Feature Selection : Selecting Informative Predictors Using Simulated Annealing and Genetic Algorithms
John Pauline Pineda
December 22, 2022
- 1.
Table of Contents
- 1.1 Sample Data
- 1.2 Data Quality Assessment
- 1.3 Data Preprocessing
- 1.4 Data Exploration
- 1.5 Simulated
Annealing (SA) and Genetic Algorithms (GA)
- 1.5.1 Random Forest Without SA and GA (RF_FULL)
- 1.5.2 Random Forest With Simulated Annealing (RF_SA)
- 1.5.3 Random Forest With Genetic Algorithms (RF_GA)
- 1.5.4 Linear Discriminant Analysis Without SA and GA (LDA_FULL)
- 1.5.5 Linear Discriminant Analysis With Simulated Annealing (LDA_SA)
- 1.5.6 Linear Discriminant Analysis With Genetic Algorithms (LDA_GA)
- 1.6 Consolidated Findings
- 2. Summary
- 3. References
1. Table of Contents
This project implements Simulated Annealing and Genetic Algorithms in selecting informative predictors for a modelling problem using the Random Forest and Linear Discriminant Analysis structures in R. The resulting predictions derived from the candidate models applying both Simulated Annealing and Genetic Algorithms were evaluated in terms of their predictive power using the accuracy metric. The accuracy values were compared to those of the baseline models which made use of the full data without any form of feature selection, or implemented a model-specific feature selection process. All results were consolidated in a Summary presented at the end of the document.
Feature selection is the process of reducing the number of input variables by eliminating redundant or unimportant features and narrowing down the set of features to those most relevant to the machine learning approach, resulting to simpler explainable models, shorter training times due to a more precise subset of features, reduction of variance, increase in precision estimates and more robust solution against the curse of high dimensionality. The algorithms applied in this study (mostly contained in the caret package) are wrapper feature selection methods which attempt to consider the task of selecting feature subsets as a search problem, whereby their quality is assessed with the preparation, evaluation, and comparison between different feature combinations.
1.1 Sample Data
The AlzheimerDisease dataset from the AppliedPredictiveModeling package was used for this illustrated example.
Preliminary dataset assessment:
[A] 333 rows (observations)
[A.1] Train Set = 267 observations
[A.2] Test Set = 66 observations
[B] 128 columns (variables)
[B.1] 1/128 response = Class variable (factor)
[B.1.1] Levels = Class=Control < Class=Impaired
[B.2] 127/128 predictors = All remaining variables (3/127 factor + 124/127 numeric)
Code Chunk | Output
##################################
# Loading R libraries
##################################
library(AppliedPredictiveModeling)
library(caret)
library(rpart)
library(lattice)
library(dplyr)
library(tidyr)
library(moments)
library(skimr)
library(RANN)
library(pls)
library(corrplot)
library(tidyverse)
library(lares)
library(DMwR2)
library(gridExtra)
library(rattle)
library(rpart.plot)
library(RColorBrewer)
library(stats)
library(nnet)
library(elasticnet)
library(earth)
library(party)
library(kernlab)
library(randomForest)
library(Cubist)
library(pROC)
library(mda)
library(klaR)
library(pamr)
library(MLmetrics)
##################################
# Loading source and
# formulating the train set
##################################
data(AlzheimerDisease)
Alzheimer <- predictors
Alzheimer$Class <- diagnosis
##################################
# Decomposing the Genotype factor
# into binary dummy variables
##################################
## Decompose the genotype factor into binary dummy variables
Alzheimer$E2 <- Alzheimer$E3 <- Alzheimer$E4 <- 0
Alzheimer$E2[grepl("2", Alzheimer$Genotype)] <- 1
Alzheimer$E3[grepl("3", Alzheimer$Genotype)] <- 1
Alzheimer$E4[grepl("4", Alzheimer$Genotype)] <- 1
Alzheimer_Original <- Alzheimer
##################################
# Removing baseline predictors
##################################
Alzheimer <- Alzheimer[,!(names(Alzheimer) %in% c("Genotype", "age", "tau", "p_tau", "Ab_42", "male"))]
##################################
# Partitoning the data into
# train and test sets
##################################
set.seed(12345678)
Alzheimer_Train_Index <- createDataPartition(Alzheimer$Class,p=0.8)[[1]]
Alzheimer_Train <- Alzheimer[ Alzheimer_Train_Index, ]
Alzheimer_Test <- Alzheimer[-Alzheimer_Train_Index, ]
##################################
# Performing a general exploration of the train set
##################################
dim(Alzheimer_Train)## [1] 267 128str(Alzheimer_Train)## 'data.frame': 267 obs. of 128 variables:
## $ ACE_CD143_Angiotensin_Converti : num 2.003 1.562 1.521 2.401 0.431 ...
## $ ACTH_Adrenocorticotropic_Hormon : num -1.386 -1.386 -1.715 -0.968 -1.273 ...
## $ AXL : num 1.098 0.683 -0.145 0.191 -0.222 ...
## $ Adiponectin : num -5.36 -5.02 -5.81 -4.78 -5.22 ...
## $ Alpha_1_Antichymotrypsin : num 1.74 1.46 1.19 2.13 1.31 ...
## $ Alpha_1_Antitrypsin : num -12.6 -11.9 -13.6 -11.1 -12.1 ...
## $ Alpha_1_Microglobulin : num -2.58 -3.24 -2.88 -2.34 -2.55 ...
## $ Alpha_2_Macroglobulin : num -72.7 -154.6 -136.5 -144.9 -154.6 ...
## $ Angiopoietin_2_ANG_2 : num 1.0647 0.7419 0.8329 0.9555 -0.0513 ...
## $ Angiotensinogen : num 2.51 2.46 1.98 2.86 2.52 ...
## $ Apolipoprotein_A_IV : num -1.43 -1.66 -1.66 -1.17 -1.39 ...
## $ Apolipoprotein_A1 : num -7.4 -7.05 -7.68 -6.73 -7.4 ...
## $ Apolipoprotein_A2 : num -0.2614 -0.8675 -0.6539 0.0953 -0.2744 ...
## $ Apolipoprotein_B : num -4.62 -6.75 -3.98 -3.38 -2.96 ...
## $ Apolipoprotein_CI : num -1.273 -1.273 -1.715 -0.755 -1.661 ...
## $ Apolipoprotein_CIII : num -2.31 -2.34 -2.75 -1.51 -2.31 ...
## $ Apolipoprotein_D : num 2.08 1.34 1.34 1.63 1.92 ...
## $ Apolipoprotein_E : num 3.755 3.097 2.753 3.067 0.591 ...
## $ Apolipoprotein_H : num -0.1573 -0.5754 -0.3448 0.6626 0.0972 ...
## $ B_Lymphocyte_Chemoattractant_BL : num 2.3 1.67 1.67 2.3 2.48 ...
## $ BMP_6 : num -2.2 -1.73 -2.06 -1.24 -1.88 ...
## $ Beta_2_Microglobulin : num 0.693 0.47 0.336 0.336 -0.545 ...
## $ Betacellulin : int 34 53 49 67 51 41 42 58 32 43 ...
## $ C_Reactive_Protein : num -4.07 -6.65 -8.05 -4.34 -7.56 ...
## $ CD40 : num -0.796 -1.273 -1.242 -0.924 -1.784 ...
## $ CD5L : num 0.0953 -0.6733 0.0953 0.3633 0.4055 ...
## $ Calbindin : num 33.2 25.3 22.2 21.8 13.2 ...
## $ Calcitonin : num 1.39 3.61 2.12 1.31 1.63 ...
## $ CgA : num 398 466 348 443 138 ...
## $ Clusterin_Apo_J : num 3.56 3.04 2.77 3.04 2.56 ...
## $ Complement_3 : num -10.4 -16.1 -16.1 -12.8 -12 ...
## $ Complement_Factor_H : num 3.57 3.6 4.47 7.25 3.57 ...
## $ Connective_Tissue_Growth_Factor : num 0.531 0.588 0.642 0.916 0.993 ...
## $ Cortisol : num 10 12 10 11 13 4.9 13 12 6.8 12 ...
## $ Creatine_Kinase_MB : num -1.71 -1.75 -1.38 -1.63 -1.67 ...
## $ Cystatin_C : num 9.04 9.07 8.95 8.98 7.84 ...
## $ EGF_R : num -0.135 -0.37 -0.733 -0.621 -1.111 ...
## $ EN_RAGE : num -3.69 -3.82 -4.76 -2.36 -3.44 ...
## $ ENA_78 : num -1.35 -1.36 -1.39 -1.34 -1.36 ...
## $ Eotaxin_3 : int 53 62 62 64 57 64 64 64 82 73 ...
## $ FAS : num -0.0834 -0.5276 -0.6349 -0.1278 -0.3285 ...
## $ FSH_Follicle_Stimulation_Hormon : num -0.652 -1.627 -1.563 -0.976 -1.683 ...
## $ Fas_Ligand : num 3.1 2.98 1.36 4.04 2.41 ...
## $ Fatty_Acid_Binding_Protein : num 2.521 2.248 0.906 2.635 0.624 ...
## $ Ferritin : num 3.33 3.93 3.18 2.69 1.85 ...
## $ Fetuin_A : num 1.28 1.19 1.41 2.15 1.48 ...
## $ Fibrinogen : num -7.04 -8.05 -7.2 -6.98 -6.44 ...
## $ GRO_alpha : num 1.38 1.37 1.41 1.4 1.4 ...
## $ Gamma_Interferon_induced_Monokin: num 2.95 2.72 2.76 2.85 2.82 ...
## $ Glutathione_S_Transferase_alpha : num 1.064 0.867 0.889 1.236 1.154 ...
## $ HB_EGF : num 6.56 8.75 7.75 7.25 6.41 ...
## $ HCC_4 : num -3.04 -4.07 -3.65 -3.15 -3.08 ...
## $ Hepatocyte_Growth_Factor_HGF : num 0.5878 0.5306 0.0953 0.5306 0.0953 ...
## $ I_309 : num 3.43 3.14 2.4 3.76 2.71 ...
## $ ICAM_1 : num -0.1908 -0.462 -0.462 0.0972 -0.9351 ...
## $ IGF_BP_2 : num 5.61 5.35 5.18 5.42 5.06 ...
## $ IL_11 : num 5.12 4.94 4.67 7.07 6.1 ...
## $ IL_13 : num 1.28 1.27 1.27 1.31 1.28 ...
## $ IL_16 : num 4.19 2.88 2.62 4.74 2.67 ...
## $ IL_17E : num 5.73 6.71 4.15 4.2 3.64 ...
## $ IL_1alpha : num -6.57 -8.05 -8.18 -6.94 -8.18 ...
## $ IL_3 : num -3.24 -3.91 -4.65 -3 -3.86 ...
## $ IL_4 : num 2.48 2.4 1.82 2.71 1.21 ...
## $ IL_5 : num 1.099 0.693 -0.248 1.163 -0.4 ...
## $ IL_6 : num 0.2694 0.0962 0.1857 -0.072 0.1857 ...
## $ IL_6_Receptor : num 0.6428 0.4312 0.0967 0.0967 -0.5173 ...
## $ IL_7 : num 4.81 3.71 1.01 4.29 2.78 ...
## $ IL_8 : num 1.71 1.68 1.69 1.76 1.71 ...
## $ IP_10_Inducible_Protein_10 : num 6.24 5.69 5.05 6.37 5.48 ...
## $ IgA : num -6.81 -6.38 -6.32 -4.65 -5.81 ...
## $ Insulin : num -0.626 -0.943 -1.447 -0.3 -1.341 ...
## $ Kidney_Injury_Molecule_1_KIM_1 : num -1.2 -1.2 -1.19 -1.16 -1.12 ...
## $ LOX_1 : num 1.705 1.526 1.163 1.361 0.642 ...
## $ Leptin : num -1.529 -1.466 -1.662 -0.915 -1.361 ...
## $ Lipoprotein_a : num -4.27 -4.93 -5.84 -2.94 -4.51 ...
## $ MCP_1 : num 6.74 6.85 6.77 6.72 6.54 ...
## $ MCP_2 : num 1.981 1.809 0.401 2.221 2.334 ...
## $ MIF : num -1.24 -1.9 -2.3 -1.9 -2.04 ...
## $ MIP_1alpha : num 4.97 3.69 4.05 6.45 4.6 ...
## $ MIP_1beta : num 3.26 3.14 2.4 3.53 2.89 ...
## $ MMP_2 : num 4.48 3.78 2.87 3.69 2.92 ...
## $ MMP_3 : num -2.21 -2.47 -2.3 -1.56 -3.04 ...
## $ MMP10 : num -3.27 -3.65 -2.73 -2.62 -3.32 ...
## $ MMP7 : num -3.774 -5.968 -4.03 -0.222 -1.922 ...
## $ Myoglobin : num -1.897 -0.755 -1.386 -1.772 -1.139 ...
## $ NT_proBNP : num 4.55 4.22 4.25 4.47 4.19 ...
## $ NrCAM : num 5 5.21 4.74 5.2 3.26 ...
## $ Osteopontin : num 5.36 6 5.02 5.69 4.74 ...
## $ PAI_1 : num 1.0035 -0.0306 0.4384 0.2523 0.4384 ...
## $ PAPP_A : num -2.9 -2.81 -2.94 -2.94 -2.94 ...
## $ PLGF : num 4.44 4.03 4.51 4.8 4.39 ...
## $ PYY : num 3.22 3.14 2.89 3.66 3.33 ...
## $ Pancreatic_polypeptide : num 0.579 0.336 -0.892 0.262 -0.478 ...
## $ Prolactin : num 0 -0.511 -0.139 0.182 -0.151 ...
## $ Prostatic_Acid_Phosphatase : num -1.62 -1.74 -1.64 -1.7 -1.76 ...
## $ Protein_S : num -1.78 -2.46 -2.26 -1.66 -2.36 ...
## $ Pulmonary_and_Activation_Regulat: num -0.844 -2.303 -1.661 -0.562 -1.171 ...
## $ RANTES : num -6.21 -6.94 -6.65 -6.32 -6.5 ...
## $ Resistin : num -16.5 -16 -16.5 -11.1 -11.3 ...
## [list output truncated]summary(Alzheimer_Train)## ACE_CD143_Angiotensin_Converti ACTH_Adrenocorticotropic_Hormon
## Min. :-0.6756 Min. :-2.207
## 1st Qu.: 0.9462 1st Qu.:-1.715
## Median : 1.3013 Median :-1.561
## Mean : 1.3198 Mean :-1.538
## 3rd Qu.: 1.7191 3rd Qu.:-1.347
## Max. : 2.8398 Max. :-0.844
## AXL Adiponectin Alpha_1_Antichymotrypsin
## Min. :-0.9230 Min. :-6.725 Min. :0.2624
## 1st Qu.: 0.0000 1st Qu.:-5.669 1st Qu.:1.1314
## Median : 0.2804 Median :-5.185 Median :1.3610
## Mean : 0.3093 Mean :-5.201 Mean :1.3605
## 3rd Qu.: 0.6077 3rd Qu.:-4.780 3rd Qu.:1.5892
## Max. : 1.5214 Max. :-3.507 Max. :2.3026
## Alpha_1_Antitrypsin Alpha_1_Microglobulin Alpha_2_Macroglobulin
## Min. :-17.028 Min. :-4.343 Min. :-289.68
## 1st Qu.:-14.071 1st Qu.:-3.270 1st Qu.:-186.64
## Median :-13.004 Median :-2.937 Median :-160.01
## Mean :-13.052 Mean :-2.932 Mean :-158.61
## 3rd Qu.:-12.096 3rd Qu.:-2.590 3rd Qu.:-134.62
## Max. : -8.192 Max. :-1.772 Max. : -59.46
## Angiopoietin_2_ANG_2 Angiotensinogen Apolipoprotein_A_IV Apolipoprotein_A1
## Min. :-0.5447 Min. :1.752 Min. :-2.9565 Min. :-8.680
## 1st Qu.: 0.4700 1st Qu.:2.119 1st Qu.:-2.1203 1st Qu.:-7.763
## Median : 0.6419 Median :2.320 Median :-1.8326 Median :-7.470
## Mean : 0.6730 Mean :2.318 Mean :-1.8544 Mean :-7.483
## 3rd Qu.: 0.8755 3rd Qu.:2.497 3rd Qu.:-1.6094 3rd Qu.:-7.209
## Max. : 1.5261 Max. :2.881 Max. :-0.7765 Max. :-6.166
## Apolipoprotein_A2 Apolipoprotein_B Apolipoprotein_CI Apolipoprotein_CIII
## Min. :-1.8971 Min. :-9.937 Min. :-3.3242 Min. :-3.689
## 1st Qu.:-0.9676 1st Qu.:-6.630 1st Qu.:-1.8326 1st Qu.:-2.773
## Median :-0.6733 Median :-5.703 Median :-1.6094 Median :-2.526
## Mean :-0.6354 Mean :-5.578 Mean :-1.5833 Mean :-2.494
## 3rd Qu.:-0.3147 3rd Qu.:-4.539 3rd Qu.:-1.3667 3rd Qu.:-2.207
## Max. : 0.9555 Max. :-2.153 Max. :-0.2744 Max. :-1.238
## Apolipoprotein_D Apolipoprotein_E Apolipoprotein_H
## Min. :0.470 Min. :0.5911 Min. :-2.23379
## 1st Qu.:1.209 1st Qu.:2.3344 1st Qu.:-0.59782
## Median :1.411 Median :2.8181 Median :-0.37005
## Mean :1.440 Mean :2.8062 Mean :-0.32122
## 3rd Qu.:1.668 3rd Qu.:3.2863 3rd Qu.:-0.06112
## Max. :2.272 Max. :5.4442 Max. : 0.92696
## B_Lymphocyte_Chemoattractant_BL BMP_6 Beta_2_Microglobulin
## Min. :0.7318 Min. :-2.7612 Min. :-0.54473
## 1st Qu.:1.6731 1st Qu.:-2.1516 1st Qu.:-0.04082
## Median :1.9805 Median :-1.8774 Median : 0.18232
## Mean :2.0175 Mean :-1.9114 Mean : 0.16757
## 3rd Qu.:2.3714 3rd Qu.:-1.6753 3rd Qu.: 0.33647
## Max. :4.0237 Max. :-0.8166 Max. : 0.99325
## Betacellulin C_Reactive_Protein CD40 CD5L
## Min. :10.00 Min. :-8.517 Min. :-1.8644 Min. :-1.23787
## 1st Qu.:42.00 1st Qu.:-6.645 1st Qu.:-1.3761 1st Qu.:-0.35667
## Median :51.00 Median :-5.843 Median :-1.2734 Median :-0.06188
## Mean :51.01 Mean :-5.874 Mean :-1.2584 Mean :-0.05310
## 3rd Qu.:59.00 3rd Qu.:-5.083 3rd Qu.:-1.1238 3rd Qu.: 0.26236
## Max. :82.00 Max. :-2.937 Max. :-0.5475 Max. : 1.16315
## Calbindin Calcitonin CgA Clusterin_Apo_J
## Min. :10.96 Min. :-0.7134 Min. :135.6 Min. :1.872
## 1st Qu.:19.77 1st Qu.: 0.9555 1st Qu.:278.0 1st Qu.:2.708
## Median :22.25 Median : 1.6487 Median :331.5 Median :2.890
## Mean :22.43 Mean : 1.6788 Mean :333.3 Mean :2.882
## 3rd Qu.:24.80 3rd Qu.: 2.2824 3rd Qu.:392.1 3rd Qu.:3.045
## Max. :33.78 Max. : 3.8918 Max. :535.4 Max. :3.584
## Complement_3 Complement_Factor_H Connective_Tissue_Growth_Factor
## Min. :-23.387 Min. :-0.8387 Min. :0.1823
## 1st Qu.:-17.567 1st Qu.: 2.7531 1st Qu.:0.6419
## Median :-15.524 Median : 3.6000 Median :0.7885
## Mean :-15.610 Mean : 3.5541 Mean :0.7739
## 3rd Qu.:-13.882 3rd Qu.: 4.2548 3rd Qu.:0.9163
## Max. : -9.563 Max. : 7.6238 Max. :1.4110
## Cortisol Creatine_Kinase_MB Cystatin_C EGF_R
## Min. : 0.10 Min. :-1.872 Min. :7.432 Min. :-1.36135
## 1st Qu.: 9.80 1st Qu.:-1.724 1st Qu.:8.321 1st Qu.:-0.85727
## Median :12.00 Median :-1.671 Median :8.564 Median :-0.68354
## Mean :11.98 Mean :-1.674 Mean :8.586 Mean :-0.70130
## 3rd Qu.:14.00 3rd Qu.:-1.626 3rd Qu.:8.839 3rd Qu.:-0.54612
## Max. :29.00 Max. :-1.384 Max. :9.694 Max. :-0.06112
## EN_RAGE ENA_78 Eotaxin_3 FAS
## Min. :-8.3774 Min. :-1.405 Min. : 7.00 Min. :-1.5141
## 1st Qu.:-4.1997 1st Qu.:-1.381 1st Qu.: 44.00 1st Qu.:-0.7133
## Median :-3.6497 Median :-1.374 Median : 59.00 Median :-0.5276
## Mean :-3.6353 Mean :-1.372 Mean : 58.17 Mean :-0.5291
## 3rd Qu.:-3.1466 3rd Qu.:-1.364 3rd Qu.: 70.00 3rd Qu.:-0.3147
## Max. :-0.3857 Max. :-1.339 Max. :107.00 Max. : 0.3365
## FSH_Follicle_Stimulation_Hormon Fas_Ligand Fatty_Acid_Binding_Protein
## Min. :-2.11511 Min. :-0.1536 Min. :-1.0441
## 1st Qu.:-1.46606 1st Qu.: 2.3415 1st Qu.: 0.7998
## Median :-1.13570 Median : 3.1015 Median : 1.3865
## Mean :-1.14259 Mean : 2.9680 Mean : 1.3529
## 3rd Qu.:-0.87620 3rd Qu.: 3.6950 3rd Qu.: 1.8847
## Max. : 0.09715 Max. : 7.6328 Max. : 3.7055
## Ferritin Fetuin_A Fibrinogen GRO_alpha
## Min. :0.6077 Min. :0.470 Min. :-8.874 Min. :1.271
## 1st Qu.:2.2895 1st Qu.:1.099 1st Qu.:-7.717 1st Qu.:1.351
## Median :2.7749 Median :1.308 Median :-7.323 Median :1.382
## Mean :2.7646 Mean :1.350 Mean :-7.356 Mean :1.378
## 3rd Qu.:3.2915 3rd Qu.:1.609 3rd Qu.:-7.013 3rd Qu.:1.406
## Max. :4.6333 Max. :2.251 Max. :-5.843 Max. :1.495
## Gamma_Interferon_induced_Monokin Glutathione_S_Transferase_alpha
## Min. :2.393 Min. :0.5238
## 1st Qu.:2.707 1st Qu.:0.8439
## Median :2.783 Median :0.9677
## Mean :2.786 Mean :0.9512
## 3rd Qu.:2.873 3rd Qu.:1.0344
## Max. :3.065 Max. :1.3176
## HB_EGF HCC_4 Hepatocyte_Growth_Factor_HGF I_309
## Min. : 2.103 Min. :-4.510 Min. :-0.6349 Min. :1.758
## 1st Qu.: 5.786 1st Qu.:-3.730 1st Qu.: 0.0000 1st Qu.:2.708
## Median : 6.703 Median :-3.507 Median : 0.1823 Median :2.944
## Mean : 6.833 Mean :-3.500 Mean : 0.1963 Mean :2.958
## 3rd Qu.: 7.865 3rd Qu.:-3.270 3rd Qu.: 0.4055 3rd Qu.:3.219
## Max. :10.695 Max. :-2.120 Max. : 0.8755 Max. :4.143
## ICAM_1 IGF_BP_2 IL_11 IL_13
## Min. :-1.5332 Min. :4.635 Min. :1.755 Min. :1.259
## 1st Qu.:-0.8298 1st Qu.:5.179 1st Qu.:3.706 1st Qu.:1.274
## Median :-0.5903 Median :5.323 Median :4.805 Median :1.283
## Mean :-0.5908 Mean :5.317 Mean :4.725 Mean :1.284
## 3rd Qu.:-0.3828 3rd Qu.:5.453 3rd Qu.:5.776 3rd Qu.:1.290
## Max. : 0.5171 Max. :5.948 Max. :8.491 Max. :1.321
## IL_16 IL_17E IL_1alpha IL_3
## Min. :1.187 Min. :1.052 Min. :-8.517 Min. :-5.915
## 1st Qu.:2.521 1st Qu.:4.149 1st Qu.:-7.824 1st Qu.:-4.269
## Median :2.909 Median :4.749 Median :-7.524 Median :-3.912
## Mean :2.929 Mean :4.855 Mean :-7.514 Mean :-3.941
## 3rd Qu.:3.351 3rd Qu.:5.631 3rd Qu.:-7.264 3rd Qu.:-3.631
## Max. :4.937 Max. :8.952 Max. :-5.952 Max. :-2.453
## IL_4 IL_5 IL_6 IL_6_Receptor
## Min. :0.5306 Min. :-1.4271 Min. :-1.5343 Min. :-0.67562
## 1st Qu.:1.4586 1st Qu.:-0.1221 1st Qu.:-0.4127 1st Qu.:-0.12541
## Median :1.8083 Median : 0.1823 Median :-0.1599 Median : 0.09669
## Mean :1.7732 Mean : 0.1866 Mean :-0.1540 Mean : 0.09492
## 3rd Qu.:2.1459 3rd Qu.: 0.4700 3rd Qu.: 0.1410 3rd Qu.: 0.35404
## Max. :3.0445 Max. : 1.9459 Max. : 1.8138 Max. : 0.83099
## IL_7 IL_8 IP_10_Inducible_Protein_10 IgA
## Min. :0.5598 Min. :1.574 Min. :4.317 Min. :-10.520
## 1st Qu.:2.1548 1st Qu.:1.680 1st Qu.:5.398 1st Qu.: -6.645
## Median :2.7934 Median :1.705 Median :5.753 Median : -6.119
## Mean :2.8392 Mean :1.704 Mean :5.755 Mean : -6.121
## 3rd Qu.:3.7055 3rd Qu.:1.728 3rd Qu.:6.064 3rd Qu.: -5.573
## Max. :5.7056 Max. :1.807 Max. :7.501 Max. : -4.200
## Insulin Kidney_Injury_Molecule_1_KIM_1 LOX_1
## Min. :-2.1692 Min. :-1.256 Min. :0.000
## 1st Qu.:-1.4466 1st Qu.:-1.204 1st Qu.:1.030
## Median :-1.2462 Median :-1.183 Median :1.281
## Mean :-1.2329 Mean :-1.185 Mean :1.283
## 3rd Qu.:-1.0340 3rd Qu.:-1.164 3rd Qu.:1.526
## Max. :-0.1586 Max. :-1.105 Max. :2.272
## Leptin Lipoprotein_a MCP_1 MCP_2
## Min. :-2.1468 Min. :-6.812 Min. :5.826 Min. :0.4006
## 1st Qu.:-1.6996 1st Qu.:-5.308 1st Qu.:6.319 1st Qu.:1.5304
## Median :-1.5047 Median :-4.605 Median :6.494 Median :1.8528
## Mean :-1.5042 Mean :-4.417 Mean :6.497 Mean :1.8691
## 3rd Qu.:-1.3295 3rd Qu.:-3.490 3rd Qu.:6.678 3rd Qu.:2.1821
## Max. :-0.6206 Max. :-1.386 Max. :7.230 Max. :4.0237
## MIF MIP_1alpha MIP_1beta MMP_2
## Min. :-2.847 Min. :0.9346 Min. :1.946 Min. :0.09809
## 1st Qu.:-2.120 1st Qu.:3.3377 1st Qu.:2.565 1st Qu.:2.33214
## Median :-1.897 Median :4.0495 Median :2.833 Median :2.81512
## Mean :-1.864 Mean :4.0489 Mean :2.814 Mean :2.87534
## 3rd Qu.:-1.661 3rd Qu.:4.6857 3rd Qu.:3.045 3rd Qu.:3.55121
## Max. :-0.844 Max. :6.7959 Max. :4.007 Max. :5.35895
## MMP_3 MMP10 MMP7 Myoglobin
## Min. :-4.4228 Min. :-4.934 Min. :-8.3975 Min. :-3.1701
## 1st Qu.:-2.7489 1st Qu.:-3.938 1st Qu.:-4.8199 1st Qu.:-2.0402
## Median :-2.4534 Median :-3.650 Median :-3.7735 Median :-1.4697
## Mean :-2.4455 Mean :-3.635 Mean :-3.7894 Mean :-1.3671
## 3rd Qu.:-2.1203 3rd Qu.:-3.352 3rd Qu.:-2.7140 3rd Qu.:-0.7988
## Max. :-0.5276 Max. :-2.207 Max. :-0.2222 Max. : 1.7750
## NT_proBNP NrCAM Osteopontin PAI_1
## Min. :3.178 Min. :2.639 Min. :4.111 Min. :-0.99085
## 1st Qu.:4.350 1st Qu.:3.998 1st Qu.:4.963 1st Qu.:-0.16655
## Median :4.554 Median :4.394 Median :5.187 Median : 0.09396
## Mean :4.552 Mean :4.362 Mean :5.204 Mean : 0.07743
## 3rd Qu.:4.775 3rd Qu.:4.749 3rd Qu.:5.442 3rd Qu.: 0.32005
## Max. :5.886 Max. :6.011 Max. :6.308 Max. : 1.16611
## PAPP_A PLGF PYY Pancreatic_polypeptide
## Min. :-3.311 Min. :2.485 Min. :2.186 Min. :-2.12026
## 1st Qu.:-2.936 1st Qu.:3.638 1st Qu.:2.833 1st Qu.:-0.52763
## Median :-2.871 Median :3.871 Median :2.996 Median :-0.04082
## Mean :-2.854 Mean :3.912 Mean :3.015 Mean :-0.01323
## 3rd Qu.:-2.749 3rd Qu.:4.205 3rd Qu.:3.178 3rd Qu.: 0.53063
## Max. :-2.520 Max. :5.170 Max. :3.932 Max. : 1.93152
## Prolactin Prostatic_Acid_Phosphatase Protein_S
## Min. :-1.30933 Min. :-1.934 Min. :-3.338
## 1st Qu.:-0.13926 1st Qu.:-1.717 1st Qu.:-2.464
## Median : 0.00000 Median :-1.690 Median :-2.259
## Mean : 0.04495 Mean :-1.685 Mean :-2.240
## 3rd Qu.: 0.25799 3rd Qu.:-1.654 3rd Qu.:-2.000
## Max. : 0.99325 Max. :-1.424 Max. :-1.221
## Pulmonary_and_Activation_Regulat RANTES Resistin
## Min. :-2.5133 Min. :-7.222 Min. :-34.967
## 1st Qu.:-1.8326 1st Qu.:-6.725 1st Qu.:-21.468
## Median :-1.5141 Median :-6.502 Median :-17.466
## Mean :-1.4880 Mean :-6.511 Mean :-17.641
## 3rd Qu.:-1.1712 3rd Qu.:-6.320 3rd Qu.:-13.501
## Max. :-0.2744 Max. :-5.547 Max. : -2.239
## S100b SGOT SHBG SOD
## Min. :0.1874 Min. :-1.3471 Min. :-4.135 Min. :4.317
## 1st Qu.:1.0012 1st Qu.:-0.6349 1st Qu.:-2.813 1st Qu.:5.094
## Median :1.2544 Median :-0.4005 Median :-2.489 Median :5.366
## Mean :1.2505 Mean :-0.4057 Mean :-2.477 Mean :5.336
## 3rd Qu.:1.4996 3rd Qu.:-0.1985 3rd Qu.:-2.120 3rd Qu.:5.583
## Max. :2.3726 Max. : 0.7419 Max. :-1.109 Max. :6.317
## Serum_Amyloid_P Sortilin Stem_Cell_Factor TGF_alpha
## Min. :-7.506 Min. :1.654 Min. :2.251 Min. : 6.843
## 1st Qu.:-6.377 1st Qu.:3.343 1st Qu.:3.045 1st Qu.: 8.859
## Median :-6.032 Median :3.867 Median :3.296 Median : 9.919
## Mean :-6.017 Mean :3.852 Mean :3.301 Mean : 9.801
## 3rd Qu.:-5.655 3rd Qu.:4.371 3rd Qu.:3.526 3rd Qu.:10.695
## Max. :-4.646 Max. :6.225 Max. :4.277 Max. :13.827
## TIMP_1 TNF_RII TRAIL_R3 TTR_prealbumin
## Min. : 1.742 Min. :-1.6607 Min. :-1.2107 Min. :2.485
## 1st Qu.:10.490 1st Qu.:-0.8210 1st Qu.:-0.7008 1st Qu.:2.773
## Median :11.565 Median :-0.5978 Median :-0.5317 Median :2.833
## Mean :11.750 Mean :-0.5939 Mean :-0.5394 Mean :2.854
## 3rd Qu.:12.697 3rd Qu.:-0.3784 3rd Qu.:-0.3849 3rd Qu.:2.944
## Max. :18.881 Max. : 0.4700 Max. : 0.2694 Max. :3.332
## Tamm_Horsfall_Protein_THP Thrombomodulin Thrombopoietin
## Min. :-3.206 Min. :-2.0377 Min. :-1.53957
## 1st Qu.:-3.137 1st Qu.:-1.6256 1st Qu.:-0.88645
## Median :-3.117 Median :-1.4920 Median :-0.75100
## Mean :-3.116 Mean :-1.5050 Mean :-0.75419
## 3rd Qu.:-3.096 3rd Qu.:-1.3406 3rd Qu.:-0.62887
## Max. :-2.995 Max. :-0.8166 Max. : 0.09762
## Thymus_Expressed_Chemokine_TECK Thyroid_Stimulating_Hormone
## Min. :1.508 Min. :-6.190
## 1st Qu.:3.343 1st Qu.:-4.962
## Median :3.810 Median :-4.510
## Mean :3.848 Mean :-4.499
## 3rd Qu.:4.316 3rd Qu.:-4.017
## Max. :6.225 Max. :-1.715
## Thyroxine_Binding_Globulin Tissue_Factor Transferrin
## Min. :-2.4769 Min. :-0.2107 Min. :1.932
## 1st Qu.:-1.7720 1st Qu.: 0.8329 1st Qu.:2.708
## Median :-1.5141 Median : 1.2238 Median :2.890
## Mean :-1.4788 Mean : 1.1702 Mean :2.909
## 3rd Qu.:-1.2379 3rd Qu.: 1.4816 3rd Qu.:3.091
## Max. :-0.2107 Max. : 2.4849 Max. :3.761
## Trefoil_Factor_3_TFF3 VCAM_1 VEGF Vitronectin
## Min. :-4.744 Min. :1.723 Min. :11.83 Min. :-1.42712
## 1st Qu.:-4.135 1st Qu.:2.485 1st Qu.:15.77 1st Qu.:-0.51083
## Median :-3.863 Median :2.708 Median :17.08 Median :-0.30111
## Mean :-3.876 Mean :2.688 Mean :16.99 Mean :-0.28473
## 3rd Qu.:-3.650 3rd Qu.:2.890 3rd Qu.:18.10 3rd Qu.:-0.03564
## Max. :-2.957 Max. :3.689 Max. :22.38 Max. : 0.53063
## von_Willebrand_Factor Class E4 E3
## Min. :-4.991 Impaired: 73 Min. :0.0000 Min. :0.0000
## 1st Qu.:-4.200 Control :194 1st Qu.:0.0000 1st Qu.:1.0000
## Median :-3.912 Median :0.0000 Median :1.0000
## Mean :-3.906 Mean :0.4007 Mean :0.9176
## 3rd Qu.:-3.612 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :-2.957 Max. :1.0000 Max. :1.0000
## E2
## Min. :0.000
## 1st Qu.:0.000
## Median :0.000
## Mean :0.161
## 3rd Qu.:0.000
## Max. :1.000##################################
# Performing a general exploration of the test set
##################################
dim(Alzheimer_Test)## [1] 66 128str(Alzheimer_Test)## 'data.frame': 66 obs. of 128 variables:
## $ ACE_CD143_Angiotensin_Converti : num 1.681 1.602 1.301 1.562 0.831 ...
## $ ACTH_Adrenocorticotropic_Hormon : num -1.61 -1.51 -1.77 -1.56 -1.97 ...
## $ AXL : num 0.6833 0.4495 -0.0201 0.5298 -0.2 ...
## $ Adiponectin : num -5.12 -5.57 -6.17 -6.07 -5.43 ...
## $ Alpha_1_Antichymotrypsin : num 1.281 1.163 1.253 0.875 1.253 ...
## $ Alpha_1_Antitrypsin : num -15.5 -12.1 -14.5 -14 -13.3 ...
## $ Alpha_1_Microglobulin : num -3.17 -2.36 -3.32 -3.19 -3.24 ...
## $ Alpha_2_Macroglobulin : num -98.4 -144.9 -204.1 -125.8 -186.6 ...
## $ Angiopoietin_2_ANG_2 : num 0.916 0.531 0.262 0.742 0 ...
## $ Angiotensinogen : num 2.38 2.26 2.03 2.25 2.05 ...
## $ Apolipoprotein_A_IV : num -2.12 -1.9 -2.04 -2.3 -1.9 ...
## $ Apolipoprotein_A1 : num -8.05 -7.14 -8.08 -7.9 -8.18 ...
## $ Apolipoprotein_A2 : num -1.238 -0.562 -0.844 -1.022 -1.022 ...
## $ Apolipoprotein_B : num -6.52 -6.41 -5.56 -5.36 -5.94 ...
## $ Apolipoprotein_CI : num -1.97 -1.51 -2.21 -1.9 -2.04 ...
## $ Apolipoprotein_CIII : num -3 -1.97 -2.94 -2.83 -2.8 ...
## $ Apolipoprotein_D : num 1.44 1.48 1.39 1.16 1.25 ...
## $ Apolipoprotein_E : num 2.37 3.7 1.33 3.19 1.53 ...
## $ Apolipoprotein_H : num -0.532 -0.125 -0.32 -0.517 -0.462 ...
## $ B_Lymphocyte_Chemoattractant_BL : num 1.981 2.182 1.853 1.274 0.927 ...
## $ BMP_6 : num -1.98 -1.88 -1.68 -2.65 -1.68 ...
## $ Beta_2_Microglobulin : num 0.642 0.182 -0.274 0.405 -0.223 ...
## $ Betacellulin : int 52 59 51 46 51 42 61 46 32 46 ...
## $ C_Reactive_Protein : num -6.21 -6.21 -6.12 -5.71 -6.93 ...
## $ CD40 : num -1.12 -1.24 -1.45 -1.07 -1.41 ...
## $ CD5L : num -0.3285 0 -1.2379 -0.0408 -0.1054 ...
## $ Calbindin : num 23.5 20.6 13.4 27.3 22.5 ...
## $ Calcitonin : num -0.151 4.111 2.303 3.091 1.281 ...
## $ CgA : num 334 323 289 412 342 ...
## $ Clusterin_Apo_J : num 2.83 3.04 2.56 3.14 2.48 ...
## $ Complement_3 : num -13.2 -13 -17.3 -14.8 -19.2 ...
## $ Complement_Factor_H : num 3.1 4.68 3.78 2.52 3.3 ...
## $ Connective_Tissue_Growth_Factor : num 0.531 0.693 0.956 0.588 0.875 ...
## $ Cortisol : num 14 17 9.2 11 12 16 6.1 10 9.8 13 ...
## $ Creatine_Kinase_MB : num -1.65 -1.63 -1.61 -1.59 -1.72 ...
## $ Cystatin_C : num 9.58 8.33 7.91 8.99 8.47 ...
## $ EGF_R : num -0.422 -0.785 -0.976 -0.561 -0.767 ...
## $ EN_RAGE : num -2.94 -3.77 -3.24 -4.2 -4.27 ...
## $ ENA_78 : num -1.37 -1.38 -1.36 -1.37 -1.39 ...
## $ Eotaxin_3 : int 44 70 70 36 39 76 44 62 82 36 ...
## $ FAS : num -0.478 -0.0726 -0.5798 -0.5276 -0.9416 ...
## $ FSH_Follicle_Stimulation_Hormon : num -0.59 -0.652 -1.559 -1.505 -1.361 ...
## $ Fas_Ligand : num 2.537 2.792 2.073 0.288 3.867 ...
## $ Fatty_Acid_Binding_Protein : num 0.624 1.143 0.624 2.379 1.424 ...
## $ Ferritin : num 3.14 2.52 1.9 4.29 1.69 ...
## $ Fetuin_A : num 0.742 1.386 1.194 0.993 1.131 ...
## $ Fibrinogen : num -7.8 -7.06 -7.45 -7.8 -7.35 ...
## $ GRO_alpha : num 1.37 1.35 1.37 1.37 1.38 ...
## $ Gamma_Interferon_induced_Monokin: num 2.89 2.78 2.69 2.69 2.7 ...
## $ Glutathione_S_Transferase_alpha : num 0.708 1.034 1.13 0.676 0.844 ...
## $ HB_EGF : num 5.95 6.11 6.11 6.56 7.75 ...
## $ HCC_4 : num -3.82 -3.24 -3.77 -3.54 -3.73 ...
## $ Hepatocyte_Growth_Factor_HGF : num 0.4055 0.1823 -0.0834 0.47 -0.1054 ...
## $ I_309 : num 3.37 3 2.83 3.14 2.83 ...
## $ ICAM_1 : num -0.857 -1.111 -0.561 -0.357 -1.064 ...
## $ IGF_BP_2 : num 5.42 5.38 5.41 5.14 4.93 ...
## $ IL_11 : num 6.22 4.59 4.1 4.52 3.22 ...
## $ IL_13 : num 1.31 1.27 1.27 1.29 1.27 ...
## $ IL_16 : num 2.44 3.48 2.88 2.81 1.9 ...
## $ IL_17E : num 4.7 3.64 5.73 4.8 4.15 ...
## $ IL_1alpha : num -7.6 -7.37 -7.85 -7.68 -8.33 ...
## $ IL_3 : num -4.27 -4.02 -4.51 -3.58 -4.69 ...
## $ IL_4 : num 1.48 1.81 1.81 2.04 1.21 ...
## $ IL_5 : num 0.788 0.182 0 0.693 -0.371 ...
## $ IL_6 : num -0.371 -1.534 0.422 -0.563 0.8 ...
## $ IL_6_Receptor : num 0.5752 0.0967 -0.5322 -0.1586 0.0967 ...
## $ IL_7 : num 2.34 2.15 1.56 3.71 2.15 ...
## $ IL_8 : num 1.72 1.7 1.69 1.69 1.7 ...
## $ IP_10_Inducible_Protein_10 : num 5.6 5.33 5.06 4.75 5.29 ...
## $ IgA : num -7.62 -5.36 -7.04 -5.6 -6.57 ...
## $ Insulin : num -1.485 -1.034 -1.569 -0.901 -1.865 ...
## $ Kidney_Injury_Molecule_1_KIM_1 : num -1.23 -1.16 -1.12 -1.21 -1.16 ...
## $ LOX_1 : num 1.224 1.131 0.588 1.308 1.308 ...
## $ Leptin : num -1.27 -1.54 -1.54 -1.36 -1.55 ...
## $ Lipoprotein_a : num -4.99 -4.2 -3.54 -4.87 -5.08 ...
## $ MCP_1 : num 6.78 6.38 6.61 6.41 6.78 ...
## $ MCP_2 : num 1.981 1.626 1.626 0.401 1.853 ...
## $ MIF : num -1.66 -1.61 -2.04 -1.97 -1.83 ...
## $ MIP_1alpha : num 4.93 4.35 3.41 2.28 1.68 ...
## $ MIP_1beta : num 3.22 2.77 2.83 2.48 2.77 ...
## $ MMP_2 : num 2.97 2.92 3.27 4.05 1.36 ...
## $ MMP_3 : num -1.77 -1.97 -2.04 -2.04 -2.21 ...
## $ MMP10 : num -4.07 -3.27 -3.02 -3.04 -4.07 ...
## $ MMP7 : num -6.86 -3 -4.36 -3.35 -4.45 ...
## $ Myoglobin : num -1.139 -1.661 0.182 -1.897 -1.204 ...
## $ NT_proBNP : num 4.11 4.52 4.44 4.61 4.51 ...
## $ NrCAM : num 4.97 4.23 3.71 4.75 4.3 ...
## $ Osteopontin : num 5.77 5.28 4.96 5.23 4.79 ...
## $ PAI_1 : num 0 -0.0957 0.4905 0.4905 -0.0957 ...
## $ PAPP_A : num -2.79 -3.03 -2.71 -3.15 -3.08 ...
## $ PLGF : num 3.43 3.69 4.08 3.85 3.76 ...
## $ PYY : num 2.83 3 2.94 2.89 2.83 ...
## $ Pancreatic_polypeptide : num -0.821 0.262 -0.105 0.262 0.182 ...
## $ Prolactin : num -0.0408 0.7419 0.3365 0 -0.2485 ...
## $ Prostatic_Acid_Phosphatase : num -1.74 -1.68 -1.68 -1.69 -1.69 ...
## $ Protein_S : num -2.7 -2.36 -2.36 -2.7 -2.58 ...
## $ Pulmonary_and_Activation_Regulat: num -1.11 -1.31 -1.97 -1.97 -1.39 ...
## $ RANTES : num -5.99 -6.73 -6.65 -6.57 -6.57 ...
## $ Resistin : num -13.5 -15.6 -18 -16 -24.4 ...
## [list output truncated]summary(Alzheimer_Test)## ACE_CD143_Angiotensin_Converti ACTH_Adrenocorticotropic_Hormon
## Min. :-0.5473 Min. :-2.2073
## 1st Qu.: 0.9462 1st Qu.:-1.7148
## Median : 1.3013 Median :-1.5374
## Mean : 1.3105 Mean :-1.5311
## 3rd Qu.: 1.6320 3rd Qu.:-1.3863
## Max. : 3.0890 Max. :-0.7985
## AXL Adiponectin Alpha_1_Antichymotrypsin
## Min. :-0.73509 Min. :-7.059 Min. :0.1823
## 1st Qu.:-0.08175 1st Qu.:-5.737 1st Qu.:1.0647
## Median : 0.28035 Median :-5.360 Median :1.3083
## Mean : 0.25373 Mean :-5.298 Mean :1.3077
## 3rd Qu.: 0.60768 3rd Qu.:-4.917 3rd Qu.:1.5686
## Max. : 1.28634 Max. :-3.474 Max. :2.2192
## Alpha_1_Antitrypsin Alpha_1_Microglobulin Alpha_2_Macroglobulin
## Min. :-18.17 Min. :-4.135 Min. :-238.64
## 1st Qu.:-14.70 1st Qu.:-3.284 1st Qu.:-186.64
## Median :-13.59 Median :-3.006 Median :-162.93
## Mean :-13.49 Mean :-2.983 Mean :-162.89
## 3rd Qu.:-12.31 3rd Qu.:-2.674 3rd Qu.:-136.53
## Max. :-10.06 Max. :-1.897 Max. : -50.17
## Angiopoietin_2_ANG_2 Angiotensinogen Apolipoprotein_A_IV Apolipoprotein_A1
## Min. :-0.05129 Min. :1.710 Min. :-2.749 Min. :-8.568
## 1st Qu.: 0.35372 1st Qu.:2.068 1st Qu.:-2.186 1st Qu.:-7.818
## Median : 0.55921 Median :2.276 Median :-1.897 Median :-7.497
## Mean : 0.60278 Mean :2.274 Mean :-1.867 Mean :-7.488
## 3rd Qu.: 0.78846 3rd Qu.:2.430 3rd Qu.:-1.526 3rd Qu.:-7.176
## Max. : 1.77495 Max. :2.752 Max. :-1.109 Max. :-6.645
## Apolipoprotein_A2 Apolipoprotein_B Apolipoprotein_CI Apolipoprotein_CIII
## Min. :-1.9661 Min. :-8.192 Min. :-2.847 Min. :-3.863
## 1st Qu.:-0.9416 1st Qu.:-6.748 1st Qu.:-1.897 1st Qu.:-2.781
## Median :-0.7032 Median :-5.819 Median :-1.609 Median :-2.557
## Mean :-0.6902 Mean :-5.649 Mean :-1.625 Mean :-2.523
## 3rd Qu.:-0.3533 3rd Qu.:-4.603 3rd Qu.:-1.309 3rd Qu.:-2.231
## Max. : 0.5306 Max. :-2.339 Max. :-0.462 Max. :-1.386
## Apolipoprotein_D Apolipoprotein_E Apolipoprotein_H
## Min. :0.2624 Min. :0.6626 Min. :-1.1609
## 1st Qu.:1.1314 1st Qu.:2.1526 1st Qu.:-0.5317
## Median :1.3863 Median :2.8181 Median :-0.2897
## Mean :1.3943 Mean :2.7160 Mean :-0.3212
## 3rd Qu.:1.6864 3rd Qu.:3.2363 3rd Qu.:-0.1032
## Max. :2.6391 Max. :4.6844 Max. : 0.4402
## B_Lymphocyte_Chemoattractant_BL BMP_6 Beta_2_Microglobulin
## Min. :0.7318 Min. :-2.669 Min. :-0.51083
## 1st Qu.:1.5304 1st Qu.:-2.152 1st Qu.:-0.06188
## Median :1.8528 Median :-1.964 Median : 0.18232
## Mean :1.8766 Mean :-1.937 Mean : 0.15566
## 3rd Qu.:2.3714 3rd Qu.:-1.675 3rd Qu.: 0.40547
## Max. :2.9757 Max. :-1.181 Max. : 0.83291
## Betacellulin C_Reactive_Protein CD40 CD5L
## Min. :32.00 Min. :-8.112 Min. :-1.9390 Min. :-1.96611
## 1st Qu.:46.00 1st Qu.:-6.725 1st Qu.:-1.4420 1st Qu.:-0.36747
## Median :51.00 Median :-6.166 Median :-1.2574 Median :-0.05135
## Mean :52.74 Mean :-5.997 Mean :-1.2773 Mean :-0.08760
## 3rd Qu.:59.75 3rd Qu.:-5.369 3rd Qu.:-1.1034 3rd Qu.: 0.24235
## Max. :80.00 Max. :-3.411 Max. :-0.7766 Max. : 0.91629
## Calbindin Calcitonin CgA Clusterin_Apo_J
## Min. :10.81 Min. :-0.7134 Min. :166.6 Min. :1.932
## 1st Qu.:18.88 1st Qu.: 1.2014 1st Qu.:268.2 1st Qu.:2.565
## Median :21.06 Median : 1.6849 Median :324.7 Median :2.833
## Mean :21.49 Mean : 1.7250 Mean :320.2 Mean :2.845
## 3rd Qu.:24.00 3rd Qu.: 2.2618 3rd Qu.:362.3 3rd Qu.:3.045
## Max. :35.36 Max. : 4.1109 Max. :494.5 Max. :3.761
## Complement_3 Complement_Factor_H Connective_Tissue_Growth_Factor
## Min. :-22.40 Min. :0.2766 Min. :0.09531
## 1st Qu.:-17.50 1st Qu.:2.6019 1st Qu.:0.58779
## Median :-15.90 Median :3.3983 Median :0.74194
## Mean :-15.91 Mean :3.3897 Mean :0.74507
## 3rd Qu.:-14.34 3rd Qu.:4.2548 3rd Qu.:0.87547
## Max. :-10.23 Max. :6.5597 Max. :1.41099
## Cortisol Creatine_Kinase_MB Cystatin_C EGF_R
## Min. : 0.10 Min. :-1.872 Min. :7.728 Min. :-1.2694
## 1st Qu.: 8.90 1st Qu.:-1.721 1st Qu.:8.301 1st Qu.:-0.8859
## Median :10.00 Median :-1.651 Median :8.544 Median :-0.6917
## Mean :10.46 Mean :-1.652 Mean :8.576 Mean :-0.6965
## 3rd Qu.:12.00 3rd Qu.:-1.590 3rd Qu.:8.837 3rd Qu.:-0.5034
## Max. :22.00 Max. :-1.434 Max. :9.694 Max. : 0.1891
## EN_RAGE ENA_78 Eotaxin_3 FAS
## Min. :-8.3774 Min. :-1.405 Min. : 23.00 Min. :-1.1087
## 1st Qu.:-4.1836 1st Qu.:-1.382 1st Qu.: 43.00 1st Qu.:-0.7133
## Median :-3.6889 Median :-1.374 Median : 54.00 Median :-0.5798
## Mean :-3.5986 Mean :-1.376 Mean : 55.55 Mean :-0.5414
## 3rd Qu.:-3.2189 3rd Qu.:-1.368 3rd Qu.: 64.00 3rd Qu.:-0.3355
## Max. :-0.8675 Max. :-1.353 Max. :107.00 Max. : 0.1823
## FSH_Follicle_Stimulation_Hormon Fas_Ligand Fatty_Acid_Binding_Protein
## Min. :-1.8101 Min. :0.288 Min. :-0.4559
## 1st Qu.:-1.2694 1st Qu.:2.073 1st Qu.: 0.7998
## Median :-0.9763 Median :2.665 Median : 1.1866
## Mean :-1.0597 Mean :2.649 Mean : 1.2884
## 3rd Qu.:-0.8068 3rd Qu.:3.162 3rd Qu.: 1.9192
## Max. :-0.4757 Max. :5.377 Max. : 3.2188
## Ferritin Fetuin_A Fibrinogen GRO_alpha
## Min. :0.8983 Min. :0.5306 Min. :-9.373 Min. :1.271
## 1st Qu.:2.1473 1st Qu.:1.0296 1st Qu.:-7.799 1st Qu.:1.351
## Median :2.6260 Median :1.3083 Median :-7.316 Median :1.372
## Mean :2.7069 Mean :1.3116 Mean :-7.360 Mean :1.378
## 3rd Qu.:3.1672 3rd Qu.:1.6094 3rd Qu.:-6.970 3rd Qu.:1.398
## Max. :4.9282 Max. :2.2083 Max. :-6.166 Max. :1.514
## Gamma_Interferon_induced_Monokin Glutathione_S_Transferase_alpha
## Min. :2.545 Min. :0.5661
## 1st Qu.:2.698 1st Qu.:0.8257
## Median :2.768 Median :0.9493
## Mean :2.772 Mean :0.9440
## 3rd Qu.:2.829 3rd Qu.:1.0457
## Max. :3.046 Max. :1.3102
## HB_EGF HCC_4 Hepatocyte_Growth_Factor_HGF I_309
## Min. : 3.521 Min. :-4.343 Min. :-0.61619 Min. :2.041
## 1st Qu.: 5.949 1st Qu.:-3.772 1st Qu.:-0.05661 1st Qu.:2.724
## Median : 6.980 Median :-3.540 Median : 0.18232 Median :2.944
## Mean : 6.844 Mean :-3.538 Mean : 0.18076 Mean :2.921
## 3rd Qu.: 7.745 3rd Qu.:-3.352 3rd Qu.: 0.33647 3rd Qu.:3.135
## Max. :10.359 Max. :-2.489 Max. : 1.09861 Max. :3.689
## ICAM_1 IGF_BP_2 IL_11 IL_13
## Min. :-1.4661 Min. :4.718 Min. :2.031 Min. :1.232
## 1st Qu.:-0.7671 1st Qu.:5.127 1st Qu.:3.960 1st Qu.:1.274
## Median :-0.5903 Median :5.255 Median :4.838 Median :1.283
## Mean :-0.5958 Mean :5.263 Mean :4.651 Mean :1.283
## 3rd Qu.:-0.3574 3rd Qu.:5.402 3rd Qu.:5.482 3rd Qu.:1.292
## Max. : 0.3602 Max. :5.916 Max. :8.692 Max. :1.310
## IL_16 IL_17E IL_1alpha IL_3
## Min. :0.9568 Min. :1.582 Min. :-8.468 Min. :-5.521
## 1st Qu.:2.4411 1st Qu.:3.637 1st Qu.:-7.849 1st Qu.:-4.324
## Median :2.8763 Median :4.723 Median :-7.562 Median :-3.963
## Mean :2.8176 Mean :4.774 Mean :-7.549 Mean :-3.976
## 3rd Qu.:3.3514 3rd Qu.:5.415 3rd Qu.:-7.279 3rd Qu.:-3.576
## Max. :4.1028 Max. :8.081 Max. :-6.377 Max. :-3.079
## IL_4 IL_5 IL_6 IL_6_Receptor
## Min. :0.5306 Min. :-1.04982 Min. :-1.53428 Min. :-0.74560
## 1st Qu.:1.4586 1st Qu.:-0.03062 1st Qu.:-0.40924 1st Qu.:-0.20131
## Median :1.7226 Median : 0.22234 Median :-0.07205 Median : 0.00000
## Mean :1.7445 Mean : 0.22853 Mean :-0.05216 Mean : 0.06213
## 3rd Qu.:2.0669 3rd Qu.: 0.53063 3rd Qu.: 0.34805 3rd Qu.: 0.27297
## Max. :2.7081 Max. : 1.13140 Max. : 1.00562 Max. : 0.77048
## IL_7 IL_8 IP_10_Inducible_Protein_10 IgA
## Min. :1.310 Min. :1.615 Min. :4.263 Min. :-7.621
## 1st Qu.:2.379 1st Qu.:1.684 1st Qu.:5.323 1st Qu.:-6.571
## Median :3.148 Median :1.702 Median :5.617 Median :-6.012
## Mean :3.143 Mean :1.704 Mean :5.636 Mean :-6.066
## 3rd Qu.:3.706 3rd Qu.:1.725 3rd Qu.:5.917 3rd Qu.:-5.606
## Max. :5.000 Max. :1.836 Max. :7.208 Max. :-4.733
## Insulin Kidney_Injury_Molecule_1_KIM_1 LOX_1
## Min. :-2.0099 Min. :-1.251 Min. :0.0000
## 1st Qu.:-1.4466 1st Qu.:-1.209 1st Qu.:0.9649
## Median :-1.2169 Median :-1.187 Median :1.2238
## Mean :-1.1998 Mean :-1.188 Mean :1.2085
## 3rd Qu.:-1.0105 3rd Qu.:-1.166 3rd Qu.:1.4351
## Max. :-0.5025 Max. :-1.124 Max. :2.3979
## Leptin Lipoprotein_a MCP_1 MCP_2
## Min. :-1.9471 Min. :-6.571 Min. :5.889 Min. :0.4006
## 1st Qu.:-1.6334 1st Qu.:-5.116 1st Qu.:6.318 1st Qu.:1.5304
## Median :-1.4294 Median :-4.657 Median :6.482 Median :1.8528
## Mean :-1.4363 Mean :-4.515 Mean :6.480 Mean :1.8104
## 3rd Qu.:-1.2409 3rd Qu.:-4.017 3rd Qu.:6.627 3rd Qu.:2.0827
## Max. :-0.8387 Max. :-2.040 Max. :7.065 Max. :3.7545
## MIF MIP_1alpha MIP_1beta MMP_2
## Min. :-2.797 Min. :1.008 Min. :1.917 Min. :0.6248
## 1st Qu.:-2.120 1st Qu.:3.302 1st Qu.:2.485 1st Qu.:2.5513
## Median :-1.966 Median :3.736 Median :2.773 Median :2.9937
## Mean :-1.932 Mean :3.898 Mean :2.784 Mean :3.0347
## 3rd Qu.:-1.715 3rd Qu.:4.686 3rd Qu.:3.079 3rd Qu.:3.4798
## Max. :-1.109 Max. :5.735 Max. :3.784 Max. :6.0996
## MMP_3 MMP10 MMP7 Myoglobin
## Min. :-3.650 Min. :-4.948 Min. :-7.5346 Min. :-3.2968
## 1st Qu.:-2.852 1st Qu.:-4.075 1st Qu.:-4.9634 1st Qu.:-2.0217
## Median :-2.532 Median :-3.612 Median :-4.0302 Median :-1.5874
## Mean :-2.490 Mean :-3.676 Mean :-4.0148 Mean :-1.4165
## 3rd Qu.:-2.120 3rd Qu.:-3.331 3rd Qu.:-3.1640 3rd Qu.:-0.7765
## Max. :-1.171 Max. :-2.900 Max. :-0.1953 Max. : 1.1314
## NT_proBNP NrCAM Osteopontin PAI_1
## Min. :3.611 Min. :2.890 Min. :4.078 Min. :-0.990849
## 1st Qu.:4.174 1st Qu.:3.871 1st Qu.:4.892 1st Qu.:-0.334043
## Median :4.477 Median :4.317 Median :5.168 Median : 0.000000
## Mean :4.488 Mean :4.291 Mean :5.177 Mean :-0.003947
## 3rd Qu.:4.794 3rd Qu.:4.725 3rd Qu.:5.410 3rd Qu.: 0.303112
## Max. :5.398 Max. :5.690 Max. :6.315 Max. : 0.885785
## PAPP_A PLGF PYY Pancreatic_polypeptide
## Min. :-3.152 Min. :2.639 Min. :2.398 Min. :-1.609438
## 1st Qu.:-2.971 1st Qu.:3.689 1st Qu.:2.833 1st Qu.:-0.506693
## Median :-2.841 Median :3.892 Median :2.996 Median : 0.138816
## Mean :-2.845 Mean :3.884 Mean :2.976 Mean :-0.005258
## 3rd Qu.:-2.719 3rd Qu.:4.123 3rd Qu.:3.178 3rd Qu.: 0.470004
## Max. :-2.488 Max. :4.710 Max. :3.738 Max. : 1.504077
## Prolactin Prostatic_Acid_Phosphatase Protein_S
## Min. :-0.38566 Min. :-1.800 Min. :-3.154
## 1st Qu.:-0.16558 1st Qu.:-1.739 1st Qu.:-2.579
## Median : 0.00000 Median :-1.690 Median :-2.259
## Mean : 0.05195 Mean :-1.692 Mean :-2.268
## 3rd Qu.: 0.18232 3rd Qu.:-1.659 3rd Qu.:-1.924
## Max. : 0.78846 Max. :-1.540 Max. :-1.547
## Pulmonary_and_Activation_Regulat RANTES Resistin
## Min. :-2.4418 Min. :-7.236 Min. :-30.156
## 1st Qu.:-1.8326 1st Qu.:-6.725 1st Qu.:-22.131
## Median :-1.5141 Median :-6.571 Median :-18.014
## Mean :-1.5007 Mean :-6.540 Mean :-18.245
## 3rd Qu.:-1.1712 3rd Qu.:-6.392 3rd Qu.:-15.202
## Max. :-0.4463 Max. :-5.843 Max. : -6.594
## S100b SGOT SHBG SOD
## Min. :0.1874 Min. :-1.8971 Min. :-3.730 Min. :4.382
## 1st Qu.:0.9600 1st Qu.:-0.7498 1st Qu.:-3.052 1st Qu.:5.006
## Median :1.1571 Median :-0.4780 Median :-2.711 Median :5.313
## Mean :1.1819 Mean :-0.4898 Mean :-2.686 Mean :5.302
## 3rd Qu.:1.3807 3rd Qu.:-0.2138 3rd Qu.:-2.343 3rd Qu.:5.547
## Max. :2.1950 Max. : 0.1823 Max. :-1.561 Max. :6.461
## Serum_Amyloid_P Sortilin Stem_Cell_Factor TGF_alpha
## Min. :-7.182 Min. :1.508 Min. :2.219 Min. : 7.500
## 1st Qu.:-6.438 1st Qu.:3.177 1st Qu.:3.045 1st Qu.: 9.062
## Median :-6.215 Median :3.867 Median :3.314 Median : 9.596
## Mean :-6.083 Mean :3.787 Mean :3.267 Mean : 9.776
## 3rd Qu.:-5.607 3rd Qu.:4.371 3rd Qu.:3.466 3rd Qu.:10.612
## Max. :-4.699 Max. :5.681 Max. :4.078 Max. :13.083
## TIMP_1 TNF_RII TRAIL_R3 TTR_prealbumin
## Min. : 8.198 Min. :-1.6607 Min. :-1.30636 Min. :2.485
## 1st Qu.:10.530 1st Qu.:-0.8675 1st Qu.:-0.73332 1st Qu.:2.773
## Median :11.341 Median :-0.6541 Median :-0.55547 Median :2.890
## Mean :11.520 Mean :-0.6270 Mean :-0.58640 Mean :2.854
## 3rd Qu.:12.352 3rd Qu.:-0.3320 3rd Qu.:-0.47065 3rd Qu.:2.944
## Max. :16.547 Max. : 0.4055 Max. : 0.09622 Max. :3.091
## Tamm_Horsfall_Protein_THP Thrombomodulin Thrombopoietin
## Min. :-3.206 Min. :-2.054 Min. :-1.5396
## 1st Qu.:-3.144 1st Qu.:-1.675 1st Qu.:-0.8383
## Median :-3.126 Median :-1.534 Median :-0.7039
## Mean :-3.123 Mean :-1.533 Mean :-0.7192
## 3rd Qu.:-3.101 3rd Qu.:-1.341 3rd Qu.:-0.6289
## Max. :-3.041 Max. :-1.019 Max. :-0.3029
## Thymus_Expressed_Chemokine_TECK Thyroid_Stimulating_Hormone
## Min. :2.141 Min. :-6.190
## 1st Qu.:3.283 1st Qu.:-4.733
## Median :3.753 Median :-4.269
## Mean :3.770 Mean :-4.221
## 3rd Qu.:4.316 3rd Qu.:-3.828
## Max. :5.681 Max. :-2.040
## Thyroxine_Binding_Globulin Tissue_Factor Transferrin
## Min. :-2.3026 Min. :0.0000 Min. :2.282
## 1st Qu.:-1.7148 1st Qu.:0.7053 1st Qu.:2.708
## Median :-1.4919 Median :1.1473 Median :2.890
## Mean :-1.4902 Mean :1.1356 Mean :2.900
## 3rd Qu.:-1.2379 3rd Qu.:1.5149 3rd Qu.:3.135
## Max. :-0.5978 Max. :2.7081 Max. :3.497
## Trefoil_Factor_3_TFF3 VCAM_1 VEGF Vitronectin
## Min. :-4.906 Min. :2.028 Min. :12.23 Min. :-1.07881
## 1st Qu.:-4.200 1st Qu.:2.420 1st Qu.:15.03 1st Qu.:-0.46204
## Median :-3.912 Median :2.674 Median :17.08 Median :-0.28106
## Mean :-3.947 Mean :2.644 Mean :16.70 Mean :-0.26833
## 3rd Qu.:-3.772 3rd Qu.:2.833 3rd Qu.:18.19 3rd Qu.:-0.05394
## Max. :-3.170 Max. :3.466 Max. :21.18 Max. : 0.40547
## von_Willebrand_Factor Class E4 E3
## Min. :-4.920 Impaired:18 Min. :0.000 Min. :0.0000
## 1st Qu.:-4.269 Control :48 1st Qu.:0.000 1st Qu.:1.0000
## Median :-4.017 Median :0.000 Median :1.0000
## Mean :-4.014 Mean :0.303 Mean :0.9848
## 3rd Qu.:-3.730 3rd Qu.:1.000 3rd Qu.:1.0000
## Max. :-3.058 Max. :1.000 Max. :1.0000
## E2
## Min. :0.00000
## 1st Qu.:0.00000
## Median :0.00000
## Mean :0.06061
## 3rd Qu.:0.00000
## Max. :1.00000##################################
# Formulating a data type assessment summary
##################################
PDA <- Alzheimer_Train
(PDA.Summary <- data.frame(
Column.Index=c(1:length(names(PDA))),
Column.Name= names(PDA),
Column.Type=sapply(PDA, function(x) class(x)),
row.names=NULL)
)## Column.Index Column.Name Column.Type
## 1 1 ACE_CD143_Angiotensin_Converti numeric
## 2 2 ACTH_Adrenocorticotropic_Hormon numeric
## 3 3 AXL numeric
## 4 4 Adiponectin numeric
## 5 5 Alpha_1_Antichymotrypsin numeric
## 6 6 Alpha_1_Antitrypsin numeric
## 7 7 Alpha_1_Microglobulin numeric
## 8 8 Alpha_2_Macroglobulin numeric
## 9 9 Angiopoietin_2_ANG_2 numeric
## 10 10 Angiotensinogen numeric
## 11 11 Apolipoprotein_A_IV numeric
## 12 12 Apolipoprotein_A1 numeric
## 13 13 Apolipoprotein_A2 numeric
## 14 14 Apolipoprotein_B numeric
## 15 15 Apolipoprotein_CI numeric
## 16 16 Apolipoprotein_CIII numeric
## 17 17 Apolipoprotein_D numeric
## 18 18 Apolipoprotein_E numeric
## 19 19 Apolipoprotein_H numeric
## 20 20 B_Lymphocyte_Chemoattractant_BL numeric
## 21 21 BMP_6 numeric
## 22 22 Beta_2_Microglobulin numeric
## 23 23 Betacellulin integer
## 24 24 C_Reactive_Protein numeric
## 25 25 CD40 numeric
## 26 26 CD5L numeric
## 27 27 Calbindin numeric
## 28 28 Calcitonin numeric
## 29 29 CgA numeric
## 30 30 Clusterin_Apo_J numeric
## 31 31 Complement_3 numeric
## 32 32 Complement_Factor_H numeric
## 33 33 Connective_Tissue_Growth_Factor numeric
## 34 34 Cortisol numeric
## 35 35 Creatine_Kinase_MB numeric
## 36 36 Cystatin_C numeric
## 37 37 EGF_R numeric
## 38 38 EN_RAGE numeric
## 39 39 ENA_78 numeric
## 40 40 Eotaxin_3 integer
## 41 41 FAS numeric
## 42 42 FSH_Follicle_Stimulation_Hormon numeric
## 43 43 Fas_Ligand numeric
## 44 44 Fatty_Acid_Binding_Protein numeric
## 45 45 Ferritin numeric
## 46 46 Fetuin_A numeric
## 47 47 Fibrinogen numeric
## 48 48 GRO_alpha numeric
## 49 49 Gamma_Interferon_induced_Monokin numeric
## 50 50 Glutathione_S_Transferase_alpha numeric
## 51 51 HB_EGF numeric
## 52 52 HCC_4 numeric
## 53 53 Hepatocyte_Growth_Factor_HGF numeric
## 54 54 I_309 numeric
## 55 55 ICAM_1 numeric
## 56 56 IGF_BP_2 numeric
## 57 57 IL_11 numeric
## 58 58 IL_13 numeric
## 59 59 IL_16 numeric
## 60 60 IL_17E numeric
## 61 61 IL_1alpha numeric
## 62 62 IL_3 numeric
## 63 63 IL_4 numeric
## 64 64 IL_5 numeric
## 65 65 IL_6 numeric
## 66 66 IL_6_Receptor numeric
## 67 67 IL_7 numeric
## 68 68 IL_8 numeric
## 69 69 IP_10_Inducible_Protein_10 numeric
## 70 70 IgA numeric
## 71 71 Insulin numeric
## 72 72 Kidney_Injury_Molecule_1_KIM_1 numeric
## 73 73 LOX_1 numeric
## 74 74 Leptin numeric
## 75 75 Lipoprotein_a numeric
## 76 76 MCP_1 numeric
## 77 77 MCP_2 numeric
## 78 78 MIF numeric
## 79 79 MIP_1alpha numeric
## 80 80 MIP_1beta numeric
## 81 81 MMP_2 numeric
## 82 82 MMP_3 numeric
## 83 83 MMP10 numeric
## 84 84 MMP7 numeric
## 85 85 Myoglobin numeric
## 86 86 NT_proBNP numeric
## 87 87 NrCAM numeric
## 88 88 Osteopontin numeric
## 89 89 PAI_1 numeric
## 90 90 PAPP_A numeric
## 91 91 PLGF numeric
## 92 92 PYY numeric
## 93 93 Pancreatic_polypeptide numeric
## 94 94 Prolactin numeric
## 95 95 Prostatic_Acid_Phosphatase numeric
## 96 96 Protein_S numeric
## 97 97 Pulmonary_and_Activation_Regulat numeric
## 98 98 RANTES numeric
## 99 99 Resistin numeric
## 100 100 S100b numeric
## 101 101 SGOT numeric
## 102 102 SHBG numeric
## 103 103 SOD numeric
## 104 104 Serum_Amyloid_P numeric
## 105 105 Sortilin numeric
## 106 106 Stem_Cell_Factor numeric
## 107 107 TGF_alpha numeric
## 108 108 TIMP_1 numeric
## 109 109 TNF_RII numeric
## 110 110 TRAIL_R3 numeric
## 111 111 TTR_prealbumin numeric
## 112 112 Tamm_Horsfall_Protein_THP numeric
## 113 113 Thrombomodulin numeric
## 114 114 Thrombopoietin numeric
## 115 115 Thymus_Expressed_Chemokine_TECK numeric
## 116 116 Thyroid_Stimulating_Hormone numeric
## 117 117 Thyroxine_Binding_Globulin numeric
## 118 118 Tissue_Factor numeric
## 119 119 Transferrin numeric
## 120 120 Trefoil_Factor_3_TFF3 numeric
## 121 121 VCAM_1 numeric
## 122 122 VEGF numeric
## 123 123 Vitronectin numeric
## 124 124 von_Willebrand_Factor numeric
## 125 125 Class factor
## 126 126 E4 numeric
## 127 127 E3 numeric
## 128 128 E2 numeric1.2 Data Quality Assessment
[A] No missing observations noted for any variable.
[B] Low variance observed for 2 variables with First.Second.Mode.Ratio>5.
[B.1] E2 variable (factor)
[B.2] E3 variable (factor)
[C] No low variance observed for any variable with Unique.Count.Ratio<0.01.
[D] No high skewness observed for any variable with Skewness>3 or Skewness<(-3).
Code Chunk | Output
##################################
# Loading dataset
##################################
DQA <- Alzheimer_Train
##################################
# Formulating an overall data quality assessment summary
##################################
(DQA.Summary <- data.frame(
Column.Index=c(1:length(names(DQA))),
Column.Name= names(DQA),
Column.Type=sapply(DQA, function(x) class(x)),
Row.Count=sapply(DQA, function(x) nrow(DQA)),
NA.Count=sapply(DQA,function(x)sum(is.na(x))),
Fill.Rate=sapply(DQA,function(x)format(round((sum(!is.na(x))/nrow(DQA)),3),nsmall=3)),
row.names=NULL)
)## Column.Index Column.Name Column.Type Row.Count
## 1 1 ACE_CD143_Angiotensin_Converti numeric 267
## 2 2 ACTH_Adrenocorticotropic_Hormon numeric 267
## 3 3 AXL numeric 267
## 4 4 Adiponectin numeric 267
## 5 5 Alpha_1_Antichymotrypsin numeric 267
## 6 6 Alpha_1_Antitrypsin numeric 267
## 7 7 Alpha_1_Microglobulin numeric 267
## 8 8 Alpha_2_Macroglobulin numeric 267
## 9 9 Angiopoietin_2_ANG_2 numeric 267
## 10 10 Angiotensinogen numeric 267
## 11 11 Apolipoprotein_A_IV numeric 267
## 12 12 Apolipoprotein_A1 numeric 267
## 13 13 Apolipoprotein_A2 numeric 267
## 14 14 Apolipoprotein_B numeric 267
## 15 15 Apolipoprotein_CI numeric 267
## 16 16 Apolipoprotein_CIII numeric 267
## 17 17 Apolipoprotein_D numeric 267
## 18 18 Apolipoprotein_E numeric 267
## 19 19 Apolipoprotein_H numeric 267
## 20 20 B_Lymphocyte_Chemoattractant_BL numeric 267
## 21 21 BMP_6 numeric 267
## 22 22 Beta_2_Microglobulin numeric 267
## 23 23 Betacellulin integer 267
## 24 24 C_Reactive_Protein numeric 267
## 25 25 CD40 numeric 267
## 26 26 CD5L numeric 267
## 27 27 Calbindin numeric 267
## 28 28 Calcitonin numeric 267
## 29 29 CgA numeric 267
## 30 30 Clusterin_Apo_J numeric 267
## 31 31 Complement_3 numeric 267
## 32 32 Complement_Factor_H numeric 267
## 33 33 Connective_Tissue_Growth_Factor numeric 267
## 34 34 Cortisol numeric 267
## 35 35 Creatine_Kinase_MB numeric 267
## 36 36 Cystatin_C numeric 267
## 37 37 EGF_R numeric 267
## 38 38 EN_RAGE numeric 267
## 39 39 ENA_78 numeric 267
## 40 40 Eotaxin_3 integer 267
## 41 41 FAS numeric 267
## 42 42 FSH_Follicle_Stimulation_Hormon numeric 267
## 43 43 Fas_Ligand numeric 267
## 44 44 Fatty_Acid_Binding_Protein numeric 267
## 45 45 Ferritin numeric 267
## 46 46 Fetuin_A numeric 267
## 47 47 Fibrinogen numeric 267
## 48 48 GRO_alpha numeric 267
## 49 49 Gamma_Interferon_induced_Monokin numeric 267
## 50 50 Glutathione_S_Transferase_alpha numeric 267
## 51 51 HB_EGF numeric 267
## 52 52 HCC_4 numeric 267
## 53 53 Hepatocyte_Growth_Factor_HGF numeric 267
## 54 54 I_309 numeric 267
## 55 55 ICAM_1 numeric 267
## 56 56 IGF_BP_2 numeric 267
## 57 57 IL_11 numeric 267
## 58 58 IL_13 numeric 267
## 59 59 IL_16 numeric 267
## 60 60 IL_17E numeric 267
## 61 61 IL_1alpha numeric 267
## 62 62 IL_3 numeric 267
## 63 63 IL_4 numeric 267
## 64 64 IL_5 numeric 267
## 65 65 IL_6 numeric 267
## 66 66 IL_6_Receptor numeric 267
## 67 67 IL_7 numeric 267
## 68 68 IL_8 numeric 267
## 69 69 IP_10_Inducible_Protein_10 numeric 267
## 70 70 IgA numeric 267
## 71 71 Insulin numeric 267
## 72 72 Kidney_Injury_Molecule_1_KIM_1 numeric 267
## 73 73 LOX_1 numeric 267
## 74 74 Leptin numeric 267
## 75 75 Lipoprotein_a numeric 267
## 76 76 MCP_1 numeric 267
## 77 77 MCP_2 numeric 267
## 78 78 MIF numeric 267
## 79 79 MIP_1alpha numeric 267
## 80 80 MIP_1beta numeric 267
## 81 81 MMP_2 numeric 267
## 82 82 MMP_3 numeric 267
## 83 83 MMP10 numeric 267
## 84 84 MMP7 numeric 267
## 85 85 Myoglobin numeric 267
## 86 86 NT_proBNP numeric 267
## 87 87 NrCAM numeric 267
## 88 88 Osteopontin numeric 267
## 89 89 PAI_1 numeric 267
## 90 90 PAPP_A numeric 267
## 91 91 PLGF numeric 267
## 92 92 PYY numeric 267
## 93 93 Pancreatic_polypeptide numeric 267
## 94 94 Prolactin numeric 267
## 95 95 Prostatic_Acid_Phosphatase numeric 267
## 96 96 Protein_S numeric 267
## 97 97 Pulmonary_and_Activation_Regulat numeric 267
## 98 98 RANTES numeric 267
## 99 99 Resistin numeric 267
## 100 100 S100b numeric 267
## 101 101 SGOT numeric 267
## 102 102 SHBG numeric 267
## 103 103 SOD numeric 267
## 104 104 Serum_Amyloid_P numeric 267
## 105 105 Sortilin numeric 267
## 106 106 Stem_Cell_Factor numeric 267
## 107 107 TGF_alpha numeric 267
## 108 108 TIMP_1 numeric 267
## 109 109 TNF_RII numeric 267
## 110 110 TRAIL_R3 numeric 267
## 111 111 TTR_prealbumin numeric 267
## 112 112 Tamm_Horsfall_Protein_THP numeric 267
## 113 113 Thrombomodulin numeric 267
## 114 114 Thrombopoietin numeric 267
## 115 115 Thymus_Expressed_Chemokine_TECK numeric 267
## 116 116 Thyroid_Stimulating_Hormone numeric 267
## 117 117 Thyroxine_Binding_Globulin numeric 267
## 118 118 Tissue_Factor numeric 267
## 119 119 Transferrin numeric 267
## 120 120 Trefoil_Factor_3_TFF3 numeric 267
## 121 121 VCAM_1 numeric 267
## 122 122 VEGF numeric 267
## 123 123 Vitronectin numeric 267
## 124 124 von_Willebrand_Factor numeric 267
## 125 125 Class factor 267
## 126 126 E4 numeric 267
## 127 127 E3 numeric 267
## 128 128 E2 numeric 267
## NA.Count Fill.Rate
## 1 0 1.000
## 2 0 1.000
## 3 0 1.000
## 4 0 1.000
## 5 0 1.000
## 6 0 1.000
## 7 0 1.000
## 8 0 1.000
## 9 0 1.000
## 10 0 1.000
## 11 0 1.000
## 12 0 1.000
## 13 0 1.000
## 14 0 1.000
## 15 0 1.000
## 16 0 1.000
## 17 0 1.000
## 18 0 1.000
## 19 0 1.000
## 20 0 1.000
## 21 0 1.000
## 22 0 1.000
## 23 0 1.000
## 24 0 1.000
## 25 0 1.000
## 26 0 1.000
## 27 0 1.000
## 28 0 1.000
## 29 0 1.000
## 30 0 1.000
## 31 0 1.000
## 32 0 1.000
## 33 0 1.000
## 34 0 1.000
## 35 0 1.000
## 36 0 1.000
## 37 0 1.000
## 38 0 1.000
## 39 0 1.000
## 40 0 1.000
## 41 0 1.000
## 42 0 1.000
## 43 0 1.000
## 44 0 1.000
## 45 0 1.000
## 46 0 1.000
## 47 0 1.000
## 48 0 1.000
## 49 0 1.000
## 50 0 1.000
## 51 0 1.000
## 52 0 1.000
## 53 0 1.000
## 54 0 1.000
## 55 0 1.000
## 56 0 1.000
## 57 0 1.000
## 58 0 1.000
## 59 0 1.000
## 60 0 1.000
## 61 0 1.000
## 62 0 1.000
## 63 0 1.000
## 64 0 1.000
## 65 0 1.000
## 66 0 1.000
## 67 0 1.000
## 68 0 1.000
## 69 0 1.000
## 70 0 1.000
## 71 0 1.000
## 72 0 1.000
## 73 0 1.000
## 74 0 1.000
## 75 0 1.000
## 76 0 1.000
## 77 0 1.000
## 78 0 1.000
## 79 0 1.000
## 80 0 1.000
## 81 0 1.000
## 82 0 1.000
## 83 0 1.000
## 84 0 1.000
## 85 0 1.000
## 86 0 1.000
## 87 0 1.000
## 88 0 1.000
## 89 0 1.000
## 90 0 1.000
## 91 0 1.000
## 92 0 1.000
## 93 0 1.000
## 94 0 1.000
## 95 0 1.000
## 96 0 1.000
## 97 0 1.000
## 98 0 1.000
## 99 0 1.000
## 100 0 1.000
## 101 0 1.000
## 102 0 1.000
## 103 0 1.000
## 104 0 1.000
## 105 0 1.000
## 106 0 1.000
## 107 0 1.000
## 108 0 1.000
## 109 0 1.000
## 110 0 1.000
## 111 0 1.000
## 112 0 1.000
## 113 0 1.000
## 114 0 1.000
## 115 0 1.000
## 116 0 1.000
## 117 0 1.000
## 118 0 1.000
## 119 0 1.000
## 120 0 1.000
## 121 0 1.000
## 122 0 1.000
## 123 0 1.000
## 124 0 1.000
## 125 0 1.000
## 126 0 1.000
## 127 0 1.000
## 128 0 1.000##################################
# Listing all predictors
##################################
DQA.Predictors <- DQA[,!names(DQA) %in% c("Class")]
##################################
# Listing all numeric predictors
##################################
DQA.Predictors.Numeric <- DQA.Predictors[,!names(DQA.Predictors) %in% c("E2","E3","E4")]
DQA.Predictors.Numeric <- as.data.frame(sapply(DQA.Predictors.Numeric,function(x) as.numeric(x)))
if (length(names(DQA.Predictors.Numeric))>0) {
print(paste0("There are ",
(length(names(DQA.Predictors.Numeric))),
" numeric predictor variable(s)."))
} else {
print("There are no numeric predictor variables.")
}## [1] "There are 124 numeric predictor variable(s)."##################################
# Listing all factor predictors
##################################
DQA.Predictors.Factor <- DQA.Predictors[,names(DQA.Predictors) %in% c("E2","E3","E4")]
DQA.Predictors.Factor <- as.data.frame(sapply(DQA.Predictors.Factor,function(x) as.factor(x)))
if (length(names(DQA.Predictors.Factor))>0) {
print(paste0("There are ",
(length(names(DQA.Predictors.Factor))),
" factor predictor variable(s)."))
} else {
print("There are no factor predictor variables.")
}## [1] "There are 3 factor predictor variable(s)."##################################
# Formulating a data quality assessment summary for factor predictors
##################################
if (length(names(DQA.Predictors.Factor))>0) {
##################################
# Formulating a function to determine the first mode
##################################
FirstModes <- function(x) {
ux <- unique(na.omit(x))
tab <- tabulate(match(x, ux))
ux[tab == max(tab)]
}
##################################
# Formulating a function to determine the second mode
##################################
SecondModes <- function(x) {
ux <- unique(na.omit(x))
tab <- tabulate(match(x, ux))
fm = ux[tab == max(tab)]
sm = x[!(x %in% fm)]
usm <- unique(sm)
tabsm <- tabulate(match(sm, usm))
ifelse(is.na(usm[tabsm == max(tabsm)])==TRUE,
return("x"),
return(usm[tabsm == max(tabsm)]))
}
(DQA.Predictors.Factor.Summary <- data.frame(
Column.Name= names(DQA.Predictors.Factor),
Column.Type=sapply(DQA.Predictors.Factor, function(x) class(x)),
Unique.Count=sapply(DQA.Predictors.Factor, function(x) length(unique(x))),
First.Mode.Value=sapply(DQA.Predictors.Factor, function(x) as.character(FirstModes(x)[1])),
Second.Mode.Value=sapply(DQA.Predictors.Factor, function(x) as.character(SecondModes(x)[1])),
First.Mode.Count=sapply(DQA.Predictors.Factor, function(x) sum(na.omit(x) == FirstModes(x)[1])),
Second.Mode.Count=sapply(DQA.Predictors.Factor, function(x) sum(na.omit(x) == SecondModes(x)[1])),
Unique.Count.Ratio=sapply(DQA.Predictors.Factor, function(x) format(round((length(unique(x))/nrow(DQA.Predictors.Factor)),3), nsmall=3)),
First.Second.Mode.Ratio=sapply(DQA.Predictors.Factor, function(x) format(round((sum(na.omit(x) == FirstModes(x)[1])/sum(na.omit(x) == SecondModes(x)[1])),3), nsmall=3)),
row.names=NULL)
)
} ## Column.Name Column.Type Unique.Count First.Mode.Value Second.Mode.Value
## 1 E4 character 2 0 1
## 2 E3 character 2 1 0
## 3 E2 character 2 0 1
## First.Mode.Count Second.Mode.Count Unique.Count.Ratio First.Second.Mode.Ratio
## 1 160 107 0.007 1.495
## 2 245 22 0.007 11.136
## 3 224 43 0.007 5.209##################################
# Formulating a data quality assessment summary for numeric predictors
##################################
if (length(names(DQA.Predictors.Numeric))>0) {
##################################
# Formulating a function to determine the first mode
##################################
FirstModes <- function(x) {
ux <- unique(na.omit(x))
tab <- tabulate(match(x, ux))
ux[tab == max(tab)]
}
##################################
# Formulating a function to determine the second mode
##################################
SecondModes <- function(x) {
ux <- unique(na.omit(x))
tab <- tabulate(match(x, ux))
fm = ux[tab == max(tab)]
sm = na.omit(x)[!(na.omit(x) %in% fm)]
usm <- unique(sm)
tabsm <- tabulate(match(sm, usm))
ifelse(is.na(usm[tabsm == max(tabsm)])==TRUE,
return(0.00001),
return(usm[tabsm == max(tabsm)]))
}
(DQA.Predictors.Numeric.Summary <- data.frame(
Column.Name= names(DQA.Predictors.Numeric),
Column.Type=sapply(DQA.Predictors.Numeric, function(x) class(x)),
Unique.Count=sapply(DQA.Predictors.Numeric, function(x) length(unique(x))),
Unique.Count.Ratio=sapply(DQA.Predictors.Numeric, function(x) format(round((length(unique(x))/nrow(DQA.Predictors.Numeric)),3), nsmall=3)),
First.Mode.Value=sapply(DQA.Predictors.Numeric, function(x) format(round((FirstModes(x)[1]),3),nsmall=3)),
Second.Mode.Value=sapply(DQA.Predictors.Numeric, function(x) format(round((SecondModes(x)[1]),3),nsmall=3)),
First.Mode.Count=sapply(DQA.Predictors.Numeric, function(x) sum(na.omit(x) == FirstModes(x)[1])),
Second.Mode.Count=sapply(DQA.Predictors.Numeric, function(x) sum(na.omit(x) == SecondModes(x)[1])),
First.Second.Mode.Ratio=sapply(DQA.Predictors.Numeric, function(x) format(round((sum(na.omit(x) == FirstModes(x)[1])/sum(na.omit(x) == SecondModes(x)[1])),3), nsmall=3)),
Minimum=sapply(DQA.Predictors.Numeric, function(x) format(round(min(x,na.rm = TRUE),3), nsmall=3)),
Mean=sapply(DQA.Predictors.Numeric, function(x) format(round(mean(x,na.rm = TRUE),3), nsmall=3)),
Median=sapply(DQA.Predictors.Numeric, function(x) format(round(median(x,na.rm = TRUE),3), nsmall=3)),
Maximum=sapply(DQA.Predictors.Numeric, function(x) format(round(max(x,na.rm = TRUE),3), nsmall=3)),
Skewness=sapply(DQA.Predictors.Numeric, function(x) format(round(skewness(x,na.rm = TRUE),3), nsmall=3)),
Kurtosis=sapply(DQA.Predictors.Numeric, function(x) format(round(kurtosis(x,na.rm = TRUE),3), nsmall=3)),
Percentile25th=sapply(DQA.Predictors.Numeric, function(x) format(round(quantile(x,probs=0.25,na.rm = TRUE),3), nsmall=3)),
Percentile75th=sapply(DQA.Predictors.Numeric, function(x) format(round(quantile(x,probs=0.75,na.rm = TRUE),3), nsmall=3)),
row.names=NULL)
)
}## Column.Name Column.Type Unique.Count
## 1 ACE_CD143_Angiotensin_Converti numeric 53
## 2 ACTH_Adrenocorticotropic_Hormon numeric 32
## 3 AXL numeric 59
## 4 Adiponectin numeric 91
## 5 Alpha_1_Antichymotrypsin numeric 65
## 6 Alpha_1_Antitrypsin numeric 64
## 7 Alpha_1_Microglobulin numeric 82
## 8 Alpha_2_Macroglobulin numeric 47
## 9 Angiopoietin_2_ANG_2 numeric 36
## 10 Angiotensinogen numeric 135
## 11 Apolipoprotein_A_IV numeric 53
## 12 Apolipoprotein_A1 numeric 83
## 13 Apolipoprotein_A2 numeric 85
## 14 Apolipoprotein_B numeric 83
## 15 Apolipoprotein_CI numeric 49
## 16 Apolipoprotein_CIII numeric 82
## 17 Apolipoprotein_D numeric 63
## 18 Apolipoprotein_E numeric 79
## 19 Apolipoprotein_H numeric 82
## 20 B_Lymphocyte_Chemoattractant_BL numeric 35
## 21 BMP_6 numeric 42
## 22 Beta_2_Microglobulin numeric 50
## 23 Betacellulin numeric 36
## 24 C_Reactive_Protein numeric 135
## 25 CD40 numeric 34
## 26 CD5L numeric 82
## 27 Calbindin numeric 139
## 28 Calcitonin numeric 93
## 29 CgA numeric 105
## 30 Clusterin_Apo_J numeric 31
## 31 Complement_3 numeric 63
## 32 Complement_Factor_H numeric 87
## 33 Connective_Tissue_Growth_Factor numeric 26
## 34 Cortisol numeric 52
## 35 Creatine_Kinase_MB numeric 32
## 36 Cystatin_C numeric 212
## 37 EGF_R numeric 59
## 38 EN_RAGE numeric 95
## 39 ENA_78 numeric 39
## 40 Eotaxin_3 numeric 42
## 41 FAS numeric 52
## 42 FSH_Follicle_Stimulation_Hormon numeric 97
## 43 Fas_Ligand numeric 57
## 44 Fatty_Acid_Binding_Protein numeric 84
## 45 Ferritin numeric 75
## 46 Fetuin_A numeric 67
## 47 Fibrinogen numeric 91
## 48 GRO_alpha numeric 25
## 49 Gamma_Interferon_induced_Monokin numeric 209
## 50 Glutathione_S_Transferase_alpha numeric 42
## 51 HB_EGF numeric 54
## 52 HCC_4 numeric 53
## 53 Hepatocyte_Growth_Factor_HGF numeric 44
## 54 I_309 numeric 45
## 55 ICAM_1 numeric 68
## 56 IGF_BP_2 numeric 126
## 57 IL_11 numeric 75
## 58 IL_13 numeric 18
## 59 IL_16 numeric 55
## 60 IL_17E numeric 44
## 61 IL_1alpha numeric 60
## 62 IL_3 numeric 58
## 63 IL_4 numeric 47
## 64 IL_5 numeric 48
## 65 IL_6 numeric 53
## 66 IL_6_Receptor numeric 53
## 67 IL_7 numeric 46
## 68 IL_8 numeric 56
## 69 IP_10_Inducible_Protein_10 numeric 211
## 70 IgA numeric 94
## 71 Insulin numeric 55
## 72 Kidney_Injury_Molecule_1_KIM_1 numeric 50
## 73 LOX_1 numeric 67
## 74 Leptin numeric 82
## 75 Lipoprotein_a numeric 128
## 76 MCP_1 numeric 219
## 77 MCP_2 numeric 39
## 78 MIF numeric 43
## 79 MIP_1alpha numeric 49
## 80 MIP_1beta numeric 47
## 81 MMP_2 numeric 48
## 82 MMP_3 numeric 80
## 83 MMP10 numeric 56
## 84 MMP7 numeric 89
## 85 Myoglobin numeric 116
## 86 NT_proBNP numeric 111
## 87 NrCAM numeric 126
## 88 Osteopontin numeric 166
## 89 PAI_1 numeric 70
## 90 PAPP_A numeric 34
## 91 PLGF numeric 86
## 92 PYY numeric 34
## 93 Pancreatic_polypeptide numeric 81
## 94 Prolactin numeric 57
## 95 Prostatic_Acid_Phosphatase numeric 43
## 96 Protein_S numeric 24
## 97 Pulmonary_and_Activation_Regulat numeric 54
## 98 RANTES numeric 39
## 99 Resistin numeric 59
## 100 S100b numeric 35
## 101 SGOT numeric 75
## 102 SHBG numeric 92
## 103 SOD numeric 164
## 104 Serum_Amyloid_P numeric 74
## 105 Sortilin numeric 65
## 106 Stem_Cell_Factor numeric 44
## 107 TGF_alpha numeric 62
## 108 TIMP_1 numeric 56
## 109 TNF_RII numeric 72
## 110 TRAIL_R3 numeric 60
## 111 TTR_prealbumin numeric 16
## 112 Tamm_Horsfall_Protein_THP numeric 60
## 113 Thrombomodulin numeric 35
## 114 Thrombopoietin numeric 54
## 115 Thymus_Expressed_Chemokine_TECK numeric 37
## 116 Thyroid_Stimulating_Hormone numeric 66
## 117 Thyroxine_Binding_Globulin numeric 49
## 118 Tissue_Factor numeric 67
## 119 Transferrin numeric 30
## 120 Trefoil_Factor_3_TFF3 numeric 37
## 121 VCAM_1 numeric 40
## 122 VEGF numeric 200
## 123 Vitronectin numeric 71
## 124 von_Willebrand_Factor numeric 43
## Unique.Count.Ratio First.Mode.Value Second.Mode.Value First.Mode.Count
## 1 0.199 1.157 1.107 14
## 2 0.120 -1.609 -1.715 20
## 3 0.221 0.191 0.530 29
## 4 0.341 -5.991 -4.200 7
## 5 0.243 1.194 1.099 12
## 6 0.240 -12.907 -13.310 11
## 7 0.307 -3.244 -3.270 13
## 8 0.176 -179.087 -194.947 21
## 9 0.135 0.531 0.642 23
## 10 0.506 2.262 2.107 9
## 11 0.199 -2.040 -1.772 30
## 12 0.311 -7.902 -7.452 8
## 13 0.318 -0.968 -0.755 9
## 14 0.311 -6.211 -7.289 11
## 15 0.184 -1.715 -1.661 23
## 16 0.307 -2.120 -2.207 17
## 17 0.236 1.308 1.386 11
## 18 0.296 2.720 4.024 11
## 19 0.307 0.097 -0.383 14
## 20 0.131 2.371 1.981 36
## 21 0.157 -1.675 -1.845 30
## 22 0.187 0.095 0.182 38
## 23 0.135 51.000 42.000 50
## 24 0.506 -5.745 -6.571 7
## 25 0.127 -1.242 -1.273 25
## 26 0.307 0.095 0.182 17
## 27 0.521 21.495 20.891 8
## 28 0.348 0.693 0.956 15
## 29 0.393 315.308 361.583 9
## 30 0.116 2.773 2.890 25
## 31 0.236 -16.545 -18.173 15
## 32 0.326 4.024 4.475 22
## 33 0.097 0.693 0.788 25
## 34 0.195 12.000 11.000 38
## 35 0.120 -1.671 -1.724 27
## 36 0.794 8.470 8.357 4
## 37 0.221 -0.590 -0.700 12
## 38 0.356 -4.200 -4.423 11
## 39 0.146 -1.368 -1.364 39
## 40 0.157 64.000 44.000 38
## 41 0.195 -0.713 -0.528 23
## 42 0.363 -1.064 -1.361 10
## 43 0.213 3.101 2.792 19
## 44 0.315 0.624 0.269 9
## 45 0.281 2.382 3.329 8
## 46 0.251 1.281 1.224 15
## 47 0.341 -6.571 -7.601 7
## 48 0.094 1.398 1.372 32
## 49 0.783 2.789 2.584 4
## 50 0.157 0.968 0.985 20
## 51 0.202 6.413 6.560 17
## 52 0.199 -3.576 -3.689 15
## 53 0.165 0.095 0.182 45
## 54 0.169 2.944 2.996 21
## 55 0.255 -0.489 -0.590 19
## 56 0.472 5.328 5.187 7
## 57 0.281 2.031 5.122 16
## 58 0.067 1.283 1.274 41
## 59 0.206 3.077 2.924 21
## 60 0.165 5.325 4.749 30
## 61 0.225 -7.264 -7.849 35
## 62 0.217 -3.912 -4.075 20
## 63 0.176 1.808 1.209 25
## 64 0.180 0.182 0.336 27
## 65 0.199 0.096 -0.242 19
## 66 0.199 0.273 0.000 26
## 67 0.172 2.155 3.476 33
## 68 0.210 1.676 1.691 15
## 69 0.790 5.687 5.050 3
## 70 0.352 -6.645 -6.502 11
## 71 0.206 -1.277 -1.341 19
## 72 0.187 -1.172 -1.144 11
## 73 0.251 1.281 1.131 13
## 74 0.307 -1.329 -1.466 17
## 75 0.479 -4.343 -4.423 8
## 76 0.820 6.213 6.293 4
## 77 0.146 1.530 1.853 32
## 78 0.161 -1.897 -2.120 29
## 79 0.184 5.359 3.690 21
## 80 0.176 2.944 2.833 22
## 81 0.180 2.332 3.266 36
## 82 0.300 -2.207 -2.120 18
## 83 0.210 -3.689 -3.963 14
## 84 0.333 -3.774 -3.345 24
## 85 0.434 -2.040 -1.609 11
## 86 0.416 4.466 4.554 8
## 87 0.472 4.489 3.912 6
## 88 0.622 5.288 5.187 6
## 89 0.262 0.094 0.177 25
## 90 0.127 -2.971 -2.902 26
## 91 0.322 3.738 3.714 10
## 92 0.127 2.833 2.996 38
## 93 0.303 0.182 0.336 14
## 94 0.213 0.095 0.182 32
## 95 0.161 -1.690 -1.710 26
## 96 0.090 -2.358 -2.259 36
## 97 0.202 -1.386 -1.772 16
## 98 0.146 -6.571 -6.502 28
## 99 0.221 -20.661 -23.322 14
## 100 0.131 0.946 1.055 22
## 101 0.281 -0.400 0.095 12
## 102 0.345 -2.207 -1.772 24
## 103 0.614 5.263 5.468 9
## 104 0.277 -6.032 -6.215 14
## 105 0.243 3.461 3.924 11
## 106 0.165 3.401 3.045 18
## 107 0.232 10.186 10.858 10
## 108 0.210 11.266 11.856 15
## 109 0.270 -0.755 -0.598 9
## 110 0.225 -0.683 -0.471 13
## 111 0.060 2.833 2.890 48
## 112 0.225 -3.096 -3.123 20
## 113 0.131 -1.579 -1.534 26
## 114 0.202 -0.886 -0.658 20
## 115 0.139 4.149 3.637 20
## 116 0.247 -6.190 -4.605 15
## 117 0.184 -1.715 -1.661 19
## 118 0.251 0.742 1.435 9
## 119 0.112 2.890 2.773 29
## 120 0.139 -4.017 -3.730 19
## 121 0.150 2.708 2.565 27
## 122 0.749 15.756 17.476 4
## 123 0.266 0.095 0.182 14
## 124 0.161 -4.269 -4.343 18
## Second.Mode.Count First.Second.Mode.Ratio Minimum Mean Median
## 1 11 1.273 -0.676 1.320 1.301
## 2 19 1.053 -2.207 -1.538 -1.561
## 3 26 1.115 -0.923 0.309 0.280
## 4 6 1.167 -6.725 -5.201 -5.185
## 5 10 1.200 0.262 1.361 1.361
## 6 10 1.100 -17.028 -13.052 -13.004
## 7 8 1.625 -4.343 -2.932 -2.937
## 8 20 1.050 -289.685 -158.615 -160.010
## 9 20 1.150 -0.545 0.673 0.642
## 10 7 1.286 1.752 2.318 2.320
## 11 21 1.429 -2.957 -1.854 -1.833
## 12 7 1.143 -8.680 -7.483 -7.470
## 13 8 1.125 -1.897 -0.635 -0.673
## 14 9 1.222 -9.937 -5.578 -5.703
## 15 18 1.278 -3.324 -1.583 -1.609
## 16 15 1.133 -3.689 -2.494 -2.526
## 17 10 1.100 0.470 1.440 1.411
## 18 10 1.100 0.591 2.806 2.818
## 19 9 1.556 -2.234 -0.321 -0.370
## 20 30 1.200 0.732 2.017 1.981
## 21 29 1.034 -2.761 -1.911 -1.877
## 22 36 1.056 -0.545 0.168 0.182
## 23 31 1.613 10.000 51.011 51.000
## 24 6 1.167 -8.517 -5.874 -5.843
## 25 20 1.250 -1.864 -1.258 -1.273
## 26 16 1.062 -1.238 -0.053 -0.062
## 27 6 1.333 10.961 22.433 22.249
## 28 13 1.154 -0.713 1.679 1.649
## 29 8 1.125 135.605 333.298 331.520
## 30 21 1.190 1.872 2.882 2.890
## 31 13 1.154 -23.387 -15.610 -15.524
## 32 19 1.158 -0.839 3.554 3.600
## 33 24 1.042 0.182 0.774 0.788
## 34 34 1.118 0.100 11.984 12.000
## 35 24 1.125 -1.872 -1.674 -1.671
## 36 3 1.333 7.432 8.586 8.564
## 37 11 1.091 -1.361 -0.701 -0.684
## 38 10 1.100 -8.377 -3.635 -3.650
## 39 22 1.773 -1.405 -1.372 -1.374
## 40 26 1.462 7.000 58.172 59.000
## 41 19 1.211 -1.514 -0.529 -0.528
## 42 9 1.111 -2.115 -1.143 -1.136
## 43 14 1.357 -0.154 2.968 3.101
## 44 8 1.125 -1.044 1.353 1.387
## 45 7 1.143 0.608 2.765 2.775
## 46 12 1.250 0.470 1.350 1.308
## 47 6 1.167 -8.874 -7.356 -7.323
## 48 28 1.143 1.271 1.378 1.382
## 49 3 1.333 2.393 2.786 2.783
## 50 18 1.111 0.524 0.951 0.968
## 51 13 1.308 2.103 6.833 6.703
## 52 14 1.071 -4.510 -3.500 -3.507
## 53 27 1.667 -0.635 0.196 0.182
## 54 19 1.105 1.758 2.958 2.944
## 55 14 1.357 -1.533 -0.591 -0.590
## 56 6 1.167 4.635 5.317 5.323
## 57 10 1.600 1.755 4.725 4.805
## 58 38 1.079 1.259 1.284 1.283
## 59 20 1.050 1.187 2.929 2.909
## 60 25 1.200 1.052 4.855 4.749
## 61 26 1.346 -8.517 -7.514 -7.524
## 62 17 1.176 -5.915 -3.941 -3.912
## 63 20 1.250 0.531 1.773 1.808
## 64 26 1.038 -1.427 0.187 0.182
## 65 16 1.188 -1.534 -0.154 -0.160
## 66 24 1.083 -0.676 0.095 0.097
## 67 18 1.833 0.560 2.839 2.793
## 68 13 1.154 1.574 1.704 1.705
## 69 2 1.500 4.317 5.755 5.753
## 70 10 1.100 -10.520 -6.121 -6.119
## 71 16 1.188 -2.169 -1.233 -1.246
## 72 10 1.100 -1.256 -1.185 -1.183
## 73 12 1.083 0.000 1.283 1.281
## 74 15 1.133 -2.147 -1.504 -1.505
## 75 7 1.143 -6.812 -4.417 -4.605
## 76 3 1.333 5.826 6.497 6.494
## 77 24 1.333 0.401 1.869 1.853
## 78 25 1.160 -2.847 -1.864 -1.897
## 79 14 1.500 0.935 4.049 4.050
## 80 21 1.048 1.946 2.814 2.833
## 81 22 1.636 0.098 2.875 2.815
## 82 17 1.059 -4.423 -2.446 -2.453
## 83 13 1.077 -4.934 -3.635 -3.650
## 84 13 1.846 -8.398 -3.789 -3.774
## 85 10 1.100 -3.170 -1.367 -1.470
## 86 7 1.143 3.178 4.552 4.554
## 87 5 1.200 2.639 4.362 4.394
## 88 5 1.200 4.111 5.204 5.187
## 89 20 1.250 -0.991 0.077 0.094
## 90 25 1.040 -3.311 -2.854 -2.871
## 91 9 1.111 2.485 3.912 3.871
## 92 27 1.407 2.186 3.015 2.996
## 93 11 1.273 -2.120 -0.013 -0.041
## 94 30 1.067 -1.309 0.045 0.000
## 95 21 1.238 -1.934 -1.685 -1.690
## 96 30 1.200 -3.338 -2.240 -2.259
## 97 14 1.143 -2.513 -1.488 -1.514
## 98 22 1.273 -7.222 -6.511 -6.502
## 99 13 1.077 -34.967 -17.641 -17.466
## 100 20 1.100 0.187 1.251 1.254
## 101 10 1.200 -1.347 -0.406 -0.400
## 102 11 2.182 -4.135 -2.477 -2.489
## 103 6 1.500 4.317 5.336 5.366
## 104 12 1.167 -7.506 -6.017 -6.032
## 105 10 1.100 1.654 3.852 3.867
## 106 15 1.200 2.251 3.301 3.296
## 107 9 1.111 6.843 9.801 9.919
## 108 13 1.154 1.742 11.750 11.565
## 109 8 1.125 -1.661 -0.594 -0.598
## 110 12 1.083 -1.211 -0.539 -0.532
## 111 47 1.021 2.485 2.854 2.833
## 112 18 1.111 -3.206 -3.116 -3.117
## 113 21 1.238 -2.038 -1.505 -1.492
## 114 17 1.176 -1.540 -0.754 -0.751
## 115 19 1.053 1.508 3.848 3.810
## 116 14 1.071 -6.190 -4.499 -4.510
## 117 18 1.056 -2.477 -1.479 -1.514
## 118 8 1.125 -0.211 1.170 1.224
## 119 28 1.036 1.932 2.909 2.890
## 120 18 1.056 -4.744 -3.876 -3.863
## 121 24 1.125 1.723 2.688 2.708
## 122 3 1.333 11.831 16.988 17.077
## 123 12 1.167 -1.427 -0.285 -0.301
## 124 17 1.059 -4.991 -3.906 -3.912
## Maximum Skewness Kurtosis Percentile25th Percentile75th
## 1 2.840 -0.101 2.975 0.946 1.719
## 2 -0.844 0.028 2.746 -1.715 -1.347
## 3 1.521 0.038 2.866 0.000 0.608
## 4 -3.507 0.108 2.713 -5.669 -4.780
## 5 2.303 0.034 3.103 1.131 1.589
## 6 -8.192 0.164 3.586 -14.071 -12.096
## 7 -1.772 0.027 2.648 -3.270 -2.590
## 8 -59.456 -0.034 3.026 -186.641 -134.622
## 9 1.526 -0.168 3.639 0.470 0.875
## 10 2.881 -0.042 2.370 2.119 2.497
## 11 -0.777 0.046 3.028 -2.120 -1.609
## 12 -6.166 -0.016 3.085 -7.763 -7.209
## 13 0.956 0.279 2.957 -0.968 -0.315
## 14 -2.153 -0.032 2.767 -6.630 -4.539
## 15 -0.274 0.088 4.317 -1.833 -1.367
## 16 -1.238 0.245 3.246 -2.773 -2.207
## 17 2.272 0.001 2.732 1.209 1.668
## 18 5.444 0.064 3.288 2.334 3.286
## 19 0.927 0.097 4.888 -0.598 -0.061
## 20 4.024 0.050 3.410 1.673 2.371
## 21 -0.817 0.055 3.667 -2.152 -1.675
## 22 0.993 -0.022 2.906 -0.041 0.336
## 23 82.000 -0.026 3.431 42.000 59.000
## 24 -2.937 0.032 2.515 -6.645 -5.083
## 25 -0.547 0.157 3.504 -1.376 -1.124
## 26 1.163 0.095 2.918 -0.357 0.262
## 27 33.777 -0.042 3.250 19.771 24.795
## 28 3.892 0.109 2.731 0.956 2.282
## 29 535.397 -0.055 2.708 278.025 392.067
## 30 3.584 -0.186 3.336 2.708 3.045
## 31 -9.563 -0.028 2.547 -17.567 -13.882
## 32 7.624 0.065 3.873 2.753 4.255
## 33 1.411 0.015 3.002 0.642 0.916
## 34 29.000 0.586 5.953 9.800 14.000
## 35 -1.384 0.086 3.197 -1.724 -1.626
## 36 9.694 0.157 3.075 8.321 8.839
## 37 -0.061 -0.163 2.797 -0.857 -0.546
## 38 -0.386 0.068 6.513 -4.200 -3.147
## 39 -1.339 0.091 2.965 -1.381 -1.364
## 40 107.000 0.074 2.842 44.000 70.000
## 41 0.336 -0.085 2.755 -0.713 -0.315
## 42 0.097 0.114 2.612 -1.466 -0.876
## 43 7.633 0.000 4.024 2.341 3.695
## 44 3.706 0.037 3.003 0.800 1.885
## 45 4.633 -0.127 2.981 2.290 3.292
## 46 2.251 0.165 2.609 1.099 1.609
## 47 -5.843 0.006 3.171 -7.717 -7.013
## 48 1.495 -0.219 2.941 1.351 1.406
## 49 3.065 -0.158 2.829 2.707 2.873
## 50 1.318 0.044 2.589 0.844 1.034
## 51 10.695 0.020 2.900 5.786 7.865
## 52 -2.120 0.260 3.591 -3.730 -3.270
## 53 0.875 -0.055 2.708 0.000 0.405
## 54 4.143 -0.174 3.467 2.708 3.219
## 55 0.517 -0.040 2.979 -0.830 -0.383
## 56 5.948 -0.110 3.296 5.179 5.453
## 57 8.491 0.000 2.480 3.706 5.776
## 58 1.321 0.402 3.316 1.274 1.290
## 59 4.937 0.175 3.117 2.521 3.351
## 60 8.952 -0.012 3.326 4.149 5.631
## 61 -5.952 0.299 3.530 -7.824 -7.264
## 62 -2.453 -0.150 3.642 -4.269 -3.631
## 63 3.045 0.004 2.822 1.459 2.146
## 64 1.946 -0.045 3.687 -0.122 0.470
## 65 1.814 0.016 4.021 -0.413 0.141
## 66 0.831 -0.132 2.443 -0.125 0.354
## 67 5.706 -0.022 2.488 2.155 3.706
## 68 1.807 -0.145 3.470 1.680 1.728
## 69 7.501 0.293 3.317 5.398 6.064
## 70 -4.200 -0.607 6.399 -6.645 -5.573
## 71 -0.159 -0.025 3.691 -1.447 -1.034
## 72 -1.105 0.012 2.880 -1.204 -1.164
## 73 2.272 -0.020 3.061 1.030 1.526
## 74 -0.621 0.053 3.019 -1.700 -1.329
## 75 -1.386 0.344 2.390 -5.308 -3.490
## 76 7.230 -0.015 2.788 6.319 6.678
## 77 4.024 0.000 3.957 1.530 2.182
## 78 -0.844 0.160 3.034 -2.120 -1.661
## 79 6.796 0.151 2.810 3.338 4.686
## 80 4.007 0.206 3.001 2.565 3.045
## 81 5.359 -0.113 2.953 2.332 3.551
## 82 -0.528 -0.114 3.615 -2.749 -2.120
## 83 -2.207 0.240 3.361 -3.938 -3.352
## 84 -0.222 -0.035 2.703 -4.820 -2.714
## 85 1.775 0.704 3.638 -2.040 -0.799
## 86 5.886 -0.160 4.130 4.350 4.775
## 87 6.011 -0.244 3.244 3.998 4.749
## 88 6.308 0.031 3.223 4.963 5.442
## 89 1.166 0.045 2.750 -0.167 0.320
## 90 -2.520 -0.029 2.698 -2.936 -2.749
## 91 5.170 -0.092 3.011 3.638 4.205
## 92 3.932 0.166 3.434 2.833 3.178
## 93 1.932 0.076 2.690 -0.528 0.531
## 94 0.993 -0.045 4.693 -0.139 0.258
## 95 -1.424 0.193 5.276 -1.717 -1.654
## 96 -1.221 0.041 3.459 -2.464 -2.000
## 97 -0.274 0.244 2.621 -1.833 -1.171
## 98 -5.547 0.170 2.912 -6.725 -6.320
## 99 -2.239 -0.050 2.997 -21.468 -13.501
## 100 2.373 -0.007 2.971 1.001 1.500
## 101 0.742 0.142 3.370 -0.635 -0.198
## 102 -1.109 -0.066 2.965 -2.813 -2.120
## 103 6.317 -0.145 3.061 5.094 5.583
## 104 -4.646 -0.127 2.900 -6.377 -5.655
## 105 6.225 0.056 2.885 3.343 4.371
## 106 4.277 0.056 2.906 3.045 3.526
## 107 13.827 -0.021 2.809 8.859 10.695
## 108 18.881 0.157 6.004 10.490 12.697
## 109 0.470 0.044 3.110 -0.821 -0.378
## 110 0.269 0.070 3.256 -0.701 -0.385
## 111 3.332 0.226 3.255 2.773 2.944
## 112 -2.995 0.059 3.762 -3.137 -3.096
## 113 -0.817 -0.024 2.875 -1.626 -1.341
## 114 0.098 0.239 3.382 -0.886 -0.629
## 115 6.225 0.032 3.693 3.343 4.316
## 116 -1.715 0.024 3.719 -4.962 -4.017
## 117 -0.211 0.331 2.879 -1.772 -1.238
## 118 2.485 -0.180 2.887 0.833 1.482
## 119 3.761 -0.035 3.828 2.708 3.091
## 120 -2.957 0.151 2.781 -4.135 -3.650
## 121 3.689 -0.064 3.124 2.485 2.890
## 122 22.380 0.102 3.290 15.773 18.095
## 123 0.531 -0.038 2.760 -0.511 -0.036
## 124 -2.957 -0.124 2.625 -4.200 -3.612##################################
# Identifying potential data quality issues
##################################
##################################
# Checking for missing observations
##################################
if ((nrow(DQA.Summary[DQA.Summary$NA.Count>0,]))>0){
print(paste0("Missing observations noted for ",
(nrow(DQA.Summary[DQA.Summary$NA.Count>0,])),
" variable(s) with NA.Count>0 and Fill.Rate<1.0."))
DQA.Summary[DQA.Summary$NA.Count>0,]
} else {
print("No missing observations noted.")
}## [1] "No missing observations noted."##################################
# Checking for zero or near-zero variance predictors
##################################
if (length(names(DQA.Predictors.Factor))==0) {
print("No factor predictors noted.")
} else if (nrow(DQA.Predictors.Factor.Summary[as.numeric(as.character(DQA.Predictors.Factor.Summary$First.Second.Mode.Ratio))>5,])>0){
print(paste0("Low variance observed for ",
(nrow(DQA.Predictors.Factor.Summary[as.numeric(as.character(DQA.Predictors.Factor.Summary$First.Second.Mode.Ratio))>5,])),
" factor variable(s) with First.Second.Mode.Ratio>5."))
DQA.Predictors.Factor.Summary[as.numeric(as.character(DQA.Predictors.Factor.Summary$First.Second.Mode.Ratio))>5,]
} else {
print("No low variance factor predictors due to high first-second mode ratio noted.")
}## [1] "Low variance observed for 2 factor variable(s) with First.Second.Mode.Ratio>5."## Column.Name Column.Type Unique.Count First.Mode.Value Second.Mode.Value
## 2 E3 character 2 1 0
## 3 E2 character 2 0 1
## First.Mode.Count Second.Mode.Count Unique.Count.Ratio First.Second.Mode.Ratio
## 2 245 22 0.007 11.136
## 3 224 43 0.007 5.209if (length(names(DQA.Predictors.Numeric))==0) {
print("No numeric predictors noted.")
} else if (nrow(DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$First.Second.Mode.Ratio))>5,])>0){
print(paste0("Low variance observed for ",
(nrow(DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$First.Second.Mode.Ratio))>5,])),
" numeric variable(s) with First.Second.Mode.Ratio>5."))
DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$First.Second.Mode.Ratio))>5,]
} else {
print("No low variance numeric predictors due to high first-second mode ratio noted.")
}## [1] "No low variance numeric predictors due to high first-second mode ratio noted."if (length(names(DQA.Predictors.Numeric))==0) {
print("No numeric predictors noted.")
} else if (nrow(DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$Unique.Count.Ratio))<0.01,])>0){
print(paste0("Low variance observed for ",
(nrow(DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$Unique.Count.Ratio))<0.01,])),
" numeric variable(s) with Unique.Count.Ratio<0.01."))
DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$Unique.Count.Ratio))<0.01,]
} else {
print("No low variance numeric predictors due to low unique count ratio noted.")
}## [1] "No low variance numeric predictors due to low unique count ratio noted."##################################
# Checking for skewed predictors
##################################
if (length(names(DQA.Predictors.Numeric))==0) {
print("No numeric predictors noted.")
} else if (nrow(DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$Skewness))>3 |
as.numeric(as.character(DQA.Predictors.Numeric.Summary$Skewness))<(-3),])>0){
print(paste0("High skewness observed for ",
(nrow(DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$Skewness))>3 |
as.numeric(as.character(DQA.Predictors.Numeric.Summary$Skewness))<(-3),])),
" numeric variable(s) with Skewness>3 or Skewness<(-3)."))
DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$Skewness))>3 |
as.numeric(as.character(DQA.Predictors.Numeric.Summary$Skewness))<(-3),]
} else {
print("No skewed numeric predictors noted.")
}## [1] "No skewed numeric predictors noted."1.3 Data Preprocessing
1.3.1 Outlier
[A] Few outliers noted for most variables with the numeric data visualized through a boxplot including observations classified as suspected outliers using the IQR criterion. The IQR criterion means that all observations above the (75th percentile + 1.5 x IQR) or below the (25th percentile - 1.5 x IQR) are suspected outliers, where IQR is the difference between the third quartile (75th percentile) and first quartile (25th percentile). Outlier treatment for numerical stability remains optional depending on potential model requirements for the subsequent steps. 6 variables were observed with at least 10 outliers listed as follows:
[A.1] Apolipoprotein_CI variable (10 outliers detected)
[A.2] Cortisol variable (11 outliers detected)
[A.3] IL_17E variable (11 outliers detected)
[A.4] IL6 variable (19 outliers detected)
[A.5] MCP_2 variable (21 outliers detected)
[A.6] Prostatic_Acid_Phospatase variable (10 outliers detected)
Code Chunk | Output
##################################
# Loading dataset
##################################
DPA <- Alzheimer_Train
##################################
# Listing all predictors
##################################
DPA.Predictors <- DPA[,!names(DPA) %in% c("Class")]
##################################
# Listing all numeric predictors
##################################
DPA.Predictors.Numeric <- DPA.Predictors[,!names(DPA.Predictors) %in% c("E2","E3","E4")]
DPA.Predictors.Numeric <- as.data.frame(sapply(DPA.Predictors.Numeric,function(x) as.numeric(x)))
##################################
# Identifying outliers for the numeric predictors
##################################
OutlierCountList <- c()
for (i in 1:ncol(DPA.Predictors.Numeric)) {
Outliers <- boxplot.stats(DPA.Predictors.Numeric[,i])$out
OutlierCount <- length(Outliers)
OutlierCountList <- append(OutlierCountList,OutlierCount)
OutlierIndices <- which(DPA.Predictors.Numeric[,i] %in% c(Outliers))
boxplot(DPA.Predictors.Numeric[,i],
ylab = names(DPA.Predictors.Numeric)[i],
main = names(DPA.Predictors.Numeric)[i],
horizontal=TRUE)
mtext(paste0(OutlierCount, " Outlier(s) Detected"))
}
OutlierCountSummary <- as.data.frame(cbind(names(DPA.Predictors.Numeric),(OutlierCountList)))
names(OutlierCountSummary) <- c("NumericPredictors","OutlierCount")
OutlierCountSummary$OutlierCount <- as.numeric(as.character(OutlierCountSummary$OutlierCount))
NumericPredictorWithOutlierCount <- nrow(OutlierCountSummary[OutlierCountSummary$OutlierCount>0,])
print(paste0(NumericPredictorWithOutlierCount, " numeric variable(s) were noted with outlier(s)." ))## [1] "105 numeric variable(s) were noted with outlier(s)."##################################
# Gathering descriptive statistics
##################################
(DPA_Skimmed <- skim(DPA.Predictors.Numeric))| Name | DPA.Predictors.Numeric |
| Number of rows | 267 |
| Number of columns | 124 |
| _______________________ | |
| Column type frequency: | |
| numeric | 124 |
| ________________________ | |
| Group variables | None |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| ACE_CD143_Angiotensin_Converti | 0 | 1 | 1.32 | 0.54 | -0.68 | 0.95 | 1.30 | 1.72 | 2.84 | ▁▃▇▇▁ |
| ACTH_Adrenocorticotropic_Hormon | 0 | 1 | -1.54 | 0.28 | -2.21 | -1.71 | -1.56 | -1.35 | -0.84 | ▂▆▇▆▂ |
| AXL | 0 | 1 | 0.31 | 0.45 | -0.92 | 0.00 | 0.28 | 0.61 | 1.52 | ▁▅▇▃▁ |
| Adiponectin | 0 | 1 | -5.20 | 0.67 | -6.73 | -5.67 | -5.18 | -4.78 | -3.51 | ▂▆▇▅▁ |
| Alpha_1_Antichymotrypsin | 0 | 1 | 1.36 | 0.36 | 0.26 | 1.13 | 1.36 | 1.59 | 2.30 | ▁▃▇▅▁ |
| Alpha_1_Antitrypsin | 0 | 1 | -13.05 | 1.48 | -17.03 | -14.07 | -13.00 | -12.10 | -8.19 | ▁▅▇▂▁ |
| Alpha_1_Microglobulin | 0 | 1 | -2.93 | 0.48 | -4.34 | -3.27 | -2.94 | -2.59 | -1.77 | ▁▅▇▇▂ |
| Alpha_2_Macroglobulin | 0 | 1 | -158.61 | 40.93 | -289.68 | -186.64 | -160.01 | -134.62 | -59.46 | ▁▂▇▅▂ |
| Angiopoietin_2_ANG_2 | 0 | 1 | 0.67 | 0.33 | -0.54 | 0.47 | 0.64 | 0.88 | 1.53 | ▁▂▇▆▂ |
| Angiotensinogen | 0 | 1 | 2.32 | 0.25 | 1.75 | 2.12 | 2.32 | 2.50 | 2.88 | ▃▆▇▇▂ |
| Apolipoprotein_A_IV | 0 | 1 | -1.85 | 0.38 | -2.96 | -2.12 | -1.83 | -1.61 | -0.78 | ▁▃▇▃▁ |
| Apolipoprotein_A1 | 0 | 1 | -7.48 | 0.44 | -8.68 | -7.76 | -7.47 | -7.21 | -6.17 | ▁▅▇▃▁ |
| Apolipoprotein_A2 | 0 | 1 | -0.64 | 0.50 | -1.90 | -0.97 | -0.67 | -0.31 | 0.96 | ▁▇▇▃▁ |
| Apolipoprotein_B | 0 | 1 | -5.58 | 1.48 | -9.94 | -6.63 | -5.70 | -4.54 | -2.15 | ▁▅▇▇▂ |
| Apolipoprotein_CI | 0 | 1 | -1.58 | 0.41 | -3.32 | -1.83 | -1.61 | -1.37 | -0.27 | ▁▁▇▅▁ |
| Apolipoprotein_CIII | 0 | 1 | -2.49 | 0.44 | -3.69 | -2.77 | -2.53 | -2.21 | -1.24 | ▁▅▇▅▁ |
| Apolipoprotein_D | 0 | 1 | 1.44 | 0.34 | 0.47 | 1.21 | 1.41 | 1.67 | 2.27 | ▁▃▇▆▂ |
| Apolipoprotein_E | 0 | 1 | 2.81 | 0.78 | 0.59 | 2.33 | 2.82 | 3.29 | 5.44 | ▁▅▇▂▁ |
| Apolipoprotein_H | 0 | 1 | -0.32 | 0.39 | -2.23 | -0.60 | -0.37 | -0.06 | 0.93 | ▁▁▇▆▁ |
| B_Lymphocyte_Chemoattractant_BL | 0 | 1 | 2.02 | 0.57 | 0.73 | 1.67 | 1.98 | 2.37 | 4.02 | ▃▇▇▁▁ |
| BMP_6 | 0 | 1 | -1.91 | 0.31 | -2.76 | -2.15 | -1.88 | -1.68 | -0.82 | ▁▅▇▂▁ |
| Beta_2_Microglobulin | 0 | 1 | 0.17 | 0.30 | -0.54 | -0.04 | 0.18 | 0.34 | 0.99 | ▂▃▇▃▁ |
| Betacellulin | 0 | 1 | 51.01 | 10.87 | 10.00 | 42.00 | 51.00 | 59.00 | 82.00 | ▁▁▇▅▁ |
| C_Reactive_Protein | 0 | 1 | -5.87 | 1.20 | -8.52 | -6.65 | -5.84 | -5.08 | -2.94 | ▃▆▇▆▂ |
| CD40 | 0 | 1 | -1.26 | 0.21 | -1.86 | -1.38 | -1.27 | -1.12 | -0.55 | ▁▆▇▃▁ |
| CD5L | 0 | 1 | -0.05 | 0.45 | -1.24 | -0.36 | -0.06 | 0.26 | 1.16 | ▁▅▇▃▁ |
| Calbindin | 0 | 1 | 22.43 | 4.11 | 10.96 | 19.77 | 22.25 | 24.80 | 33.78 | ▁▃▇▃▁ |
| Calcitonin | 0 | 1 | 1.68 | 0.87 | -0.71 | 0.96 | 1.65 | 2.28 | 3.89 | ▁▆▇▅▂ |
| CgA | 0 | 1 | 333.30 | 83.67 | 135.60 | 278.02 | 331.52 | 392.07 | 535.40 | ▂▆▇▅▂ |
| Clusterin_Apo_J | 0 | 1 | 2.88 | 0.29 | 1.87 | 2.71 | 2.89 | 3.04 | 3.58 | ▁▂▇▆▂ |
| Complement_3 | 0 | 1 | -15.61 | 2.46 | -23.39 | -17.57 | -15.52 | -13.88 | -9.56 | ▁▆▇▇▂ |
| Complement_Factor_H | 0 | 1 | 3.55 | 1.25 | -0.84 | 2.75 | 3.60 | 4.25 | 7.62 | ▁▃▇▅▁ |
| Connective_Tissue_Growth_Factor | 0 | 1 | 0.77 | 0.20 | 0.18 | 0.64 | 0.79 | 0.92 | 1.41 | ▁▅▇▃▁ |
| Cortisol | 0 | 1 | 11.98 | 3.95 | 0.10 | 9.80 | 12.00 | 14.00 | 29.00 | ▁▇▇▁▁ |
| Creatine_Kinase_MB | 0 | 1 | -1.67 | 0.09 | -1.87 | -1.72 | -1.67 | -1.63 | -1.38 | ▃▅▇▂▁ |
| Cystatin_C | 0 | 1 | 8.59 | 0.40 | 7.43 | 8.32 | 8.56 | 8.84 | 9.69 | ▁▅▇▃▁ |
| EGF_R | 0 | 1 | -0.70 | 0.22 | -1.36 | -0.86 | -0.68 | -0.55 | -0.06 | ▁▃▇▅▁ |
| EN_RAGE | 0 | 1 | -3.64 | 0.88 | -8.38 | -4.20 | -3.65 | -3.15 | -0.39 | ▁▁▇▆▁ |
| ENA_78 | 0 | 1 | -1.37 | 0.01 | -1.41 | -1.38 | -1.37 | -1.36 | -1.34 | ▁▅▇▅▁ |
| Eotaxin_3 | 0 | 1 | 58.17 | 15.83 | 7.00 | 44.00 | 59.00 | 70.00 | 107.00 | ▁▆▇▅▁ |
| FAS | 0 | 1 | -0.53 | 0.30 | -1.51 | -0.71 | -0.53 | -0.31 | 0.34 | ▁▃▇▆▁ |
| FSH_Follicle_Stimulation_Hormon | 0 | 1 | -1.14 | 0.42 | -2.12 | -1.47 | -1.14 | -0.88 | 0.10 | ▂▇▇▃▁ |
| Fas_Ligand | 0 | 1 | 2.97 | 1.09 | -0.15 | 2.34 | 3.10 | 3.70 | 7.63 | ▂▇▇▁▁ |
| Fatty_Acid_Binding_Protein | 0 | 1 | 1.35 | 0.78 | -1.04 | 0.80 | 1.39 | 1.88 | 3.71 | ▁▅▇▅▁ |
| Ferritin | 0 | 1 | 2.76 | 0.76 | 0.61 | 2.29 | 2.77 | 3.29 | 4.63 | ▁▃▇▆▂ |
| Fetuin_A | 0 | 1 | 1.35 | 0.37 | 0.47 | 1.10 | 1.31 | 1.61 | 2.25 | ▂▆▇▅▂ |
| Fibrinogen | 0 | 1 | -7.36 | 0.57 | -8.87 | -7.72 | -7.32 | -7.01 | -5.84 | ▁▅▇▅▁ |
| GRO_alpha | 0 | 1 | 1.38 | 0.04 | 1.27 | 1.35 | 1.38 | 1.41 | 1.49 | ▂▃▇▅▁ |
| Gamma_Interferon_induced_Monokin | 0 | 1 | 2.79 | 0.11 | 2.39 | 2.71 | 2.78 | 2.87 | 3.07 | ▁▂▇▆▂ |
| Glutathione_S_Transferase_alpha | 0 | 1 | 0.95 | 0.16 | 0.52 | 0.84 | 0.97 | 1.03 | 1.32 | ▁▃▇▅▂ |
| HB_EGF | 0 | 1 | 6.83 | 1.51 | 2.10 | 5.79 | 6.70 | 7.86 | 10.70 | ▁▃▇▆▂ |
| HCC_4 | 0 | 1 | -3.50 | 0.36 | -4.51 | -3.73 | -3.51 | -3.27 | -2.12 | ▂▇▇▂▁ |
| Hepatocyte_Growth_Factor_HGF | 0 | 1 | 0.20 | 0.29 | -0.63 | 0.00 | 0.18 | 0.41 | 0.88 | ▁▃▇▅▂ |
| I_309 | 0 | 1 | 2.96 | 0.37 | 1.76 | 2.71 | 2.94 | 3.22 | 4.14 | ▁▅▇▃▁ |
| ICAM_1 | 0 | 1 | -0.59 | 0.33 | -1.53 | -0.83 | -0.59 | -0.38 | 0.52 | ▁▅▇▃▁ |
| IGF_BP_2 | 0 | 1 | 5.32 | 0.20 | 4.63 | 5.18 | 5.32 | 5.45 | 5.95 | ▁▃▇▅▁ |
| IL_11 | 0 | 1 | 4.72 | 1.45 | 1.75 | 3.71 | 4.81 | 5.78 | 8.49 | ▃▆▇▅▁ |
| IL_13 | 0 | 1 | 1.28 | 0.01 | 1.26 | 1.27 | 1.28 | 1.29 | 1.32 | ▂▇▆▂▁ |
| IL_16 | 0 | 1 | 2.93 | 0.66 | 1.19 | 2.52 | 2.91 | 3.35 | 4.94 | ▁▆▇▃▁ |
| IL_17E | 0 | 1 | 4.85 | 1.34 | 1.05 | 4.15 | 4.75 | 5.63 | 8.95 | ▁▆▇▃▁ |
| IL_1alpha | 0 | 1 | -7.51 | 0.39 | -8.52 | -7.82 | -7.52 | -7.26 | -5.95 | ▂▇▇▂▁ |
| IL_3 | 0 | 1 | -3.94 | 0.50 | -5.91 | -4.27 | -3.91 | -3.63 | -2.45 | ▁▂▇▅▁ |
| IL_4 | 0 | 1 | 1.77 | 0.51 | 0.53 | 1.46 | 1.81 | 2.15 | 3.04 | ▂▅▇▅▂ |
| IL_5 | 0 | 1 | 0.19 | 0.46 | -1.43 | -0.12 | 0.18 | 0.47 | 1.95 | ▁▃▇▂▁ |
| IL_6 | 0 | 1 | -0.15 | 0.55 | -1.53 | -0.41 | -0.16 | 0.14 | 1.81 | ▂▆▇▂▁ |
| IL_6_Receptor | 0 | 1 | 0.09 | 0.32 | -0.68 | -0.13 | 0.10 | 0.35 | 0.83 | ▂▆▇▆▂ |
| IL_7 | 0 | 1 | 2.84 | 1.05 | 0.56 | 2.15 | 2.79 | 3.71 | 5.71 | ▃▇▇▆▁ |
| IL_8 | 0 | 1 | 1.70 | 0.04 | 1.57 | 1.68 | 1.71 | 1.73 | 1.81 | ▁▂▇▆▁ |
| IP_10_Inducible_Protein_10 | 0 | 1 | 5.75 | 0.51 | 4.32 | 5.40 | 5.75 | 6.06 | 7.50 | ▁▆▇▂▁ |
| IgA | 0 | 1 | -6.12 | 0.76 | -10.52 | -6.65 | -6.12 | -5.57 | -4.20 | ▁▁▂▇▂ |
| Insulin | 0 | 1 | -1.23 | 0.34 | -2.17 | -1.45 | -1.25 | -1.03 | -0.16 | ▁▃▇▂▁ |
| Kidney_Injury_Molecule_1_KIM_1 | 0 | 1 | -1.18 | 0.03 | -1.26 | -1.20 | -1.18 | -1.16 | -1.10 | ▁▇▇▅▁ |
| LOX_1 | 0 | 1 | 1.28 | 0.40 | 0.00 | 1.03 | 1.28 | 1.53 | 2.27 | ▁▂▇▅▂ |
| Leptin | 0 | 1 | -1.50 | 0.27 | -2.15 | -1.70 | -1.50 | -1.33 | -0.62 | ▂▇▇▂▁ |
| Lipoprotein_a | 0 | 1 | -4.42 | 1.11 | -6.81 | -5.31 | -4.61 | -3.49 | -1.39 | ▂▇▅▅▁ |
| MCP_1 | 0 | 1 | 6.50 | 0.26 | 5.83 | 6.32 | 6.49 | 6.68 | 7.23 | ▂▅▇▅▁ |
| MCP_2 | 0 | 1 | 1.87 | 0.65 | 0.40 | 1.53 | 1.85 | 2.18 | 4.02 | ▂▆▇▂▁ |
| MIF | 0 | 1 | -1.86 | 0.34 | -2.85 | -2.12 | -1.90 | -1.66 | -0.84 | ▁▃▇▃▁ |
| MIP_1alpha | 0 | 1 | 4.05 | 1.01 | 0.93 | 3.34 | 4.05 | 4.69 | 6.80 | ▁▅▇▅▂ |
| MIP_1beta | 0 | 1 | 2.81 | 0.38 | 1.95 | 2.56 | 2.83 | 3.04 | 4.01 | ▂▅▇▂▁ |
| MMP_2 | 0 | 1 | 2.88 | 0.93 | 0.10 | 2.33 | 2.82 | 3.55 | 5.36 | ▁▃▇▆▁ |
| MMP_3 | 0 | 1 | -2.45 | 0.57 | -4.42 | -2.75 | -2.45 | -2.12 | -0.53 | ▁▂▇▃▁ |
| MMP10 | 0 | 1 | -3.63 | 0.43 | -4.93 | -3.94 | -3.65 | -3.35 | -2.21 | ▁▆▇▃▁ |
| MMP7 | 0 | 1 | -3.79 | 1.55 | -8.40 | -4.82 | -3.77 | -2.71 | -0.22 | ▁▃▇▅▂ |
| Myoglobin | 0 | 1 | -1.37 | 0.95 | -3.17 | -2.04 | -1.47 | -0.80 | 1.77 | ▅▇▆▂▁ |
| NT_proBNP | 0 | 1 | 4.55 | 0.38 | 3.18 | 4.35 | 4.55 | 4.77 | 5.89 | ▁▂▇▃▁ |
| NrCAM | 0 | 1 | 4.36 | 0.57 | 2.64 | 4.00 | 4.39 | 4.75 | 6.01 | ▁▃▇▅▁ |
| Osteopontin | 0 | 1 | 5.20 | 0.39 | 4.11 | 4.96 | 5.19 | 5.44 | 6.31 | ▁▅▇▃▁ |
| PAI_1 | 0 | 1 | 0.08 | 0.41 | -0.99 | -0.17 | 0.09 | 0.32 | 1.17 | ▂▃▇▅▂ |
| PAPP_A | 0 | 1 | -2.85 | 0.14 | -3.31 | -2.94 | -2.87 | -2.75 | -2.52 | ▁▂▇▅▂ |
| PLGF | 0 | 1 | 3.91 | 0.41 | 2.48 | 3.64 | 3.87 | 4.20 | 5.17 | ▁▃▇▆▁ |
| PYY | 0 | 1 | 3.02 | 0.29 | 2.19 | 2.83 | 3.00 | 3.18 | 3.93 | ▁▅▇▃▁ |
| Pancreatic_polypeptide | 0 | 1 | -0.01 | 0.72 | -2.12 | -0.53 | -0.04 | 0.53 | 1.93 | ▁▅▇▆▁ |
| Prolactin | 0 | 1 | 0.04 | 0.30 | -1.31 | -0.14 | 0.00 | 0.26 | 0.99 | ▁▁▇▇▁ |
| Prostatic_Acid_Phosphatase | 0 | 1 | -1.69 | 0.06 | -1.93 | -1.72 | -1.69 | -1.65 | -1.42 | ▁▂▇▂▁ |
| Protein_S | 0 | 1 | -2.24 | 0.35 | -3.34 | -2.46 | -2.26 | -2.00 | -1.22 | ▁▃▇▃▁ |
| Pulmonary_and_Activation_Regulat | 0 | 1 | -1.49 | 0.45 | -2.51 | -1.83 | -1.51 | -1.17 | -0.27 | ▂▇▇▃▂ |
| RANTES | 0 | 1 | -6.51 | 0.32 | -7.22 | -6.73 | -6.50 | -6.32 | -5.55 | ▃▇▇▃▁ |
| Resistin | 0 | 1 | -17.64 | 5.82 | -34.97 | -21.47 | -17.47 | -13.50 | -2.24 | ▁▃▇▆▁ |
| S100b | 0 | 1 | 1.25 | 0.34 | 0.19 | 1.00 | 1.25 | 1.50 | 2.37 | ▁▆▇▅▁ |
| SGOT | 0 | 1 | -0.41 | 0.35 | -1.35 | -0.63 | -0.40 | -0.20 | 0.74 | ▁▅▇▂▁ |
| SHBG | 0 | 1 | -2.48 | 0.58 | -4.14 | -2.81 | -2.49 | -2.12 | -1.11 | ▁▃▇▆▂ |
| SOD | 0 | 1 | 5.34 | 0.38 | 4.32 | 5.09 | 5.37 | 5.58 | 6.32 | ▁▅▇▅▁ |
| Serum_Amyloid_P | 0 | 1 | -6.02 | 0.56 | -7.51 | -6.38 | -6.03 | -5.65 | -4.65 | ▁▅▇▅▂ |
| Sortilin | 0 | 1 | 3.85 | 0.87 | 1.65 | 3.34 | 3.87 | 4.37 | 6.23 | ▁▅▇▃▁ |
| Stem_Cell_Factor | 0 | 1 | 3.30 | 0.36 | 2.25 | 3.04 | 3.30 | 3.53 | 4.28 | ▁▅▇▅▁ |
| TGF_alpha | 0 | 1 | 9.80 | 1.32 | 6.84 | 8.86 | 9.92 | 10.70 | 13.83 | ▂▆▇▂▁ |
| TIMP_1 | 0 | 1 | 11.75 | 1.90 | 1.74 | 10.49 | 11.56 | 12.70 | 18.88 | ▁▁▇▅▁ |
| TNF_RII | 0 | 1 | -0.59 | 0.33 | -1.66 | -0.82 | -0.60 | -0.38 | 0.47 | ▁▃▇▃▁ |
| TRAIL_R3 | 0 | 1 | -0.54 | 0.24 | -1.21 | -0.70 | -0.53 | -0.38 | 0.27 | ▁▆▇▂▁ |
| TTR_prealbumin | 0 | 1 | 2.85 | 0.14 | 2.48 | 2.77 | 2.83 | 2.94 | 3.33 | ▂▅▇▃▁ |
| Tamm_Horsfall_Protein_THP | 0 | 1 | -3.12 | 0.03 | -3.21 | -3.14 | -3.12 | -3.10 | -2.99 | ▁▇▇▂▁ |
| Thrombomodulin | 0 | 1 | -1.51 | 0.22 | -2.04 | -1.63 | -1.49 | -1.34 | -0.82 | ▂▆▇▃▁ |
| Thrombopoietin | 0 | 1 | -0.75 | 0.24 | -1.54 | -0.89 | -0.75 | -0.63 | 0.10 | ▁▅▇▂▁ |
| Thymus_Expressed_Chemokine_TECK | 0 | 1 | 3.85 | 0.80 | 1.51 | 3.34 | 3.81 | 4.32 | 6.23 | ▁▃▇▃▁ |
| Thyroid_Stimulating_Hormone | 0 | 1 | -4.50 | 0.75 | -6.19 | -4.96 | -4.51 | -4.02 | -1.71 | ▂▇▆▁▁ |
| Thyroxine_Binding_Globulin | 0 | 1 | -1.48 | 0.40 | -2.48 | -1.77 | -1.51 | -1.24 | -0.21 | ▂▇▇▃▁ |
| Tissue_Factor | 0 | 1 | 1.17 | 0.50 | -0.21 | 0.83 | 1.22 | 1.48 | 2.48 | ▁▅▇▆▁ |
| Transferrin | 0 | 1 | 2.91 | 0.27 | 1.93 | 2.71 | 2.89 | 3.09 | 3.76 | ▁▂▇▅▁ |
| Trefoil_Factor_3_TFF3 | 0 | 1 | -3.88 | 0.34 | -4.74 | -4.14 | -3.86 | -3.65 | -2.96 | ▁▅▇▃▁ |
| VCAM_1 | 0 | 1 | 2.69 | 0.32 | 1.72 | 2.48 | 2.71 | 2.89 | 3.69 | ▁▃▇▃▁ |
| VEGF | 0 | 1 | 16.99 | 1.81 | 11.83 | 15.77 | 17.08 | 18.10 | 22.38 | ▁▅▇▃▁ |
| Vitronectin | 0 | 1 | -0.28 | 0.33 | -1.43 | -0.51 | -0.30 | -0.04 | 0.53 | ▁▃▇▇▂ |
| von_Willebrand_Factor | 0 | 1 | -3.91 | 0.38 | -4.99 | -4.20 | -3.91 | -3.61 | -2.96 | ▁▅▇▆▂ |
###################################
# Verifying the data dimensions
###################################
dim(DPA.Predictors.Numeric)## [1] 267 1241.3.2 Zero and Near-Zero Variance
[A] Low variance noted for 2 variables from the previous data quality assessment using a lower threshold.
[B] No low variance noted for any variable using a preprocessing summary from the caret package. The nearZeroVar method using both the freqCut and uniqueCut criteria set at 95/5 and 10, respectively, were applied on the dataset.
Code Chunk | Output
##################################
# Loading dataset
##################################
DPA <- DPA.Predictors
##################################
# Gathering descriptive statistics
##################################
(DPA_Skimmed <- skim(DPA))| Name | DPA |
| Number of rows | 267 |
| Number of columns | 127 |
| _______________________ | |
| Column type frequency: | |
| numeric | 127 |
| ________________________ | |
| Group variables | None |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| ACE_CD143_Angiotensin_Converti | 0 | 1 | 1.32 | 0.54 | -0.68 | 0.95 | 1.30 | 1.72 | 2.84 | ▁▃▇▇▁ |
| ACTH_Adrenocorticotropic_Hormon | 0 | 1 | -1.54 | 0.28 | -2.21 | -1.71 | -1.56 | -1.35 | -0.84 | ▂▆▇▆▂ |
| AXL | 0 | 1 | 0.31 | 0.45 | -0.92 | 0.00 | 0.28 | 0.61 | 1.52 | ▁▅▇▃▁ |
| Adiponectin | 0 | 1 | -5.20 | 0.67 | -6.73 | -5.67 | -5.18 | -4.78 | -3.51 | ▂▆▇▅▁ |
| Alpha_1_Antichymotrypsin | 0 | 1 | 1.36 | 0.36 | 0.26 | 1.13 | 1.36 | 1.59 | 2.30 | ▁▃▇▅▁ |
| Alpha_1_Antitrypsin | 0 | 1 | -13.05 | 1.48 | -17.03 | -14.07 | -13.00 | -12.10 | -8.19 | ▁▅▇▂▁ |
| Alpha_1_Microglobulin | 0 | 1 | -2.93 | 0.48 | -4.34 | -3.27 | -2.94 | -2.59 | -1.77 | ▁▅▇▇▂ |
| Alpha_2_Macroglobulin | 0 | 1 | -158.61 | 40.93 | -289.68 | -186.64 | -160.01 | -134.62 | -59.46 | ▁▂▇▅▂ |
| Angiopoietin_2_ANG_2 | 0 | 1 | 0.67 | 0.33 | -0.54 | 0.47 | 0.64 | 0.88 | 1.53 | ▁▂▇▆▂ |
| Angiotensinogen | 0 | 1 | 2.32 | 0.25 | 1.75 | 2.12 | 2.32 | 2.50 | 2.88 | ▃▆▇▇▂ |
| Apolipoprotein_A_IV | 0 | 1 | -1.85 | 0.38 | -2.96 | -2.12 | -1.83 | -1.61 | -0.78 | ▁▃▇▃▁ |
| Apolipoprotein_A1 | 0 | 1 | -7.48 | 0.44 | -8.68 | -7.76 | -7.47 | -7.21 | -6.17 | ▁▅▇▃▁ |
| Apolipoprotein_A2 | 0 | 1 | -0.64 | 0.50 | -1.90 | -0.97 | -0.67 | -0.31 | 0.96 | ▁▇▇▃▁ |
| Apolipoprotein_B | 0 | 1 | -5.58 | 1.48 | -9.94 | -6.63 | -5.70 | -4.54 | -2.15 | ▁▅▇▇▂ |
| Apolipoprotein_CI | 0 | 1 | -1.58 | 0.41 | -3.32 | -1.83 | -1.61 | -1.37 | -0.27 | ▁▁▇▅▁ |
| Apolipoprotein_CIII | 0 | 1 | -2.49 | 0.44 | -3.69 | -2.77 | -2.53 | -2.21 | -1.24 | ▁▅▇▅▁ |
| Apolipoprotein_D | 0 | 1 | 1.44 | 0.34 | 0.47 | 1.21 | 1.41 | 1.67 | 2.27 | ▁▃▇▆▂ |
| Apolipoprotein_E | 0 | 1 | 2.81 | 0.78 | 0.59 | 2.33 | 2.82 | 3.29 | 5.44 | ▁▅▇▂▁ |
| Apolipoprotein_H | 0 | 1 | -0.32 | 0.39 | -2.23 | -0.60 | -0.37 | -0.06 | 0.93 | ▁▁▇▆▁ |
| B_Lymphocyte_Chemoattractant_BL | 0 | 1 | 2.02 | 0.57 | 0.73 | 1.67 | 1.98 | 2.37 | 4.02 | ▃▇▇▁▁ |
| BMP_6 | 0 | 1 | -1.91 | 0.31 | -2.76 | -2.15 | -1.88 | -1.68 | -0.82 | ▁▅▇▂▁ |
| Beta_2_Microglobulin | 0 | 1 | 0.17 | 0.30 | -0.54 | -0.04 | 0.18 | 0.34 | 0.99 | ▂▃▇▃▁ |
| Betacellulin | 0 | 1 | 51.01 | 10.87 | 10.00 | 42.00 | 51.00 | 59.00 | 82.00 | ▁▁▇▅▁ |
| C_Reactive_Protein | 0 | 1 | -5.87 | 1.20 | -8.52 | -6.65 | -5.84 | -5.08 | -2.94 | ▃▆▇▆▂ |
| CD40 | 0 | 1 | -1.26 | 0.21 | -1.86 | -1.38 | -1.27 | -1.12 | -0.55 | ▁▆▇▃▁ |
| CD5L | 0 | 1 | -0.05 | 0.45 | -1.24 | -0.36 | -0.06 | 0.26 | 1.16 | ▁▅▇▃▁ |
| Calbindin | 0 | 1 | 22.43 | 4.11 | 10.96 | 19.77 | 22.25 | 24.80 | 33.78 | ▁▃▇▃▁ |
| Calcitonin | 0 | 1 | 1.68 | 0.87 | -0.71 | 0.96 | 1.65 | 2.28 | 3.89 | ▁▆▇▅▂ |
| CgA | 0 | 1 | 333.30 | 83.67 | 135.60 | 278.02 | 331.52 | 392.07 | 535.40 | ▂▆▇▅▂ |
| Clusterin_Apo_J | 0 | 1 | 2.88 | 0.29 | 1.87 | 2.71 | 2.89 | 3.04 | 3.58 | ▁▂▇▆▂ |
| Complement_3 | 0 | 1 | -15.61 | 2.46 | -23.39 | -17.57 | -15.52 | -13.88 | -9.56 | ▁▆▇▇▂ |
| Complement_Factor_H | 0 | 1 | 3.55 | 1.25 | -0.84 | 2.75 | 3.60 | 4.25 | 7.62 | ▁▃▇▅▁ |
| Connective_Tissue_Growth_Factor | 0 | 1 | 0.77 | 0.20 | 0.18 | 0.64 | 0.79 | 0.92 | 1.41 | ▁▅▇▃▁ |
| Cortisol | 0 | 1 | 11.98 | 3.95 | 0.10 | 9.80 | 12.00 | 14.00 | 29.00 | ▁▇▇▁▁ |
| Creatine_Kinase_MB | 0 | 1 | -1.67 | 0.09 | -1.87 | -1.72 | -1.67 | -1.63 | -1.38 | ▃▅▇▂▁ |
| Cystatin_C | 0 | 1 | 8.59 | 0.40 | 7.43 | 8.32 | 8.56 | 8.84 | 9.69 | ▁▅▇▃▁ |
| EGF_R | 0 | 1 | -0.70 | 0.22 | -1.36 | -0.86 | -0.68 | -0.55 | -0.06 | ▁▃▇▅▁ |
| EN_RAGE | 0 | 1 | -3.64 | 0.88 | -8.38 | -4.20 | -3.65 | -3.15 | -0.39 | ▁▁▇▆▁ |
| ENA_78 | 0 | 1 | -1.37 | 0.01 | -1.41 | -1.38 | -1.37 | -1.36 | -1.34 | ▁▅▇▅▁ |
| Eotaxin_3 | 0 | 1 | 58.17 | 15.83 | 7.00 | 44.00 | 59.00 | 70.00 | 107.00 | ▁▆▇▅▁ |
| FAS | 0 | 1 | -0.53 | 0.30 | -1.51 | -0.71 | -0.53 | -0.31 | 0.34 | ▁▃▇▆▁ |
| FSH_Follicle_Stimulation_Hormon | 0 | 1 | -1.14 | 0.42 | -2.12 | -1.47 | -1.14 | -0.88 | 0.10 | ▂▇▇▃▁ |
| Fas_Ligand | 0 | 1 | 2.97 | 1.09 | -0.15 | 2.34 | 3.10 | 3.70 | 7.63 | ▂▇▇▁▁ |
| Fatty_Acid_Binding_Protein | 0 | 1 | 1.35 | 0.78 | -1.04 | 0.80 | 1.39 | 1.88 | 3.71 | ▁▅▇▅▁ |
| Ferritin | 0 | 1 | 2.76 | 0.76 | 0.61 | 2.29 | 2.77 | 3.29 | 4.63 | ▁▃▇▆▂ |
| Fetuin_A | 0 | 1 | 1.35 | 0.37 | 0.47 | 1.10 | 1.31 | 1.61 | 2.25 | ▂▆▇▅▂ |
| Fibrinogen | 0 | 1 | -7.36 | 0.57 | -8.87 | -7.72 | -7.32 | -7.01 | -5.84 | ▁▅▇▅▁ |
| GRO_alpha | 0 | 1 | 1.38 | 0.04 | 1.27 | 1.35 | 1.38 | 1.41 | 1.49 | ▂▃▇▅▁ |
| Gamma_Interferon_induced_Monokin | 0 | 1 | 2.79 | 0.11 | 2.39 | 2.71 | 2.78 | 2.87 | 3.07 | ▁▂▇▆▂ |
| Glutathione_S_Transferase_alpha | 0 | 1 | 0.95 | 0.16 | 0.52 | 0.84 | 0.97 | 1.03 | 1.32 | ▁▃▇▅▂ |
| HB_EGF | 0 | 1 | 6.83 | 1.51 | 2.10 | 5.79 | 6.70 | 7.86 | 10.70 | ▁▃▇▆▂ |
| HCC_4 | 0 | 1 | -3.50 | 0.36 | -4.51 | -3.73 | -3.51 | -3.27 | -2.12 | ▂▇▇▂▁ |
| Hepatocyte_Growth_Factor_HGF | 0 | 1 | 0.20 | 0.29 | -0.63 | 0.00 | 0.18 | 0.41 | 0.88 | ▁▃▇▅▂ |
| I_309 | 0 | 1 | 2.96 | 0.37 | 1.76 | 2.71 | 2.94 | 3.22 | 4.14 | ▁▅▇▃▁ |
| ICAM_1 | 0 | 1 | -0.59 | 0.33 | -1.53 | -0.83 | -0.59 | -0.38 | 0.52 | ▁▅▇▃▁ |
| IGF_BP_2 | 0 | 1 | 5.32 | 0.20 | 4.63 | 5.18 | 5.32 | 5.45 | 5.95 | ▁▃▇▅▁ |
| IL_11 | 0 | 1 | 4.72 | 1.45 | 1.75 | 3.71 | 4.81 | 5.78 | 8.49 | ▃▆▇▅▁ |
| IL_13 | 0 | 1 | 1.28 | 0.01 | 1.26 | 1.27 | 1.28 | 1.29 | 1.32 | ▂▇▆▂▁ |
| IL_16 | 0 | 1 | 2.93 | 0.66 | 1.19 | 2.52 | 2.91 | 3.35 | 4.94 | ▁▆▇▃▁ |
| IL_17E | 0 | 1 | 4.85 | 1.34 | 1.05 | 4.15 | 4.75 | 5.63 | 8.95 | ▁▆▇▃▁ |
| IL_1alpha | 0 | 1 | -7.51 | 0.39 | -8.52 | -7.82 | -7.52 | -7.26 | -5.95 | ▂▇▇▂▁ |
| IL_3 | 0 | 1 | -3.94 | 0.50 | -5.91 | -4.27 | -3.91 | -3.63 | -2.45 | ▁▂▇▅▁ |
| IL_4 | 0 | 1 | 1.77 | 0.51 | 0.53 | 1.46 | 1.81 | 2.15 | 3.04 | ▂▅▇▅▂ |
| IL_5 | 0 | 1 | 0.19 | 0.46 | -1.43 | -0.12 | 0.18 | 0.47 | 1.95 | ▁▃▇▂▁ |
| IL_6 | 0 | 1 | -0.15 | 0.55 | -1.53 | -0.41 | -0.16 | 0.14 | 1.81 | ▂▆▇▂▁ |
| IL_6_Receptor | 0 | 1 | 0.09 | 0.32 | -0.68 | -0.13 | 0.10 | 0.35 | 0.83 | ▂▆▇▆▂ |
| IL_7 | 0 | 1 | 2.84 | 1.05 | 0.56 | 2.15 | 2.79 | 3.71 | 5.71 | ▃▇▇▆▁ |
| IL_8 | 0 | 1 | 1.70 | 0.04 | 1.57 | 1.68 | 1.71 | 1.73 | 1.81 | ▁▂▇▆▁ |
| IP_10_Inducible_Protein_10 | 0 | 1 | 5.75 | 0.51 | 4.32 | 5.40 | 5.75 | 6.06 | 7.50 | ▁▆▇▂▁ |
| IgA | 0 | 1 | -6.12 | 0.76 | -10.52 | -6.65 | -6.12 | -5.57 | -4.20 | ▁▁▂▇▂ |
| Insulin | 0 | 1 | -1.23 | 0.34 | -2.17 | -1.45 | -1.25 | -1.03 | -0.16 | ▁▃▇▂▁ |
| Kidney_Injury_Molecule_1_KIM_1 | 0 | 1 | -1.18 | 0.03 | -1.26 | -1.20 | -1.18 | -1.16 | -1.10 | ▁▇▇▅▁ |
| LOX_1 | 0 | 1 | 1.28 | 0.40 | 0.00 | 1.03 | 1.28 | 1.53 | 2.27 | ▁▂▇▅▂ |
| Leptin | 0 | 1 | -1.50 | 0.27 | -2.15 | -1.70 | -1.50 | -1.33 | -0.62 | ▂▇▇▂▁ |
| Lipoprotein_a | 0 | 1 | -4.42 | 1.11 | -6.81 | -5.31 | -4.61 | -3.49 | -1.39 | ▂▇▅▅▁ |
| MCP_1 | 0 | 1 | 6.50 | 0.26 | 5.83 | 6.32 | 6.49 | 6.68 | 7.23 | ▂▅▇▅▁ |
| MCP_2 | 0 | 1 | 1.87 | 0.65 | 0.40 | 1.53 | 1.85 | 2.18 | 4.02 | ▂▆▇▂▁ |
| MIF | 0 | 1 | -1.86 | 0.34 | -2.85 | -2.12 | -1.90 | -1.66 | -0.84 | ▁▃▇▃▁ |
| MIP_1alpha | 0 | 1 | 4.05 | 1.01 | 0.93 | 3.34 | 4.05 | 4.69 | 6.80 | ▁▅▇▅▂ |
| MIP_1beta | 0 | 1 | 2.81 | 0.38 | 1.95 | 2.56 | 2.83 | 3.04 | 4.01 | ▂▅▇▂▁ |
| MMP_2 | 0 | 1 | 2.88 | 0.93 | 0.10 | 2.33 | 2.82 | 3.55 | 5.36 | ▁▃▇▆▁ |
| MMP_3 | 0 | 1 | -2.45 | 0.57 | -4.42 | -2.75 | -2.45 | -2.12 | -0.53 | ▁▂▇▃▁ |
| MMP10 | 0 | 1 | -3.63 | 0.43 | -4.93 | -3.94 | -3.65 | -3.35 | -2.21 | ▁▆▇▃▁ |
| MMP7 | 0 | 1 | -3.79 | 1.55 | -8.40 | -4.82 | -3.77 | -2.71 | -0.22 | ▁▃▇▅▂ |
| Myoglobin | 0 | 1 | -1.37 | 0.95 | -3.17 | -2.04 | -1.47 | -0.80 | 1.77 | ▅▇▆▂▁ |
| NT_proBNP | 0 | 1 | 4.55 | 0.38 | 3.18 | 4.35 | 4.55 | 4.77 | 5.89 | ▁▂▇▃▁ |
| NrCAM | 0 | 1 | 4.36 | 0.57 | 2.64 | 4.00 | 4.39 | 4.75 | 6.01 | ▁▃▇▅▁ |
| Osteopontin | 0 | 1 | 5.20 | 0.39 | 4.11 | 4.96 | 5.19 | 5.44 | 6.31 | ▁▅▇▃▁ |
| PAI_1 | 0 | 1 | 0.08 | 0.41 | -0.99 | -0.17 | 0.09 | 0.32 | 1.17 | ▂▃▇▅▂ |
| PAPP_A | 0 | 1 | -2.85 | 0.14 | -3.31 | -2.94 | -2.87 | -2.75 | -2.52 | ▁▂▇▅▂ |
| PLGF | 0 | 1 | 3.91 | 0.41 | 2.48 | 3.64 | 3.87 | 4.20 | 5.17 | ▁▃▇▆▁ |
| PYY | 0 | 1 | 3.02 | 0.29 | 2.19 | 2.83 | 3.00 | 3.18 | 3.93 | ▁▅▇▃▁ |
| Pancreatic_polypeptide | 0 | 1 | -0.01 | 0.72 | -2.12 | -0.53 | -0.04 | 0.53 | 1.93 | ▁▅▇▆▁ |
| Prolactin | 0 | 1 | 0.04 | 0.30 | -1.31 | -0.14 | 0.00 | 0.26 | 0.99 | ▁▁▇▇▁ |
| Prostatic_Acid_Phosphatase | 0 | 1 | -1.69 | 0.06 | -1.93 | -1.72 | -1.69 | -1.65 | -1.42 | ▁▂▇▂▁ |
| Protein_S | 0 | 1 | -2.24 | 0.35 | -3.34 | -2.46 | -2.26 | -2.00 | -1.22 | ▁▃▇▃▁ |
| Pulmonary_and_Activation_Regulat | 0 | 1 | -1.49 | 0.45 | -2.51 | -1.83 | -1.51 | -1.17 | -0.27 | ▂▇▇▃▂ |
| RANTES | 0 | 1 | -6.51 | 0.32 | -7.22 | -6.73 | -6.50 | -6.32 | -5.55 | ▃▇▇▃▁ |
| Resistin | 0 | 1 | -17.64 | 5.82 | -34.97 | -21.47 | -17.47 | -13.50 | -2.24 | ▁▃▇▆▁ |
| S100b | 0 | 1 | 1.25 | 0.34 | 0.19 | 1.00 | 1.25 | 1.50 | 2.37 | ▁▆▇▅▁ |
| SGOT | 0 | 1 | -0.41 | 0.35 | -1.35 | -0.63 | -0.40 | -0.20 | 0.74 | ▁▅▇▂▁ |
| SHBG | 0 | 1 | -2.48 | 0.58 | -4.14 | -2.81 | -2.49 | -2.12 | -1.11 | ▁▃▇▆▂ |
| SOD | 0 | 1 | 5.34 | 0.38 | 4.32 | 5.09 | 5.37 | 5.58 | 6.32 | ▁▅▇▅▁ |
| Serum_Amyloid_P | 0 | 1 | -6.02 | 0.56 | -7.51 | -6.38 | -6.03 | -5.65 | -4.65 | ▁▅▇▅▂ |
| Sortilin | 0 | 1 | 3.85 | 0.87 | 1.65 | 3.34 | 3.87 | 4.37 | 6.23 | ▁▅▇▃▁ |
| Stem_Cell_Factor | 0 | 1 | 3.30 | 0.36 | 2.25 | 3.04 | 3.30 | 3.53 | 4.28 | ▁▅▇▅▁ |
| TGF_alpha | 0 | 1 | 9.80 | 1.32 | 6.84 | 8.86 | 9.92 | 10.70 | 13.83 | ▂▆▇▂▁ |
| TIMP_1 | 0 | 1 | 11.75 | 1.90 | 1.74 | 10.49 | 11.56 | 12.70 | 18.88 | ▁▁▇▅▁ |
| TNF_RII | 0 | 1 | -0.59 | 0.33 | -1.66 | -0.82 | -0.60 | -0.38 | 0.47 | ▁▃▇▃▁ |
| TRAIL_R3 | 0 | 1 | -0.54 | 0.24 | -1.21 | -0.70 | -0.53 | -0.38 | 0.27 | ▁▆▇▂▁ |
| TTR_prealbumin | 0 | 1 | 2.85 | 0.14 | 2.48 | 2.77 | 2.83 | 2.94 | 3.33 | ▂▅▇▃▁ |
| Tamm_Horsfall_Protein_THP | 0 | 1 | -3.12 | 0.03 | -3.21 | -3.14 | -3.12 | -3.10 | -2.99 | ▁▇▇▂▁ |
| Thrombomodulin | 0 | 1 | -1.51 | 0.22 | -2.04 | -1.63 | -1.49 | -1.34 | -0.82 | ▂▆▇▃▁ |
| Thrombopoietin | 0 | 1 | -0.75 | 0.24 | -1.54 | -0.89 | -0.75 | -0.63 | 0.10 | ▁▅▇▂▁ |
| Thymus_Expressed_Chemokine_TECK | 0 | 1 | 3.85 | 0.80 | 1.51 | 3.34 | 3.81 | 4.32 | 6.23 | ▁▃▇▃▁ |
| Thyroid_Stimulating_Hormone | 0 | 1 | -4.50 | 0.75 | -6.19 | -4.96 | -4.51 | -4.02 | -1.71 | ▂▇▆▁▁ |
| Thyroxine_Binding_Globulin | 0 | 1 | -1.48 | 0.40 | -2.48 | -1.77 | -1.51 | -1.24 | -0.21 | ▂▇▇▃▁ |
| Tissue_Factor | 0 | 1 | 1.17 | 0.50 | -0.21 | 0.83 | 1.22 | 1.48 | 2.48 | ▁▅▇▆▁ |
| Transferrin | 0 | 1 | 2.91 | 0.27 | 1.93 | 2.71 | 2.89 | 3.09 | 3.76 | ▁▂▇▅▁ |
| Trefoil_Factor_3_TFF3 | 0 | 1 | -3.88 | 0.34 | -4.74 | -4.14 | -3.86 | -3.65 | -2.96 | ▁▅▇▃▁ |
| VCAM_1 | 0 | 1 | 2.69 | 0.32 | 1.72 | 2.48 | 2.71 | 2.89 | 3.69 | ▁▃▇▃▁ |
| VEGF | 0 | 1 | 16.99 | 1.81 | 11.83 | 15.77 | 17.08 | 18.10 | 22.38 | ▁▅▇▃▁ |
| Vitronectin | 0 | 1 | -0.28 | 0.33 | -1.43 | -0.51 | -0.30 | -0.04 | 0.53 | ▁▃▇▇▂ |
| von_Willebrand_Factor | 0 | 1 | -3.91 | 0.38 | -4.99 | -4.20 | -3.91 | -3.61 | -2.96 | ▁▅▇▆▂ |
| E4 | 0 | 1 | 0.40 | 0.49 | 0.00 | 0.00 | 0.00 | 1.00 | 1.00 | ▇▁▁▁▆ |
| E3 | 0 | 1 | 0.92 | 0.28 | 0.00 | 1.00 | 1.00 | 1.00 | 1.00 | ▁▁▁▁▇ |
| E2 | 0 | 1 | 0.16 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | ▇▁▁▁▂ |
##################################
# Identifying columns with low variance
###################################
DPA_LowVariance <- nearZeroVar(DPA,
freqCut = 95/5,
uniqueCut = 10,
saveMetrics= TRUE)
(DPA_LowVariance[DPA_LowVariance$nzv,])## [1] freqRatio percentUnique zeroVar nzv
## <0 rows> (or 0-length row.names)if ((nrow(DPA_LowVariance[DPA_LowVariance$nzv,]))==0){
print("No low variance predictors noted.")
} else {
print(paste0("Low variance observed for ",
(nrow(DPA_LowVariance[DPA_LowVariance$nzv,])),
" numeric variable(s) with First.Second.Mode.Ratio>4 and Unique.Count.Ratio<0.10."))
DPA_LowVarianceForRemoval <- (nrow(DPA_LowVariance[DPA_LowVariance$nzv,]))
print(paste0("Low variance can be resolved by removing ",
(nrow(DPA_LowVariance[DPA_LowVariance$nzv,])),
" numeric variable(s)."))
for (j in 1:DPA_LowVarianceForRemoval) {
DPA_LowVarianceRemovedVariable <- rownames(DPA_LowVariance[DPA_LowVariance$nzv,])[j]
print(paste0("Variable ",
j,
" for removal: ",
DPA_LowVarianceRemovedVariable))
}
DPA %>%
skim() %>%
dplyr::filter(skim_variable %in% rownames(DPA_LowVariance[DPA_LowVariance$nzv,]))
##################################
# Filtering out columns with low variance
#################################
DPA_ExcludedLowVariance <- DPA[,!names(DPA) %in% rownames(DPA_LowVariance[DPA_LowVariance$nzv,])]
##################################
# Gathering descriptive statistics
##################################
(DPA_ExcludedLowVariance_Skimmed <- skim(DPA_ExcludedLowVariance))
}## [1] "No low variance predictors noted."1.3.3 Collinearity
[A] No high correlation > 95% were noted for any variable pair as confirmed using the preprocessing summaries from the caret and lares packages.
Code Chunk | Output
##################################
# Loading dataset
##################################
DPA <- Alzheimer_Train
##################################
# Listing all predictors
##################################
DPA.Predictors <- DPA[,!names(DPA) %in% c("Class")]
##################################
# Listing all numeric predictors
##################################
DPA.Predictors.Numeric <- DPA.Predictors[,!names(DPA.Predictors) %in% c("E2","E3","E4")]
DPA.Predictors.Numeric <- as.data.frame(sapply(DPA.Predictors.Numeric,function(x) as.numeric(x)))
##################################
# Visualizing pairwise correlation between predictors
##################################
DPA_CorrelationTest <- cor.mtest(DPA.Predictors.Numeric,
method = "pearson",
conf.level = .95)
corrplot(cor(DPA.Predictors.Numeric,
method = "pearson",
use="pairwise.complete.obs"),
method = "circle",
type = "upper",
order = "original",
tl.col = "black",
tl.cex = 0.75,
tl.srt = 90,
sig.level = 0.05,
p.mat = DPA_CorrelationTest$p,
insig = "blank")
##################################
# Identifying the highly correlated variables
##################################
DPA_Correlation <- cor(DPA.Predictors.Numeric,
method = "pearson",
use="pairwise.complete.obs")
(DPA_HighlyCorrelatedCount <- sum(abs(DPA_Correlation[upper.tri(DPA_Correlation)]) > 0.95))## [1] 0if (DPA_HighlyCorrelatedCount == 0) {
print("No highly correlated predictors noted.")
} else {
print(paste0("High correlation observed for ",
(DPA_HighlyCorrelatedCount),
" pairs of numeric variable(s) with Correlation.Coefficient>0.95."))
(DPA_HighlyCorrelatedPairs <- corr_cross(DPA.Predictors.Numeric,
max_pvalue = 0.05,
top = DPA_HighlyCorrelatedCount,
rm.na = TRUE,
grid = FALSE
))
}## [1] "No highly correlated predictors noted."if (DPA_HighlyCorrelatedCount > 0) {
DPA_HighlyCorrelated <- findCorrelation(DPA_Correlation, cutoff = 0.95)
(DPA_HighlyCorrelatedForRemoval <- length(DPA_HighlyCorrelated))
print(paste0("High correlation can be resolved by removing ",
(DPA_HighlyCorrelatedForRemoval),
" numeric variable(s)."))
for (j in 1:DPA_HighlyCorrelatedForRemoval) {
DPA_HighlyCorrelatedRemovedVariable <- colnames(DPA.Predictors.Numeric)[DPA_HighlyCorrelated[j]]
print(paste0("Variable ",
j,
" for removal: ",
DPA_HighlyCorrelatedRemovedVariable))
}
##################################
# Filtering out columns with high correlation
#################################
DPA_ExcludedHighCorrelation <- DPA[,-DPA_HighlyCorrelated]
##################################
# Gathering descriptive statistics
##################################
(DPA_ExcludedHighCorrelation_Skimmed <- skim(DPA_ExcludedHighCorrelation))
}1.3.4 Linear Dependencies
[A] No linear dependencies noted for any subset of variables using the preprocessing summary from the caret package applying the findLinearCombos method which utilizes the QR decomposition of a matrix to enumerate sets of linear combinations (if they exist).
Code Chunk | Output
##################################
# Loading dataset
##################################
DPA <- Alzheimer_Train
##################################
# Listing all predictors
##################################
DPA.Predictors <- DPA[,!names(DPA) %in% c("Class")]
##################################
# Listing all numeric predictors
##################################
DPA.Predictors.Numeric <- DPA.Predictors[,!names(DPA.Predictors) %in% c("E2","E3","E4")]
DPA.Predictors.Numeric <- as.data.frame(sapply(DPA.Predictors.Numeric,function(x) as.numeric(x)))
##################################
# Identifying the linearly dependent variables
##################################
DPA_LinearlyDependent <- findLinearCombos(DPA.Predictors.Numeric)
(DPA_LinearlyDependentCount <- length(DPA_LinearlyDependent$linearCombos))## [1] 0if (DPA_LinearlyDependentCount == 0) {
print("No linearly dependent predictors noted.")
} else {
print(paste0("Linear dependency observed for ",
(DPA_LinearlyDependentCount),
" subset(s) of numeric variable(s)."))
for (i in 1:DPA_LinearlyDependentCount) {
DPA_LinearlyDependentSubset <- colnames(DPA.Predictors.Numeric)[DPA_LinearlyDependent$linearCombos[[i]]]
print(paste0("Linear dependent variable(s) for subset ",
i,
" include: ",
DPA_LinearlyDependentSubset))
}
}## [1] "No linearly dependent predictors noted."##################################
# Identifying the linearly dependent variables for removal
##################################
if (DPA_LinearlyDependentCount > 0) {
DPA_LinearlyDependent <- findLinearCombos(DPA.Predictors.Numeric)
DPA_LinearlyDependentForRemoval <- length(DPA_LinearlyDependent$remove)
print(paste0("Linear dependency can be resolved by removing ",
(DPA_LinearlyDependentForRemoval),
" numeric variable(s)."))
for (j in 1:DPA_LinearlyDependentForRemoval) {
DPA_LinearlyDependentRemovedVariable <- colnames(DPA.Predictors.Numeric)[DPA_LinearlyDependent$remove[j]]
print(paste0("Variable ",
j,
" for removal: ",
DPA_LinearlyDependentRemovedVariable))
}
##################################
# Filtering out columns with linear dependency
#################################
DPA_ExcludedLinearlyDependent <- DPA[,-DPA_LinearlyDependent$remove]
##################################
# Gathering descriptive statistics
##################################
(DPA_ExcludedLinearlyDependent_Skimmed <- skim(DPA_ExcludedLinearlyDependent))
}1.3.5 Pre-Processed Dataset
[A] 333 rows (observations)
[A.1] Train Set = 267 observations
[A.2] Test Set = 66 observations
[B] 128 columns (variables)
[B.1] 1/128 response = Class variable (factor)
[B.1.1] Levels = Class=Control < Class=Impaired
[B.2] 127/128 predictors = All remaining variables (3/127 factor + 124/127 numeric)
[C] No pre-processing actions applied:
[C.1] No shape transformation applied since distributions were fairly normal
[C.2] Centering and scaling may be necessary due to the differences in ranges for the numeric variables however, these will be selectively applied based on model requirements
[C.2] No outlier treatment applied since the high values noted were minimal and contextually valid
[C.3] No predictors removed due to zero or near-zero variance
[C.4] No predictors removed due to high correlation
[C.5] No predictors removed due to linear dependencies
Code Chunk | Output
##################################
# Creating the pre-modelling
# train set
##################################
PMA_PreModelling_Train <- Alzheimer_Train
PMA_PreModelling_Train$Class <- as.factor(PMA_PreModelling_Train$Class)
PMA_PreModelling_Train$E2 <- as.factor(PMA_PreModelling_Train$E2)
PMA_PreModelling_Train$E3 <- as.factor(PMA_PreModelling_Train$E3)
PMA_PreModelling_Train$E4 <- as.factor(PMA_PreModelling_Train$E4)
##################################
# Gathering descriptive statistics
##################################
(PMA_PreModelling_Train_Skimmed <- skim(PMA_PreModelling_Train))| Name | PMA_PreModelling_Train |
| Number of rows | 267 |
| Number of columns | 128 |
| _______________________ | |
| Column type frequency: | |
| factor | 4 |
| numeric | 124 |
| ________________________ | |
| Group variables | None |
Variable type: factor
| skim_variable | n_missing | complete_rate | ordered | n_unique | top_counts |
|---|---|---|---|---|---|
| Class | 0 | 1 | FALSE | 2 | Con: 194, Imp: 73 |
| E4 | 0 | 1 | FALSE | 2 | 0: 160, 1: 107 |
| E3 | 0 | 1 | FALSE | 2 | 1: 245, 0: 22 |
| E2 | 0 | 1 | FALSE | 2 | 0: 224, 1: 43 |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| ACE_CD143_Angiotensin_Converti | 0 | 1 | 1.32 | 0.54 | -0.68 | 0.95 | 1.30 | 1.72 | 2.84 | ▁▃▇▇▁ |
| ACTH_Adrenocorticotropic_Hormon | 0 | 1 | -1.54 | 0.28 | -2.21 | -1.71 | -1.56 | -1.35 | -0.84 | ▂▆▇▆▂ |
| AXL | 0 | 1 | 0.31 | 0.45 | -0.92 | 0.00 | 0.28 | 0.61 | 1.52 | ▁▅▇▃▁ |
| Adiponectin | 0 | 1 | -5.20 | 0.67 | -6.73 | -5.67 | -5.18 | -4.78 | -3.51 | ▂▆▇▅▁ |
| Alpha_1_Antichymotrypsin | 0 | 1 | 1.36 | 0.36 | 0.26 | 1.13 | 1.36 | 1.59 | 2.30 | ▁▃▇▅▁ |
| Alpha_1_Antitrypsin | 0 | 1 | -13.05 | 1.48 | -17.03 | -14.07 | -13.00 | -12.10 | -8.19 | ▁▅▇▂▁ |
| Alpha_1_Microglobulin | 0 | 1 | -2.93 | 0.48 | -4.34 | -3.27 | -2.94 | -2.59 | -1.77 | ▁▅▇▇▂ |
| Alpha_2_Macroglobulin | 0 | 1 | -158.61 | 40.93 | -289.68 | -186.64 | -160.01 | -134.62 | -59.46 | ▁▂▇▅▂ |
| Angiopoietin_2_ANG_2 | 0 | 1 | 0.67 | 0.33 | -0.54 | 0.47 | 0.64 | 0.88 | 1.53 | ▁▂▇▆▂ |
| Angiotensinogen | 0 | 1 | 2.32 | 0.25 | 1.75 | 2.12 | 2.32 | 2.50 | 2.88 | ▃▆▇▇▂ |
| Apolipoprotein_A_IV | 0 | 1 | -1.85 | 0.38 | -2.96 | -2.12 | -1.83 | -1.61 | -0.78 | ▁▃▇▃▁ |
| Apolipoprotein_A1 | 0 | 1 | -7.48 | 0.44 | -8.68 | -7.76 | -7.47 | -7.21 | -6.17 | ▁▅▇▃▁ |
| Apolipoprotein_A2 | 0 | 1 | -0.64 | 0.50 | -1.90 | -0.97 | -0.67 | -0.31 | 0.96 | ▁▇▇▃▁ |
| Apolipoprotein_B | 0 | 1 | -5.58 | 1.48 | -9.94 | -6.63 | -5.70 | -4.54 | -2.15 | ▁▅▇▇▂ |
| Apolipoprotein_CI | 0 | 1 | -1.58 | 0.41 | -3.32 | -1.83 | -1.61 | -1.37 | -0.27 | ▁▁▇▅▁ |
| Apolipoprotein_CIII | 0 | 1 | -2.49 | 0.44 | -3.69 | -2.77 | -2.53 | -2.21 | -1.24 | ▁▅▇▅▁ |
| Apolipoprotein_D | 0 | 1 | 1.44 | 0.34 | 0.47 | 1.21 | 1.41 | 1.67 | 2.27 | ▁▃▇▆▂ |
| Apolipoprotein_E | 0 | 1 | 2.81 | 0.78 | 0.59 | 2.33 | 2.82 | 3.29 | 5.44 | ▁▅▇▂▁ |
| Apolipoprotein_H | 0 | 1 | -0.32 | 0.39 | -2.23 | -0.60 | -0.37 | -0.06 | 0.93 | ▁▁▇▆▁ |
| B_Lymphocyte_Chemoattractant_BL | 0 | 1 | 2.02 | 0.57 | 0.73 | 1.67 | 1.98 | 2.37 | 4.02 | ▃▇▇▁▁ |
| BMP_6 | 0 | 1 | -1.91 | 0.31 | -2.76 | -2.15 | -1.88 | -1.68 | -0.82 | ▁▅▇▂▁ |
| Beta_2_Microglobulin | 0 | 1 | 0.17 | 0.30 | -0.54 | -0.04 | 0.18 | 0.34 | 0.99 | ▂▃▇▃▁ |
| Betacellulin | 0 | 1 | 51.01 | 10.87 | 10.00 | 42.00 | 51.00 | 59.00 | 82.00 | ▁▁▇▅▁ |
| C_Reactive_Protein | 0 | 1 | -5.87 | 1.20 | -8.52 | -6.65 | -5.84 | -5.08 | -2.94 | ▃▆▇▆▂ |
| CD40 | 0 | 1 | -1.26 | 0.21 | -1.86 | -1.38 | -1.27 | -1.12 | -0.55 | ▁▆▇▃▁ |
| CD5L | 0 | 1 | -0.05 | 0.45 | -1.24 | -0.36 | -0.06 | 0.26 | 1.16 | ▁▅▇▃▁ |
| Calbindin | 0 | 1 | 22.43 | 4.11 | 10.96 | 19.77 | 22.25 | 24.80 | 33.78 | ▁▃▇▃▁ |
| Calcitonin | 0 | 1 | 1.68 | 0.87 | -0.71 | 0.96 | 1.65 | 2.28 | 3.89 | ▁▆▇▅▂ |
| CgA | 0 | 1 | 333.30 | 83.67 | 135.60 | 278.02 | 331.52 | 392.07 | 535.40 | ▂▆▇▅▂ |
| Clusterin_Apo_J | 0 | 1 | 2.88 | 0.29 | 1.87 | 2.71 | 2.89 | 3.04 | 3.58 | ▁▂▇▆▂ |
| Complement_3 | 0 | 1 | -15.61 | 2.46 | -23.39 | -17.57 | -15.52 | -13.88 | -9.56 | ▁▆▇▇▂ |
| Complement_Factor_H | 0 | 1 | 3.55 | 1.25 | -0.84 | 2.75 | 3.60 | 4.25 | 7.62 | ▁▃▇▅▁ |
| Connective_Tissue_Growth_Factor | 0 | 1 | 0.77 | 0.20 | 0.18 | 0.64 | 0.79 | 0.92 | 1.41 | ▁▅▇▃▁ |
| Cortisol | 0 | 1 | 11.98 | 3.95 | 0.10 | 9.80 | 12.00 | 14.00 | 29.00 | ▁▇▇▁▁ |
| Creatine_Kinase_MB | 0 | 1 | -1.67 | 0.09 | -1.87 | -1.72 | -1.67 | -1.63 | -1.38 | ▃▅▇▂▁ |
| Cystatin_C | 0 | 1 | 8.59 | 0.40 | 7.43 | 8.32 | 8.56 | 8.84 | 9.69 | ▁▅▇▃▁ |
| EGF_R | 0 | 1 | -0.70 | 0.22 | -1.36 | -0.86 | -0.68 | -0.55 | -0.06 | ▁▃▇▅▁ |
| EN_RAGE | 0 | 1 | -3.64 | 0.88 | -8.38 | -4.20 | -3.65 | -3.15 | -0.39 | ▁▁▇▆▁ |
| ENA_78 | 0 | 1 | -1.37 | 0.01 | -1.41 | -1.38 | -1.37 | -1.36 | -1.34 | ▁▅▇▅▁ |
| Eotaxin_3 | 0 | 1 | 58.17 | 15.83 | 7.00 | 44.00 | 59.00 | 70.00 | 107.00 | ▁▆▇▅▁ |
| FAS | 0 | 1 | -0.53 | 0.30 | -1.51 | -0.71 | -0.53 | -0.31 | 0.34 | ▁▃▇▆▁ |
| FSH_Follicle_Stimulation_Hormon | 0 | 1 | -1.14 | 0.42 | -2.12 | -1.47 | -1.14 | -0.88 | 0.10 | ▂▇▇▃▁ |
| Fas_Ligand | 0 | 1 | 2.97 | 1.09 | -0.15 | 2.34 | 3.10 | 3.70 | 7.63 | ▂▇▇▁▁ |
| Fatty_Acid_Binding_Protein | 0 | 1 | 1.35 | 0.78 | -1.04 | 0.80 | 1.39 | 1.88 | 3.71 | ▁▅▇▅▁ |
| Ferritin | 0 | 1 | 2.76 | 0.76 | 0.61 | 2.29 | 2.77 | 3.29 | 4.63 | ▁▃▇▆▂ |
| Fetuin_A | 0 | 1 | 1.35 | 0.37 | 0.47 | 1.10 | 1.31 | 1.61 | 2.25 | ▂▆▇▅▂ |
| Fibrinogen | 0 | 1 | -7.36 | 0.57 | -8.87 | -7.72 | -7.32 | -7.01 | -5.84 | ▁▅▇▅▁ |
| GRO_alpha | 0 | 1 | 1.38 | 0.04 | 1.27 | 1.35 | 1.38 | 1.41 | 1.49 | ▂▃▇▅▁ |
| Gamma_Interferon_induced_Monokin | 0 | 1 | 2.79 | 0.11 | 2.39 | 2.71 | 2.78 | 2.87 | 3.07 | ▁▂▇▆▂ |
| Glutathione_S_Transferase_alpha | 0 | 1 | 0.95 | 0.16 | 0.52 | 0.84 | 0.97 | 1.03 | 1.32 | ▁▃▇▅▂ |
| HB_EGF | 0 | 1 | 6.83 | 1.51 | 2.10 | 5.79 | 6.70 | 7.86 | 10.70 | ▁▃▇▆▂ |
| HCC_4 | 0 | 1 | -3.50 | 0.36 | -4.51 | -3.73 | -3.51 | -3.27 | -2.12 | ▂▇▇▂▁ |
| Hepatocyte_Growth_Factor_HGF | 0 | 1 | 0.20 | 0.29 | -0.63 | 0.00 | 0.18 | 0.41 | 0.88 | ▁▃▇▅▂ |
| I_309 | 0 | 1 | 2.96 | 0.37 | 1.76 | 2.71 | 2.94 | 3.22 | 4.14 | ▁▅▇▃▁ |
| ICAM_1 | 0 | 1 | -0.59 | 0.33 | -1.53 | -0.83 | -0.59 | -0.38 | 0.52 | ▁▅▇▃▁ |
| IGF_BP_2 | 0 | 1 | 5.32 | 0.20 | 4.63 | 5.18 | 5.32 | 5.45 | 5.95 | ▁▃▇▅▁ |
| IL_11 | 0 | 1 | 4.72 | 1.45 | 1.75 | 3.71 | 4.81 | 5.78 | 8.49 | ▃▆▇▅▁ |
| IL_13 | 0 | 1 | 1.28 | 0.01 | 1.26 | 1.27 | 1.28 | 1.29 | 1.32 | ▂▇▆▂▁ |
| IL_16 | 0 | 1 | 2.93 | 0.66 | 1.19 | 2.52 | 2.91 | 3.35 | 4.94 | ▁▆▇▃▁ |
| IL_17E | 0 | 1 | 4.85 | 1.34 | 1.05 | 4.15 | 4.75 | 5.63 | 8.95 | ▁▆▇▃▁ |
| IL_1alpha | 0 | 1 | -7.51 | 0.39 | -8.52 | -7.82 | -7.52 | -7.26 | -5.95 | ▂▇▇▂▁ |
| IL_3 | 0 | 1 | -3.94 | 0.50 | -5.91 | -4.27 | -3.91 | -3.63 | -2.45 | ▁▂▇▅▁ |
| IL_4 | 0 | 1 | 1.77 | 0.51 | 0.53 | 1.46 | 1.81 | 2.15 | 3.04 | ▂▅▇▅▂ |
| IL_5 | 0 | 1 | 0.19 | 0.46 | -1.43 | -0.12 | 0.18 | 0.47 | 1.95 | ▁▃▇▂▁ |
| IL_6 | 0 | 1 | -0.15 | 0.55 | -1.53 | -0.41 | -0.16 | 0.14 | 1.81 | ▂▆▇▂▁ |
| IL_6_Receptor | 0 | 1 | 0.09 | 0.32 | -0.68 | -0.13 | 0.10 | 0.35 | 0.83 | ▂▆▇▆▂ |
| IL_7 | 0 | 1 | 2.84 | 1.05 | 0.56 | 2.15 | 2.79 | 3.71 | 5.71 | ▃▇▇▆▁ |
| IL_8 | 0 | 1 | 1.70 | 0.04 | 1.57 | 1.68 | 1.71 | 1.73 | 1.81 | ▁▂▇▆▁ |
| IP_10_Inducible_Protein_10 | 0 | 1 | 5.75 | 0.51 | 4.32 | 5.40 | 5.75 | 6.06 | 7.50 | ▁▆▇▂▁ |
| IgA | 0 | 1 | -6.12 | 0.76 | -10.52 | -6.65 | -6.12 | -5.57 | -4.20 | ▁▁▂▇▂ |
| Insulin | 0 | 1 | -1.23 | 0.34 | -2.17 | -1.45 | -1.25 | -1.03 | -0.16 | ▁▃▇▂▁ |
| Kidney_Injury_Molecule_1_KIM_1 | 0 | 1 | -1.18 | 0.03 | -1.26 | -1.20 | -1.18 | -1.16 | -1.10 | ▁▇▇▅▁ |
| LOX_1 | 0 | 1 | 1.28 | 0.40 | 0.00 | 1.03 | 1.28 | 1.53 | 2.27 | ▁▂▇▅▂ |
| Leptin | 0 | 1 | -1.50 | 0.27 | -2.15 | -1.70 | -1.50 | -1.33 | -0.62 | ▂▇▇▂▁ |
| Lipoprotein_a | 0 | 1 | -4.42 | 1.11 | -6.81 | -5.31 | -4.61 | -3.49 | -1.39 | ▂▇▅▅▁ |
| MCP_1 | 0 | 1 | 6.50 | 0.26 | 5.83 | 6.32 | 6.49 | 6.68 | 7.23 | ▂▅▇▅▁ |
| MCP_2 | 0 | 1 | 1.87 | 0.65 | 0.40 | 1.53 | 1.85 | 2.18 | 4.02 | ▂▆▇▂▁ |
| MIF | 0 | 1 | -1.86 | 0.34 | -2.85 | -2.12 | -1.90 | -1.66 | -0.84 | ▁▃▇▃▁ |
| MIP_1alpha | 0 | 1 | 4.05 | 1.01 | 0.93 | 3.34 | 4.05 | 4.69 | 6.80 | ▁▅▇▅▂ |
| MIP_1beta | 0 | 1 | 2.81 | 0.38 | 1.95 | 2.56 | 2.83 | 3.04 | 4.01 | ▂▅▇▂▁ |
| MMP_2 | 0 | 1 | 2.88 | 0.93 | 0.10 | 2.33 | 2.82 | 3.55 | 5.36 | ▁▃▇▆▁ |
| MMP_3 | 0 | 1 | -2.45 | 0.57 | -4.42 | -2.75 | -2.45 | -2.12 | -0.53 | ▁▂▇▃▁ |
| MMP10 | 0 | 1 | -3.63 | 0.43 | -4.93 | -3.94 | -3.65 | -3.35 | -2.21 | ▁▆▇▃▁ |
| MMP7 | 0 | 1 | -3.79 | 1.55 | -8.40 | -4.82 | -3.77 | -2.71 | -0.22 | ▁▃▇▅▂ |
| Myoglobin | 0 | 1 | -1.37 | 0.95 | -3.17 | -2.04 | -1.47 | -0.80 | 1.77 | ▅▇▆▂▁ |
| NT_proBNP | 0 | 1 | 4.55 | 0.38 | 3.18 | 4.35 | 4.55 | 4.77 | 5.89 | ▁▂▇▃▁ |
| NrCAM | 0 | 1 | 4.36 | 0.57 | 2.64 | 4.00 | 4.39 | 4.75 | 6.01 | ▁▃▇▅▁ |
| Osteopontin | 0 | 1 | 5.20 | 0.39 | 4.11 | 4.96 | 5.19 | 5.44 | 6.31 | ▁▅▇▃▁ |
| PAI_1 | 0 | 1 | 0.08 | 0.41 | -0.99 | -0.17 | 0.09 | 0.32 | 1.17 | ▂▃▇▅▂ |
| PAPP_A | 0 | 1 | -2.85 | 0.14 | -3.31 | -2.94 | -2.87 | -2.75 | -2.52 | ▁▂▇▅▂ |
| PLGF | 0 | 1 | 3.91 | 0.41 | 2.48 | 3.64 | 3.87 | 4.20 | 5.17 | ▁▃▇▆▁ |
| PYY | 0 | 1 | 3.02 | 0.29 | 2.19 | 2.83 | 3.00 | 3.18 | 3.93 | ▁▅▇▃▁ |
| Pancreatic_polypeptide | 0 | 1 | -0.01 | 0.72 | -2.12 | -0.53 | -0.04 | 0.53 | 1.93 | ▁▅▇▆▁ |
| Prolactin | 0 | 1 | 0.04 | 0.30 | -1.31 | -0.14 | 0.00 | 0.26 | 0.99 | ▁▁▇▇▁ |
| Prostatic_Acid_Phosphatase | 0 | 1 | -1.69 | 0.06 | -1.93 | -1.72 | -1.69 | -1.65 | -1.42 | ▁▂▇▂▁ |
| Protein_S | 0 | 1 | -2.24 | 0.35 | -3.34 | -2.46 | -2.26 | -2.00 | -1.22 | ▁▃▇▃▁ |
| Pulmonary_and_Activation_Regulat | 0 | 1 | -1.49 | 0.45 | -2.51 | -1.83 | -1.51 | -1.17 | -0.27 | ▂▇▇▃▂ |
| RANTES | 0 | 1 | -6.51 | 0.32 | -7.22 | -6.73 | -6.50 | -6.32 | -5.55 | ▃▇▇▃▁ |
| Resistin | 0 | 1 | -17.64 | 5.82 | -34.97 | -21.47 | -17.47 | -13.50 | -2.24 | ▁▃▇▆▁ |
| S100b | 0 | 1 | 1.25 | 0.34 | 0.19 | 1.00 | 1.25 | 1.50 | 2.37 | ▁▆▇▅▁ |
| SGOT | 0 | 1 | -0.41 | 0.35 | -1.35 | -0.63 | -0.40 | -0.20 | 0.74 | ▁▅▇▂▁ |
| SHBG | 0 | 1 | -2.48 | 0.58 | -4.14 | -2.81 | -2.49 | -2.12 | -1.11 | ▁▃▇▆▂ |
| SOD | 0 | 1 | 5.34 | 0.38 | 4.32 | 5.09 | 5.37 | 5.58 | 6.32 | ▁▅▇▅▁ |
| Serum_Amyloid_P | 0 | 1 | -6.02 | 0.56 | -7.51 | -6.38 | -6.03 | -5.65 | -4.65 | ▁▅▇▅▂ |
| Sortilin | 0 | 1 | 3.85 | 0.87 | 1.65 | 3.34 | 3.87 | 4.37 | 6.23 | ▁▅▇▃▁ |
| Stem_Cell_Factor | 0 | 1 | 3.30 | 0.36 | 2.25 | 3.04 | 3.30 | 3.53 | 4.28 | ▁▅▇▅▁ |
| TGF_alpha | 0 | 1 | 9.80 | 1.32 | 6.84 | 8.86 | 9.92 | 10.70 | 13.83 | ▂▆▇▂▁ |
| TIMP_1 | 0 | 1 | 11.75 | 1.90 | 1.74 | 10.49 | 11.56 | 12.70 | 18.88 | ▁▁▇▅▁ |
| TNF_RII | 0 | 1 | -0.59 | 0.33 | -1.66 | -0.82 | -0.60 | -0.38 | 0.47 | ▁▃▇▃▁ |
| TRAIL_R3 | 0 | 1 | -0.54 | 0.24 | -1.21 | -0.70 | -0.53 | -0.38 | 0.27 | ▁▆▇▂▁ |
| TTR_prealbumin | 0 | 1 | 2.85 | 0.14 | 2.48 | 2.77 | 2.83 | 2.94 | 3.33 | ▂▅▇▃▁ |
| Tamm_Horsfall_Protein_THP | 0 | 1 | -3.12 | 0.03 | -3.21 | -3.14 | -3.12 | -3.10 | -2.99 | ▁▇▇▂▁ |
| Thrombomodulin | 0 | 1 | -1.51 | 0.22 | -2.04 | -1.63 | -1.49 | -1.34 | -0.82 | ▂▆▇▃▁ |
| Thrombopoietin | 0 | 1 | -0.75 | 0.24 | -1.54 | -0.89 | -0.75 | -0.63 | 0.10 | ▁▅▇▂▁ |
| Thymus_Expressed_Chemokine_TECK | 0 | 1 | 3.85 | 0.80 | 1.51 | 3.34 | 3.81 | 4.32 | 6.23 | ▁▃▇▃▁ |
| Thyroid_Stimulating_Hormone | 0 | 1 | -4.50 | 0.75 | -6.19 | -4.96 | -4.51 | -4.02 | -1.71 | ▂▇▆▁▁ |
| Thyroxine_Binding_Globulin | 0 | 1 | -1.48 | 0.40 | -2.48 | -1.77 | -1.51 | -1.24 | -0.21 | ▂▇▇▃▁ |
| Tissue_Factor | 0 | 1 | 1.17 | 0.50 | -0.21 | 0.83 | 1.22 | 1.48 | 2.48 | ▁▅▇▆▁ |
| Transferrin | 0 | 1 | 2.91 | 0.27 | 1.93 | 2.71 | 2.89 | 3.09 | 3.76 | ▁▂▇▅▁ |
| Trefoil_Factor_3_TFF3 | 0 | 1 | -3.88 | 0.34 | -4.74 | -4.14 | -3.86 | -3.65 | -2.96 | ▁▅▇▃▁ |
| VCAM_1 | 0 | 1 | 2.69 | 0.32 | 1.72 | 2.48 | 2.71 | 2.89 | 3.69 | ▁▃▇▃▁ |
| VEGF | 0 | 1 | 16.99 | 1.81 | 11.83 | 15.77 | 17.08 | 18.10 | 22.38 | ▁▅▇▃▁ |
| Vitronectin | 0 | 1 | -0.28 | 0.33 | -1.43 | -0.51 | -0.30 | -0.04 | 0.53 | ▁▃▇▇▂ |
| von_Willebrand_Factor | 0 | 1 | -3.91 | 0.38 | -4.99 | -4.20 | -3.91 | -3.61 | -2.96 | ▁▅▇▆▂ |
###################################
# Verifying the data dimensions
# for the train set
###################################
dim(PMA_PreModelling_Train)## [1] 267 128##################################
# Formulating the test set
##################################
PMA_PreModelling_Test <- Alzheimer_Test
PMA_PreModelling_Test$Class <- as.factor(PMA_PreModelling_Test$Class)
PMA_PreModelling_Test$E2 <- as.factor(PMA_PreModelling_Test$E2)
PMA_PreModelling_Test$E3 <- as.factor(PMA_PreModelling_Test$E3)
PMA_PreModelling_Test$E4 <- as.factor(PMA_PreModelling_Test$E4)
##################################
# Gathering descriptive statistics
##################################
(PMA_PreModelling_Test_Skimmed <- skim(PMA_PreModelling_Test))| Name | PMA_PreModelling_Test |
| Number of rows | 66 |
| Number of columns | 128 |
| _______________________ | |
| Column type frequency: | |
| factor | 4 |
| numeric | 124 |
| ________________________ | |
| Group variables | None |
Variable type: factor
| skim_variable | n_missing | complete_rate | ordered | n_unique | top_counts |
|---|---|---|---|---|---|
| Class | 0 | 1 | FALSE | 2 | Con: 48, Imp: 18 |
| E4 | 0 | 1 | FALSE | 2 | 0: 46, 1: 20 |
| E3 | 0 | 1 | FALSE | 2 | 1: 65, 0: 1 |
| E2 | 0 | 1 | FALSE | 2 | 0: 62, 1: 4 |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| ACE_CD143_Angiotensin_Converti | 0 | 1 | 1.31 | 0.59 | -0.55 | 0.95 | 1.30 | 1.63 | 3.09 | ▁▃▇▃▁ |
| ACTH_Adrenocorticotropic_Hormon | 0 | 1 | -1.53 | 0.25 | -2.21 | -1.71 | -1.54 | -1.39 | -0.80 | ▁▃▇▃▁ |
| AXL | 0 | 1 | 0.25 | 0.45 | -0.74 | -0.08 | 0.28 | 0.61 | 1.29 | ▃▃▇▅▂ |
| Adiponectin | 0 | 1 | -5.30 | 0.66 | -7.06 | -5.74 | -5.36 | -4.92 | -3.47 | ▁▅▇▃▁ |
| Alpha_1_Antichymotrypsin | 0 | 1 | 1.31 | 0.38 | 0.18 | 1.06 | 1.31 | 1.57 | 2.22 | ▁▃▇▆▂ |
| Alpha_1_Antitrypsin | 0 | 1 | -13.49 | 1.76 | -18.17 | -14.70 | -13.59 | -12.31 | -10.06 | ▁▃▇▆▃ |
| Alpha_1_Microglobulin | 0 | 1 | -2.98 | 0.49 | -4.14 | -3.28 | -3.01 | -2.67 | -1.90 | ▂▅▇▅▂ |
| Alpha_2_Macroglobulin | 0 | 1 | -162.89 | 40.98 | -238.64 | -186.64 | -162.93 | -136.53 | -50.17 | ▃▇▇▃▁ |
| Angiopoietin_2_ANG_2 | 0 | 1 | 0.60 | 0.35 | -0.05 | 0.35 | 0.56 | 0.79 | 1.77 | ▃▇▅▁▁ |
| Angiotensinogen | 0 | 1 | 2.27 | 0.23 | 1.71 | 2.07 | 2.28 | 2.43 | 2.75 | ▁▇▇▇▂ |
| Apolipoprotein_A_IV | 0 | 1 | -1.87 | 0.38 | -2.75 | -2.19 | -1.90 | -1.53 | -1.11 | ▂▆▇▆▅ |
| Apolipoprotein_A1 | 0 | 1 | -7.49 | 0.42 | -8.57 | -7.82 | -7.50 | -7.18 | -6.65 | ▁▆▇▇▃ |
| Apolipoprotein_A2 | 0 | 1 | -0.69 | 0.48 | -1.97 | -0.94 | -0.70 | -0.35 | 0.53 | ▁▃▇▅▁ |
| Apolipoprotein_B | 0 | 1 | -5.65 | 1.34 | -8.19 | -6.75 | -5.82 | -4.60 | -2.34 | ▃▇▅▅▂ |
| Apolipoprotein_CI | 0 | 1 | -1.63 | 0.45 | -2.85 | -1.90 | -1.61 | -1.31 | -0.46 | ▂▅▇▅▁ |
| Apolipoprotein_CIII | 0 | 1 | -2.52 | 0.46 | -3.86 | -2.78 | -2.56 | -2.23 | -1.39 | ▁▂▇▃▂ |
| Apolipoprotein_D | 0 | 1 | 1.39 | 0.41 | 0.26 | 1.13 | 1.39 | 1.69 | 2.64 | ▁▇▇▅▁ |
| Apolipoprotein_E | 0 | 1 | 2.72 | 0.88 | 0.66 | 2.15 | 2.82 | 3.24 | 4.68 | ▂▅▇▅▂ |
| Apolipoprotein_H | 0 | 1 | -0.32 | 0.33 | -1.16 | -0.53 | -0.29 | -0.10 | 0.44 | ▂▅▇▆▂ |
| B_Lymphocyte_Chemoattractant_BL | 0 | 1 | 1.88 | 0.57 | 0.73 | 1.53 | 1.85 | 2.37 | 2.98 | ▂▆▇▆▃ |
| BMP_6 | 0 | 1 | -1.94 | 0.35 | -2.67 | -2.15 | -1.96 | -1.68 | -1.18 | ▃▃▇▆▂ |
| Beta_2_Microglobulin | 0 | 1 | 0.16 | 0.31 | -0.51 | -0.06 | 0.18 | 0.41 | 0.83 | ▂▇▇▆▂ |
| Betacellulin | 0 | 1 | 52.74 | 10.58 | 32.00 | 46.00 | 51.00 | 59.75 | 80.00 | ▂▇▅▃▁ |
| C_Reactive_Protein | 0 | 1 | -6.00 | 1.17 | -8.11 | -6.73 | -6.17 | -5.37 | -3.41 | ▃▇▇▃▃ |
| CD40 | 0 | 1 | -1.28 | 0.24 | -1.94 | -1.44 | -1.26 | -1.10 | -0.78 | ▂▃▅▇▂ |
| CD5L | 0 | 1 | -0.09 | 0.49 | -1.97 | -0.37 | -0.05 | 0.24 | 0.92 | ▁▁▃▇▂ |
| Calbindin | 0 | 1 | 21.49 | 4.49 | 10.81 | 18.88 | 21.06 | 24.00 | 35.36 | ▂▆▇▂▁ |
| Calcitonin | 0 | 1 | 1.73 | 0.89 | -0.71 | 1.20 | 1.68 | 2.26 | 4.11 | ▁▅▇▅▁ |
| CgA | 0 | 1 | 320.22 | 75.26 | 166.55 | 268.21 | 324.75 | 362.27 | 494.53 | ▃▃▇▃▂ |
| Clusterin_Apo_J | 0 | 1 | 2.85 | 0.35 | 1.93 | 2.56 | 2.83 | 3.04 | 3.76 | ▁▆▇▅▁ |
| Complement_3 | 0 | 1 | -15.91 | 2.60 | -22.40 | -17.50 | -15.90 | -14.34 | -10.23 | ▁▃▇▃▂ |
| Complement_Factor_H | 0 | 1 | 3.39 | 1.26 | 0.28 | 2.60 | 3.40 | 4.25 | 6.56 | ▁▅▇▅▁ |
| Connective_Tissue_Growth_Factor | 0 | 1 | 0.75 | 0.22 | 0.10 | 0.59 | 0.74 | 0.88 | 1.41 | ▁▃▇▃▁ |
| Cortisol | 0 | 1 | 10.46 | 3.85 | 0.10 | 8.90 | 10.00 | 12.00 | 22.00 | ▁▂▇▂▁ |
| Creatine_Kinase_MB | 0 | 1 | -1.65 | 0.10 | -1.87 | -1.72 | -1.65 | -1.59 | -1.43 | ▂▅▇▅▂ |
| Cystatin_C | 0 | 1 | 8.58 | 0.42 | 7.73 | 8.30 | 8.54 | 8.84 | 9.69 | ▃▇▇▃▂ |
| EGF_R | 0 | 1 | -0.70 | 0.26 | -1.27 | -0.89 | -0.69 | -0.50 | 0.19 | ▂▆▇▁▁ |
| EN_RAGE | 0 | 1 | -3.60 | 0.98 | -8.38 | -4.18 | -3.69 | -3.22 | -0.87 | ▁▁▅▇▁ |
| ENA_78 | 0 | 1 | -1.38 | 0.01 | -1.41 | -1.38 | -1.37 | -1.37 | -1.35 | ▂▂▆▇▂ |
| Eotaxin_3 | 0 | 1 | 55.55 | 18.33 | 23.00 | 43.00 | 54.00 | 64.00 | 107.00 | ▅▇▆▂▁ |
| FAS | 0 | 1 | -0.54 | 0.30 | -1.11 | -0.71 | -0.58 | -0.34 | 0.18 | ▃▇▇▅▂ |
| FSH_Follicle_Stimulation_Hormon | 0 | 1 | -1.06 | 0.34 | -1.81 | -1.27 | -0.98 | -0.81 | -0.48 | ▂▂▅▇▃ |
| Fas_Ligand | 0 | 1 | 2.65 | 1.02 | 0.29 | 2.07 | 2.67 | 3.16 | 5.38 | ▂▅▇▃▁ |
| Fatty_Acid_Binding_Protein | 0 | 1 | 1.29 | 0.79 | -0.46 | 0.80 | 1.19 | 1.92 | 3.22 | ▂▇▆▆▂ |
| Ferritin | 0 | 1 | 2.71 | 0.87 | 0.90 | 2.15 | 2.63 | 3.17 | 4.93 | ▂▆▇▂▂ |
| Fetuin_A | 0 | 1 | 1.31 | 0.41 | 0.53 | 1.03 | 1.31 | 1.61 | 2.21 | ▅▇▇▇▂ |
| Fibrinogen | 0 | 1 | -7.36 | 0.63 | -9.37 | -7.80 | -7.32 | -6.97 | -6.17 | ▁▂▇▇▅ |
| GRO_alpha | 0 | 1 | 1.38 | 0.04 | 1.27 | 1.35 | 1.37 | 1.40 | 1.51 | ▁▇▇▂▁ |
| Gamma_Interferon_induced_Monokin | 0 | 1 | 2.77 | 0.12 | 2.54 | 2.70 | 2.77 | 2.83 | 3.05 | ▂▅▇▂▂ |
| Glutathione_S_Transferase_alpha | 0 | 1 | 0.94 | 0.17 | 0.57 | 0.83 | 0.95 | 1.05 | 1.31 | ▃▅▇▇▂ |
| HB_EGF | 0 | 1 | 6.84 | 1.43 | 3.52 | 5.95 | 6.98 | 7.75 | 10.36 | ▂▆▇▇▂ |
| HCC_4 | 0 | 1 | -3.54 | 0.35 | -4.34 | -3.77 | -3.54 | -3.35 | -2.49 | ▂▇▇▃▁ |
| Hepatocyte_Growth_Factor_HGF | 0 | 1 | 0.18 | 0.34 | -0.62 | -0.06 | 0.18 | 0.34 | 1.10 | ▁▆▇▃▁ |
| I_309 | 0 | 1 | 2.92 | 0.36 | 2.04 | 2.72 | 2.94 | 3.14 | 3.69 | ▂▂▇▃▂ |
| ICAM_1 | 0 | 1 | -0.60 | 0.35 | -1.47 | -0.77 | -0.59 | -0.36 | 0.36 | ▂▂▇▅▁ |
| IGF_BP_2 | 0 | 1 | 5.26 | 0.22 | 4.72 | 5.13 | 5.25 | 5.40 | 5.92 | ▁▅▇▂▁ |
| IL_11 | 0 | 1 | 4.65 | 1.33 | 2.03 | 3.96 | 4.84 | 5.48 | 8.69 | ▃▅▇▂▁ |
| IL_13 | 0 | 1 | 1.28 | 0.01 | 1.23 | 1.27 | 1.28 | 1.29 | 1.31 | ▁▁▇▇▃ |
| IL_16 | 0 | 1 | 2.82 | 0.70 | 0.96 | 2.44 | 2.88 | 3.35 | 4.10 | ▂▂▇▇▅ |
| IL_17E | 0 | 1 | 4.77 | 1.33 | 1.58 | 3.64 | 4.72 | 5.41 | 8.08 | ▁▇▇▃▂ |
| IL_1alpha | 0 | 1 | -7.55 | 0.44 | -8.47 | -7.85 | -7.56 | -7.28 | -6.38 | ▂▇▇▃▁ |
| IL_3 | 0 | 1 | -3.98 | 0.52 | -5.52 | -4.32 | -3.96 | -3.58 | -3.08 | ▁▃▇▇▆ |
| IL_4 | 0 | 1 | 1.74 | 0.52 | 0.53 | 1.46 | 1.72 | 2.07 | 2.71 | ▁▅▇▃▅ |
| IL_5 | 0 | 1 | 0.23 | 0.44 | -1.05 | -0.03 | 0.22 | 0.53 | 1.13 | ▁▂▇▇▂ |
| IL_6 | 0 | 1 | -0.05 | 0.52 | -1.53 | -0.41 | -0.07 | 0.35 | 1.01 | ▁▂▇▇▂ |
| IL_6_Receptor | 0 | 1 | 0.06 | 0.35 | -0.75 | -0.20 | 0.00 | 0.27 | 0.77 | ▂▇▇▆▅ |
| IL_7 | 0 | 1 | 3.14 | 0.85 | 1.31 | 2.38 | 3.15 | 3.71 | 5.00 | ▁▇▅▆▂ |
| IL_8 | 0 | 1 | 1.70 | 0.04 | 1.62 | 1.68 | 1.70 | 1.73 | 1.84 | ▂▇▆▂▁ |
| IP_10_Inducible_Protein_10 | 0 | 1 | 5.64 | 0.51 | 4.26 | 5.32 | 5.62 | 5.92 | 7.21 | ▁▅▇▃▁ |
| IgA | 0 | 1 | -6.07 | 0.64 | -7.62 | -6.57 | -6.01 | -5.61 | -4.73 | ▁▆▇▇▂ |
| Insulin | 0 | 1 | -1.20 | 0.32 | -2.01 | -1.45 | -1.22 | -1.01 | -0.50 | ▂▆▇▇▃ |
| Kidney_Injury_Molecule_1_KIM_1 | 0 | 1 | -1.19 | 0.03 | -1.25 | -1.21 | -1.19 | -1.17 | -1.12 | ▃▇▇▇▂ |
| LOX_1 | 0 | 1 | 1.21 | 0.45 | 0.00 | 0.96 | 1.22 | 1.44 | 2.40 | ▁▃▇▃▁ |
| Leptin | 0 | 1 | -1.44 | 0.25 | -1.95 | -1.63 | -1.43 | -1.24 | -0.84 | ▃▇▆▇▂ |
| Lipoprotein_a | 0 | 1 | -4.51 | 0.91 | -6.57 | -5.12 | -4.66 | -4.02 | -2.04 | ▂▇▇▅▁ |
| MCP_1 | 0 | 1 | 6.48 | 0.25 | 5.89 | 6.32 | 6.48 | 6.63 | 7.06 | ▁▅▇▅▂ |
| MCP_2 | 0 | 1 | 1.81 | 0.60 | 0.40 | 1.53 | 1.85 | 2.08 | 3.75 | ▂▅▇▁▁ |
| MIF | 0 | 1 | -1.93 | 0.31 | -2.80 | -2.12 | -1.97 | -1.71 | -1.11 | ▁▃▇▃▁ |
| MIP_1alpha | 0 | 1 | 3.90 | 1.04 | 1.01 | 3.30 | 3.74 | 4.69 | 5.74 | ▁▂▇▆▅ |
| MIP_1beta | 0 | 1 | 2.78 | 0.39 | 1.92 | 2.48 | 2.77 | 3.08 | 3.78 | ▃▆▇▆▁ |
| MMP_2 | 0 | 1 | 3.03 | 0.95 | 0.62 | 2.55 | 2.99 | 3.48 | 6.10 | ▁▃▇▁▁ |
| MMP_3 | 0 | 1 | -2.49 | 0.59 | -3.65 | -2.85 | -2.53 | -2.12 | -1.17 | ▃▆▇▅▂ |
| MMP10 | 0 | 1 | -3.68 | 0.44 | -4.95 | -4.07 | -3.61 | -3.33 | -2.90 | ▁▃▆▇▅ |
| MMP7 | 0 | 1 | -4.01 | 1.55 | -7.53 | -4.96 | -4.03 | -3.16 | -0.20 | ▂▃▇▂▁ |
| Myoglobin | 0 | 1 | -1.42 | 0.91 | -3.30 | -2.02 | -1.59 | -0.78 | 1.13 | ▂▇▆▃▁ |
| NT_proBNP | 0 | 1 | 4.49 | 0.39 | 3.61 | 4.17 | 4.48 | 4.79 | 5.40 | ▂▇▇▆▂ |
| NrCAM | 0 | 1 | 4.29 | 0.58 | 2.89 | 3.87 | 4.32 | 4.72 | 5.69 | ▂▆▇▆▁ |
| Osteopontin | 0 | 1 | 5.18 | 0.40 | 4.08 | 4.89 | 5.17 | 5.41 | 6.32 | ▁▆▇▃▁ |
| PAI_1 | 0 | 1 | 0.00 | 0.41 | -0.99 | -0.33 | 0.00 | 0.30 | 0.89 | ▂▆▇▇▂ |
| PAPP_A | 0 | 1 | -2.84 | 0.14 | -3.15 | -2.97 | -2.84 | -2.72 | -2.49 | ▂▇▇▆▁ |
| PLGF | 0 | 1 | 3.88 | 0.38 | 2.64 | 3.69 | 3.89 | 4.12 | 4.71 | ▁▂▇▇▂ |
| PYY | 0 | 1 | 2.98 | 0.29 | 2.40 | 2.83 | 3.00 | 3.18 | 3.74 | ▃▇▇▅▁ |
| Pancreatic_polypeptide | 0 | 1 | -0.01 | 0.70 | -1.61 | -0.51 | 0.14 | 0.47 | 1.50 | ▂▅▅▇▁ |
| Prolactin | 0 | 1 | 0.05 | 0.29 | -0.39 | -0.17 | 0.00 | 0.18 | 0.79 | ▇▇▆▃▂ |
| Prostatic_Acid_Phosphatase | 0 | 1 | -1.69 | 0.05 | -1.80 | -1.74 | -1.69 | -1.66 | -1.54 | ▂▇▇▂▁ |
| Protein_S | 0 | 1 | -2.27 | 0.41 | -3.15 | -2.58 | -2.26 | -1.92 | -1.55 | ▃▅▇▇▆ |
| Pulmonary_and_Activation_Regulat | 0 | 1 | -1.50 | 0.45 | -2.44 | -1.83 | -1.51 | -1.17 | -0.45 | ▃▇▆▇▂ |
| RANTES | 0 | 1 | -6.54 | 0.29 | -7.24 | -6.73 | -6.57 | -6.39 | -5.84 | ▁▆▇▃▂ |
| Resistin | 0 | 1 | -18.24 | 5.18 | -30.16 | -22.13 | -18.01 | -15.20 | -6.59 | ▂▅▇▅▂ |
| S100b | 0 | 1 | 1.18 | 0.37 | 0.19 | 0.96 | 1.16 | 1.38 | 2.20 | ▁▃▇▂▁ |
| SGOT | 0 | 1 | -0.49 | 0.37 | -1.90 | -0.75 | -0.48 | -0.21 | 0.18 | ▁▁▆▇▅ |
| SHBG | 0 | 1 | -2.69 | 0.49 | -3.73 | -3.05 | -2.71 | -2.34 | -1.56 | ▂▇▇▆▂ |
| SOD | 0 | 1 | 5.30 | 0.41 | 4.38 | 5.01 | 5.31 | 5.55 | 6.46 | ▂▇▇▃▁ |
| Serum_Amyloid_P | 0 | 1 | -6.08 | 0.52 | -7.18 | -6.44 | -6.21 | -5.61 | -4.70 | ▂▇▅▃▁ |
| Sortilin | 0 | 1 | 3.79 | 0.87 | 1.51 | 3.18 | 3.87 | 4.37 | 5.68 | ▂▅▇▆▃ |
| Stem_Cell_Factor | 0 | 1 | 3.27 | 0.35 | 2.22 | 3.04 | 3.31 | 3.47 | 4.08 | ▁▅▇▇▂ |
| TGF_alpha | 0 | 1 | 9.78 | 1.11 | 7.50 | 9.06 | 9.60 | 10.61 | 13.08 | ▃▇▆▃▁ |
| TIMP_1 | 0 | 1 | 11.52 | 1.64 | 8.20 | 10.53 | 11.34 | 12.35 | 16.55 | ▅▇▇▃▁ |
| TNF_RII | 0 | 1 | -0.63 | 0.36 | -1.66 | -0.87 | -0.65 | -0.33 | 0.41 | ▁▅▇▅▁ |
| TRAIL_R3 | 0 | 1 | -0.59 | 0.23 | -1.31 | -0.73 | -0.56 | -0.47 | 0.10 | ▁▃▇▂▁ |
| TTR_prealbumin | 0 | 1 | 2.85 | 0.14 | 2.48 | 2.77 | 2.89 | 2.94 | 3.09 | ▁▃▅▇▅ |
| Tamm_Horsfall_Protein_THP | 0 | 1 | -3.12 | 0.03 | -3.21 | -3.14 | -3.13 | -3.10 | -3.04 | ▁▅▇▃▂ |
| Thrombomodulin | 0 | 1 | -1.53 | 0.25 | -2.05 | -1.68 | -1.53 | -1.34 | -1.02 | ▂▆▇▆▂ |
| Thrombopoietin | 0 | 1 | -0.72 | 0.21 | -1.54 | -0.84 | -0.70 | -0.63 | -0.30 | ▁▁▆▇▃ |
| Thymus_Expressed_Chemokine_TECK | 0 | 1 | 3.77 | 0.73 | 2.14 | 3.28 | 3.75 | 4.32 | 5.68 | ▃▆▇▅▂ |
| Thyroid_Stimulating_Hormone | 0 | 1 | -4.22 | 0.79 | -6.19 | -4.73 | -4.27 | -3.83 | -2.04 | ▁▅▇▃▁ |
| Thyroxine_Binding_Globulin | 0 | 1 | -1.49 | 0.40 | -2.30 | -1.71 | -1.49 | -1.24 | -0.60 | ▃▅▇▆▂ |
| Tissue_Factor | 0 | 1 | 1.14 | 0.54 | 0.00 | 0.71 | 1.15 | 1.51 | 2.71 | ▂▆▇▂▁ |
| Transferrin | 0 | 1 | 2.90 | 0.29 | 2.28 | 2.71 | 2.89 | 3.14 | 3.50 | ▃▃▇▅▃ |
| Trefoil_Factor_3_TFF3 | 0 | 1 | -3.95 | 0.34 | -4.91 | -4.20 | -3.91 | -3.77 | -3.17 | ▁▂▇▆▂ |
| VCAM_1 | 0 | 1 | 2.64 | 0.32 | 2.03 | 2.42 | 2.67 | 2.83 | 3.47 | ▅▃▇▃▁ |
| VEGF | 0 | 1 | 16.70 | 2.10 | 12.23 | 15.03 | 17.08 | 18.19 | 21.18 | ▃▇▇▆▂ |
| Vitronectin | 0 | 1 | -0.27 | 0.32 | -1.08 | -0.46 | -0.28 | -0.05 | 0.41 | ▁▅▇▆▂ |
| von_Willebrand_Factor | 0 | 1 | -4.01 | 0.38 | -4.92 | -4.27 | -4.02 | -3.73 | -3.06 | ▂▇▇▆▂ |
###################################
# Verifying the data dimensions
# for the test set
###################################
dim(PMA_PreModelling_Test)## [1] 66 1281.4 Data Exploration
[A] Numeric variables which demonstrated differential relationships with the Class response variable include:
[A.1] Fibrinogen variable (numeric)
[A.2] GRO_alpha variable (numeric)
[A.3] FAS variable (numeric)
[A.4] Eotaxin_3 variable (numeric)
[A.5] Creatine_Kinase_MB variable (numeric)
[A.6] IGF_BP2 variable (numeric)
[A.7] Gamma_Interferon_Induced_Monokin variable (numeric)
[A.8] MCP_2 variable (numeric)
[A.9] MIF variable (numeric)
[A.10] Pancreatic_polypteptide variable (numeric)
[A.11] PAI_1 variable (numeric)
[A.12] NT_proBNP variable (numeric)
[A.13] MMP10 variable (numeric)
[A.14] MMP7 variable (numeric)
[A.15] TRAIL_R3 variable (numeric)
[A.16] Pulmonary_and_Activation_Regulat variable (numeric)
[A.17] Resistin variable (numeric)
[A.18] VEGF variable (numeric)
[A.19] Thrombopoietin variable (numeric)
[A.20] Thymus_Expressed_Chemokine_TECK variable (numeric)
[B] Factor variables which demonstrated relatively better differentiation of the Class response variable between its Control and Impaired levels include:
[B.1] E2 variable (factor)
[B.2] E4 variable (factor)
Code Chunk | Output
##################################
# Loading dataset
##################################
EDA <- PMA_PreModelling_Train
##################################
# Listing all predictors
##################################
EDA.Predictors <- EDA[,!names(EDA) %in% c("Class")]
##################################
# Listing all numeric predictors
##################################
EDA.Predictors.Numeric <- EDA.Predictors[,sapply(EDA.Predictors, is.numeric)]
ncol(EDA.Predictors.Numeric)## [1] 124names(EDA.Predictors.Numeric)## [1] "ACE_CD143_Angiotensin_Converti" "ACTH_Adrenocorticotropic_Hormon"
## [3] "AXL" "Adiponectin"
## [5] "Alpha_1_Antichymotrypsin" "Alpha_1_Antitrypsin"
## [7] "Alpha_1_Microglobulin" "Alpha_2_Macroglobulin"
## [9] "Angiopoietin_2_ANG_2" "Angiotensinogen"
## [11] "Apolipoprotein_A_IV" "Apolipoprotein_A1"
## [13] "Apolipoprotein_A2" "Apolipoprotein_B"
## [15] "Apolipoprotein_CI" "Apolipoprotein_CIII"
## [17] "Apolipoprotein_D" "Apolipoprotein_E"
## [19] "Apolipoprotein_H" "B_Lymphocyte_Chemoattractant_BL"
## [21] "BMP_6" "Beta_2_Microglobulin"
## [23] "Betacellulin" "C_Reactive_Protein"
## [25] "CD40" "CD5L"
## [27] "Calbindin" "Calcitonin"
## [29] "CgA" "Clusterin_Apo_J"
## [31] "Complement_3" "Complement_Factor_H"
## [33] "Connective_Tissue_Growth_Factor" "Cortisol"
## [35] "Creatine_Kinase_MB" "Cystatin_C"
## [37] "EGF_R" "EN_RAGE"
## [39] "ENA_78" "Eotaxin_3"
## [41] "FAS" "FSH_Follicle_Stimulation_Hormon"
## [43] "Fas_Ligand" "Fatty_Acid_Binding_Protein"
## [45] "Ferritin" "Fetuin_A"
## [47] "Fibrinogen" "GRO_alpha"
## [49] "Gamma_Interferon_induced_Monokin" "Glutathione_S_Transferase_alpha"
## [51] "HB_EGF" "HCC_4"
## [53] "Hepatocyte_Growth_Factor_HGF" "I_309"
## [55] "ICAM_1" "IGF_BP_2"
## [57] "IL_11" "IL_13"
## [59] "IL_16" "IL_17E"
## [61] "IL_1alpha" "IL_3"
## [63] "IL_4" "IL_5"
## [65] "IL_6" "IL_6_Receptor"
## [67] "IL_7" "IL_8"
## [69] "IP_10_Inducible_Protein_10" "IgA"
## [71] "Insulin" "Kidney_Injury_Molecule_1_KIM_1"
## [73] "LOX_1" "Leptin"
## [75] "Lipoprotein_a" "MCP_1"
## [77] "MCP_2" "MIF"
## [79] "MIP_1alpha" "MIP_1beta"
## [81] "MMP_2" "MMP_3"
## [83] "MMP10" "MMP7"
## [85] "Myoglobin" "NT_proBNP"
## [87] "NrCAM" "Osteopontin"
## [89] "PAI_1" "PAPP_A"
## [91] "PLGF" "PYY"
## [93] "Pancreatic_polypeptide" "Prolactin"
## [95] "Prostatic_Acid_Phosphatase" "Protein_S"
## [97] "Pulmonary_and_Activation_Regulat" "RANTES"
## [99] "Resistin" "S100b"
## [101] "SGOT" "SHBG"
## [103] "SOD" "Serum_Amyloid_P"
## [105] "Sortilin" "Stem_Cell_Factor"
## [107] "TGF_alpha" "TIMP_1"
## [109] "TNF_RII" "TRAIL_R3"
## [111] "TTR_prealbumin" "Tamm_Horsfall_Protein_THP"
## [113] "Thrombomodulin" "Thrombopoietin"
## [115] "Thymus_Expressed_Chemokine_TECK" "Thyroid_Stimulating_Hormone"
## [117] "Thyroxine_Binding_Globulin" "Tissue_Factor"
## [119] "Transferrin" "Trefoil_Factor_3_TFF3"
## [121] "VCAM_1" "VEGF"
## [123] "Vitronectin" "von_Willebrand_Factor"##################################
# Listing all factor predictors
##################################
EDA.Predictors.Factor <- EDA.Predictors[,sapply(EDA.Predictors, is.factor)]
ncol(EDA.Predictors.Factor)## [1] 3names(EDA.Predictors.Factor)## [1] "E4" "E3" "E2"##################################
# Formulating the box plots
##################################
featurePlot(x = EDA.Predictors.Numeric[1:124],
y = EDA$Class,
plot = "box",
scales = list(x = list(relation="free", rot = 90),
y = list(relation="free")),
adjust = 1.5,
pch = "|",
layout=(c(4,4)))
##################################
# Restructuring the dataset for
# for barchart analysis
##################################
EDA.Bar.Source <- as.data.frame(cbind(EDA$Class,
EDA.Predictors.Factor))
names(EDA.Bar.Source) <- c("Class",names(EDA.Predictors.Factor))
ncol(EDA.Bar.Source)## [1] 4##################################
# Creating a function to formulate
# the proportions table
##################################
EDA.PropTable.Function <- function(FactorVar) {
EDA.Bar.Source.FactorVar <- EDA.Bar.Source[,c("Class",
FactorVar)]
EDA.Bar.Source.FactorVar.Prop <- as.data.frame(prop.table(table(EDA.Bar.Source.FactorVar), 2))
names(EDA.Bar.Source.FactorVar.Prop)[2] <- "Class"
EDA.Bar.Source.FactorVar.Prop$Variable <- rep(FactorVar,nrow(EDA.Bar.Source.FactorVar.Prop))
return(EDA.Bar.Source.FactorVar.Prop)
}
EDA.Bar.Source.FactorVar.Prop <- rbind(EDA.PropTable.Function("E2"),
EDA.PropTable.Function("E3"),
EDA.PropTable.Function("E4"))
(EDA.Barchart.FactorVar <- barchart(EDA.Bar.Source.FactorVar.Prop[,3] ~
EDA.Bar.Source.FactorVar.Prop[,2] | EDA.Bar.Source.FactorVar.Prop[,4],
data=EDA.Bar.Source.FactorVar.Prop,
groups = EDA.Bar.Source.FactorVar.Prop[,1],
stack=TRUE,
ylab = "Proportion",
xlab = "Class",
auto.key = list(adj = 1),
layout=(c(3,1))))
1.5 Simulated Annealing (SA) and Genetic Algorithms (GA)
1.5.1 Random Forest Without SA and GA (RF_FULL)
Random Forest is an ensemble learning method made up of a large set of small decision trees called estimators, with each producing its own prediction. The random forest model aggregates the predictions of the estimators to produce a more accurate prediction. The algorithm involves bootstrap aggregating (where smaller subsets of the training data are repeatedly subsampled with replacement), random subspacing (where a subset of features are sampled and used to train each individual estimator), estimator training (where unpruned decision trees are formulated for each estimator) and inference by aggregating the predictions of all estimators.
[A] The random forest model from the randomForest package was implemented without simulated annealing and genetic algorithms through the caret package.
[B] The model contains 1 hyperparameter:
[B.1] mtry = number of randomly selected predictors held constant at a value of 11
[C] The cross-validated model performance of the final model is summarized as follows:
[C.1] Final model configuration involves mtry=11
[C.2] Accuracy = 0.77975
[D] The model allows for ranking of predictors in terms of variable importance. The top-performing predictors in the model are as follows:
[D.1] MMP10 variable (numeric)
[D.2] Crystatin_C variable (numeric)
[D.3] TRAIL_R3 variable (numeric)
[D.4] VEGF variable (numeric)
[D.5] MCP_2 variable (numeric)
[E] The independent test model performance of the final model is summarized as follows:
[E.1] Accuracy = 0.80303
Code Chunk | Output
##################################
# Converting all predictors to numeric
# for both train and test data
##################################
for (i in 1:ncol(PMA_PreModelling_Train)){
if (names(PMA_PreModelling_Train)[i]!="Class"){
PMA_PreModelling_Train[,i] <- as.numeric(PMA_PreModelling_Train[,i])
}
}
summary(PMA_PreModelling_Train)## ACE_CD143_Angiotensin_Converti ACTH_Adrenocorticotropic_Hormon
## Min. :-0.6756 Min. :-2.207
## 1st Qu.: 0.9462 1st Qu.:-1.715
## Median : 1.3013 Median :-1.561
## Mean : 1.3198 Mean :-1.538
## 3rd Qu.: 1.7191 3rd Qu.:-1.347
## Max. : 2.8398 Max. :-0.844
## AXL Adiponectin Alpha_1_Antichymotrypsin
## Min. :-0.9230 Min. :-6.725 Min. :0.2624
## 1st Qu.: 0.0000 1st Qu.:-5.669 1st Qu.:1.1314
## Median : 0.2804 Median :-5.185 Median :1.3610
## Mean : 0.3093 Mean :-5.201 Mean :1.3605
## 3rd Qu.: 0.6077 3rd Qu.:-4.780 3rd Qu.:1.5892
## Max. : 1.5214 Max. :-3.507 Max. :2.3026
## Alpha_1_Antitrypsin Alpha_1_Microglobulin Alpha_2_Macroglobulin
## Min. :-17.028 Min. :-4.343 Min. :-289.68
## 1st Qu.:-14.071 1st Qu.:-3.270 1st Qu.:-186.64
## Median :-13.004 Median :-2.937 Median :-160.01
## Mean :-13.052 Mean :-2.932 Mean :-158.61
## 3rd Qu.:-12.096 3rd Qu.:-2.590 3rd Qu.:-134.62
## Max. : -8.192 Max. :-1.772 Max. : -59.46
## Angiopoietin_2_ANG_2 Angiotensinogen Apolipoprotein_A_IV Apolipoprotein_A1
## Min. :-0.5447 Min. :1.752 Min. :-2.9565 Min. :-8.680
## 1st Qu.: 0.4700 1st Qu.:2.119 1st Qu.:-2.1203 1st Qu.:-7.763
## Median : 0.6419 Median :2.320 Median :-1.8326 Median :-7.470
## Mean : 0.6730 Mean :2.318 Mean :-1.8544 Mean :-7.483
## 3rd Qu.: 0.8755 3rd Qu.:2.497 3rd Qu.:-1.6094 3rd Qu.:-7.209
## Max. : 1.5261 Max. :2.881 Max. :-0.7765 Max. :-6.166
## Apolipoprotein_A2 Apolipoprotein_B Apolipoprotein_CI Apolipoprotein_CIII
## Min. :-1.8971 Min. :-9.937 Min. :-3.3242 Min. :-3.689
## 1st Qu.:-0.9676 1st Qu.:-6.630 1st Qu.:-1.8326 1st Qu.:-2.773
## Median :-0.6733 Median :-5.703 Median :-1.6094 Median :-2.526
## Mean :-0.6354 Mean :-5.578 Mean :-1.5833 Mean :-2.494
## 3rd Qu.:-0.3147 3rd Qu.:-4.539 3rd Qu.:-1.3667 3rd Qu.:-2.207
## Max. : 0.9555 Max. :-2.153 Max. :-0.2744 Max. :-1.238
## Apolipoprotein_D Apolipoprotein_E Apolipoprotein_H
## Min. :0.470 Min. :0.5911 Min. :-2.23379
## 1st Qu.:1.209 1st Qu.:2.3344 1st Qu.:-0.59782
## Median :1.411 Median :2.8181 Median :-0.37005
## Mean :1.440 Mean :2.8062 Mean :-0.32122
## 3rd Qu.:1.668 3rd Qu.:3.2863 3rd Qu.:-0.06112
## Max. :2.272 Max. :5.4442 Max. : 0.92696
## B_Lymphocyte_Chemoattractant_BL BMP_6 Beta_2_Microglobulin
## Min. :0.7318 Min. :-2.7612 Min. :-0.54473
## 1st Qu.:1.6731 1st Qu.:-2.1516 1st Qu.:-0.04082
## Median :1.9805 Median :-1.8774 Median : 0.18232
## Mean :2.0175 Mean :-1.9114 Mean : 0.16757
## 3rd Qu.:2.3714 3rd Qu.:-1.6753 3rd Qu.: 0.33647
## Max. :4.0237 Max. :-0.8166 Max. : 0.99325
## Betacellulin C_Reactive_Protein CD40 CD5L
## Min. :10.00 Min. :-8.517 Min. :-1.8644 Min. :-1.23787
## 1st Qu.:42.00 1st Qu.:-6.645 1st Qu.:-1.3761 1st Qu.:-0.35667
## Median :51.00 Median :-5.843 Median :-1.2734 Median :-0.06188
## Mean :51.01 Mean :-5.874 Mean :-1.2584 Mean :-0.05310
## 3rd Qu.:59.00 3rd Qu.:-5.083 3rd Qu.:-1.1238 3rd Qu.: 0.26236
## Max. :82.00 Max. :-2.937 Max. :-0.5475 Max. : 1.16315
## Calbindin Calcitonin CgA Clusterin_Apo_J
## Min. :10.96 Min. :-0.7134 Min. :135.6 Min. :1.872
## 1st Qu.:19.77 1st Qu.: 0.9555 1st Qu.:278.0 1st Qu.:2.708
## Median :22.25 Median : 1.6487 Median :331.5 Median :2.890
## Mean :22.43 Mean : 1.6788 Mean :333.3 Mean :2.882
## 3rd Qu.:24.80 3rd Qu.: 2.2824 3rd Qu.:392.1 3rd Qu.:3.045
## Max. :33.78 Max. : 3.8918 Max. :535.4 Max. :3.584
## Complement_3 Complement_Factor_H Connective_Tissue_Growth_Factor
## Min. :-23.387 Min. :-0.8387 Min. :0.1823
## 1st Qu.:-17.567 1st Qu.: 2.7531 1st Qu.:0.6419
## Median :-15.524 Median : 3.6000 Median :0.7885
## Mean :-15.610 Mean : 3.5541 Mean :0.7739
## 3rd Qu.:-13.882 3rd Qu.: 4.2548 3rd Qu.:0.9163
## Max. : -9.563 Max. : 7.6238 Max. :1.4110
## Cortisol Creatine_Kinase_MB Cystatin_C EGF_R
## Min. : 0.10 Min. :-1.872 Min. :7.432 Min. :-1.36135
## 1st Qu.: 9.80 1st Qu.:-1.724 1st Qu.:8.321 1st Qu.:-0.85727
## Median :12.00 Median :-1.671 Median :8.564 Median :-0.68354
## Mean :11.98 Mean :-1.674 Mean :8.586 Mean :-0.70130
## 3rd Qu.:14.00 3rd Qu.:-1.626 3rd Qu.:8.839 3rd Qu.:-0.54612
## Max. :29.00 Max. :-1.384 Max. :9.694 Max. :-0.06112
## EN_RAGE ENA_78 Eotaxin_3 FAS
## Min. :-8.3774 Min. :-1.405 Min. : 7.00 Min. :-1.5141
## 1st Qu.:-4.1997 1st Qu.:-1.381 1st Qu.: 44.00 1st Qu.:-0.7133
## Median :-3.6497 Median :-1.374 Median : 59.00 Median :-0.5276
## Mean :-3.6353 Mean :-1.372 Mean : 58.17 Mean :-0.5291
## 3rd Qu.:-3.1466 3rd Qu.:-1.364 3rd Qu.: 70.00 3rd Qu.:-0.3147
## Max. :-0.3857 Max. :-1.339 Max. :107.00 Max. : 0.3365
## FSH_Follicle_Stimulation_Hormon Fas_Ligand Fatty_Acid_Binding_Protein
## Min. :-2.11511 Min. :-0.1536 Min. :-1.0441
## 1st Qu.:-1.46606 1st Qu.: 2.3415 1st Qu.: 0.7998
## Median :-1.13570 Median : 3.1015 Median : 1.3865
## Mean :-1.14259 Mean : 2.9680 Mean : 1.3529
## 3rd Qu.:-0.87620 3rd Qu.: 3.6950 3rd Qu.: 1.8847
## Max. : 0.09715 Max. : 7.6328 Max. : 3.7055
## Ferritin Fetuin_A Fibrinogen GRO_alpha
## Min. :0.6077 Min. :0.470 Min. :-8.874 Min. :1.271
## 1st Qu.:2.2895 1st Qu.:1.099 1st Qu.:-7.717 1st Qu.:1.351
## Median :2.7749 Median :1.308 Median :-7.323 Median :1.382
## Mean :2.7646 Mean :1.350 Mean :-7.356 Mean :1.378
## 3rd Qu.:3.2915 3rd Qu.:1.609 3rd Qu.:-7.013 3rd Qu.:1.406
## Max. :4.6333 Max. :2.251 Max. :-5.843 Max. :1.495
## Gamma_Interferon_induced_Monokin Glutathione_S_Transferase_alpha
## Min. :2.393 Min. :0.5238
## 1st Qu.:2.707 1st Qu.:0.8439
## Median :2.783 Median :0.9677
## Mean :2.786 Mean :0.9512
## 3rd Qu.:2.873 3rd Qu.:1.0344
## Max. :3.065 Max. :1.3176
## HB_EGF HCC_4 Hepatocyte_Growth_Factor_HGF I_309
## Min. : 2.103 Min. :-4.510 Min. :-0.6349 Min. :1.758
## 1st Qu.: 5.786 1st Qu.:-3.730 1st Qu.: 0.0000 1st Qu.:2.708
## Median : 6.703 Median :-3.507 Median : 0.1823 Median :2.944
## Mean : 6.833 Mean :-3.500 Mean : 0.1963 Mean :2.958
## 3rd Qu.: 7.865 3rd Qu.:-3.270 3rd Qu.: 0.4055 3rd Qu.:3.219
## Max. :10.695 Max. :-2.120 Max. : 0.8755 Max. :4.143
## ICAM_1 IGF_BP_2 IL_11 IL_13
## Min. :-1.5332 Min. :4.635 Min. :1.755 Min. :1.259
## 1st Qu.:-0.8298 1st Qu.:5.179 1st Qu.:3.706 1st Qu.:1.274
## Median :-0.5903 Median :5.323 Median :4.805 Median :1.283
## Mean :-0.5908 Mean :5.317 Mean :4.725 Mean :1.284
## 3rd Qu.:-0.3828 3rd Qu.:5.453 3rd Qu.:5.776 3rd Qu.:1.290
## Max. : 0.5171 Max. :5.948 Max. :8.491 Max. :1.321
## IL_16 IL_17E IL_1alpha IL_3
## Min. :1.187 Min. :1.052 Min. :-8.517 Min. :-5.915
## 1st Qu.:2.521 1st Qu.:4.149 1st Qu.:-7.824 1st Qu.:-4.269
## Median :2.909 Median :4.749 Median :-7.524 Median :-3.912
## Mean :2.929 Mean :4.855 Mean :-7.514 Mean :-3.941
## 3rd Qu.:3.351 3rd Qu.:5.631 3rd Qu.:-7.264 3rd Qu.:-3.631
## Max. :4.937 Max. :8.952 Max. :-5.952 Max. :-2.453
## IL_4 IL_5 IL_6 IL_6_Receptor
## Min. :0.5306 Min. :-1.4271 Min. :-1.5343 Min. :-0.67562
## 1st Qu.:1.4586 1st Qu.:-0.1221 1st Qu.:-0.4127 1st Qu.:-0.12541
## Median :1.8083 Median : 0.1823 Median :-0.1599 Median : 0.09669
## Mean :1.7732 Mean : 0.1866 Mean :-0.1540 Mean : 0.09492
## 3rd Qu.:2.1459 3rd Qu.: 0.4700 3rd Qu.: 0.1410 3rd Qu.: 0.35404
## Max. :3.0445 Max. : 1.9459 Max. : 1.8138 Max. : 0.83099
## IL_7 IL_8 IP_10_Inducible_Protein_10 IgA
## Min. :0.5598 Min. :1.574 Min. :4.317 Min. :-10.520
## 1st Qu.:2.1548 1st Qu.:1.680 1st Qu.:5.398 1st Qu.: -6.645
## Median :2.7934 Median :1.705 Median :5.753 Median : -6.119
## Mean :2.8392 Mean :1.704 Mean :5.755 Mean : -6.121
## 3rd Qu.:3.7055 3rd Qu.:1.728 3rd Qu.:6.064 3rd Qu.: -5.573
## Max. :5.7056 Max. :1.807 Max. :7.501 Max. : -4.200
## Insulin Kidney_Injury_Molecule_1_KIM_1 LOX_1
## Min. :-2.1692 Min. :-1.256 Min. :0.000
## 1st Qu.:-1.4466 1st Qu.:-1.204 1st Qu.:1.030
## Median :-1.2462 Median :-1.183 Median :1.281
## Mean :-1.2329 Mean :-1.185 Mean :1.283
## 3rd Qu.:-1.0340 3rd Qu.:-1.164 3rd Qu.:1.526
## Max. :-0.1586 Max. :-1.105 Max. :2.272
## Leptin Lipoprotein_a MCP_1 MCP_2
## Min. :-2.1468 Min. :-6.812 Min. :5.826 Min. :0.4006
## 1st Qu.:-1.6996 1st Qu.:-5.308 1st Qu.:6.319 1st Qu.:1.5304
## Median :-1.5047 Median :-4.605 Median :6.494 Median :1.8528
## Mean :-1.5042 Mean :-4.417 Mean :6.497 Mean :1.8691
## 3rd Qu.:-1.3295 3rd Qu.:-3.490 3rd Qu.:6.678 3rd Qu.:2.1821
## Max. :-0.6206 Max. :-1.386 Max. :7.230 Max. :4.0237
## MIF MIP_1alpha MIP_1beta MMP_2
## Min. :-2.847 Min. :0.9346 Min. :1.946 Min. :0.09809
## 1st Qu.:-2.120 1st Qu.:3.3377 1st Qu.:2.565 1st Qu.:2.33214
## Median :-1.897 Median :4.0495 Median :2.833 Median :2.81512
## Mean :-1.864 Mean :4.0489 Mean :2.814 Mean :2.87534
## 3rd Qu.:-1.661 3rd Qu.:4.6857 3rd Qu.:3.045 3rd Qu.:3.55121
## Max. :-0.844 Max. :6.7959 Max. :4.007 Max. :5.35895
## MMP_3 MMP10 MMP7 Myoglobin
## Min. :-4.4228 Min. :-4.934 Min. :-8.3975 Min. :-3.1701
## 1st Qu.:-2.7489 1st Qu.:-3.938 1st Qu.:-4.8199 1st Qu.:-2.0402
## Median :-2.4534 Median :-3.650 Median :-3.7735 Median :-1.4697
## Mean :-2.4455 Mean :-3.635 Mean :-3.7894 Mean :-1.3671
## 3rd Qu.:-2.1203 3rd Qu.:-3.352 3rd Qu.:-2.7140 3rd Qu.:-0.7988
## Max. :-0.5276 Max. :-2.207 Max. :-0.2222 Max. : 1.7750
## NT_proBNP NrCAM Osteopontin PAI_1
## Min. :3.178 Min. :2.639 Min. :4.111 Min. :-0.99085
## 1st Qu.:4.350 1st Qu.:3.998 1st Qu.:4.963 1st Qu.:-0.16655
## Median :4.554 Median :4.394 Median :5.187 Median : 0.09396
## Mean :4.552 Mean :4.362 Mean :5.204 Mean : 0.07743
## 3rd Qu.:4.775 3rd Qu.:4.749 3rd Qu.:5.442 3rd Qu.: 0.32005
## Max. :5.886 Max. :6.011 Max. :6.308 Max. : 1.16611
## PAPP_A PLGF PYY Pancreatic_polypeptide
## Min. :-3.311 Min. :2.485 Min. :2.186 Min. :-2.12026
## 1st Qu.:-2.936 1st Qu.:3.638 1st Qu.:2.833 1st Qu.:-0.52763
## Median :-2.871 Median :3.871 Median :2.996 Median :-0.04082
## Mean :-2.854 Mean :3.912 Mean :3.015 Mean :-0.01323
## 3rd Qu.:-2.749 3rd Qu.:4.205 3rd Qu.:3.178 3rd Qu.: 0.53063
## Max. :-2.520 Max. :5.170 Max. :3.932 Max. : 1.93152
## Prolactin Prostatic_Acid_Phosphatase Protein_S
## Min. :-1.30933 Min. :-1.934 Min. :-3.338
## 1st Qu.:-0.13926 1st Qu.:-1.717 1st Qu.:-2.464
## Median : 0.00000 Median :-1.690 Median :-2.259
## Mean : 0.04495 Mean :-1.685 Mean :-2.240
## 3rd Qu.: 0.25799 3rd Qu.:-1.654 3rd Qu.:-2.000
## Max. : 0.99325 Max. :-1.424 Max. :-1.221
## Pulmonary_and_Activation_Regulat RANTES Resistin
## Min. :-2.5133 Min. :-7.222 Min. :-34.967
## 1st Qu.:-1.8326 1st Qu.:-6.725 1st Qu.:-21.468
## Median :-1.5141 Median :-6.502 Median :-17.466
## Mean :-1.4880 Mean :-6.511 Mean :-17.641
## 3rd Qu.:-1.1712 3rd Qu.:-6.320 3rd Qu.:-13.501
## Max. :-0.2744 Max. :-5.547 Max. : -2.239
## S100b SGOT SHBG SOD
## Min. :0.1874 Min. :-1.3471 Min. :-4.135 Min. :4.317
## 1st Qu.:1.0012 1st Qu.:-0.6349 1st Qu.:-2.813 1st Qu.:5.094
## Median :1.2544 Median :-0.4005 Median :-2.489 Median :5.366
## Mean :1.2505 Mean :-0.4057 Mean :-2.477 Mean :5.336
## 3rd Qu.:1.4996 3rd Qu.:-0.1985 3rd Qu.:-2.120 3rd Qu.:5.583
## Max. :2.3726 Max. : 0.7419 Max. :-1.109 Max. :6.317
## Serum_Amyloid_P Sortilin Stem_Cell_Factor TGF_alpha
## Min. :-7.506 Min. :1.654 Min. :2.251 Min. : 6.843
## 1st Qu.:-6.377 1st Qu.:3.343 1st Qu.:3.045 1st Qu.: 8.859
## Median :-6.032 Median :3.867 Median :3.296 Median : 9.919
## Mean :-6.017 Mean :3.852 Mean :3.301 Mean : 9.801
## 3rd Qu.:-5.655 3rd Qu.:4.371 3rd Qu.:3.526 3rd Qu.:10.695
## Max. :-4.646 Max. :6.225 Max. :4.277 Max. :13.827
## TIMP_1 TNF_RII TRAIL_R3 TTR_prealbumin
## Min. : 1.742 Min. :-1.6607 Min. :-1.2107 Min. :2.485
## 1st Qu.:10.490 1st Qu.:-0.8210 1st Qu.:-0.7008 1st Qu.:2.773
## Median :11.565 Median :-0.5978 Median :-0.5317 Median :2.833
## Mean :11.750 Mean :-0.5939 Mean :-0.5394 Mean :2.854
## 3rd Qu.:12.697 3rd Qu.:-0.3784 3rd Qu.:-0.3849 3rd Qu.:2.944
## Max. :18.881 Max. : 0.4700 Max. : 0.2694 Max. :3.332
## Tamm_Horsfall_Protein_THP Thrombomodulin Thrombopoietin
## Min. :-3.206 Min. :-2.0377 Min. :-1.53957
## 1st Qu.:-3.137 1st Qu.:-1.6256 1st Qu.:-0.88645
## Median :-3.117 Median :-1.4920 Median :-0.75100
## Mean :-3.116 Mean :-1.5050 Mean :-0.75419
## 3rd Qu.:-3.096 3rd Qu.:-1.3406 3rd Qu.:-0.62887
## Max. :-2.995 Max. :-0.8166 Max. : 0.09762
## Thymus_Expressed_Chemokine_TECK Thyroid_Stimulating_Hormone
## Min. :1.508 Min. :-6.190
## 1st Qu.:3.343 1st Qu.:-4.962
## Median :3.810 Median :-4.510
## Mean :3.848 Mean :-4.499
## 3rd Qu.:4.316 3rd Qu.:-4.017
## Max. :6.225 Max. :-1.715
## Thyroxine_Binding_Globulin Tissue_Factor Transferrin
## Min. :-2.4769 Min. :-0.2107 Min. :1.932
## 1st Qu.:-1.7720 1st Qu.: 0.8329 1st Qu.:2.708
## Median :-1.5141 Median : 1.2238 Median :2.890
## Mean :-1.4788 Mean : 1.1702 Mean :2.909
## 3rd Qu.:-1.2379 3rd Qu.: 1.4816 3rd Qu.:3.091
## Max. :-0.2107 Max. : 2.4849 Max. :3.761
## Trefoil_Factor_3_TFF3 VCAM_1 VEGF Vitronectin
## Min. :-4.744 Min. :1.723 Min. :11.83 Min. :-1.42712
## 1st Qu.:-4.135 1st Qu.:2.485 1st Qu.:15.77 1st Qu.:-0.51083
## Median :-3.863 Median :2.708 Median :17.08 Median :-0.30111
## Mean :-3.876 Mean :2.688 Mean :16.99 Mean :-0.28473
## 3rd Qu.:-3.650 3rd Qu.:2.890 3rd Qu.:18.10 3rd Qu.:-0.03564
## Max. :-2.957 Max. :3.689 Max. :22.38 Max. : 0.53063
## von_Willebrand_Factor Class E4 E3
## Min. :-4.991 Impaired: 73 Min. :1.000 Min. :1.000
## 1st Qu.:-4.200 Control :194 1st Qu.:1.000 1st Qu.:2.000
## Median :-3.912 Median :1.000 Median :2.000
## Mean :-3.906 Mean :1.401 Mean :1.918
## 3rd Qu.:-3.612 3rd Qu.:2.000 3rd Qu.:2.000
## Max. :-2.957 Max. :2.000 Max. :2.000
## E2
## Min. :1.000
## 1st Qu.:1.000
## Median :1.000
## Mean :1.161
## 3rd Qu.:1.000
## Max. :2.000for (i in 1:ncol(PMA_PreModelling_Test)){
if (names(PMA_PreModelling_Test)[i]!="Class"){
PMA_PreModelling_Test[,i] <- as.numeric(PMA_PreModelling_Test[,i])
}
}
summary(PMA_PreModelling_Test)## ACE_CD143_Angiotensin_Converti ACTH_Adrenocorticotropic_Hormon
## Min. :-0.5473 Min. :-2.2073
## 1st Qu.: 0.9462 1st Qu.:-1.7148
## Median : 1.3013 Median :-1.5374
## Mean : 1.3105 Mean :-1.5311
## 3rd Qu.: 1.6320 3rd Qu.:-1.3863
## Max. : 3.0890 Max. :-0.7985
## AXL Adiponectin Alpha_1_Antichymotrypsin
## Min. :-0.73509 Min. :-7.059 Min. :0.1823
## 1st Qu.:-0.08175 1st Qu.:-5.737 1st Qu.:1.0647
## Median : 0.28035 Median :-5.360 Median :1.3083
## Mean : 0.25373 Mean :-5.298 Mean :1.3077
## 3rd Qu.: 0.60768 3rd Qu.:-4.917 3rd Qu.:1.5686
## Max. : 1.28634 Max. :-3.474 Max. :2.2192
## Alpha_1_Antitrypsin Alpha_1_Microglobulin Alpha_2_Macroglobulin
## Min. :-18.17 Min. :-4.135 Min. :-238.64
## 1st Qu.:-14.70 1st Qu.:-3.284 1st Qu.:-186.64
## Median :-13.59 Median :-3.006 Median :-162.93
## Mean :-13.49 Mean :-2.983 Mean :-162.89
## 3rd Qu.:-12.31 3rd Qu.:-2.674 3rd Qu.:-136.53
## Max. :-10.06 Max. :-1.897 Max. : -50.17
## Angiopoietin_2_ANG_2 Angiotensinogen Apolipoprotein_A_IV Apolipoprotein_A1
## Min. :-0.05129 Min. :1.710 Min. :-2.749 Min. :-8.568
## 1st Qu.: 0.35372 1st Qu.:2.068 1st Qu.:-2.186 1st Qu.:-7.818
## Median : 0.55921 Median :2.276 Median :-1.897 Median :-7.497
## Mean : 0.60278 Mean :2.274 Mean :-1.867 Mean :-7.488
## 3rd Qu.: 0.78846 3rd Qu.:2.430 3rd Qu.:-1.526 3rd Qu.:-7.176
## Max. : 1.77495 Max. :2.752 Max. :-1.109 Max. :-6.645
## Apolipoprotein_A2 Apolipoprotein_B Apolipoprotein_CI Apolipoprotein_CIII
## Min. :-1.9661 Min. :-8.192 Min. :-2.847 Min. :-3.863
## 1st Qu.:-0.9416 1st Qu.:-6.748 1st Qu.:-1.897 1st Qu.:-2.781
## Median :-0.7032 Median :-5.819 Median :-1.609 Median :-2.557
## Mean :-0.6902 Mean :-5.649 Mean :-1.625 Mean :-2.523
## 3rd Qu.:-0.3533 3rd Qu.:-4.603 3rd Qu.:-1.309 3rd Qu.:-2.231
## Max. : 0.5306 Max. :-2.339 Max. :-0.462 Max. :-1.386
## Apolipoprotein_D Apolipoprotein_E Apolipoprotein_H
## Min. :0.2624 Min. :0.6626 Min. :-1.1609
## 1st Qu.:1.1314 1st Qu.:2.1526 1st Qu.:-0.5317
## Median :1.3863 Median :2.8181 Median :-0.2897
## Mean :1.3943 Mean :2.7160 Mean :-0.3212
## 3rd Qu.:1.6864 3rd Qu.:3.2363 3rd Qu.:-0.1032
## Max. :2.6391 Max. :4.6844 Max. : 0.4402
## B_Lymphocyte_Chemoattractant_BL BMP_6 Beta_2_Microglobulin
## Min. :0.7318 Min. :-2.669 Min. :-0.51083
## 1st Qu.:1.5304 1st Qu.:-2.152 1st Qu.:-0.06188
## Median :1.8528 Median :-1.964 Median : 0.18232
## Mean :1.8766 Mean :-1.937 Mean : 0.15566
## 3rd Qu.:2.3714 3rd Qu.:-1.675 3rd Qu.: 0.40547
## Max. :2.9757 Max. :-1.181 Max. : 0.83291
## Betacellulin C_Reactive_Protein CD40 CD5L
## Min. :32.00 Min. :-8.112 Min. :-1.9390 Min. :-1.96611
## 1st Qu.:46.00 1st Qu.:-6.725 1st Qu.:-1.4420 1st Qu.:-0.36747
## Median :51.00 Median :-6.166 Median :-1.2574 Median :-0.05135
## Mean :52.74 Mean :-5.997 Mean :-1.2773 Mean :-0.08760
## 3rd Qu.:59.75 3rd Qu.:-5.369 3rd Qu.:-1.1034 3rd Qu.: 0.24235
## Max. :80.00 Max. :-3.411 Max. :-0.7766 Max. : 0.91629
## Calbindin Calcitonin CgA Clusterin_Apo_J
## Min. :10.81 Min. :-0.7134 Min. :166.6 Min. :1.932
## 1st Qu.:18.88 1st Qu.: 1.2014 1st Qu.:268.2 1st Qu.:2.565
## Median :21.06 Median : 1.6849 Median :324.7 Median :2.833
## Mean :21.49 Mean : 1.7250 Mean :320.2 Mean :2.845
## 3rd Qu.:24.00 3rd Qu.: 2.2618 3rd Qu.:362.3 3rd Qu.:3.045
## Max. :35.36 Max. : 4.1109 Max. :494.5 Max. :3.761
## Complement_3 Complement_Factor_H Connective_Tissue_Growth_Factor
## Min. :-22.40 Min. :0.2766 Min. :0.09531
## 1st Qu.:-17.50 1st Qu.:2.6019 1st Qu.:0.58779
## Median :-15.90 Median :3.3983 Median :0.74194
## Mean :-15.91 Mean :3.3897 Mean :0.74507
## 3rd Qu.:-14.34 3rd Qu.:4.2548 3rd Qu.:0.87547
## Max. :-10.23 Max. :6.5597 Max. :1.41099
## Cortisol Creatine_Kinase_MB Cystatin_C EGF_R
## Min. : 0.10 Min. :-1.872 Min. :7.728 Min. :-1.2694
## 1st Qu.: 8.90 1st Qu.:-1.721 1st Qu.:8.301 1st Qu.:-0.8859
## Median :10.00 Median :-1.651 Median :8.544 Median :-0.6917
## Mean :10.46 Mean :-1.652 Mean :8.576 Mean :-0.6965
## 3rd Qu.:12.00 3rd Qu.:-1.590 3rd Qu.:8.837 3rd Qu.:-0.5034
## Max. :22.00 Max. :-1.434 Max. :9.694 Max. : 0.1891
## EN_RAGE ENA_78 Eotaxin_3 FAS
## Min. :-8.3774 Min. :-1.405 Min. : 23.00 Min. :-1.1087
## 1st Qu.:-4.1836 1st Qu.:-1.382 1st Qu.: 43.00 1st Qu.:-0.7133
## Median :-3.6889 Median :-1.374 Median : 54.00 Median :-0.5798
## Mean :-3.5986 Mean :-1.376 Mean : 55.55 Mean :-0.5414
## 3rd Qu.:-3.2189 3rd Qu.:-1.368 3rd Qu.: 64.00 3rd Qu.:-0.3355
## Max. :-0.8675 Max. :-1.353 Max. :107.00 Max. : 0.1823
## FSH_Follicle_Stimulation_Hormon Fas_Ligand Fatty_Acid_Binding_Protein
## Min. :-1.8101 Min. :0.288 Min. :-0.4559
## 1st Qu.:-1.2694 1st Qu.:2.073 1st Qu.: 0.7998
## Median :-0.9763 Median :2.665 Median : 1.1866
## Mean :-1.0597 Mean :2.649 Mean : 1.2884
## 3rd Qu.:-0.8068 3rd Qu.:3.162 3rd Qu.: 1.9192
## Max. :-0.4757 Max. :5.377 Max. : 3.2188
## Ferritin Fetuin_A Fibrinogen GRO_alpha
## Min. :0.8983 Min. :0.5306 Min. :-9.373 Min. :1.271
## 1st Qu.:2.1473 1st Qu.:1.0296 1st Qu.:-7.799 1st Qu.:1.351
## Median :2.6260 Median :1.3083 Median :-7.316 Median :1.372
## Mean :2.7069 Mean :1.3116 Mean :-7.360 Mean :1.378
## 3rd Qu.:3.1672 3rd Qu.:1.6094 3rd Qu.:-6.970 3rd Qu.:1.398
## Max. :4.9282 Max. :2.2083 Max. :-6.166 Max. :1.514
## Gamma_Interferon_induced_Monokin Glutathione_S_Transferase_alpha
## Min. :2.545 Min. :0.5661
## 1st Qu.:2.698 1st Qu.:0.8257
## Median :2.768 Median :0.9493
## Mean :2.772 Mean :0.9440
## 3rd Qu.:2.829 3rd Qu.:1.0457
## Max. :3.046 Max. :1.3102
## HB_EGF HCC_4 Hepatocyte_Growth_Factor_HGF I_309
## Min. : 3.521 Min. :-4.343 Min. :-0.61619 Min. :2.041
## 1st Qu.: 5.949 1st Qu.:-3.772 1st Qu.:-0.05661 1st Qu.:2.724
## Median : 6.980 Median :-3.540 Median : 0.18232 Median :2.944
## Mean : 6.844 Mean :-3.538 Mean : 0.18076 Mean :2.921
## 3rd Qu.: 7.745 3rd Qu.:-3.352 3rd Qu.: 0.33647 3rd Qu.:3.135
## Max. :10.359 Max. :-2.489 Max. : 1.09861 Max. :3.689
## ICAM_1 IGF_BP_2 IL_11 IL_13
## Min. :-1.4661 Min. :4.718 Min. :2.031 Min. :1.232
## 1st Qu.:-0.7671 1st Qu.:5.127 1st Qu.:3.960 1st Qu.:1.274
## Median :-0.5903 Median :5.255 Median :4.838 Median :1.283
## Mean :-0.5958 Mean :5.263 Mean :4.651 Mean :1.283
## 3rd Qu.:-0.3574 3rd Qu.:5.402 3rd Qu.:5.482 3rd Qu.:1.292
## Max. : 0.3602 Max. :5.916 Max. :8.692 Max. :1.310
## IL_16 IL_17E IL_1alpha IL_3
## Min. :0.9568 Min. :1.582 Min. :-8.468 Min. :-5.521
## 1st Qu.:2.4411 1st Qu.:3.637 1st Qu.:-7.849 1st Qu.:-4.324
## Median :2.8763 Median :4.723 Median :-7.562 Median :-3.963
## Mean :2.8176 Mean :4.774 Mean :-7.549 Mean :-3.976
## 3rd Qu.:3.3514 3rd Qu.:5.415 3rd Qu.:-7.279 3rd Qu.:-3.576
## Max. :4.1028 Max. :8.081 Max. :-6.377 Max. :-3.079
## IL_4 IL_5 IL_6 IL_6_Receptor
## Min. :0.5306 Min. :-1.04982 Min. :-1.53428 Min. :-0.74560
## 1st Qu.:1.4586 1st Qu.:-0.03062 1st Qu.:-0.40924 1st Qu.:-0.20131
## Median :1.7226 Median : 0.22234 Median :-0.07205 Median : 0.00000
## Mean :1.7445 Mean : 0.22853 Mean :-0.05216 Mean : 0.06213
## 3rd Qu.:2.0669 3rd Qu.: 0.53063 3rd Qu.: 0.34805 3rd Qu.: 0.27297
## Max. :2.7081 Max. : 1.13140 Max. : 1.00562 Max. : 0.77048
## IL_7 IL_8 IP_10_Inducible_Protein_10 IgA
## Min. :1.310 Min. :1.615 Min. :4.263 Min. :-7.621
## 1st Qu.:2.379 1st Qu.:1.684 1st Qu.:5.323 1st Qu.:-6.571
## Median :3.148 Median :1.702 Median :5.617 Median :-6.012
## Mean :3.143 Mean :1.704 Mean :5.636 Mean :-6.066
## 3rd Qu.:3.706 3rd Qu.:1.725 3rd Qu.:5.917 3rd Qu.:-5.606
## Max. :5.000 Max. :1.836 Max. :7.208 Max. :-4.733
## Insulin Kidney_Injury_Molecule_1_KIM_1 LOX_1
## Min. :-2.0099 Min. :-1.251 Min. :0.0000
## 1st Qu.:-1.4466 1st Qu.:-1.209 1st Qu.:0.9649
## Median :-1.2169 Median :-1.187 Median :1.2238
## Mean :-1.1998 Mean :-1.188 Mean :1.2085
## 3rd Qu.:-1.0105 3rd Qu.:-1.166 3rd Qu.:1.4351
## Max. :-0.5025 Max. :-1.124 Max. :2.3979
## Leptin Lipoprotein_a MCP_1 MCP_2
## Min. :-1.9471 Min. :-6.571 Min. :5.889 Min. :0.4006
## 1st Qu.:-1.6334 1st Qu.:-5.116 1st Qu.:6.318 1st Qu.:1.5304
## Median :-1.4294 Median :-4.657 Median :6.482 Median :1.8528
## Mean :-1.4363 Mean :-4.515 Mean :6.480 Mean :1.8104
## 3rd Qu.:-1.2409 3rd Qu.:-4.017 3rd Qu.:6.627 3rd Qu.:2.0827
## Max. :-0.8387 Max. :-2.040 Max. :7.065 Max. :3.7545
## MIF MIP_1alpha MIP_1beta MMP_2
## Min. :-2.797 Min. :1.008 Min. :1.917 Min. :0.6248
## 1st Qu.:-2.120 1st Qu.:3.302 1st Qu.:2.485 1st Qu.:2.5513
## Median :-1.966 Median :3.736 Median :2.773 Median :2.9937
## Mean :-1.932 Mean :3.898 Mean :2.784 Mean :3.0347
## 3rd Qu.:-1.715 3rd Qu.:4.686 3rd Qu.:3.079 3rd Qu.:3.4798
## Max. :-1.109 Max. :5.735 Max. :3.784 Max. :6.0996
## MMP_3 MMP10 MMP7 Myoglobin
## Min. :-3.650 Min. :-4.948 Min. :-7.5346 Min. :-3.2968
## 1st Qu.:-2.852 1st Qu.:-4.075 1st Qu.:-4.9634 1st Qu.:-2.0217
## Median :-2.532 Median :-3.612 Median :-4.0302 Median :-1.5874
## Mean :-2.490 Mean :-3.676 Mean :-4.0148 Mean :-1.4165
## 3rd Qu.:-2.120 3rd Qu.:-3.331 3rd Qu.:-3.1640 3rd Qu.:-0.7765
## Max. :-1.171 Max. :-2.900 Max. :-0.1953 Max. : 1.1314
## NT_proBNP NrCAM Osteopontin PAI_1
## Min. :3.611 Min. :2.890 Min. :4.078 Min. :-0.990849
## 1st Qu.:4.174 1st Qu.:3.871 1st Qu.:4.892 1st Qu.:-0.334043
## Median :4.477 Median :4.317 Median :5.168 Median : 0.000000
## Mean :4.488 Mean :4.291 Mean :5.177 Mean :-0.003947
## 3rd Qu.:4.794 3rd Qu.:4.725 3rd Qu.:5.410 3rd Qu.: 0.303112
## Max. :5.398 Max. :5.690 Max. :6.315 Max. : 0.885785
## PAPP_A PLGF PYY Pancreatic_polypeptide
## Min. :-3.152 Min. :2.639 Min. :2.398 Min. :-1.609438
## 1st Qu.:-2.971 1st Qu.:3.689 1st Qu.:2.833 1st Qu.:-0.506693
## Median :-2.841 Median :3.892 Median :2.996 Median : 0.138816
## Mean :-2.845 Mean :3.884 Mean :2.976 Mean :-0.005258
## 3rd Qu.:-2.719 3rd Qu.:4.123 3rd Qu.:3.178 3rd Qu.: 0.470004
## Max. :-2.488 Max. :4.710 Max. :3.738 Max. : 1.504077
## Prolactin Prostatic_Acid_Phosphatase Protein_S
## Min. :-0.38566 Min. :-1.800 Min. :-3.154
## 1st Qu.:-0.16558 1st Qu.:-1.739 1st Qu.:-2.579
## Median : 0.00000 Median :-1.690 Median :-2.259
## Mean : 0.05195 Mean :-1.692 Mean :-2.268
## 3rd Qu.: 0.18232 3rd Qu.:-1.659 3rd Qu.:-1.924
## Max. : 0.78846 Max. :-1.540 Max. :-1.547
## Pulmonary_and_Activation_Regulat RANTES Resistin
## Min. :-2.4418 Min. :-7.236 Min. :-30.156
## 1st Qu.:-1.8326 1st Qu.:-6.725 1st Qu.:-22.131
## Median :-1.5141 Median :-6.571 Median :-18.014
## Mean :-1.5007 Mean :-6.540 Mean :-18.245
## 3rd Qu.:-1.1712 3rd Qu.:-6.392 3rd Qu.:-15.202
## Max. :-0.4463 Max. :-5.843 Max. : -6.594
## S100b SGOT SHBG SOD
## Min. :0.1874 Min. :-1.8971 Min. :-3.730 Min. :4.382
## 1st Qu.:0.9600 1st Qu.:-0.7498 1st Qu.:-3.052 1st Qu.:5.006
## Median :1.1571 Median :-0.4780 Median :-2.711 Median :5.313
## Mean :1.1819 Mean :-0.4898 Mean :-2.686 Mean :5.302
## 3rd Qu.:1.3807 3rd Qu.:-0.2138 3rd Qu.:-2.343 3rd Qu.:5.547
## Max. :2.1950 Max. : 0.1823 Max. :-1.561 Max. :6.461
## Serum_Amyloid_P Sortilin Stem_Cell_Factor TGF_alpha
## Min. :-7.182 Min. :1.508 Min. :2.219 Min. : 7.500
## 1st Qu.:-6.438 1st Qu.:3.177 1st Qu.:3.045 1st Qu.: 9.062
## Median :-6.215 Median :3.867 Median :3.314 Median : 9.596
## Mean :-6.083 Mean :3.787 Mean :3.267 Mean : 9.776
## 3rd Qu.:-5.607 3rd Qu.:4.371 3rd Qu.:3.466 3rd Qu.:10.612
## Max. :-4.699 Max. :5.681 Max. :4.078 Max. :13.083
## TIMP_1 TNF_RII TRAIL_R3 TTR_prealbumin
## Min. : 8.198 Min. :-1.6607 Min. :-1.30636 Min. :2.485
## 1st Qu.:10.530 1st Qu.:-0.8675 1st Qu.:-0.73332 1st Qu.:2.773
## Median :11.341 Median :-0.6541 Median :-0.55547 Median :2.890
## Mean :11.520 Mean :-0.6270 Mean :-0.58640 Mean :2.854
## 3rd Qu.:12.352 3rd Qu.:-0.3320 3rd Qu.:-0.47065 3rd Qu.:2.944
## Max. :16.547 Max. : 0.4055 Max. : 0.09622 Max. :3.091
## Tamm_Horsfall_Protein_THP Thrombomodulin Thrombopoietin
## Min. :-3.206 Min. :-2.054 Min. :-1.5396
## 1st Qu.:-3.144 1st Qu.:-1.675 1st Qu.:-0.8383
## Median :-3.126 Median :-1.534 Median :-0.7039
## Mean :-3.123 Mean :-1.533 Mean :-0.7192
## 3rd Qu.:-3.101 3rd Qu.:-1.341 3rd Qu.:-0.6289
## Max. :-3.041 Max. :-1.019 Max. :-0.3029
## Thymus_Expressed_Chemokine_TECK Thyroid_Stimulating_Hormone
## Min. :2.141 Min. :-6.190
## 1st Qu.:3.283 1st Qu.:-4.733
## Median :3.753 Median :-4.269
## Mean :3.770 Mean :-4.221
## 3rd Qu.:4.316 3rd Qu.:-3.828
## Max. :5.681 Max. :-2.040
## Thyroxine_Binding_Globulin Tissue_Factor Transferrin
## Min. :-2.3026 Min. :0.0000 Min. :2.282
## 1st Qu.:-1.7148 1st Qu.:0.7053 1st Qu.:2.708
## Median :-1.4919 Median :1.1473 Median :2.890
## Mean :-1.4902 Mean :1.1356 Mean :2.900
## 3rd Qu.:-1.2379 3rd Qu.:1.5149 3rd Qu.:3.135
## Max. :-0.5978 Max. :2.7081 Max. :3.497
## Trefoil_Factor_3_TFF3 VCAM_1 VEGF Vitronectin
## Min. :-4.906 Min. :2.028 Min. :12.23 Min. :-1.07881
## 1st Qu.:-4.200 1st Qu.:2.420 1st Qu.:15.03 1st Qu.:-0.46204
## Median :-3.912 Median :2.674 Median :17.08 Median :-0.28106
## Mean :-3.947 Mean :2.644 Mean :16.70 Mean :-0.26833
## 3rd Qu.:-3.772 3rd Qu.:2.833 3rd Qu.:18.19 3rd Qu.:-0.05394
## Max. :-3.170 Max. :3.466 Max. :21.18 Max. : 0.40547
## von_Willebrand_Factor Class E4 E3
## Min. :-4.920 Impaired:18 Min. :1.000 Min. :1.000
## 1st Qu.:-4.269 Control :48 1st Qu.:1.000 1st Qu.:2.000
## Median :-4.017 Median :1.000 Median :2.000
## Mean :-4.014 Mean :1.303 Mean :1.985
## 3rd Qu.:-3.730 3rd Qu.:2.000 3rd Qu.:2.000
## Max. :-3.058 Max. :2.000 Max. :2.000
## E2
## Min. :1.000
## 1st Qu.:1.000
## Median :1.000
## Mean :1.061
## 3rd Qu.:1.000
## Max. :2.000##################################
# Creating consistent fold assignments
# for the Cross Validation process
##################################
set.seed(12345678)
KFold_Indices <- createFolds(PMA_PreModelling_Train$Class ,
k = 10,
returnTrain=TRUE)
##################################
# Formulating a function to summarize
# model performance metrics
##################################
FiveMetricsSummary <- function(...) c(twoClassSummary(...), defaultSummary(...))
##################################
# Formulating the controls for the
# model training process
##################################
KFold_TrainControl <- trainControl(method = "cv",
summaryFunction = FiveMetricsSummary,
classProbs = TRUE,
index = KFold_Indices)
##################################
# Running the random forest model
# by setting the caret method to 'rf'
##################################
set.seed(12345678)
RF_FULL_Tune <- caret::train(x = PMA_PreModelling_Train[,!names(PMA_PreModelling_Train) %in% c("Class")],
y = PMA_PreModelling_Train$Class,
method = "rf",
metric = "Accuracy",
tuneGrid = data.frame(mtry = floor(sqrt(length(names(PMA_PreModelling_Train) %in% c("Class"))))),
ntree = 50,
trControl = KFold_TrainControl)
##################################
# Reporting the cross-validation results
# for the train set
##################################
RF_FULL_Tune## Random Forest
##
## 267 samples
## 127 predictors
## 2 classes: 'Impaired', 'Control'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 240, 239, 241, 240, 241, 241, ...
## Resampling results:
##
## ROC Sens Spec Accuracy Kappa
## 0.7645982 0.3178571 0.9536842 0.7797517 0.3186583
##
## Tuning parameter 'mtry' was held constant at a value of 11RF_FULL_Tune$finalModel##
## Call:
## randomForest(x = x, y = y, ntree = 50, mtry = param$mtry)
## Type of random forest: classification
## Number of trees: 50
## No. of variables tried at each split: 11
##
## OOB estimate of error rate: 23.6%
## Confusion matrix:
## Impaired Control class.error
## Impaired 24 49 0.67123288
## Control 14 180 0.07216495RF_FULL_Tune$results## mtry ROC Sens Spec Accuracy Kappa ROCSD SensSD
## 1 11 0.7645982 0.3178571 0.9536842 0.7797517 0.3186583 0.1373713 0.1832328
## SpecSD AccuracySD KappaSD
## 1 0.03791666 0.06273494 0.218025(RF_FULL_Train_Accuracy <- RF_FULL_Tune$results[,c("Accuracy")])## [1] 0.7797517##################################
# Identifying and plotting the
# best model predictors
##################################
RF_FULL_VarImp <- varImp(RF_FULL_Tune, scale = TRUE)
plot(RF_FULL_VarImp,
top=25,
scales=list(y=list(cex = .95)),
main="Ranked Variable Importance : Random Forest",
xlab="Scaled Variable Importance Metrics",
ylab="Predictors",
cex=2,
origin=0,
alpha=0.45)
##################################
# Independently evaluating the model and
# reporting the independent evaluation results
# on the test set
##################################
RF_FULL_Test <- data.frame(RF_FULL_Observed = PMA_PreModelling_Test$Class,
RF_FULL_Predicted = predict(RF_FULL_Tune,
PMA_PreModelling_Test[,!names(PMA_PreModelling_Test) %in% c("Class")],
type = "raw"))
RF_FULL_Test## RF_FULL_Observed RF_FULL_Predicted
## 1 Control Control
## 2 Impaired Control
## 3 Impaired Control
## 4 Control Control
## 5 Impaired Control
## 6 Impaired Control
## 7 Impaired Control
## 8 Control Control
## 9 Impaired Impaired
## 10 Control Control
## 11 Control Control
## 12 Control Control
## 13 Control Control
## 14 Impaired Control
## 15 Control Control
## 16 Control Control
## 17 Control Control
## 18 Impaired Impaired
## 19 Control Control
## 20 Control Control
## 21 Control Control
## 22 Control Control
## 23 Control Control
## 24 Control Control
## 25 Control Control
## 26 Control Control
## 27 Control Control
## 28 Control Control
## 29 Control Control
## 30 Control Control
## 31 Impaired Control
## 32 Control Control
## 33 Control Control
## 34 Control Control
## 35 Control Control
## 36 Control Control
## 37 Control Control
## 38 Control Control
## 39 Impaired Control
## 40 Control Control
## 41 Control Control
## 42 Control Control
## 43 Control Control
## 44 Impaired Impaired
## 45 Control Control
## 46 Control Control
## 47 Control Control
## 48 Impaired Control
## 49 Control Control
## 50 Impaired Control
## 51 Control Control
## 52 Impaired Impaired
## 53 Impaired Control
## 54 Control Control
## 55 Control Control
## 56 Control Control
## 57 Control Control
## 58 Impaired Control
## 59 Control Control
## 60 Impaired Impaired
## 61 Control Control
## 62 Control Control
## 63 Impaired Control
## 64 Control Control
## 65 Control Control
## 66 Control Control##################################
# Reporting the independent evaluation results
# for the test set
##################################
(RF_FULL_Test_Accuracy <- Accuracy(y_pred = RF_FULL_Test$RF_FULL_Predicted,
y_true = RF_FULL_Test$RF_FULL_Observed))## [1] 0.80303031.5.2 Random Forest With Simulated Annealing (RF_SA)
Random Forest is an ensemble learning method made up of a large set of small decision trees called estimators, with each producing its own prediction. The random forest model aggregates the predictions of the estimators to produce a more accurate prediction. The algorithm involves bootstrap aggregating (where smaller subsets of the training data are repeatedly subsampled with replacement), random subspacing (where a subset of features are sampled and used to train each individual estimator), estimator training (where unpruned decision trees are formulated for each estimator) and inference by aggregating the predictions of all estimators
Simulated Annealing is a global search method that makes small random changes or perturbations to an initial candidate solution. If the performance value for the perturbed value is better than the previous solution, the new solution is accepted. If not, an acceptance probability is determined based on the difference between the two performance values and the current iteration of the search. From this, a sub-optimal solution can be accepted on the off-change that it may eventually produce a better solution in subsequent iterations. In the context of feature selection, a solution is a binary vector that describes the current subset. The subset is perturbed by randomly changing a small number of members in the subset.
[A] The random forest model from the randomForest package was implemented with simulated annealing through the caret package.
[B] The model contains 1 hyperparameter:
[B.1] mtry = number of randomly selected predictors held constant at a value of 5
[C] Simulated annealing was applied with results as follows:
[C.1] 30 predictors were selected using the training data at iteration 8.
[C.2] Resampling showed that approximately 28 variables were selected.
[C.3] The top 5 variables identified were tied among too many predictors.
[D] The cross-validated model performance of the final model is summarized as follows:
[D.1] Final model configuration involves variable subset=23 to 33
[D.2] Accuracy = 0.77618
[E] The independent test model performance of the final model is summarized as follows:
[E.1] Accuracy = 0.77272
Code Chunk | Output
##################################
# Formulating the controls for the
# simulated annealing process
##################################
KFold_SAControl <- safsControl(method = "cv",
verbose = TRUE,
functions = rfSA,
index = KFold_Indices,
returnResamp = "final",
improve = 25)
##################################
# Running the random forest model
# by setting the caret method to 'rf'
# with implementation of simulated annealing
##################################
set.seed(12345678)
RF_SA_Tune <- caret::safs(x = PMA_PreModelling_Train[,!names(PMA_PreModelling_Train) %in% c("Class")],
y = PMA_PreModelling_Train$Class,
iters = 10,
ntree = 50,
safsControl = KFold_SAControl)## Fold01 1 0.7333333 (26)
## Fold01 2 0.7333333->0.6958333 (26+1, 96.3%) 0.9027833 A
## Fold01 3 0.7333333->0.7166667 (26+0, 92.6%) 0.9340906 A
## Fold01 4 0.7333333->0.7291667 (26+1, 89.3%) 0.977529 A
## Fold01 5 0.7333333->0.7291667 (26+2, 86.2%) 0.9719907 A
## Fold01 6 0.7333333->0.7208333 (26+3, 83.3%) 0.9027833 A
## Fold01 7 0.7333333->0.7125 (26+4, 80.6%) 0.8196617 A
## Fold01 8 0.7333333->0.7166667 (26+5, 78.1%) 0.8337529 A
## Fold01 9 0.7333333->0.7208333 (26+4, 75.0%) 0.8577787 A
## Fold01 10 0.7333333->0.7416667 (26+5, 72.7%) *
## Fold02 1 0.7322176 (26)
## Fold02 2 0.7322176->0.7656904 (26+1, 96.3%) *
## Fold02 3 0.7656904->0.7238494 (27-1, 96.3%) 0.8487977 A
## Fold02 4 0.7656904->0.748954 (27+0, 92.9%) 0.9162815 A
## Fold02 5 0.7656904->0.748954 (27+1, 89.7%) 0.8964707 A
## Fold02 6 0.7656904->0.7656904 (27+2, 86.7%) 1 A
## Fold02 7 0.7656904->0.7238494 (27+3, 83.9%) 0.6821446 A
## Fold02 8 0.7656904->0.748954 (27+2, 80.6%) 0.8395717 A
## Fold02 9 0.7656904->0.7238494 (27+1, 77.4%) 0.6115227 A
## Fold02 10 0.7656904->0.7782427 (27+2, 75.0%) *
## Fold03 1 0.7385892 (26)
## Fold03 2 0.7385892->0.7510373 (26-1, 96.2%) *
## Fold03 3 0.7510373->0.7427386 (25+1, 96.2%) 0.9673942 A
## Fold03 4 0.7510373->0.7219917 (25+2, 92.6%) 0.8566755 A
## Fold03 5 0.7510373->0.7427386 (25+3, 89.3%) 0.9462499 A
## Fold03 6 0.7510373->0.7178423 (25+4, 86.2%) 0.7670576 A
## Fold03 7 0.7510373->0.7427386 (25+5, 83.3%) 0.9255676 A
## Fold03 8 0.7510373->0.7302905 (25+6, 80.6%) 0.8017211 A
## Fold03 9 0.7510373->0.7385892 (25+7, 78.1%) 0.8614216 A
## Fold03 10 0.7510373->0.7261411 (25+8, 75.8%) 0.7178521 A
## Fold04 1 0.7291667 (26)
## Fold04 2 0.7291667->0.75 (26+1, 96.3%) *
## Fold04 3 0.75->0.7625 (27-1, 96.3%) *
## Fold04 4 0.7625->0.7291667 (26+1, 96.3%) 0.8395717 A
## Fold04 5 0.7625->0.7583333 (26+2, 92.9%) 0.9730475 A
## Fold04 6 0.7625->0.725 (26+3, 89.7%) 0.7444706 A
## Fold04 7 0.7625->0.7041667 (26+4, 86.7%) 0.5853653
## Fold04 8 0.7625->0.75 (26+2, 86.2%) 0.8770884 A
## Fold04 9 0.7625->0.75 (26+3, 83.3%) 0.8628271 A
## Fold04 10 0.7625->0.75 (26+4, 80.6%) 0.8487977 A
## Fold05 1 0.7095436 (26)
## Fold05 2 0.7095436->0.7385892 (26+1, 96.3%) *
## Fold05 3 0.7385892->0.7427386 (27-1, 96.3%) *
## Fold05 4 0.7427386->0.7344398 (26-1, 96.2%) 0.9562913 A
## Fold05 5 0.7427386->0.7302905 (26-2, 92.3%) 0.9196162 A
## Fold05 6 0.7427386->0.7261411 (26-3, 88.5%) 0.8745217
## Fold05 7 0.7427386->0.7676349 (26-3, 88.5%) *
## Fold05 8 0.7676349->0.7053942 (23+1, 95.8%) 0.5227517 A
## Fold05 9 0.7676349->0.7095436 (23+2, 92.0%) 0.5060696
## Fold05 10 0.7676349->0.7676349 (23+2, 92.0%) 1 A
## Fold06 1 0.7551867 (26)
## Fold06 2 0.7551867->0.7385892 (26-1, 96.2%) 0.956996 A
## Fold06 3 0.7551867->0.6929461 (26+0, 92.6%) 0.7809433 A
## Fold06 4 0.7551867->0.7551867 (26+1, 89.3%) 1 A
## Fold06 5 0.7551867->0.7053942 (26+2, 86.2%) 0.7191608
## Fold06 6 0.7551867->0.7012448 (26+2, 86.2%) 0.6514391 A
## Fold06 7 0.7551867->0.7261411 (26+3, 83.3%) 0.7639669 A
## Fold06 8 0.7551867->0.7053942 (26+4, 80.6%) 0.5900945 A
## Fold06 9 0.7551867->0.7427386 (26+5, 78.1%) 0.8621279 A
## Fold06 10 0.7551867->0.746888 (26+4, 75.0%) 0.8959326
## Fold07 1 0.7427386 (26)
## Fold07 2 0.7427386->0.7178423 (26+1, 96.3%) 0.9351586 A
## Fold07 3 0.7427386->0.7385892 (26+2, 92.9%) 0.9833799 A
## Fold07 4 0.7427386->0.7095436 (26+3, 89.7%) 0.8362974 A
## Fold07 5 0.7427386->0.7385892 (26+2, 86.2%) 0.9724536 A
## Fold07 6 0.7427386->0.7053942 (26+3, 83.3%) 0.7395777 A
## Fold07 7 0.7427386->0.7261411 (26+4, 80.6%) 0.855196 A
## Fold07 8 0.7427386->0.746888 (26+5, 78.1%) *
## Fold07 9 0.746888->0.7427386 (31+1, 96.9%) 0.9512294 A
## Fold07 10 0.746888->0.7427386 (31+0, 93.8%) 0.9459595 A
## Fold08 1 0.725 (26)
## Fold08 2 0.725->0.7208333 (26+1, 96.3%) 0.9885716 A
## Fold08 3 0.725->0.7083333 (26+2, 92.9%) 0.9333589 A
## Fold08 4 0.725->0.7375 (26+3, 89.7%) *
## Fold08 5 0.7375->0.7541667 (29+1, 96.7%) *
## Fold08 6 0.7541667->0.7375 (30+1, 96.8%) 0.8758183 A
## Fold08 7 0.7541667->0.7708333 (30+2, 93.8%) *
## Fold08 8 0.7708333->0.775 (32+1, 97.0%) *
## Fold08 9 0.775->0.7333333 (33-1, 97.0%) 0.6163927 A
## Fold08 10 0.775->0.7458333 (33-2, 93.9%) 0.6863661
## Fold09 1 0.7447699 (26)
## Fold09 2 0.7447699->0.748954 (26+1, 96.3%) *
## Fold09 3 0.748954->0.7447699 (27+1, 96.4%) 0.9833799 A
## Fold09 4 0.748954->0.7280335 (27+2, 93.1%) 0.894284
## Fold09 5 0.748954->0.707113 (27+2, 93.1%) 0.7562906 A
## Fold09 6 0.748954->0.7364017 (27+1, 89.7%) 0.9043321 A
## Fold09 7 0.748954->0.7322176 (27+2, 86.7%) 0.855196 A
## Fold09 8 0.748954->0.7405858 (27+3, 83.9%) 0.914493 A
## Fold09 9 0.748954->0.7112971 (27+4, 81.2%) 0.6360272 A
## Fold09 10 0.748954->0.7447699 (27+5, 78.8%) 0.9456659 A
## Fold10 1 0.7385892 (26)
## Fold10 2 0.7385892->0.7344398 (26+1, 96.3%) 0.9888269 A
## Fold10 3 0.7385892->0.7302905 (26+2, 92.9%) 0.9668539 A
## Fold10 4 0.7385892->0.7344398 (26+3, 89.7%) 0.9777787 A
## Fold10 5 0.7385892->0.7427386 (26+4, 86.7%) *
## Fold10 6 0.7427386->0.7510373 (30-1, 96.7%) *
## Fold10 7 0.7510373->0.7385892 (29+1, 96.7%) 0.8904555
## Fold10 8 0.7510373->0.7136929 (29-1, 96.6%) 0.6718031
## Fold10 9 0.7510373->0.7385892 (29-1, 96.6%) 0.8614216 A
## Fold10 10 0.7510373->0.7593361 (29-2, 93.1%) *
## + final SA
## 1 0.7490637 (26)
## 2 0.7490637->0.741573 (26+1, 96.3%) 0.9801987 A
## 3 0.7490637->0.7790262 (26+2, 92.9%) *
## 4 0.7790262->0.741573 (28+1, 96.6%) 0.825053 A
## 5 0.7790262->0.7303371 (28+2, 93.3%) 0.7316156 A
## 6 0.7790262->0.7378277 (28+3, 90.3%) 0.7281067
## 7 0.7790262->0.741573 (28+3, 90.3%) 0.7142384 A
## 8 0.7790262->0.7490637 (28+2, 87.1%) 0.7351415 A
## 9 0.7790262->0.7378277 (28+3, 84.4%) 0.6212874 A
## 10 0.7790262->0.7453184 (28+4, 81.8%) 0.6487601 A
## + final model##################################
# Reporting the cross-validation results
# for the train set
##################################
RF_SA_Tune##
## Simulated Annealing Feature Selection
##
## 267 samples
## 127 predictors
## 2 classes: 'Impaired', 'Control'
##
## Maximum search iterations: 10
## Restart after 25 iterations without improvement (0 restarts on average)
##
## Internal performance values: Accuracy, Kappa
## Subset selection driven to maximize internal Accuracy
##
## External performance values: Accuracy, Kappa
## Best iteration chose by maximizing external Accuracy
## External resampling method: Cross-Validated (10 fold)
##
## During resampling:
## * the top 5 selected variables (out of a possible 127):
## Alpha_1_Microglobulin (50%), IL_3 (50%), Osteopontin (50%), Beta_2_Microglobulin (40%), BMP_6 (40%)
## * on average, 27.8 variables were selected (min = 23, max = 33)
##
## In the final search using the entire training set:
## * 30 features selected at iteration 8 including:
## ACTH_Adrenocorticotropic_Hormon, Angiotensinogen, Apolipoprotein_A2, Apolipoprotein_B, Apolipoprotein_CI ...
## * external performance at this iteration is
##
## Accuracy Kappa
## 0.7762 0.3061RF_SA_Tune$fit##
## Call:
## randomForest(x = x, y = y, ntree = 50)
## Type of random forest: classification
## Number of trees: 50
## No. of variables tried at each split: 5
##
## OOB estimate of error rate: 25.47%
## Confusion matrix:
## Impaired Control class.error
## Impaired 19 54 0.73972603
## Control 14 180 0.07216495RF_SA_Tune$averages## Iter Accuracy Kappa
## 1 1 0.7238604 0.1488856
## 2 2 0.7380037 0.2028418
## 3 3 0.7493895 0.2403309
## 4 4 0.7684778 0.2964909
## 5 5 0.7683557 0.2916946
## 6 6 0.7389703 0.1972777
## 7 7 0.7576516 0.2461292
## 8 8 0.7761803 0.3061366
## 9 9 0.7680810 0.2678226
## 10 10 0.7609381 0.2700777(RF_SA_Train_Accuracy <- RF_SA_Tune$averages[RF_SA_Tune$averages$Accuracy==max(RF_SA_Tune$averages$Accuracy),
c("Accuracy")])## [1] 0.7761803##################################
# Independently evaluating the model and
# reporting the independent evaluation results
# on the test set
##################################
RF_SA_Test <- data.frame(RF_SA_Observed = PMA_PreModelling_Test$Class,
RF_SA_Predicted = predict(RF_SA_Tune,
PMA_PreModelling_Test[,!names(PMA_PreModelling_Test) %in% c("Class")],
type = "raw"))
RF_SA_Test## RF_SA_Observed RF_SA_Predicted.pred RF_SA_Predicted.Impaired
## 4 Control Control 0.20
## 10 Impaired Control 0.34
## 13 Impaired Control 0.24
## 15 Control Control 0.10
## 27 Impaired Control 0.14
## 32 Impaired Control 0.04
## 33 Impaired Control 0.30
## 49 Control Control 0.08
## 52 Impaired Impaired 0.84
## 54 Control Control 0.10
## 58 Control Control 0.38
## 66 Control Control 0.26
## 79 Control Control 0.14
## 87 Impaired Control 0.28
## 89 Control Control 0.34
## 91 Control Control 0.34
## 92 Control Control 0.20
## 101 Impaired Impaired 0.72
## 102 Control Control 0.22
## 106 Control Control 0.14
## 116 Control Control 0.30
## 119 Control Control 0.12
## 120 Control Control 0.10
## 122 Control Control 0.22
## 125 Control Control 0.18
## 127 Control Control 0.10
## 138 Control Control 0.28
## 142 Control Control 0.34
## 150 Control Control 0.36
## 151 Control Control 0.26
## 164 Impaired Control 0.32
## 173 Control Control 0.12
## 187 Control Control 0.06
## 188 Control Control 0.32
## 196 Control Control 0.24
## 199 Control Control 0.48
## 203 Control Control 0.12
## 204 Control Control 0.32
## 206 Impaired Control 0.42
## 207 Control Control 0.24
## 209 Control Control 0.22
## 211 Control Control 0.04
## 217 Control Control 0.44
## 221 Impaired Impaired 0.54
## 222 Control Control 0.10
## 235 Control Control 0.10
## 238 Control Control 0.18
## 248 Impaired Control 0.24
## 252 Control Control 0.24
## 259 Impaired Control 0.10
## 266 Control Control 0.26
## 276 Impaired Control 0.38
## 280 Impaired Control 0.26
## 284 Control Control 0.18
## 285 Control Control 0.08
## 286 Control Control 0.06
## 288 Control Control 0.08
## 293 Impaired Control 0.22
## 295 Control Control 0.26
## 296 Impaired Impaired 0.64
## 300 Control Impaired 0.58
## 309 Control Control 0.08
## 310 Impaired Control 0.28
## 318 Control Control 0.12
## 319 Control Control 0.14
## 328 Control Control 0.28
## RF_SA_Predicted.Control
## 4 0.80
## 10 0.66
## 13 0.76
## 15 0.90
## 27 0.86
## 32 0.96
## 33 0.70
## 49 0.92
## 52 0.16
## 54 0.90
## 58 0.62
## 66 0.74
## 79 0.86
## 87 0.72
## 89 0.66
## 91 0.66
## 92 0.80
## 101 0.28
## 102 0.78
## 106 0.86
## 116 0.70
## 119 0.88
## 120 0.90
## 122 0.78
## 125 0.82
## 127 0.90
## 138 0.72
## 142 0.66
## 150 0.64
## 151 0.74
## 164 0.68
## 173 0.88
## 187 0.94
## 188 0.68
## 196 0.76
## 199 0.52
## 203 0.88
## 204 0.68
## 206 0.58
## 207 0.76
## 209 0.78
## 211 0.96
## 217 0.56
## 221 0.46
## 222 0.90
## 235 0.90
## 238 0.82
## 248 0.76
## 252 0.76
## 259 0.90
## 266 0.74
## 276 0.62
## 280 0.74
## 284 0.82
## 285 0.92
## 286 0.94
## 288 0.92
## 293 0.78
## 295 0.74
## 296 0.36
## 300 0.42
## 309 0.92
## 310 0.72
## 318 0.88
## 319 0.86
## 328 0.72##################################
# Reporting the independent evaluation results
# for the test set
##################################
(RF_SA_Test_Accuracy <- Accuracy(y_pred = RF_SA_Test$RF_SA_Predicted.pred,
y_true = RF_SA_Test$RF_SA_Observed))## [1] 0.77272731.5.3 Random Forest With Genetic Algorithms (RF_GA)
Random Forest is an ensemble learning method made up of a large set of small decision trees called estimators, with each producing its own prediction. The random forest model aggregates the predictions of the estimators to produce a more accurate prediction. The algorithm involves bootstrap aggregating (where smaller subsets of the training data are repeatedly subsampled with replacement), random subspacing (where a subset of features are sampled and used to train each individual estimator), estimator training (where unpruned decision trees are formulated for each estimator) and inference by aggregating the predictions of all estimators
Genetic Algorithms mimic Darwinian forces of natural selection to find optimal values of some function. An initial set of candidate solutions are created and their corresponding fitness values are calculated (where larger values are better). This set of solutions is referred to as a population and each solution as an individual. The individuals with the best fitness values are combined randomly to produce offsprings which make up the next population. To do so, individual are selected and undergo cross-over (mimicking genetic reproduction) and also are subject to random mutations. This process is repeated again and again and many generations are produced resulting to iterations of the search procedure that should create better and better solutions. For feature selection, the individuals are subsets of predictors that are encoded as binary representing a feature being either included or not in the subset. The fitness values applied are existing measurea of model performance.
[A] The random forest model from the randomForest package was implemented with genetic algorithms through the caret package.
[B] The model contains 1 hyperparameter:
[B.1] mtry = number of randomly selected predictors held constant at a value of 9
[C] Genetic algorithms was applied with results as follows:
[C.1] 93 predictors were selected using the training data at iteration 1.
[C.2] Resampling showed that approximately 63 variables were selected.
[C.3] The top 5 variables identified were tied among too many predictors.
[D] The cross-validated model performance of the final model is summarized as follows:
[D.1] Final model configuration involves variable subset=45 to 101
[D.2] Accuracy = 0.79842
[E] The independent test model performance of the final model is summarized as follows:
[E.1] Accuracy = 0.78787
Code Chunk | Output
##################################
# Formulating the controls for the
# genetic algorithms process
##################################
KFold_GAControl <- gafsControl(method = "cv",
verbose = TRUE,
functions = rfGA,
index = KFold_Indices,
returnResamp = "final")
##################################
# Running the random forest model
# by setting the caret method to 'rf'
# with implementation of genetic algorithms
##################################
set.seed(12345678)
RF_GA_Tune <- caret::gafs(x = PMA_PreModelling_Train[,!names(PMA_PreModelling_Train) %in% c("Class")],
y = PMA_PreModelling_Train$Class,
iters = 10,
ntree = 50,
gafsControl = KFold_GAControl)## Fold01 1 0.7833333 (81)
## Fold01 2 0.7833333->0.7791667 ( 81-> 84, 48.6%)
## Fold01 3 0.7833333->0.7875 ( 81-> 76, 48.1%) *
## Fold01 4 0.7875->0.7875 ( 76-> 78, 45.3%)
## Fold01 5 0.7875->0.8 ( 76-> 81, 46.7%) *
## Fold01 6 0.8->0.8083333 ( 81-> 81, 55.8%) *
## Fold01 7 0.8083333->0.7791667 ( 81-> 73, 51.0%)
## Fold01 8 0.8083333->0.7916667 ( 81-> 67, 41.0%)
## Fold01 9 0.8083333->0.7875 ( 81-> 69, 41.5%)
## Fold01 10 0.8083333->0.7958333 ( 81-> 71, 50.5%)
## Fold02 1 0.790795 (61)
## Fold02 2 0.790795->0.7991632 ( 61-> 23, 18.3%) *
## Fold02 3 0.7991632->0.8200837 ( 23-> 64, 14.5%) *
## Fold02 4 0.8200837->0.7949791 ( 64-> 97, 40.0%)
## Fold02 5 0.8200837->0.8033473 ( 64-> 73, 82.7%)
## Fold02 6 0.8200837->0.7991632 ( 64-> 73, 71.2%)
## Fold02 7 0.8200837->0.8033473 ( 64-> 88, 42.1%)
## Fold02 8 0.8200837->0.7991632 ( 64-> 81, 54.3%)
## Fold02 9 0.8200837->0.8075314 ( 64-> 76, 44.3%)
## Fold02 10 0.8200837->0.7991632 ( 64-> 71, 58.8%)
## Fold03 1 0.780083 (103)
## Fold03 2 0.780083->0.7883817 (103-> 47, 31.6%) *
## Fold03 3 0.7883817->0.780083 ( 47-> 89, 33.3%)
## Fold03 4 0.7883817->0.780083 ( 47-> 54, 23.2%)
## Fold03 5 0.7883817->0.7925311 ( 47-> 47, 27.0%) *
## Fold03 6 0.7925311->0.8008299 ( 47-> 72, 26.6%) *
## Fold03 7 0.8008299->0.7966805 ( 72-> 73, 70.6%)
## Fold03 8 0.8008299->0.7966805 ( 72-> 63, 87.5%)
## Fold03 9 0.8008299->0.8049793 ( 72-> 62, 78.7%) *
## Fold03 10 0.8049793->0.7925311 ( 62-> 49, 60.9%)
## Fold04 1 0.7708333 (107)
## Fold04 2 0.7708333->0.7791667 (107->106, 99.1%) *
## Fold04 3 0.7791667->0.7875 (106-> 75, 50.8%) *
## Fold04 4 0.7875->0.8 ( 75-> 75, 100.0%) *
## Fold04 5 0.8->0.7958333 ( 75-> 82, 42.7%)
## Fold04 6 0.8->0.7875 ( 75-> 59, 50.6%)
## Fold04 7 0.8->0.7833333 ( 75-> 79, 42.6%)
## Fold04 8 0.8->0.8 ( 75-> 73, 78.3%)
## Fold04 9 0.8->0.7833333 ( 75-> 67, 54.3%)
## Fold04 10 0.8->0.8 ( 75-> 92, 50.5%)
## Fold05 1 0.7842324 (99)
## Fold05 2 0.7842324->0.780083 ( 99-> 30, 22.9%)
## Fold05 3 0.7842324->0.7925311 ( 99-> 40, 31.1%) *
## Fold05 4 0.7925311->0.7966805 ( 40-> 88, 25.5%) *
## Fold05 5 0.7966805->0.8008299 ( 88-> 50, 34.0%) *
## Fold05 6 0.8008299->0.780083 ( 50-> 48, 81.5%)
## Fold05 7 0.8008299->0.8008299 ( 50-> 35, 28.8%)
## Fold05 8 0.8008299->0.7925311 ( 50-> 52, 29.1%)
## Fold05 9 0.8008299->0.8008299 ( 50-> 51, 34.7%)
## Fold05 10 0.8008299->0.7925311 ( 50-> 51, 34.7%)
## Fold06 1 0.7759336 (11)
## Fold06 2 0.7759336->0.7759336 ( 11-> 70, 9.5%)
## Fold06 3 0.7759336->0.7759336 ( 11-> 56, 6.3%)
## Fold06 4 0.7759336->0.7842324 ( 11-> 66, 8.5%) *
## Fold06 5 0.7842324->0.7842324 ( 66-> 70, 54.5%)
## Fold06 6 0.7842324->0.780083 ( 66-> 61, 47.7%)
## Fold06 7 0.7842324->0.7883817 ( 66-> 53, 45.1%) *
## Fold06 8 0.7883817->0.7925311 ( 53-> 53, 49.3%) *
## Fold06 9 0.7925311->0.7925311 ( 53-> 71, 51.2%)
## Fold06 10 0.7925311->0.7925311 ( 53-> 31, 47.4%)
## Fold07 1 0.7883817 (90)
## Fold07 2 0.7883817->0.7966805 ( 90-> 34, 21.6%) *
## Fold07 3 0.7966805->0.8049793 ( 34-> 69, 22.6%) *
## Fold07 4 0.8049793->0.7925311 ( 69-> 89, 50.5%)
## Fold07 5 0.8049793->0.8008299 ( 69-> 99, 42.4%)
## Fold07 6 0.8049793->0.8174274 ( 69->101, 42.9%) *
## Fold07 7 0.8174274->0.7966805 (101-> 76, 56.6%)
## Fold07 8 0.8174274->0.8049793 (101-> 72, 57.3%)
## Fold07 9 0.8174274->0.813278 (101-> 61, 48.6%)
## Fold07 10 0.8174274->0.8008299 (101-> 61, 48.6%)
## Fold08 1 0.7875 (76)
## Fold08 2 0.7875->0.7958333 ( 76->111, 55.8%) *
## Fold08 3 0.7958333->0.7791667 (111-> 67, 50.8%)
## Fold08 4 0.7958333->0.7875 (111-> 57, 46.1%)
## Fold08 5 0.7958333->0.7916667 (111-> 52, 40.5%)
## Fold08 6 0.7958333->0.8 (111-> 69, 52.5%) *
## Fold08 7 0.8->0.8 ( 69-> 55, 39.3%)
## Fold08 8 0.8->0.7958333 ( 69-> 62, 42.4%)
## Fold08 9 0.8->0.7833333 ( 69-> 70, 51.1%)
## Fold08 10 0.8->0.8125 ( 69-> 45, 37.3%) *
## Fold09 1 0.7991632 (61)
## Fold09 2 0.7991632->0.7949791 ( 61->113, 46.2%)
## Fold09 3 0.7991632->0.7991632 ( 61-> 79, 38.6%)
## Fold09 4 0.7991632->0.7866109 ( 61-> 32, 32.9%)
## Fold09 5 0.7991632->0.8117155 ( 61-> 55, 46.8%) *
## Fold09 6 0.8117155->0.7991632 ( 55-> 76, 32.3%)
## Fold09 7 0.8117155->0.7949791 ( 55-> 47, 32.5%)
## Fold09 8 0.8117155->0.8033473 ( 55-> 67, 31.2%)
## Fold09 9 0.8117155->0.8075314 ( 55-> 44, 32.0%)
## Fold09 10 0.8117155->0.8075314 ( 55-> 55, 27.9%)
## Fold10 1 0.7925311 (86)
## Fold10 2 0.7925311->0.7883817 ( 86-> 77, 49.5%)
## Fold10 3 0.7925311->0.7925311 ( 86-> 77, 49.5%)
## Fold10 4 0.7925311->0.7966805 ( 86-> 95, 52.1%) *
## Fold10 5 0.7966805->0.8049793 ( 95-> 45, 33.3%) *
## Fold10 6 0.8049793->0.8008299 ( 45-> 45, 100.0%)
## Fold10 7 0.8049793->0.8008299 ( 45-> 71, 33.3%)
## Fold10 8 0.8049793->0.7883817 ( 45-> 96, 33.0%)
## Fold10 9 0.8049793->0.780083 ( 45-> 85, 36.8%)
## Fold10 10 0.8049793->0.8008299 ( 45-> 64, 65.2%)
## + final GA
## 1 0.7865169 (93)
## 2 0.7865169->0.8052434 ( 93-> 23, 16.0%) *
## 3 0.8052434->0.8089888 ( 23-> 72, 20.3%) *
## 4 0.8089888->0.7940075 ( 72-> 87, 54.4%)
## 5 0.8089888->0.7940075 ( 72-> 65, 38.4%)
## 6 0.8089888->0.7865169 ( 72->100, 55.0%)
## 7 0.8089888->0.8052434 ( 72->100, 49.6%)
## 8 0.8089888->0.8164794 ( 72-> 79, 48.0%) *
## 9 0.8164794->0.7940075 ( 79->100, 62.7%)
## 10 0.8164794->0.8014981 ( 79->103, 64.0%)
## + final model##################################
# Reporting the cross-validation results
# for the train set
##################################
RF_GA_Tune##
## Genetic Algorithm Feature Selection
##
## 267 samples
## 127 predictors
## 2 classes: 'Impaired', 'Control'
##
## Maximum generations: 10
## Population per generation: 50
## Crossover probability: 0.8
## Mutation probability: 0.1
## Elitism: 0
##
## Internal performance values: Accuracy, Kappa
## Subset selection driven to maximize internal Accuracy
##
## External performance values: Accuracy, Kappa
## Best iteration chose by maximizing external Accuracy
## External resampling method: Cross-Validated (10 fold)
##
## During resampling:
## * the top 5 selected variables (out of a possible 127):
## MMP10 (100%), Cystatin_C (90%), PAI_1 (90%), Angiotensinogen (80%), Calbindin (80%)
## * on average, 63.1 variables were selected (min = 45, max = 101)
##
## In the final search using the entire training set:
## * 93 features selected at iteration 1 including:
## ACE_CD143_Angiotensin_Converti, ACTH_Adrenocorticotropic_Hormon, AXL, Alpha_1_Antichymotrypsin, Alpha_1_Microglobulin ...
## * external performance at this iteration is
##
## Accuracy Kappa
## 0.7984 0.3829RF_GA_Tune$fit##
## Call:
## randomForest(x = x, y = y, ntree = 50)
## Type of random forest: classification
## Number of trees: 50
## No. of variables tried at each split: 9
##
## OOB estimate of error rate: 22.1%
## Confusion matrix:
## Impaired Control class.error
## Impaired 27 46 0.63013699
## Control 13 181 0.06701031RF_GA_Tune$averages## Iter Accuracy Kappa
## 1 1 0.7984229 0.3828759
## 2 2 0.7800265 0.3073912
## 3 3 0.7752137 0.3112097
## 4 4 0.7875865 0.3592537
## 5 5 0.7649267 0.2534131
## 6 6 0.7908730 0.3560893
## 7 7 0.7874339 0.3312224
## 8 8 0.7687729 0.2740272
## 9 9 0.7794770 0.3112902
## 10 10 0.7803114 0.3393190(RF_GA_Train_Accuracy <- RF_GA_Tune$averages[RF_GA_Tune$averages$Accuracy==max(RF_GA_Tune$averages$Accuracy),
c("Accuracy")])## [1] 0.7984229##################################
# Independently evaluating the model and
# reporting the independent evaluation results
# on the test set
##################################
RF_GA_Test <- data.frame(RF_GA_Observed = PMA_PreModelling_Test$Class,
RF_GA_Predicted = predict(RF_GA_Tune,
PMA_PreModelling_Test[,!names(PMA_PreModelling_Test) %in% c("Class")],
type = "raw"))
RF_GA_Test## RF_GA_Observed RF_GA_Predicted.pred RF_GA_Predicted.Impaired
## 4 Control Control 0.20
## 10 Impaired Control 0.28
## 13 Impaired Control 0.14
## 15 Control Control 0.26
## 27 Impaired Control 0.18
## 32 Impaired Control 0.16
## 33 Impaired Control 0.26
## 49 Control Control 0.06
## 52 Impaired Impaired 0.68
## 54 Control Control 0.14
## 58 Control Control 0.42
## 66 Control Control 0.14
## 79 Control Control 0.16
## 87 Impaired Control 0.30
## 89 Control Control 0.20
## 91 Control Control 0.38
## 92 Control Control 0.10
## 101 Impaired Impaired 0.60
## 102 Control Control 0.10
## 106 Control Control 0.32
## 116 Control Control 0.30
## 119 Control Control 0.18
## 120 Control Control 0.12
## 122 Control Control 0.18
## 125 Control Control 0.22
## 127 Control Control 0.16
## 138 Control Control 0.44
## 142 Control Control 0.24
## 150 Control Control 0.18
## 151 Control Control 0.30
## 164 Impaired Control 0.24
## 173 Control Control 0.14
## 187 Control Control 0.18
## 188 Control Control 0.20
## 196 Control Impaired 0.50
## 199 Control Control 0.26
## 203 Control Control 0.28
## 204 Control Control 0.42
## 206 Impaired Impaired 0.58
## 207 Control Control 0.12
## 209 Control Control 0.16
## 211 Control Control 0.06
## 217 Control Control 0.22
## 221 Impaired Impaired 0.54
## 222 Control Control 0.26
## 235 Control Control 0.06
## 238 Control Control 0.22
## 248 Impaired Control 0.20
## 252 Control Control 0.08
## 259 Impaired Control 0.28
## 266 Control Control 0.14
## 276 Impaired Impaired 0.58
## 280 Impaired Control 0.26
## 284 Control Control 0.28
## 285 Control Control 0.12
## 286 Control Control 0.12
## 288 Control Control 0.06
## 293 Impaired Control 0.26
## 295 Control Control 0.26
## 296 Impaired Control 0.46
## 300 Control Control 0.38
## 309 Control Control 0.14
## 310 Impaired Control 0.30
## 318 Control Control 0.22
## 319 Control Control 0.16
## 328 Control Control 0.08
## RF_GA_Predicted.Control
## 4 0.80
## 10 0.72
## 13 0.86
## 15 0.74
## 27 0.82
## 32 0.84
## 33 0.74
## 49 0.94
## 52 0.32
## 54 0.86
## 58 0.58
## 66 0.86
## 79 0.84
## 87 0.70
## 89 0.80
## 91 0.62
## 92 0.90
## 101 0.40
## 102 0.90
## 106 0.68
## 116 0.70
## 119 0.82
## 120 0.88
## 122 0.82
## 125 0.78
## 127 0.84
## 138 0.56
## 142 0.76
## 150 0.82
## 151 0.70
## 164 0.76
## 173 0.86
## 187 0.82
## 188 0.80
## 196 0.50
## 199 0.74
## 203 0.72
## 204 0.58
## 206 0.42
## 207 0.88
## 209 0.84
## 211 0.94
## 217 0.78
## 221 0.46
## 222 0.74
## 235 0.94
## 238 0.78
## 248 0.80
## 252 0.92
## 259 0.72
## 266 0.86
## 276 0.42
## 280 0.74
## 284 0.72
## 285 0.88
## 286 0.88
## 288 0.94
## 293 0.74
## 295 0.74
## 296 0.54
## 300 0.62
## 309 0.86
## 310 0.70
## 318 0.78
## 319 0.84
## 328 0.92##################################
# Reporting the independent evaluation results
# for the test set
##################################
(RF_GA_Test_Accuracy <- Accuracy(y_pred = RF_GA_Test$RF_GA_Predicted.pred,
y_true = RF_GA_Test$RF_GA_Observed))## [1] 0.78787881.5.4 Linear Discriminant Analysis Without SA and GA (LDA_FULL)
Linear Discriminant Analysis finds a linear combination of features that best separates the classes in a data set by projecting the data onto a lower-dimensional space that maximizes the separation between the classes. The algorithm searches for a set of linear discriminants that maximize the ratio of between-class variance to within-class variance by evaluating directions in the feature space that best separate the different classes of data. LDA assumes that the data has a Gaussian distribution and that the covariance matrices of the different classes are equal, in addition to the data being linearly separable by the presence of a linear decision boundary can accurately classify the different classes.
[A] The linear discriminant analysis model from the MASS package was implemented without simulated annealing and genetic algorithms through the caret package.
[B] The model does not contain any hyperparameter.
[C] The cross-validated model performance of the final model is summarized as follows:
[C.1] Final model configuration is fixed due to the absence of a hyperparameter
[C.2] Accuracy = 0.76754
[D] The model does not allow for ranking of predictors in terms of variable importance.
[E] The independent test model performance of the final model is summarized as follows:
[E.1] Accuracy = 0.75757
Code Chunk | Output
##################################
# Converting all predictors to numeric
# for both train and test data
##################################
for (i in 1:ncol(PMA_PreModelling_Train)){
if (names(PMA_PreModelling_Train)[i]!="Class"){
PMA_PreModelling_Train[,i] <- as.numeric(PMA_PreModelling_Train[,i])
}
}
summary(PMA_PreModelling_Train)## ACE_CD143_Angiotensin_Converti ACTH_Adrenocorticotropic_Hormon
## Min. :-0.6756 Min. :-2.207
## 1st Qu.: 0.9462 1st Qu.:-1.715
## Median : 1.3013 Median :-1.561
## Mean : 1.3198 Mean :-1.538
## 3rd Qu.: 1.7191 3rd Qu.:-1.347
## Max. : 2.8398 Max. :-0.844
## AXL Adiponectin Alpha_1_Antichymotrypsin
## Min. :-0.9230 Min. :-6.725 Min. :0.2624
## 1st Qu.: 0.0000 1st Qu.:-5.669 1st Qu.:1.1314
## Median : 0.2804 Median :-5.185 Median :1.3610
## Mean : 0.3093 Mean :-5.201 Mean :1.3605
## 3rd Qu.: 0.6077 3rd Qu.:-4.780 3rd Qu.:1.5892
## Max. : 1.5214 Max. :-3.507 Max. :2.3026
## Alpha_1_Antitrypsin Alpha_1_Microglobulin Alpha_2_Macroglobulin
## Min. :-17.028 Min. :-4.343 Min. :-289.68
## 1st Qu.:-14.071 1st Qu.:-3.270 1st Qu.:-186.64
## Median :-13.004 Median :-2.937 Median :-160.01
## Mean :-13.052 Mean :-2.932 Mean :-158.61
## 3rd Qu.:-12.096 3rd Qu.:-2.590 3rd Qu.:-134.62
## Max. : -8.192 Max. :-1.772 Max. : -59.46
## Angiopoietin_2_ANG_2 Angiotensinogen Apolipoprotein_A_IV Apolipoprotein_A1
## Min. :-0.5447 Min. :1.752 Min. :-2.9565 Min. :-8.680
## 1st Qu.: 0.4700 1st Qu.:2.119 1st Qu.:-2.1203 1st Qu.:-7.763
## Median : 0.6419 Median :2.320 Median :-1.8326 Median :-7.470
## Mean : 0.6730 Mean :2.318 Mean :-1.8544 Mean :-7.483
## 3rd Qu.: 0.8755 3rd Qu.:2.497 3rd Qu.:-1.6094 3rd Qu.:-7.209
## Max. : 1.5261 Max. :2.881 Max. :-0.7765 Max. :-6.166
## Apolipoprotein_A2 Apolipoprotein_B Apolipoprotein_CI Apolipoprotein_CIII
## Min. :-1.8971 Min. :-9.937 Min. :-3.3242 Min. :-3.689
## 1st Qu.:-0.9676 1st Qu.:-6.630 1st Qu.:-1.8326 1st Qu.:-2.773
## Median :-0.6733 Median :-5.703 Median :-1.6094 Median :-2.526
## Mean :-0.6354 Mean :-5.578 Mean :-1.5833 Mean :-2.494
## 3rd Qu.:-0.3147 3rd Qu.:-4.539 3rd Qu.:-1.3667 3rd Qu.:-2.207
## Max. : 0.9555 Max. :-2.153 Max. :-0.2744 Max. :-1.238
## Apolipoprotein_D Apolipoprotein_E Apolipoprotein_H
## Min. :0.470 Min. :0.5911 Min. :-2.23379
## 1st Qu.:1.209 1st Qu.:2.3344 1st Qu.:-0.59782
## Median :1.411 Median :2.8181 Median :-0.37005
## Mean :1.440 Mean :2.8062 Mean :-0.32122
## 3rd Qu.:1.668 3rd Qu.:3.2863 3rd Qu.:-0.06112
## Max. :2.272 Max. :5.4442 Max. : 0.92696
## B_Lymphocyte_Chemoattractant_BL BMP_6 Beta_2_Microglobulin
## Min. :0.7318 Min. :-2.7612 Min. :-0.54473
## 1st Qu.:1.6731 1st Qu.:-2.1516 1st Qu.:-0.04082
## Median :1.9805 Median :-1.8774 Median : 0.18232
## Mean :2.0175 Mean :-1.9114 Mean : 0.16757
## 3rd Qu.:2.3714 3rd Qu.:-1.6753 3rd Qu.: 0.33647
## Max. :4.0237 Max. :-0.8166 Max. : 0.99325
## Betacellulin C_Reactive_Protein CD40 CD5L
## Min. :10.00 Min. :-8.517 Min. :-1.8644 Min. :-1.23787
## 1st Qu.:42.00 1st Qu.:-6.645 1st Qu.:-1.3761 1st Qu.:-0.35667
## Median :51.00 Median :-5.843 Median :-1.2734 Median :-0.06188
## Mean :51.01 Mean :-5.874 Mean :-1.2584 Mean :-0.05310
## 3rd Qu.:59.00 3rd Qu.:-5.083 3rd Qu.:-1.1238 3rd Qu.: 0.26236
## Max. :82.00 Max. :-2.937 Max. :-0.5475 Max. : 1.16315
## Calbindin Calcitonin CgA Clusterin_Apo_J
## Min. :10.96 Min. :-0.7134 Min. :135.6 Min. :1.872
## 1st Qu.:19.77 1st Qu.: 0.9555 1st Qu.:278.0 1st Qu.:2.708
## Median :22.25 Median : 1.6487 Median :331.5 Median :2.890
## Mean :22.43 Mean : 1.6788 Mean :333.3 Mean :2.882
## 3rd Qu.:24.80 3rd Qu.: 2.2824 3rd Qu.:392.1 3rd Qu.:3.045
## Max. :33.78 Max. : 3.8918 Max. :535.4 Max. :3.584
## Complement_3 Complement_Factor_H Connective_Tissue_Growth_Factor
## Min. :-23.387 Min. :-0.8387 Min. :0.1823
## 1st Qu.:-17.567 1st Qu.: 2.7531 1st Qu.:0.6419
## Median :-15.524 Median : 3.6000 Median :0.7885
## Mean :-15.610 Mean : 3.5541 Mean :0.7739
## 3rd Qu.:-13.882 3rd Qu.: 4.2548 3rd Qu.:0.9163
## Max. : -9.563 Max. : 7.6238 Max. :1.4110
## Cortisol Creatine_Kinase_MB Cystatin_C EGF_R
## Min. : 0.10 Min. :-1.872 Min. :7.432 Min. :-1.36135
## 1st Qu.: 9.80 1st Qu.:-1.724 1st Qu.:8.321 1st Qu.:-0.85727
## Median :12.00 Median :-1.671 Median :8.564 Median :-0.68354
## Mean :11.98 Mean :-1.674 Mean :8.586 Mean :-0.70130
## 3rd Qu.:14.00 3rd Qu.:-1.626 3rd Qu.:8.839 3rd Qu.:-0.54612
## Max. :29.00 Max. :-1.384 Max. :9.694 Max. :-0.06112
## EN_RAGE ENA_78 Eotaxin_3 FAS
## Min. :-8.3774 Min. :-1.405 Min. : 7.00 Min. :-1.5141
## 1st Qu.:-4.1997 1st Qu.:-1.381 1st Qu.: 44.00 1st Qu.:-0.7133
## Median :-3.6497 Median :-1.374 Median : 59.00 Median :-0.5276
## Mean :-3.6353 Mean :-1.372 Mean : 58.17 Mean :-0.5291
## 3rd Qu.:-3.1466 3rd Qu.:-1.364 3rd Qu.: 70.00 3rd Qu.:-0.3147
## Max. :-0.3857 Max. :-1.339 Max. :107.00 Max. : 0.3365
## FSH_Follicle_Stimulation_Hormon Fas_Ligand Fatty_Acid_Binding_Protein
## Min. :-2.11511 Min. :-0.1536 Min. :-1.0441
## 1st Qu.:-1.46606 1st Qu.: 2.3415 1st Qu.: 0.7998
## Median :-1.13570 Median : 3.1015 Median : 1.3865
## Mean :-1.14259 Mean : 2.9680 Mean : 1.3529
## 3rd Qu.:-0.87620 3rd Qu.: 3.6950 3rd Qu.: 1.8847
## Max. : 0.09715 Max. : 7.6328 Max. : 3.7055
## Ferritin Fetuin_A Fibrinogen GRO_alpha
## Min. :0.6077 Min. :0.470 Min. :-8.874 Min. :1.271
## 1st Qu.:2.2895 1st Qu.:1.099 1st Qu.:-7.717 1st Qu.:1.351
## Median :2.7749 Median :1.308 Median :-7.323 Median :1.382
## Mean :2.7646 Mean :1.350 Mean :-7.356 Mean :1.378
## 3rd Qu.:3.2915 3rd Qu.:1.609 3rd Qu.:-7.013 3rd Qu.:1.406
## Max. :4.6333 Max. :2.251 Max. :-5.843 Max. :1.495
## Gamma_Interferon_induced_Monokin Glutathione_S_Transferase_alpha
## Min. :2.393 Min. :0.5238
## 1st Qu.:2.707 1st Qu.:0.8439
## Median :2.783 Median :0.9677
## Mean :2.786 Mean :0.9512
## 3rd Qu.:2.873 3rd Qu.:1.0344
## Max. :3.065 Max. :1.3176
## HB_EGF HCC_4 Hepatocyte_Growth_Factor_HGF I_309
## Min. : 2.103 Min. :-4.510 Min. :-0.6349 Min. :1.758
## 1st Qu.: 5.786 1st Qu.:-3.730 1st Qu.: 0.0000 1st Qu.:2.708
## Median : 6.703 Median :-3.507 Median : 0.1823 Median :2.944
## Mean : 6.833 Mean :-3.500 Mean : 0.1963 Mean :2.958
## 3rd Qu.: 7.865 3rd Qu.:-3.270 3rd Qu.: 0.4055 3rd Qu.:3.219
## Max. :10.695 Max. :-2.120 Max. : 0.8755 Max. :4.143
## ICAM_1 IGF_BP_2 IL_11 IL_13
## Min. :-1.5332 Min. :4.635 Min. :1.755 Min. :1.259
## 1st Qu.:-0.8298 1st Qu.:5.179 1st Qu.:3.706 1st Qu.:1.274
## Median :-0.5903 Median :5.323 Median :4.805 Median :1.283
## Mean :-0.5908 Mean :5.317 Mean :4.725 Mean :1.284
## 3rd Qu.:-0.3828 3rd Qu.:5.453 3rd Qu.:5.776 3rd Qu.:1.290
## Max. : 0.5171 Max. :5.948 Max. :8.491 Max. :1.321
## IL_16 IL_17E IL_1alpha IL_3
## Min. :1.187 Min. :1.052 Min. :-8.517 Min. :-5.915
## 1st Qu.:2.521 1st Qu.:4.149 1st Qu.:-7.824 1st Qu.:-4.269
## Median :2.909 Median :4.749 Median :-7.524 Median :-3.912
## Mean :2.929 Mean :4.855 Mean :-7.514 Mean :-3.941
## 3rd Qu.:3.351 3rd Qu.:5.631 3rd Qu.:-7.264 3rd Qu.:-3.631
## Max. :4.937 Max. :8.952 Max. :-5.952 Max. :-2.453
## IL_4 IL_5 IL_6 IL_6_Receptor
## Min. :0.5306 Min. :-1.4271 Min. :-1.5343 Min. :-0.67562
## 1st Qu.:1.4586 1st Qu.:-0.1221 1st Qu.:-0.4127 1st Qu.:-0.12541
## Median :1.8083 Median : 0.1823 Median :-0.1599 Median : 0.09669
## Mean :1.7732 Mean : 0.1866 Mean :-0.1540 Mean : 0.09492
## 3rd Qu.:2.1459 3rd Qu.: 0.4700 3rd Qu.: 0.1410 3rd Qu.: 0.35404
## Max. :3.0445 Max. : 1.9459 Max. : 1.8138 Max. : 0.83099
## IL_7 IL_8 IP_10_Inducible_Protein_10 IgA
## Min. :0.5598 Min. :1.574 Min. :4.317 Min. :-10.520
## 1st Qu.:2.1548 1st Qu.:1.680 1st Qu.:5.398 1st Qu.: -6.645
## Median :2.7934 Median :1.705 Median :5.753 Median : -6.119
## Mean :2.8392 Mean :1.704 Mean :5.755 Mean : -6.121
## 3rd Qu.:3.7055 3rd Qu.:1.728 3rd Qu.:6.064 3rd Qu.: -5.573
## Max. :5.7056 Max. :1.807 Max. :7.501 Max. : -4.200
## Insulin Kidney_Injury_Molecule_1_KIM_1 LOX_1
## Min. :-2.1692 Min. :-1.256 Min. :0.000
## 1st Qu.:-1.4466 1st Qu.:-1.204 1st Qu.:1.030
## Median :-1.2462 Median :-1.183 Median :1.281
## Mean :-1.2329 Mean :-1.185 Mean :1.283
## 3rd Qu.:-1.0340 3rd Qu.:-1.164 3rd Qu.:1.526
## Max. :-0.1586 Max. :-1.105 Max. :2.272
## Leptin Lipoprotein_a MCP_1 MCP_2
## Min. :-2.1468 Min. :-6.812 Min. :5.826 Min. :0.4006
## 1st Qu.:-1.6996 1st Qu.:-5.308 1st Qu.:6.319 1st Qu.:1.5304
## Median :-1.5047 Median :-4.605 Median :6.494 Median :1.8528
## Mean :-1.5042 Mean :-4.417 Mean :6.497 Mean :1.8691
## 3rd Qu.:-1.3295 3rd Qu.:-3.490 3rd Qu.:6.678 3rd Qu.:2.1821
## Max. :-0.6206 Max. :-1.386 Max. :7.230 Max. :4.0237
## MIF MIP_1alpha MIP_1beta MMP_2
## Min. :-2.847 Min. :0.9346 Min. :1.946 Min. :0.09809
## 1st Qu.:-2.120 1st Qu.:3.3377 1st Qu.:2.565 1st Qu.:2.33214
## Median :-1.897 Median :4.0495 Median :2.833 Median :2.81512
## Mean :-1.864 Mean :4.0489 Mean :2.814 Mean :2.87534
## 3rd Qu.:-1.661 3rd Qu.:4.6857 3rd Qu.:3.045 3rd Qu.:3.55121
## Max. :-0.844 Max. :6.7959 Max. :4.007 Max. :5.35895
## MMP_3 MMP10 MMP7 Myoglobin
## Min. :-4.4228 Min. :-4.934 Min. :-8.3975 Min. :-3.1701
## 1st Qu.:-2.7489 1st Qu.:-3.938 1st Qu.:-4.8199 1st Qu.:-2.0402
## Median :-2.4534 Median :-3.650 Median :-3.7735 Median :-1.4697
## Mean :-2.4455 Mean :-3.635 Mean :-3.7894 Mean :-1.3671
## 3rd Qu.:-2.1203 3rd Qu.:-3.352 3rd Qu.:-2.7140 3rd Qu.:-0.7988
## Max. :-0.5276 Max. :-2.207 Max. :-0.2222 Max. : 1.7750
## NT_proBNP NrCAM Osteopontin PAI_1
## Min. :3.178 Min. :2.639 Min. :4.111 Min. :-0.99085
## 1st Qu.:4.350 1st Qu.:3.998 1st Qu.:4.963 1st Qu.:-0.16655
## Median :4.554 Median :4.394 Median :5.187 Median : 0.09396
## Mean :4.552 Mean :4.362 Mean :5.204 Mean : 0.07743
## 3rd Qu.:4.775 3rd Qu.:4.749 3rd Qu.:5.442 3rd Qu.: 0.32005
## Max. :5.886 Max. :6.011 Max. :6.308 Max. : 1.16611
## PAPP_A PLGF PYY Pancreatic_polypeptide
## Min. :-3.311 Min. :2.485 Min. :2.186 Min. :-2.12026
## 1st Qu.:-2.936 1st Qu.:3.638 1st Qu.:2.833 1st Qu.:-0.52763
## Median :-2.871 Median :3.871 Median :2.996 Median :-0.04082
## Mean :-2.854 Mean :3.912 Mean :3.015 Mean :-0.01323
## 3rd Qu.:-2.749 3rd Qu.:4.205 3rd Qu.:3.178 3rd Qu.: 0.53063
## Max. :-2.520 Max. :5.170 Max. :3.932 Max. : 1.93152
## Prolactin Prostatic_Acid_Phosphatase Protein_S
## Min. :-1.30933 Min. :-1.934 Min. :-3.338
## 1st Qu.:-0.13926 1st Qu.:-1.717 1st Qu.:-2.464
## Median : 0.00000 Median :-1.690 Median :-2.259
## Mean : 0.04495 Mean :-1.685 Mean :-2.240
## 3rd Qu.: 0.25799 3rd Qu.:-1.654 3rd Qu.:-2.000
## Max. : 0.99325 Max. :-1.424 Max. :-1.221
## Pulmonary_and_Activation_Regulat RANTES Resistin
## Min. :-2.5133 Min. :-7.222 Min. :-34.967
## 1st Qu.:-1.8326 1st Qu.:-6.725 1st Qu.:-21.468
## Median :-1.5141 Median :-6.502 Median :-17.466
## Mean :-1.4880 Mean :-6.511 Mean :-17.641
## 3rd Qu.:-1.1712 3rd Qu.:-6.320 3rd Qu.:-13.501
## Max. :-0.2744 Max. :-5.547 Max. : -2.239
## S100b SGOT SHBG SOD
## Min. :0.1874 Min. :-1.3471 Min. :-4.135 Min. :4.317
## 1st Qu.:1.0012 1st Qu.:-0.6349 1st Qu.:-2.813 1st Qu.:5.094
## Median :1.2544 Median :-0.4005 Median :-2.489 Median :5.366
## Mean :1.2505 Mean :-0.4057 Mean :-2.477 Mean :5.336
## 3rd Qu.:1.4996 3rd Qu.:-0.1985 3rd Qu.:-2.120 3rd Qu.:5.583
## Max. :2.3726 Max. : 0.7419 Max. :-1.109 Max. :6.317
## Serum_Amyloid_P Sortilin Stem_Cell_Factor TGF_alpha
## Min. :-7.506 Min. :1.654 Min. :2.251 Min. : 6.843
## 1st Qu.:-6.377 1st Qu.:3.343 1st Qu.:3.045 1st Qu.: 8.859
## Median :-6.032 Median :3.867 Median :3.296 Median : 9.919
## Mean :-6.017 Mean :3.852 Mean :3.301 Mean : 9.801
## 3rd Qu.:-5.655 3rd Qu.:4.371 3rd Qu.:3.526 3rd Qu.:10.695
## Max. :-4.646 Max. :6.225 Max. :4.277 Max. :13.827
## TIMP_1 TNF_RII TRAIL_R3 TTR_prealbumin
## Min. : 1.742 Min. :-1.6607 Min. :-1.2107 Min. :2.485
## 1st Qu.:10.490 1st Qu.:-0.8210 1st Qu.:-0.7008 1st Qu.:2.773
## Median :11.565 Median :-0.5978 Median :-0.5317 Median :2.833
## Mean :11.750 Mean :-0.5939 Mean :-0.5394 Mean :2.854
## 3rd Qu.:12.697 3rd Qu.:-0.3784 3rd Qu.:-0.3849 3rd Qu.:2.944
## Max. :18.881 Max. : 0.4700 Max. : 0.2694 Max. :3.332
## Tamm_Horsfall_Protein_THP Thrombomodulin Thrombopoietin
## Min. :-3.206 Min. :-2.0377 Min. :-1.53957
## 1st Qu.:-3.137 1st Qu.:-1.6256 1st Qu.:-0.88645
## Median :-3.117 Median :-1.4920 Median :-0.75100
## Mean :-3.116 Mean :-1.5050 Mean :-0.75419
## 3rd Qu.:-3.096 3rd Qu.:-1.3406 3rd Qu.:-0.62887
## Max. :-2.995 Max. :-0.8166 Max. : 0.09762
## Thymus_Expressed_Chemokine_TECK Thyroid_Stimulating_Hormone
## Min. :1.508 Min. :-6.190
## 1st Qu.:3.343 1st Qu.:-4.962
## Median :3.810 Median :-4.510
## Mean :3.848 Mean :-4.499
## 3rd Qu.:4.316 3rd Qu.:-4.017
## Max. :6.225 Max. :-1.715
## Thyroxine_Binding_Globulin Tissue_Factor Transferrin
## Min. :-2.4769 Min. :-0.2107 Min. :1.932
## 1st Qu.:-1.7720 1st Qu.: 0.8329 1st Qu.:2.708
## Median :-1.5141 Median : 1.2238 Median :2.890
## Mean :-1.4788 Mean : 1.1702 Mean :2.909
## 3rd Qu.:-1.2379 3rd Qu.: 1.4816 3rd Qu.:3.091
## Max. :-0.2107 Max. : 2.4849 Max. :3.761
## Trefoil_Factor_3_TFF3 VCAM_1 VEGF Vitronectin
## Min. :-4.744 Min. :1.723 Min. :11.83 Min. :-1.42712
## 1st Qu.:-4.135 1st Qu.:2.485 1st Qu.:15.77 1st Qu.:-0.51083
## Median :-3.863 Median :2.708 Median :17.08 Median :-0.30111
## Mean :-3.876 Mean :2.688 Mean :16.99 Mean :-0.28473
## 3rd Qu.:-3.650 3rd Qu.:2.890 3rd Qu.:18.10 3rd Qu.:-0.03564
## Max. :-2.957 Max. :3.689 Max. :22.38 Max. : 0.53063
## von_Willebrand_Factor Class E4 E3
## Min. :-4.991 Impaired: 73 Min. :1.000 Min. :1.000
## 1st Qu.:-4.200 Control :194 1st Qu.:1.000 1st Qu.:2.000
## Median :-3.912 Median :1.000 Median :2.000
## Mean :-3.906 Mean :1.401 Mean :1.918
## 3rd Qu.:-3.612 3rd Qu.:2.000 3rd Qu.:2.000
## Max. :-2.957 Max. :2.000 Max. :2.000
## E2
## Min. :1.000
## 1st Qu.:1.000
## Median :1.000
## Mean :1.161
## 3rd Qu.:1.000
## Max. :2.000for (i in 1:ncol(PMA_PreModelling_Test)){
if (names(PMA_PreModelling_Test)[i]!="Class"){
PMA_PreModelling_Test[,i] <- as.numeric(PMA_PreModelling_Test[,i])
}
}
summary(PMA_PreModelling_Test)## ACE_CD143_Angiotensin_Converti ACTH_Adrenocorticotropic_Hormon
## Min. :-0.5473 Min. :-2.2073
## 1st Qu.: 0.9462 1st Qu.:-1.7148
## Median : 1.3013 Median :-1.5374
## Mean : 1.3105 Mean :-1.5311
## 3rd Qu.: 1.6320 3rd Qu.:-1.3863
## Max. : 3.0890 Max. :-0.7985
## AXL Adiponectin Alpha_1_Antichymotrypsin
## Min. :-0.73509 Min. :-7.059 Min. :0.1823
## 1st Qu.:-0.08175 1st Qu.:-5.737 1st Qu.:1.0647
## Median : 0.28035 Median :-5.360 Median :1.3083
## Mean : 0.25373 Mean :-5.298 Mean :1.3077
## 3rd Qu.: 0.60768 3rd Qu.:-4.917 3rd Qu.:1.5686
## Max. : 1.28634 Max. :-3.474 Max. :2.2192
## Alpha_1_Antitrypsin Alpha_1_Microglobulin Alpha_2_Macroglobulin
## Min. :-18.17 Min. :-4.135 Min. :-238.64
## 1st Qu.:-14.70 1st Qu.:-3.284 1st Qu.:-186.64
## Median :-13.59 Median :-3.006 Median :-162.93
## Mean :-13.49 Mean :-2.983 Mean :-162.89
## 3rd Qu.:-12.31 3rd Qu.:-2.674 3rd Qu.:-136.53
## Max. :-10.06 Max. :-1.897 Max. : -50.17
## Angiopoietin_2_ANG_2 Angiotensinogen Apolipoprotein_A_IV Apolipoprotein_A1
## Min. :-0.05129 Min. :1.710 Min. :-2.749 Min. :-8.568
## 1st Qu.: 0.35372 1st Qu.:2.068 1st Qu.:-2.186 1st Qu.:-7.818
## Median : 0.55921 Median :2.276 Median :-1.897 Median :-7.497
## Mean : 0.60278 Mean :2.274 Mean :-1.867 Mean :-7.488
## 3rd Qu.: 0.78846 3rd Qu.:2.430 3rd Qu.:-1.526 3rd Qu.:-7.176
## Max. : 1.77495 Max. :2.752 Max. :-1.109 Max. :-6.645
## Apolipoprotein_A2 Apolipoprotein_B Apolipoprotein_CI Apolipoprotein_CIII
## Min. :-1.9661 Min. :-8.192 Min. :-2.847 Min. :-3.863
## 1st Qu.:-0.9416 1st Qu.:-6.748 1st Qu.:-1.897 1st Qu.:-2.781
## Median :-0.7032 Median :-5.819 Median :-1.609 Median :-2.557
## Mean :-0.6902 Mean :-5.649 Mean :-1.625 Mean :-2.523
## 3rd Qu.:-0.3533 3rd Qu.:-4.603 3rd Qu.:-1.309 3rd Qu.:-2.231
## Max. : 0.5306 Max. :-2.339 Max. :-0.462 Max. :-1.386
## Apolipoprotein_D Apolipoprotein_E Apolipoprotein_H
## Min. :0.2624 Min. :0.6626 Min. :-1.1609
## 1st Qu.:1.1314 1st Qu.:2.1526 1st Qu.:-0.5317
## Median :1.3863 Median :2.8181 Median :-0.2897
## Mean :1.3943 Mean :2.7160 Mean :-0.3212
## 3rd Qu.:1.6864 3rd Qu.:3.2363 3rd Qu.:-0.1032
## Max. :2.6391 Max. :4.6844 Max. : 0.4402
## B_Lymphocyte_Chemoattractant_BL BMP_6 Beta_2_Microglobulin
## Min. :0.7318 Min. :-2.669 Min. :-0.51083
## 1st Qu.:1.5304 1st Qu.:-2.152 1st Qu.:-0.06188
## Median :1.8528 Median :-1.964 Median : 0.18232
## Mean :1.8766 Mean :-1.937 Mean : 0.15566
## 3rd Qu.:2.3714 3rd Qu.:-1.675 3rd Qu.: 0.40547
## Max. :2.9757 Max. :-1.181 Max. : 0.83291
## Betacellulin C_Reactive_Protein CD40 CD5L
## Min. :32.00 Min. :-8.112 Min. :-1.9390 Min. :-1.96611
## 1st Qu.:46.00 1st Qu.:-6.725 1st Qu.:-1.4420 1st Qu.:-0.36747
## Median :51.00 Median :-6.166 Median :-1.2574 Median :-0.05135
## Mean :52.74 Mean :-5.997 Mean :-1.2773 Mean :-0.08760
## 3rd Qu.:59.75 3rd Qu.:-5.369 3rd Qu.:-1.1034 3rd Qu.: 0.24235
## Max. :80.00 Max. :-3.411 Max. :-0.7766 Max. : 0.91629
## Calbindin Calcitonin CgA Clusterin_Apo_J
## Min. :10.81 Min. :-0.7134 Min. :166.6 Min. :1.932
## 1st Qu.:18.88 1st Qu.: 1.2014 1st Qu.:268.2 1st Qu.:2.565
## Median :21.06 Median : 1.6849 Median :324.7 Median :2.833
## Mean :21.49 Mean : 1.7250 Mean :320.2 Mean :2.845
## 3rd Qu.:24.00 3rd Qu.: 2.2618 3rd Qu.:362.3 3rd Qu.:3.045
## Max. :35.36 Max. : 4.1109 Max. :494.5 Max. :3.761
## Complement_3 Complement_Factor_H Connective_Tissue_Growth_Factor
## Min. :-22.40 Min. :0.2766 Min. :0.09531
## 1st Qu.:-17.50 1st Qu.:2.6019 1st Qu.:0.58779
## Median :-15.90 Median :3.3983 Median :0.74194
## Mean :-15.91 Mean :3.3897 Mean :0.74507
## 3rd Qu.:-14.34 3rd Qu.:4.2548 3rd Qu.:0.87547
## Max. :-10.23 Max. :6.5597 Max. :1.41099
## Cortisol Creatine_Kinase_MB Cystatin_C EGF_R
## Min. : 0.10 Min. :-1.872 Min. :7.728 Min. :-1.2694
## 1st Qu.: 8.90 1st Qu.:-1.721 1st Qu.:8.301 1st Qu.:-0.8859
## Median :10.00 Median :-1.651 Median :8.544 Median :-0.6917
## Mean :10.46 Mean :-1.652 Mean :8.576 Mean :-0.6965
## 3rd Qu.:12.00 3rd Qu.:-1.590 3rd Qu.:8.837 3rd Qu.:-0.5034
## Max. :22.00 Max. :-1.434 Max. :9.694 Max. : 0.1891
## EN_RAGE ENA_78 Eotaxin_3 FAS
## Min. :-8.3774 Min. :-1.405 Min. : 23.00 Min. :-1.1087
## 1st Qu.:-4.1836 1st Qu.:-1.382 1st Qu.: 43.00 1st Qu.:-0.7133
## Median :-3.6889 Median :-1.374 Median : 54.00 Median :-0.5798
## Mean :-3.5986 Mean :-1.376 Mean : 55.55 Mean :-0.5414
## 3rd Qu.:-3.2189 3rd Qu.:-1.368 3rd Qu.: 64.00 3rd Qu.:-0.3355
## Max. :-0.8675 Max. :-1.353 Max. :107.00 Max. : 0.1823
## FSH_Follicle_Stimulation_Hormon Fas_Ligand Fatty_Acid_Binding_Protein
## Min. :-1.8101 Min. :0.288 Min. :-0.4559
## 1st Qu.:-1.2694 1st Qu.:2.073 1st Qu.: 0.7998
## Median :-0.9763 Median :2.665 Median : 1.1866
## Mean :-1.0597 Mean :2.649 Mean : 1.2884
## 3rd Qu.:-0.8068 3rd Qu.:3.162 3rd Qu.: 1.9192
## Max. :-0.4757 Max. :5.377 Max. : 3.2188
## Ferritin Fetuin_A Fibrinogen GRO_alpha
## Min. :0.8983 Min. :0.5306 Min. :-9.373 Min. :1.271
## 1st Qu.:2.1473 1st Qu.:1.0296 1st Qu.:-7.799 1st Qu.:1.351
## Median :2.6260 Median :1.3083 Median :-7.316 Median :1.372
## Mean :2.7069 Mean :1.3116 Mean :-7.360 Mean :1.378
## 3rd Qu.:3.1672 3rd Qu.:1.6094 3rd Qu.:-6.970 3rd Qu.:1.398
## Max. :4.9282 Max. :2.2083 Max. :-6.166 Max. :1.514
## Gamma_Interferon_induced_Monokin Glutathione_S_Transferase_alpha
## Min. :2.545 Min. :0.5661
## 1st Qu.:2.698 1st Qu.:0.8257
## Median :2.768 Median :0.9493
## Mean :2.772 Mean :0.9440
## 3rd Qu.:2.829 3rd Qu.:1.0457
## Max. :3.046 Max. :1.3102
## HB_EGF HCC_4 Hepatocyte_Growth_Factor_HGF I_309
## Min. : 3.521 Min. :-4.343 Min. :-0.61619 Min. :2.041
## 1st Qu.: 5.949 1st Qu.:-3.772 1st Qu.:-0.05661 1st Qu.:2.724
## Median : 6.980 Median :-3.540 Median : 0.18232 Median :2.944
## Mean : 6.844 Mean :-3.538 Mean : 0.18076 Mean :2.921
## 3rd Qu.: 7.745 3rd Qu.:-3.352 3rd Qu.: 0.33647 3rd Qu.:3.135
## Max. :10.359 Max. :-2.489 Max. : 1.09861 Max. :3.689
## ICAM_1 IGF_BP_2 IL_11 IL_13
## Min. :-1.4661 Min. :4.718 Min. :2.031 Min. :1.232
## 1st Qu.:-0.7671 1st Qu.:5.127 1st Qu.:3.960 1st Qu.:1.274
## Median :-0.5903 Median :5.255 Median :4.838 Median :1.283
## Mean :-0.5958 Mean :5.263 Mean :4.651 Mean :1.283
## 3rd Qu.:-0.3574 3rd Qu.:5.402 3rd Qu.:5.482 3rd Qu.:1.292
## Max. : 0.3602 Max. :5.916 Max. :8.692 Max. :1.310
## IL_16 IL_17E IL_1alpha IL_3
## Min. :0.9568 Min. :1.582 Min. :-8.468 Min. :-5.521
## 1st Qu.:2.4411 1st Qu.:3.637 1st Qu.:-7.849 1st Qu.:-4.324
## Median :2.8763 Median :4.723 Median :-7.562 Median :-3.963
## Mean :2.8176 Mean :4.774 Mean :-7.549 Mean :-3.976
## 3rd Qu.:3.3514 3rd Qu.:5.415 3rd Qu.:-7.279 3rd Qu.:-3.576
## Max. :4.1028 Max. :8.081 Max. :-6.377 Max. :-3.079
## IL_4 IL_5 IL_6 IL_6_Receptor
## Min. :0.5306 Min. :-1.04982 Min. :-1.53428 Min. :-0.74560
## 1st Qu.:1.4586 1st Qu.:-0.03062 1st Qu.:-0.40924 1st Qu.:-0.20131
## Median :1.7226 Median : 0.22234 Median :-0.07205 Median : 0.00000
## Mean :1.7445 Mean : 0.22853 Mean :-0.05216 Mean : 0.06213
## 3rd Qu.:2.0669 3rd Qu.: 0.53063 3rd Qu.: 0.34805 3rd Qu.: 0.27297
## Max. :2.7081 Max. : 1.13140 Max. : 1.00562 Max. : 0.77048
## IL_7 IL_8 IP_10_Inducible_Protein_10 IgA
## Min. :1.310 Min. :1.615 Min. :4.263 Min. :-7.621
## 1st Qu.:2.379 1st Qu.:1.684 1st Qu.:5.323 1st Qu.:-6.571
## Median :3.148 Median :1.702 Median :5.617 Median :-6.012
## Mean :3.143 Mean :1.704 Mean :5.636 Mean :-6.066
## 3rd Qu.:3.706 3rd Qu.:1.725 3rd Qu.:5.917 3rd Qu.:-5.606
## Max. :5.000 Max. :1.836 Max. :7.208 Max. :-4.733
## Insulin Kidney_Injury_Molecule_1_KIM_1 LOX_1
## Min. :-2.0099 Min. :-1.251 Min. :0.0000
## 1st Qu.:-1.4466 1st Qu.:-1.209 1st Qu.:0.9649
## Median :-1.2169 Median :-1.187 Median :1.2238
## Mean :-1.1998 Mean :-1.188 Mean :1.2085
## 3rd Qu.:-1.0105 3rd Qu.:-1.166 3rd Qu.:1.4351
## Max. :-0.5025 Max. :-1.124 Max. :2.3979
## Leptin Lipoprotein_a MCP_1 MCP_2
## Min. :-1.9471 Min. :-6.571 Min. :5.889 Min. :0.4006
## 1st Qu.:-1.6334 1st Qu.:-5.116 1st Qu.:6.318 1st Qu.:1.5304
## Median :-1.4294 Median :-4.657 Median :6.482 Median :1.8528
## Mean :-1.4363 Mean :-4.515 Mean :6.480 Mean :1.8104
## 3rd Qu.:-1.2409 3rd Qu.:-4.017 3rd Qu.:6.627 3rd Qu.:2.0827
## Max. :-0.8387 Max. :-2.040 Max. :7.065 Max. :3.7545
## MIF MIP_1alpha MIP_1beta MMP_2
## Min. :-2.797 Min. :1.008 Min. :1.917 Min. :0.6248
## 1st Qu.:-2.120 1st Qu.:3.302 1st Qu.:2.485 1st Qu.:2.5513
## Median :-1.966 Median :3.736 Median :2.773 Median :2.9937
## Mean :-1.932 Mean :3.898 Mean :2.784 Mean :3.0347
## 3rd Qu.:-1.715 3rd Qu.:4.686 3rd Qu.:3.079 3rd Qu.:3.4798
## Max. :-1.109 Max. :5.735 Max. :3.784 Max. :6.0996
## MMP_3 MMP10 MMP7 Myoglobin
## Min. :-3.650 Min. :-4.948 Min. :-7.5346 Min. :-3.2968
## 1st Qu.:-2.852 1st Qu.:-4.075 1st Qu.:-4.9634 1st Qu.:-2.0217
## Median :-2.532 Median :-3.612 Median :-4.0302 Median :-1.5874
## Mean :-2.490 Mean :-3.676 Mean :-4.0148 Mean :-1.4165
## 3rd Qu.:-2.120 3rd Qu.:-3.331 3rd Qu.:-3.1640 3rd Qu.:-0.7765
## Max. :-1.171 Max. :-2.900 Max. :-0.1953 Max. : 1.1314
## NT_proBNP NrCAM Osteopontin PAI_1
## Min. :3.611 Min. :2.890 Min. :4.078 Min. :-0.990849
## 1st Qu.:4.174 1st Qu.:3.871 1st Qu.:4.892 1st Qu.:-0.334043
## Median :4.477 Median :4.317 Median :5.168 Median : 0.000000
## Mean :4.488 Mean :4.291 Mean :5.177 Mean :-0.003947
## 3rd Qu.:4.794 3rd Qu.:4.725 3rd Qu.:5.410 3rd Qu.: 0.303112
## Max. :5.398 Max. :5.690 Max. :6.315 Max. : 0.885785
## PAPP_A PLGF PYY Pancreatic_polypeptide
## Min. :-3.152 Min. :2.639 Min. :2.398 Min. :-1.609438
## 1st Qu.:-2.971 1st Qu.:3.689 1st Qu.:2.833 1st Qu.:-0.506693
## Median :-2.841 Median :3.892 Median :2.996 Median : 0.138816
## Mean :-2.845 Mean :3.884 Mean :2.976 Mean :-0.005258
## 3rd Qu.:-2.719 3rd Qu.:4.123 3rd Qu.:3.178 3rd Qu.: 0.470004
## Max. :-2.488 Max. :4.710 Max. :3.738 Max. : 1.504077
## Prolactin Prostatic_Acid_Phosphatase Protein_S
## Min. :-0.38566 Min. :-1.800 Min. :-3.154
## 1st Qu.:-0.16558 1st Qu.:-1.739 1st Qu.:-2.579
## Median : 0.00000 Median :-1.690 Median :-2.259
## Mean : 0.05195 Mean :-1.692 Mean :-2.268
## 3rd Qu.: 0.18232 3rd Qu.:-1.659 3rd Qu.:-1.924
## Max. : 0.78846 Max. :-1.540 Max. :-1.547
## Pulmonary_and_Activation_Regulat RANTES Resistin
## Min. :-2.4418 Min. :-7.236 Min. :-30.156
## 1st Qu.:-1.8326 1st Qu.:-6.725 1st Qu.:-22.131
## Median :-1.5141 Median :-6.571 Median :-18.014
## Mean :-1.5007 Mean :-6.540 Mean :-18.245
## 3rd Qu.:-1.1712 3rd Qu.:-6.392 3rd Qu.:-15.202
## Max. :-0.4463 Max. :-5.843 Max. : -6.594
## S100b SGOT SHBG SOD
## Min. :0.1874 Min. :-1.8971 Min. :-3.730 Min. :4.382
## 1st Qu.:0.9600 1st Qu.:-0.7498 1st Qu.:-3.052 1st Qu.:5.006
## Median :1.1571 Median :-0.4780 Median :-2.711 Median :5.313
## Mean :1.1819 Mean :-0.4898 Mean :-2.686 Mean :5.302
## 3rd Qu.:1.3807 3rd Qu.:-0.2138 3rd Qu.:-2.343 3rd Qu.:5.547
## Max. :2.1950 Max. : 0.1823 Max. :-1.561 Max. :6.461
## Serum_Amyloid_P Sortilin Stem_Cell_Factor TGF_alpha
## Min. :-7.182 Min. :1.508 Min. :2.219 Min. : 7.500
## 1st Qu.:-6.438 1st Qu.:3.177 1st Qu.:3.045 1st Qu.: 9.062
## Median :-6.215 Median :3.867 Median :3.314 Median : 9.596
## Mean :-6.083 Mean :3.787 Mean :3.267 Mean : 9.776
## 3rd Qu.:-5.607 3rd Qu.:4.371 3rd Qu.:3.466 3rd Qu.:10.612
## Max. :-4.699 Max. :5.681 Max. :4.078 Max. :13.083
## TIMP_1 TNF_RII TRAIL_R3 TTR_prealbumin
## Min. : 8.198 Min. :-1.6607 Min. :-1.30636 Min. :2.485
## 1st Qu.:10.530 1st Qu.:-0.8675 1st Qu.:-0.73332 1st Qu.:2.773
## Median :11.341 Median :-0.6541 Median :-0.55547 Median :2.890
## Mean :11.520 Mean :-0.6270 Mean :-0.58640 Mean :2.854
## 3rd Qu.:12.352 3rd Qu.:-0.3320 3rd Qu.:-0.47065 3rd Qu.:2.944
## Max. :16.547 Max. : 0.4055 Max. : 0.09622 Max. :3.091
## Tamm_Horsfall_Protein_THP Thrombomodulin Thrombopoietin
## Min. :-3.206 Min. :-2.054 Min. :-1.5396
## 1st Qu.:-3.144 1st Qu.:-1.675 1st Qu.:-0.8383
## Median :-3.126 Median :-1.534 Median :-0.7039
## Mean :-3.123 Mean :-1.533 Mean :-0.7192
## 3rd Qu.:-3.101 3rd Qu.:-1.341 3rd Qu.:-0.6289
## Max. :-3.041 Max. :-1.019 Max. :-0.3029
## Thymus_Expressed_Chemokine_TECK Thyroid_Stimulating_Hormone
## Min. :2.141 Min. :-6.190
## 1st Qu.:3.283 1st Qu.:-4.733
## Median :3.753 Median :-4.269
## Mean :3.770 Mean :-4.221
## 3rd Qu.:4.316 3rd Qu.:-3.828
## Max. :5.681 Max. :-2.040
## Thyroxine_Binding_Globulin Tissue_Factor Transferrin
## Min. :-2.3026 Min. :0.0000 Min. :2.282
## 1st Qu.:-1.7148 1st Qu.:0.7053 1st Qu.:2.708
## Median :-1.4919 Median :1.1473 Median :2.890
## Mean :-1.4902 Mean :1.1356 Mean :2.900
## 3rd Qu.:-1.2379 3rd Qu.:1.5149 3rd Qu.:3.135
## Max. :-0.5978 Max. :2.7081 Max. :3.497
## Trefoil_Factor_3_TFF3 VCAM_1 VEGF Vitronectin
## Min. :-4.906 Min. :2.028 Min. :12.23 Min. :-1.07881
## 1st Qu.:-4.200 1st Qu.:2.420 1st Qu.:15.03 1st Qu.:-0.46204
## Median :-3.912 Median :2.674 Median :17.08 Median :-0.28106
## Mean :-3.947 Mean :2.644 Mean :16.70 Mean :-0.26833
## 3rd Qu.:-3.772 3rd Qu.:2.833 3rd Qu.:18.19 3rd Qu.:-0.05394
## Max. :-3.170 Max. :3.466 Max. :21.18 Max. : 0.40547
## von_Willebrand_Factor Class E4 E3
## Min. :-4.920 Impaired:18 Min. :1.000 Min. :1.000
## 1st Qu.:-4.269 Control :48 1st Qu.:1.000 1st Qu.:2.000
## Median :-4.017 Median :1.000 Median :2.000
## Mean :-4.014 Mean :1.303 Mean :1.985
## 3rd Qu.:-3.730 3rd Qu.:2.000 3rd Qu.:2.000
## Max. :-3.058 Max. :2.000 Max. :2.000
## E2
## Min. :1.000
## 1st Qu.:1.000
## Median :1.000
## Mean :1.061
## 3rd Qu.:1.000
## Max. :2.000##################################
# Creating consistent fold assignments
# for the Cross Validation process
##################################
set.seed(12345678)
KFold_Indices <- createFolds(PMA_PreModelling_Train$Class ,
k = 10,
returnTrain=TRUE)
##################################
# Formulating a function to summarize
# model performance metrics
##################################
FiveMetricsSummary <- function(...) c(twoClassSummary(...), defaultSummary(...))
##################################
# Formulating the controls for the
# model training process
##################################
KFold_TrainControl <- trainControl(method = "cv",
summaryFunction = FiveMetricsSummary,
classProbs = TRUE,
index = KFold_Indices)
##################################
# Running the linear discriminant analysis model
# by setting the caret method to 'lda'
##################################
set.seed(12345678)
LDA_FULL_Tune <- caret::train(x = PMA_PreModelling_Train[,!names(PMA_PreModelling_Train) %in% c("Class")],
y = PMA_PreModelling_Train$Class,
method = "lda",
metric = "Accuracy",
tol = 1.0e-12,
trControl = KFold_TrainControl)
##################################
# Reporting the cross-validation results
# for the train set
##################################
LDA_FULL_Tune## Linear Discriminant Analysis
##
## 267 samples
## 127 predictors
## 2 classes: 'Impaired', 'Control'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 240, 239, 241, 240, 241, 241, ...
## Resampling results:
##
## ROC Sens Spec Accuracy Kappa
## 0.8015132 0.6428571 0.8142105 0.7675417 0.4377465LDA_FULL_Tune$finalModel## Call:
## lda(x, y, tol = 1e-12)
##
## Prior probabilities of groups:
## Impaired Control
## 0.2734082 0.7265918
##
## Group means:
## ACE_CD143_Angiotensin_Converti ACTH_Adrenocorticotropic_Hormon
## Impaired 1.291830 -1.512663
## Control 1.330372 -1.547922
## AXL Adiponectin Alpha_1_Antichymotrypsin Alpha_1_Antitrypsin
## Impaired 0.3606134 -5.062015 1.461656 -12.54310
## Control 0.2900390 -5.252821 1.322478 -13.24365
## Alpha_1_Microglobulin Alpha_2_Macroglobulin Angiopoietin_2_ANG_2
## Impaired -2.812275 -149.8084 0.7189962
## Control -2.977260 -161.9286 0.6556583
## Angiotensinogen Apolipoprotein_A_IV Apolipoprotein_A1
## Impaired 2.358407 -1.836798 -7.489153
## Control 2.302900 -1.861029 -7.480003
## Apolipoprotein_A2 Apolipoprotein_B Apolipoprotein_CI
## Impaired -0.6028357 -5.290980 -1.557583
## Control -0.6475857 -5.686514 -1.592933
## Apolipoprotein_CIII Apolipoprotein_D Apolipoprotein_E Apolipoprotein_H
## Impaired -2.402152 1.534726 2.774604 -0.2462583
## Control -2.528993 1.404988 2.818067 -0.3494279
## B_Lymphocyte_Chemoattractant_BL BMP_6 Beta_2_Microglobulin
## Impaired 2.191212 -1.906947 0.2010301
## Control 1.952112 -1.913117 0.1549796
## Betacellulin C_Reactive_Protein CD40 CD5L Calbindin
## Impaired 51.17808 -6.014766 -1.259173 0.05894109 23.27885
## Control 50.94845 -5.820661 -1.258089 -0.09525496 22.11405
## Calcitonin CgA Clusterin_Apo_J Complement_3 Complement_Factor_H
## Impaired 1.676591 334.8176 2.952344 -14.85689 3.557332
## Control 1.679652 332.7262 2.855998 -15.89379 3.552854
## Connective_Tissue_Growth_Factor Cortisol Creatine_Kinase_MB Cystatin_C
## Impaired 0.7947004 13.42740 -1.702831 8.472553
## Control 0.7660980 11.44124 -1.663646 8.628643
## EGF_R EN_RAGE ENA_78 Eotaxin_3 FAS
## Impaired -0.6825736 -3.643713 -1.372875 64.00000 -0.3996292
## Control -0.7083446 -3.632086 -1.372303 55.97938 -0.5778808
## FSH_Follicle_Stimulation_Hormon Fas_Ligand Fatty_Acid_Binding_Protein
## Impaired -1.153392 3.240515 1.614389
## Control -1.138530 2.865447 1.254534
## Ferritin Fetuin_A Fibrinogen GRO_alpha
## Impaired 2.931628 1.434358 -7.090535 1.399543
## Control 2.701751 1.318421 -7.456059 1.370087
## Gamma_Interferon_induced_Monokin Glutathione_S_Transferase_alpha
## Impaired 2.829613 0.9529078
## Control 2.769219 0.9505496
## HB_EGF HCC_4 Hepatocyte_Growth_Factor_HGF I_309 ICAM_1
## Impaired 7.177725 -3.394734 0.2821109 3.023617 -0.5474443
## Control 6.703511 -3.539563 0.1639794 2.933276 -0.6071264
## IGF_BP_2 IL_11 IL_13 IL_16 IL_17E IL_1alpha IL_3
## Impaired 5.384293 4.680067 1.283034 2.919439 4.671603 -7.477581 -3.987613
## Control 5.291718 4.741512 1.283942 2.933033 4.923843 -7.527105 -3.923848
## IL_4 IL_5 IL_6 IL_6_Receptor IL_7 IL_8
## Impaired 1.753057 0.1442299 -0.09617877 0.10115529 2.525637 1.713003
## Control 1.780749 0.2025861 -0.17580453 0.09257149 2.957174 1.701045
## IP_10_Inducible_Protein_10 IgA Insulin
## Impaired 5.875371 -5.928985 -1.262448
## Control 5.709495 -6.193464 -1.221804
## Kidney_Injury_Molecule_1_KIM_1 LOX_1 Leptin Lipoprotein_a
## Impaired -1.179252 1.272405 -1.544007 -4.277014
## Control -1.186509 1.286978 -1.489273 -4.470063
## MCP_1 MCP_2 MIF MIP_1alpha MIP_1beta MMP_2 MMP_3
## Impaired 6.548438 2.104018 -1.724998 4.281621 2.877145 2.781498 -2.324019
## Control 6.477030 1.780639 -1.916871 3.961372 2.790792 2.910655 -2.491243
## MMP10 MMP7 Myoglobin NT_proBNP NrCAM Osteopontin
## Impaired -3.404275 -3.156452 -1.246804 4.720840 4.330498 5.313664
## Control -3.721335 -4.027631 -1.412393 4.488264 4.373735 5.162882
## PAI_1 PAPP_A PLGF PYY Pancreatic_polypeptide
## Impaired 0.275440319 -2.843776 4.012400 3.033706 0.3059723
## Control 0.002927648 -2.857862 3.874869 3.008467 -0.1333379
## Prolactin Prostatic_Acid_Phosphatase Protein_S
## Impaired 0.07862477 -1.673206 -2.161885
## Control 0.03227524 -1.689756 -2.268898
## Pulmonary_and_Activation_Regulat RANTES Resistin S100b
## Impaired -1.368849 -6.453900 -15.66720 1.339447
## Control -1.532822 -6.532627 -18.38319 1.217084
## SGOT SHBG SOD Serum_Amyloid_P Sortilin
## Impaired -0.3863058 -2.373962 5.389265 -5.975203 4.101578
## Control -0.4130533 -2.515326 5.316217 -6.032948 3.757482
## Stem_Cell_Factor TGF_alpha TIMP_1 TNF_RII TRAIL_R3
## Impaired 3.289750 9.950444 12.17891 -0.4725251 -0.4163806
## Control 3.305627 9.744131 11.58805 -0.6396312 -0.5856845
## TTR_prealbumin Tamm_Horsfall_Protein_THP Thrombomodulin Thrombopoietin
## Impaired 2.845662 -3.113195 -1.448956 -0.8002665
## Control 2.857278 -3.116753 -1.526102 -0.7368538
## Thymus_Expressed_Chemokine_TECK Thyroid_Stimulating_Hormone
## Impaired 4.152730 -4.494425
## Control 3.733299 -4.500959
## Thyroxine_Binding_Globulin Tissue_Factor Transferrin
## Impaired -1.413281 1.185679 2.920215
## Control -1.503474 1.164395 2.904860
## Trefoil_Factor_3_TFF3 VCAM_1 VEGF Vitronectin
## Impaired -3.841630 2.750947 16.49858 -0.2877221
## Control -3.889182 2.663773 17.17183 -0.2836034
## von_Willebrand_Factor E4 E3 E2
## Impaired -3.848044 1.589041 1.890411 1.082192
## Control -3.927726 1.329897 1.927835 1.190722
##
## Coefficients of linear discriminants:
## LD1
## ACE_CD143_Angiotensin_Converti 0.569504941
## ACTH_Adrenocorticotropic_Hormon -0.895338194
## AXL -0.821182573
## Adiponectin -0.135161947
## Alpha_1_Antichymotrypsin -0.041071635
## Alpha_1_Antitrypsin -0.059362982
## Alpha_1_Microglobulin -0.786319216
## Alpha_2_Macroglobulin 0.012875285
## Angiopoietin_2_ANG_2 -0.797385222
## Angiotensinogen -0.296477791
## Apolipoprotein_A_IV 0.226600353
## Apolipoprotein_A1 2.489443027
## Apolipoprotein_A2 0.596888238
## Apolipoprotein_B -0.076453360
## Apolipoprotein_CI -1.119275874
## Apolipoprotein_CIII -0.629834266
## Apolipoprotein_D -0.052057126
## Apolipoprotein_E 0.569408798
## Apolipoprotein_H -0.102695136
## B_Lymphocyte_Chemoattractant_BL 0.318850160
## BMP_6 -0.212091110
## Beta_2_Microglobulin 1.498295786
## Betacellulin -0.028149817
## C_Reactive_Protein -0.228407589
## CD40 -0.972360146
## CD5L -0.039003898
## Calbindin 0.004420323
## Calcitonin 0.200564040
## CgA -0.002357913
## Clusterin_Apo_J -3.921135761
## Complement_3 -0.131845987
## Complement_Factor_H 0.187804895
## Connective_Tissue_Growth_Factor -2.065196644
## Cortisol -0.102529183
## Creatine_Kinase_MB -0.987522965
## Cystatin_C 1.821906379
## EGF_R 0.985441261
## EN_RAGE -0.088123902
## ENA_78 18.288727363
## Eotaxin_3 -0.012987019
## FAS -0.553120590
## FSH_Follicle_Stimulation_Hormon 0.187421956
## Fas_Ligand -0.022180189
## Fatty_Acid_Binding_Protein -0.714514954
## Ferritin -0.332781446
## Fetuin_A -1.495223078
## Fibrinogen -0.372424062
## GRO_alpha -3.624048833
## Gamma_Interferon_induced_Monokin 2.828644960
## Glutathione_S_Transferase_alpha -0.214189905
## HB_EGF 0.019575787
## HCC_4 0.109076895
## Hepatocyte_Growth_Factor_HGF -1.870434054
## I_309 1.431656002
## ICAM_1 0.122494244
## IGF_BP_2 0.550693401
## IL_11 0.288369179
## IL_13 -14.463595889
## IL_16 0.614118828
## IL_17E -0.019224225
## IL_1alpha -0.002997531
## IL_3 -0.430747600
## IL_4 -0.230035338
## IL_5 0.332906195
## IL_6 0.167908082
## IL_6_Receptor 0.136225541
## IL_7 0.159315144
## IL_8 1.388397550
## IP_10_Inducible_Protein_10 -0.026249724
## IgA 0.260463630
## Insulin -0.506328776
## Kidney_Injury_Molecule_1_KIM_1 10.757005612
## LOX_1 1.050265777
## Leptin 0.759660525
## Lipoprotein_a -0.046808860
## MCP_1 -0.236939879
## MCP_2 -0.323106590
## MIF 0.102910171
## MIP_1alpha -0.048747819
## MIP_1beta -0.234755079
## MMP_2 -0.296947941
## MMP_3 -0.314383059
## MMP10 -0.871312465
## MMP7 -0.001813268
## Myoglobin 0.371661604
## NT_proBNP -1.025594984
## NrCAM 1.863397920
## Osteopontin -0.240002679
## PAI_1 -1.168572932
## PAPP_A -1.466741892
## PLGF 0.086854139
## PYY -0.783593964
## Pancreatic_polypeptide -0.172598415
## Prolactin -0.675392299
## Prostatic_Acid_Phosphatase -2.017922226
## Protein_S 2.074044988
## Pulmonary_and_Activation_Regulat -0.463430382
## RANTES 1.787930693
## Resistin -0.041841639
## S100b 0.840086713
## SGOT -0.175139101
## SHBG 0.100971900
## SOD -2.830930524
## Serum_Amyloid_P 0.279417654
## Sortilin -0.001487249
## Stem_Cell_Factor 0.688548628
## TGF_alpha -0.422316280
## TIMP_1 0.013526273
## TNF_RII -2.577558465
## TRAIL_R3 -0.802371183
## TTR_prealbumin 0.343654701
## Tamm_Horsfall_Protein_THP 0.463766273
## Thrombomodulin 1.153883219
## Thrombopoietin -1.543486362
## Thymus_Expressed_Chemokine_TECK 0.137644167
## Thyroid_Stimulating_Hormone 0.133797927
## Thyroxine_Binding_Globulin -0.493144003
## Tissue_Factor -0.601270799
## Transferrin 0.207970519
## Trefoil_Factor_3_TFF3 0.697235040
## VCAM_1 0.391948501
## VEGF 0.502708648
## Vitronectin 0.441995676
## von_Willebrand_Factor 0.769056331
## E4 0.263306628
## E3 -0.165457885
## E2 0.052923879LDA_FULL_Tune$results## parameter ROC Sens Spec Accuracy Kappa ROCSD
## 1 none 0.8015132 0.6428571 0.8142105 0.7675417 0.4377465 0.07919456
## SensSD SpecSD AccuracySD KappaSD
## 1 0.1295925 0.05582698 0.05778037 0.1370938(LDA_FULL_Train_Accuracy <- LDA_FULL_Tune$results[,c("Accuracy")])## [1] 0.7675417##################################
# Independently evaluating the model and
# reporting the independent evaluation results
# on the test set
##################################
LDA_FULL_Test <- data.frame(LDA_FULL_Observed = PMA_PreModelling_Test$Class,
LDA_FULL_Predicted = predict(LDA_FULL_Tune,
PMA_PreModelling_Test[,!names(PMA_PreModelling_Test) %in% c("Class")],
type = "raw"))
LDA_FULL_Test## LDA_FULL_Observed LDA_FULL_Predicted
## 1 Control Control
## 2 Impaired Impaired
## 3 Impaired Impaired
## 4 Control Impaired
## 5 Impaired Control
## 6 Impaired Control
## 7 Impaired Impaired
## 8 Control Impaired
## 9 Impaired Impaired
## 10 Control Control
## 11 Control Impaired
## 12 Control Control
## 13 Control Control
## 14 Impaired Control
## 15 Control Control
## 16 Control Control
## 17 Control Control
## 18 Impaired Impaired
## 19 Control Control
## 20 Control Control
## 21 Control Control
## 22 Control Control
## 23 Control Control
## 24 Control Impaired
## 25 Control Control
## 26 Control Impaired
## 27 Control Control
## 28 Control Control
## 29 Control Impaired
## 30 Control Control
## 31 Impaired Impaired
## 32 Control Control
## 33 Control Control
## 34 Control Control
## 35 Control Impaired
## 36 Control Impaired
## 37 Control Control
## 38 Control Control
## 39 Impaired Control
## 40 Control Control
## 41 Control Control
## 42 Control Control
## 43 Control Control
## 44 Impaired Impaired
## 45 Control Control
## 46 Control Control
## 47 Control Control
## 48 Impaired Impaired
## 49 Control Control
## 50 Impaired Impaired
## 51 Control Impaired
## 52 Impaired Impaired
## 53 Impaired Impaired
## 54 Control Control
## 55 Control Control
## 56 Control Control
## 57 Control Control
## 58 Impaired Control
## 59 Control Control
## 60 Impaired Control
## 61 Control Control
## 62 Control Control
## 63 Impaired Control
## 64 Control Control
## 65 Control Control
## 66 Control Control##################################
# Reporting the independent evaluation results
# for the test set
##################################
(LDA_FULL_Test_Accuracy <- Accuracy(y_pred = LDA_FULL_Test$LDA_FULL_Predicted,
y_true = LDA_FULL_Test$LDA_FULL_Observed))## [1] 0.75757581.5.5 Linear Discriminant Analysis With Simulated Annealing (LDA_SA)
Linear Discriminant Analysis finds a linear combination of features that best separates the classes in a data set by projecting the data onto a lower-dimensional space that maximizes the separation between the classes. The algorithm searches for a set of linear discriminants that maximize the ratio of between-class variance to within-class variance by evaluating directions in the feature space that best separate the different classes of data. LDA assumes that the data has a Gaussian distribution and that the covariance matrices of the different classes are equal, in addition to the data being linearly separable by the presence of a linear decision boundary can accurately classify the different classes.
Simulated Annealing is a global search method that makes small random changes or perturbations to an initial candidate solution. If the performance value for the perturbed value is better than the previous solution, the new solution is accepted. If not, an acceptance probability is determined based on the difference between the two performance values and the current iteration of the search. From this, a sub-optimal solution can be accepted on the off-change that it may eventually produce a better solution in subsequent iterations. In the context of feature selection, a solution is a binary vector that describes the current subset. The subset is perturbed by randomly changing a small number of members in the subset.
[A] The linear discriminant analysis model from the MASS package was implemented with simulated annealing through the caret package.
[B] The model does not contain any hyperparameter.
[C] Simulated annealing was applied with results as follows:
[C.1] 31 predictors were selected using the training data at iteration 9.
[C.2] Resampling showed that approximately 29 variables were selected.
[C.3] The top 5 variables identified were tied among too many predictors.
[D] The cross-validated model performance of the final model is summarized as follows:
[D.1] Final model configuration involves variable subset=26 to 34
[D.2] Accuracy = 0.80941
[E] The independent test model performance of the final model is summarized as follows:
[E.1] Accuracy = 0.81818
Code Chunk | Output
##################################
# Creating consistent fold assignments
# for the Cross Validation process
##################################
set.seed(12345678)
KFold_Indices <- createFolds(PMA_PreModelling_Train$Class ,
k = 10,
returnTrain=TRUE)
##################################
# Formulating the controls for the
# model training process
##################################
KFold_TrainControl <- trainControl(method = "cv",
classProbs = TRUE)
##################################
# Formulating the controls for the
# simulated annealing process
##################################
KFold_SAControl <- safsControl(method = "cv",
verbose = TRUE,
functions = caretSA,
index = KFold_Indices,
returnResamp = "final")
##################################
# Running the linear discriminant analysis model
# by setting the caret method to 'lda'
# with implementation of simulated annealing
##################################
set.seed(12345678)
LDA_SA_Tune <- caret::safs(x = PMA_PreModelling_Train[,!names(PMA_PreModelling_Train) %in% c("Class")],
y = PMA_PreModelling_Train$Class,
iters = 10,
method = "lda",
metric = "Accuracy",
safsControl = KFold_SAControl,
trControl = KFold_TrainControl)## Fold01 1 0.7751739 (26)
## Fold01 2 0.7751739->0.7614638 (26+1, 96.3%) 0.9652452 A
## Fold01 3 0.7751739->0.7333406 (26+2, 92.9%) 0.850527 A
## Fold01 4 0.7751739->0.7506087 (26+3, 89.7%) 0.8809453 A
## Fold01 5 0.7751739->0.7832536 (26+4, 86.7%) *
## Fold01 6 0.7832536->0.7340072 (30+1, 96.8%) 0.6857483 A
## Fold01 7 0.7832536->0.753058 (30+0, 93.5%) 0.7634857 A
## Fold01 8 0.7832536->0.729029 (30-1, 90.3%) 0.5747386 A
## Fold01 9 0.7832536->0.7373116 (30+0, 87.5%) 0.5898433 A
## Fold01 10 0.7832536->0.7457029 (30+1, 84.8%) 0.6191426 A
## Fold02 1 0.7823116 (26)
## Fold02 2 0.7823116->0.7867971 (26-1, 96.2%) *
## Fold02 3 0.7867971->0.7750725 (25-1, 96.0%) 0.9562794 A
## Fold02 4 0.7867971->0.7756159 (25+0, 92.3%) 0.9447415 A
## Fold02 5 0.7867971->0.7992029 (25+1, 88.9%) *
## Fold02 6 0.7992029->0.7784348 (26+1, 96.3%) 0.8556309 A
## Fold02 7 0.7992029->0.7745072 (26+2, 92.9%) 0.8054916 A
## Fold02 8 0.7992029->0.7707101 (26+3, 89.7%) 0.7518551 A
## Fold02 9 0.7992029->0.7695797 (26+4, 86.7%) 0.7163451 A
## Fold02 10 0.7992029->0.7703551 (26+5, 83.9%) 0.6970086
## Fold03 1 0.8017174 (26)
## Fold03 2 0.8017174->0.8004783 (26+1, 96.3%) 0.9969136 A
## Fold03 3 0.8017174->0.7878333 (26+2, 92.9%) 0.9493728 A
## Fold03 4 0.8017174->0.7882826 (26+3, 89.7%) 0.9351671 A
## Fold03 5 0.8017174->0.8058986 (26+4, 86.7%) *
## Fold03 6 0.8058986->0.8002609 (30+1, 96.8%) 0.9588955 A
## Fold03 7 0.8058986->0.8052029 (30+2, 93.8%) 0.9939758 A
## Fold03 8 0.8058986->0.8091884 (30+3, 90.9%) *
## Fold03 9 0.8091884->0.8185217 (33+1, 97.1%) *
## Fold03 10 0.8185217->0.7680217 (34+1, 97.1%) 0.5395791 A
## Fold04 1 0.7625217 (26)
## Fold04 2 0.7625217->0.7456594 (26+1, 96.3%) 0.956736 A
## Fold04 3 0.7625217->0.7572391 (26+2, 92.9%) 0.979431 A
## Fold04 4 0.7625217->0.7510507 (26+3, 89.7%) 0.9416006 A
## Fold04 5 0.7625217->0.7569565 (26+4, 86.7%) 0.9641656 A
## Fold04 6 0.7625217->0.7542029 (26+5, 83.9%) 0.9366385 A
## Fold04 7 0.7625217->0.7449855 (26+6, 81.2%) 0.8513059 A
## Fold04 8 0.7625217->0.7251449 (26+5, 78.1%) 0.6756102 A
## Fold04 9 0.7625217->0.7412826 (26+4, 75.0%) 0.7782681
## Fold04 10 0.7625217->0.7142971 (26+6, 75.8%) 0.5312959 A
## Fold05 1 0.7475507 (26)
## Fold05 2 0.7475507->0.7764348 (26+1, 96.3%) *
## Fold05 3 0.7764348->0.7591739 (27+1, 96.4%) 0.9354825 A
## Fold05 4 0.7764348->0.7691739 (27+2, 93.1%) 0.9632848 A
## Fold05 5 0.7764348->0.763913 (27+1, 89.7%) 0.9225293 A
## Fold05 6 0.7764348->0.7957536 (27+2, 86.7%) *
## Fold05 7 0.7957536->0.7841739 (29+1, 96.7%) 0.9031531 A
## Fold05 8 0.7957536->0.7632464 (29+2, 93.5%) 0.7212228 A
## Fold05 9 0.7957536->0.7806884 (29+3, 90.6%) 0.8433374 A
## Fold05 10 0.7957536->0.7716739 (29+4, 87.9%) 0.7388927 A
## Fold06 1 0.779413 (26)
## Fold06 2 0.779413->0.7506594 (26+1, 96.3%) 0.9288735 A
## Fold06 3 0.779413->0.7377101 (26+0, 92.6%) 0.8517037 A
## Fold06 4 0.779413->0.7638696 (26+1, 89.3%) 0.9233285 A
## Fold06 5 0.779413->0.7623406 (26+2, 86.2%) 0.8962631 A
## Fold06 6 0.779413->0.7332101 (26+3, 83.3%) 0.7007006 A
## Fold06 7 0.779413->0.7501594 (26+4, 80.6%) 0.7689493 A
## Fold06 8 0.779413->0.770587 (26+5, 78.1%) 0.9133902 A
## Fold06 9 0.779413->0.7271087 (26+6, 75.8%) 0.5466393
## Fold06 10 0.779413->0.7338261 (26+6, 75.8%) 0.5571681
## Fold07 1 0.7296087 (26)
## Fold07 2 0.7296087->0.7389203 (26+1, 96.3%) *
## Fold07 3 0.7389203->0.7727174 (27+1, 96.4%) *
## Fold07 4 0.7727174->0.7933261 (28-1, 96.4%) *
## Fold07 5 0.7933261->0.759587 (27-1, 96.3%) 0.8084443
## Fold07 6 0.7933261->0.7762391 (27+1, 96.4%) 0.8787716 A
## Fold07 7 0.7933261->0.7712319 (27+2, 93.1%) 0.8228753 A
## Fold07 8 0.7933261->0.7515507 (27+3, 90.0%) 0.6562142
## Fold07 9 0.7933261->0.7595217 (27+3, 90.0%) 0.6814733 A
## Fold07 10 0.7933261->0.7556884 (27+4, 87.1%) 0.6222403 A
## Fold08 1 0.7746449 (26)
## Fold08 2 0.7746449->0.7797319 (26+1, 96.3%) *
## Fold08 3 0.7797319->0.7954928 (27+1, 96.4%) *
## Fold08 4 0.7954928->0.7618406 (28+1, 96.6%) 0.844328 A
## Fold08 5 0.7954928->0.777558 (28+2, 93.3%) 0.8933941 A
## Fold08 6 0.7954928->0.7839783 (28+3, 90.3%) 0.9168164 A
## Fold08 7 0.7954928->0.7912029 (28+4, 87.5%) 0.9629547 A
## Fold08 8 0.7954928->0.8132174 (28+3, 84.4%) *
## Fold08 9 0.8132174->0.7797826 (31+1, 96.9%) 0.6907151 A
## Fold08 10 0.8132174->0.7911594 (31+2, 93.9%) 0.762431
## Fold09 1 0.743587 (26)
## Fold09 2 0.743587->0.7562899 (26+1, 96.3%) *
## Fold09 3 0.7562899->0.7617681 (27+1, 96.4%) *
## Fold09 4 0.7617681->0.7535145 (28+1, 96.6%) 0.9575864
## Fold09 5 0.7617681->0.7571957 (28+1, 96.6%) 0.9704337 A
## Fold09 6 0.7617681->0.7708116 (28+2, 93.3%) *
## Fold09 7 0.7708116->0.7666304 (30+1, 96.8%) 0.9627413 A
## Fold09 8 0.7708116->0.7657826 (30+2, 93.8%) 0.9491445 A
## Fold09 9 0.7708116->0.7662826 (30+3, 90.9%) 0.9484934 A
## Fold09 10 0.7708116->0.7874928 (30+2, 87.9%) *
## Fold10 1 0.8297319 (26)
## Fold10 2 0.8297319->0.820913 (26+1, 96.3%) 0.9789673 A
## Fold10 3 0.8297319->0.8252609 (26+2, 92.9%) 0.9839644 A
## Fold10 4 0.8297319->0.8415652 (26+3, 89.7%) *
## Fold10 5 0.8415652->0.8382826 (29-1, 96.6%) 0.980686 A
## Fold10 6 0.8415652->0.8041739 (29+0, 93.3%) 0.7659917 A
## Fold10 7 0.8415652->0.8286884 (29-1, 90.0%) 0.8984294
## Fold10 8 0.8415652->0.8181884 (29-1, 90.0%) 0.8007374 A
## Fold10 9 0.8415652->0.8162029 (29-2, 86.7%) 0.7624383 A
## Fold10 10 0.8415652->0.8097029 (29-1, 90.0%) 0.6848141
## + final SA
## 1 0.8057184 (26)
## 2 0.8057184->0.8016484 (26-1, 96.2%) 0.9899481 A
## 3 0.8057184->0.7710826 (26+0, 92.6%) 0.8790072 A
## 4 0.8057184->0.7639499 (26+1, 89.3%) 0.8127271 A
## 5 0.8057184->0.7681726 (26+2, 86.2%) 0.792157 A
## 6 0.8057184->0.7752239 (26+3, 83.3%) 0.7968526
## 7 0.8057184->0.7646418 (26+3, 83.3%) 0.6998644 A
## 8 0.8057184->0.7796296 (26+4, 80.6%) 0.7717955 A
## 9 0.8057184->0.783547 (26+5, 78.1%) 0.7806273 A
## 10 0.8057184->0.7682641 (26+4, 75.0%) 0.6282263 A
## + final model##################################
# Reporting the cross-validation results
# for the train set
##################################
LDA_SA_Tune##
## Simulated Annealing Feature Selection
##
## 267 samples
## 127 predictors
## 2 classes: 'Impaired', 'Control'
##
## Maximum search iterations: 10
##
## Internal performance values: Accuracy, Kappa
## Subset selection driven to maximize internal Accuracy
##
## External performance values: Accuracy, Kappa
## Best iteration chose by maximizing external Accuracy
## External resampling method: Cross-Validated (10 fold)
##
## During resampling:
## * the top 5 selected variables (out of a possible 127):
## Apolipoprotein_D (50%), Fatty_Acid_Binding_Protein (50%), HCC_4 (50%), IL_3 (50%), MCP_2 (50%)
## * on average, 29 variables were selected (min = 26, max = 34)
##
## In the final search using the entire training set:
## * 31 features selected at iteration 9 including:
## ACTH_Adrenocorticotropic_Hormon, Apolipoprotein_A2, Apolipoprotein_CI, Beta_2_Microglobulin, Connective_Tissue_Growth_Factor ...
## * external performance at this iteration is
##
## Accuracy Kappa
## 0.8094 0.4720LDA_SA_Tune$fit## Linear Discriminant Analysis
##
## 267 samples
## 31 predictor
## 2 classes: 'Impaired', 'Control'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 241, 239, 241, 239, 241, 241, ...
## Resampling results:
##
## Accuracy Kappa
## 0.7912393 0.4781993LDA_SA_Tune$averages## Iter Accuracy Kappa
## 1 1 0.7752137 0.3711203
## 2 2 0.7791921 0.3847643
## 3 3 0.7796093 0.3924960
## 4 4 0.7986976 0.4407613
## 5 5 0.7988400 0.4446132
## 6 6 0.7949939 0.4313315
## 7 7 0.8024115 0.4469942
## 8 8 0.7910155 0.4216211
## 9 9 0.8094119 0.4720489
## 10 10 0.8020045 0.4529000(LDA_SA_Train_Accuracy <- LDA_SA_Tune$averages[LDA_SA_Tune$averages$Accuracy==max(LDA_SA_Tune$averages$Accuracy),
c("Accuracy")])## [1] 0.8094119##################################
# Independently evaluating the model and
# reporting the independent evaluation results
# on the test set
##################################
LDA_SA_Test <- data.frame(LDA_SA_Observed = PMA_PreModelling_Test$Class,
LDA_SA_Predicted = predict(LDA_SA_Tune,
PMA_PreModelling_Test[,!names(PMA_PreModelling_Test) %in% c("Class")],
type = "raw"))
LDA_SA_Test## LDA_SA_Observed LDA_SA_Predicted.pred LDA_SA_Predicted.Impaired
## 4 Control Control 0.001117002
## 10 Impaired Control 0.202015024
## 13 Impaired Impaired 0.634018751
## 15 Control Control 0.056100052
## 27 Impaired Control 0.077386757
## 32 Impaired Control 0.002428007
## 33 Impaired Impaired 0.927490529
## 49 Control Control 0.118022391
## 52 Impaired Impaired 0.991362989
## 54 Control Control 0.003531488
## 58 Control Control 0.466873059
## 66 Control Control 0.327480206
## 79 Control Control 0.136651720
## 87 Impaired Control 0.328440901
## 89 Control Impaired 0.658809127
## 91 Control Control 0.021986699
## 92 Control Control 0.003566254
## 101 Impaired Impaired 0.997353376
## 102 Control Control 0.467304220
## 106 Control Control 0.001837830
## 116 Control Control 0.003090223
## 119 Control Control 0.167828034
## 120 Control Control 0.011248641
## 122 Control Control 0.020045395
## 125 Control Control 0.015035653
## 127 Control Control 0.364697923
## 138 Control Control 0.131881702
## 142 Control Control 0.049538373
## 150 Control Control 0.208472331
## 151 Control Control 0.169587439
## 164 Impaired Control 0.059932561
## 173 Control Control 0.001724339
## 187 Control Control 0.018097307
## 188 Control Control 0.109212518
## 196 Control Impaired 0.684300481
## 199 Control Impaired 0.784693963
## 203 Control Control 0.008990814
## 204 Control Control 0.376566904
## 206 Impaired Impaired 0.790240075
## 207 Control Control 0.006595012
## 209 Control Control 0.082794730
## 211 Control Control 0.083738824
## 217 Control Control 0.314585693
## 221 Impaired Impaired 0.699416176
## 222 Control Control 0.012729950
## 235 Control Control 0.016102086
## 238 Control Control 0.132841555
## 248 Impaired Control 0.190389435
## 252 Control Control 0.017958343
## 259 Impaired Control 0.094014109
## 266 Control Control 0.130070036
## 276 Impaired Impaired 0.785507425
## 280 Impaired Control 0.490750839
## 284 Control Control 0.046257225
## 285 Control Control 0.094341516
## 286 Control Control 0.047203239
## 288 Control Control 0.123262019
## 293 Impaired Control 0.008037950
## 295 Control Control 0.087466091
## 296 Impaired Impaired 0.702170305
## 300 Control Control 0.410044571
## 309 Control Control 0.063964905
## 310 Impaired Impaired 0.580402992
## 318 Control Control 0.074637291
## 319 Control Control 0.034766067
## 328 Control Control 0.043932395
## LDA_SA_Predicted.Control
## 4 0.998882998
## 10 0.797984976
## 13 0.365981249
## 15 0.943899948
## 27 0.922613243
## 32 0.997571993
## 33 0.072509471
## 49 0.881977609
## 52 0.008637011
## 54 0.996468512
## 58 0.533126941
## 66 0.672519794
## 79 0.863348280
## 87 0.671559099
## 89 0.341190873
## 91 0.978013301
## 92 0.996433746
## 101 0.002646624
## 102 0.532695780
## 106 0.998162170
## 116 0.996909777
## 119 0.832171966
## 120 0.988751359
## 122 0.979954605
## 125 0.984964347
## 127 0.635302077
## 138 0.868118298
## 142 0.950461627
## 150 0.791527669
## 151 0.830412561
## 164 0.940067439
## 173 0.998275661
## 187 0.981902693
## 188 0.890787482
## 196 0.315699519
## 199 0.215306037
## 203 0.991009186
## 204 0.623433096
## 206 0.209759925
## 207 0.993404988
## 209 0.917205270
## 211 0.916261176
## 217 0.685414307
## 221 0.300583824
## 222 0.987270050
## 235 0.983897914
## 238 0.867158445
## 248 0.809610565
## 252 0.982041657
## 259 0.905985891
## 266 0.869929964
## 276 0.214492575
## 280 0.509249161
## 284 0.953742775
## 285 0.905658484
## 286 0.952796761
## 288 0.876737981
## 293 0.991962050
## 295 0.912533909
## 296 0.297829695
## 300 0.589955429
## 309 0.936035095
## 310 0.419597008
## 318 0.925362709
## 319 0.965233933
## 328 0.956067605##################################
# Reporting the independent evaluation results
# for the test set
##################################
(LDA_SA_Test_Accuracy <- Accuracy(y_pred = LDA_SA_Test$LDA_SA_Predicted.pred,
y_true = LDA_SA_Test$LDA_SA_Observed))## [1] 0.81818181.5.6 Linear Discriminant Analysis With Genetic Algorithms (LDA_GA)
Linear Discriminant Analysis finds a linear combination of features that best separates the classes in a data set by projecting the data onto a lower-dimensional space that maximizes the separation between the classes. The algorithm searches for a set of linear discriminants that maximize the ratio of between-class variance to within-class variance by evaluating directions in the feature space that best separate the different classes of data. LDA assumes that the data has a Gaussian distribution and that the covariance matrices of the different classes are equal, in addition to the data being linearly separable by the presence of a linear decision boundary can accurately classify the different classes.
Genetic Algorithms mimic Darwinian forces of natural selection to find optimal values of some function. An initial set of candidate solutions are created and their corresponding fitness values are calculated (where larger values are better). This set of solutions is referred to as a population and each solution as an individual. The individuals with the best fitness values are combined randomly to produce offsprings which make up the next population. To do so, individual are selected and undergo cross-over (mimicking genetic reproduction) and also are subject to random mutations. This process is repeated again and again and many generations are produced resulting to iterations of the search procedure that should create better and better solutions. For feature selection, the individuals are subsets of predictors that are encoded as binary representing a feature being either included or not in the subset. The fitness values applied are existing measurea of model performance.
[A] The linear discriminant analysis model from the MASS package was implemented with genetic algorithms through the caret package.
[B] The model does not contain any hyperparameter.
[C] Genetic algorithms was applied with results as follows:
[C.1] 61 predictors were selected using the training data at iteration 4.
[C.2] Resampling showed that approximately 47 variables were selected.
[C.3] The top 5 variables identified were tied among too many predictors.
[D] The cross-validated model performance of the final model is summarized as follows:
[D.1] Final model configuration involves variable subset=30 to 62
[D.2] Accuracy = 0.79402
[E] The independent test model peLDAormance of the final model is summarized as follows:
[E.1] Accuracy = 0.84848
Code Chunk | Output
##################################
# Creating consistent fold assignments
# for the Cross Validation process
##################################
set.seed(12345678)
KFold_Indices <- createFolds(PMA_PreModelling_Train$Class ,
k = 10,
returnTrain=TRUE)
##################################
# Formulating the controls for the
# model training process
##################################
KFold_TrainControl <- trainControl(method = "cv",
classProbs = TRUE)
##################################
# Formulating the controls for the
# genetic algorithms process
##################################
KFold_GAControl <- gafsControl(method = "cv",
verbose = TRUE,
functions = caretGA,
index = KFold_Indices,
returnResamp = "final")
##################################
# Running the linear discriminant analysis model
# by setting the caret method to 'lda'
# with implementation of genetic algorithms
##################################
set.seed(12345678)
LDA_GA_Tune <- caret::gafs(x = PMA_PreModelling_Train[,!names(PMA_PreModelling_Train) %in% c("Class")],
y = PMA_PreModelling_Train$Class,
iters = 10,
method = "lda",
metric = "Accuracy",
gafsControl = KFold_GAControl,
trControl = KFold_TrainControl)## Fold01 1 0.7999638 (57)
## Fold01 2 0.7999638->0.8011014 ( 57-> 69, 38.5%) *
## Fold01 3 0.8011014->0.8135362 ( 69-> 69, 38.0%) *
## Fold01 4 0.8135362->0.8290362 ( 69-> 62, 84.5%) *
## Fold01 5 0.8290362->0.8302754 ( 62-> 80, 35.2%) *
## Fold01 6 0.8302754->0.8375 ( 80-> 51, 33.7%) *
## Fold01 7 0.8375->0.8418406 ( 51-> 53, 40.5%) *
## Fold01 8 0.8418406->0.8459928 ( 53-> 44, 31.1%) *
## Fold01 9 0.8459928->0.8467609 ( 44-> 43, 97.7%) *
## Fold01 10 0.8467609->0.8461087 ( 43-> 61, 36.8%)
## Fold02 1 0.8119783 (47)
## Fold02 2 0.8119783->0.8330217 ( 47-> 36, 15.3%) *
## Fold02 3 0.8330217->0.8460797 ( 36-> 40, 22.6%) *
## Fold02 4 0.8460797->0.8445362 ( 40-> 51, 35.8%)
## Fold02 5 0.8460797->0.8447826 ( 40-> 60, 20.5%)
## Fold02 6 0.8460797->0.8534203 ( 40-> 32, 20.0%) *
## Fold02 7 0.8534203->0.8498696 ( 32-> 44, 20.6%)
## Fold02 8 0.8534203->0.8532174 ( 32-> 44, 16.9%)
## Fold02 9 0.8534203->0.8618406 ( 32-> 36, 21.4%) *
## Fold02 10 0.8618406->0.8616594 ( 36-> 31, 42.6%)
## Fold03 1 0.8178841 (35)
## Fold03 2 0.8178841->0.817971 ( 35-> 32, 19.6%) *
## Fold03 3 0.817971->0.8378841 ( 32-> 51, 22.1%) *
## Fold03 4 0.8378841->0.8265362 ( 51-> 54, 52.2%)
## Fold03 5 0.8378841->0.845913 ( 51-> 49, 44.9%) *
## Fold03 6 0.845913->0.8508043 ( 49-> 49, 100.0%) *
## Fold03 7 0.8508043->0.8461884 ( 49-> 49, 100.0%)
## Fold03 8 0.8508043->0.8595942 ( 49-> 47, 71.4%) *
## Fold03 9 0.8595942->0.8596522 ( 47-> 43, 60.7%) *
## Fold03 10 0.8596522->0.850913 ( 43-> 47, 60.7%)
## Fold04 1 0.8170507 (32)
## Fold04 2 0.8170507->0.8165942 ( 32-> 32, 100.0%)
## Fold04 3 0.8170507->0.8254565 ( 32-> 31, 85.3%) *
## Fold04 4 0.8254565->0.8448696 ( 31-> 43, 39.6%) *
## Fold04 5 0.8448696->0.8333986 ( 43-> 43, 30.3%)
## Fold04 6 0.8448696->0.845913 ( 43-> 50, 45.3%) *
## Fold04 7 0.845913->0.8462174 ( 50-> 28, 39.3%) *
## Fold04 8 0.8462174->0.8424565 ( 28-> 39, 48.9%)
## Fold04 9 0.8462174->0.8538841 ( 28-> 30, 70.6%) *
## Fold04 10 0.8538841->0.8333551 ( 30-> 39, 43.8%)
## Fold05 1 0.8092754 (67)
## Fold05 2 0.8092754->0.8378406 ( 67-> 69, 37.4%) *
## Fold05 3 0.8378406->0.8456884 ( 69-> 71, 84.2%) *
## Fold05 4 0.8456884->0.8268696 ( 71-> 71, 91.9%)
## Fold05 5 0.8456884->0.846942 ( 71-> 66, 90.3%) *
## Fold05 6 0.846942->0.8836377 ( 66-> 45, 48.0%) *
## Fold05 7 0.8836377->0.8668841 ( 45-> 45, 100.0%)
## Fold05 8 0.8836377->0.8505507 ( 45-> 45, 100.0%)
## Fold05 9 0.8836377->0.8546087 ( 45-> 46, 97.8%)
## Fold05 10 0.8836377->0.8471377 ( 45-> 65, 44.7%)
## Fold06 1 0.8087174 (72)
## Fold06 2 0.8087174->0.8260217 ( 72-> 70, 94.5%) *
## Fold06 3 0.8260217->0.8293696 ( 70-> 71, 41.0%) *
## Fold06 4 0.8293696->0.8300362 ( 71-> 52, 32.3%) *
## Fold06 5 0.8300362->0.8503333 ( 52-> 55, 27.4%) *
## Fold06 6 0.8503333->0.8466377 ( 55-> 51, 92.7%)
## Fold06 7 0.8503333->0.8307464 ( 55-> 55, 52.8%)
## Fold06 8 0.8503333->0.8346377 ( 55-> 81, 51.1%)
## Fold06 9 0.8503333->0.8380362 ( 55-> 60, 40.2%)
## Fold06 10 0.8503333->0.8471087 ( 55-> 64, 70.0%)
## Fold07 1 0.8303116 (28)
## Fold07 2 0.8303116->0.8220652 ( 28-> 28, 93.1%)
## Fold07 3 0.8303116->0.8140217 ( 28-> 34, 8.8%)
## Fold07 4 0.8303116->0.8302754 ( 28-> 34, 8.8%)
## Fold07 5 0.8303116->0.8350072 ( 28-> 63, 16.7%) *
## Fold07 6 0.8350072->0.8328986 ( 63-> 39, 52.2%)
## Fold07 7 0.8350072->0.8387754 ( 63-> 60, 57.7%) *
## Fold07 8 0.8387754->0.8338116 ( 60-> 46, 73.8%)
## Fold07 9 0.8387754->0.8296449 ( 60-> 46, 23.3%)
## Fold07 10 0.8387754->0.8305217 ( 60-> 50, 41.0%)
## Fold08 1 0.8138696 (41)
## Fold08 2 0.8138696->0.8082971 ( 41->102, 32.4%)
## Fold08 3 0.8138696->0.8217029 ( 41-> 48, 21.9%) *
## Fold08 4 0.8217029->0.8337754 ( 48-> 50, 88.5%) *
## Fold08 5 0.8337754->0.8240072 ( 50-> 51, 18.8%)
## Fold08 6 0.8337754->0.8549275 ( 50-> 55, 25.0%) *
## Fold08 7 0.8549275->0.8390652 ( 55-> 55, 100.0%)
## Fold08 8 0.8549275->0.8376884 ( 55-> 46, 80.4%)
## Fold08 9 0.8549275->0.8584275 ( 55-> 62, 62.5%) *
## Fold08 10 0.8584275->0.8488406 ( 62-> 62, 100.0%)
## Fold09 1 0.8156739 (81)
## Fold09 2 0.8156739->0.8160507 ( 81-> 62, 36.2%) *
## Fold09 3 0.8160507->0.8321304 ( 62-> 67, 31.6%) *
## Fold09 4 0.8321304->0.8493986 ( 67-> 84, 36.0%) *
## Fold09 5 0.8493986->0.833087 ( 84-> 63, 41.3%)
## Fold09 6 0.8493986->0.8457029 ( 84-> 64, 64.4%)
## Fold09 7 0.8493986->0.8576884 ( 84-> 37, 23.5%) *
## Fold09 8 0.8576884->0.8613406 ( 37-> 35, 84.6%) *
## Fold09 9 0.8613406->0.8532971 ( 35-> 37, 84.6%)
## Fold09 10 0.8613406->0.8661449 ( 35-> 46, 58.8%) *
## Fold10 1 0.8305652 (62)
## Fold10 2 0.8305652->0.8277464 ( 62-> 61, 39.8%)
## Fold10 3 0.8305652->0.8218986 ( 62-> 34, 23.1%)
## Fold10 4 0.8305652->0.8673986 ( 62-> 68, 44.4%) *
## Fold10 5 0.8673986->0.8713841 ( 68-> 55, 78.3%) *
## Fold10 6 0.8713841->0.850913 ( 55-> 58, 59.2%)
## Fold10 7 0.8713841->0.8545942 ( 55-> 75, 38.3%)
## Fold10 8 0.8713841->0.8721232 ( 55-> 47, 37.8%) *
## Fold10 9 0.8721232->0.8506594 ( 47-> 58, 72.1%)
## Fold10 10 0.8721232->0.8673043 ( 47-> 45, 37.3%)
## + final GA
## 1 0.8164733 (41)
## 2 0.8164733->0.808893 ( 41-> 25, 11.9%)
## 3 0.8164733->0.8281441 ( 41-> 41, 100.0%) *
## 4 0.8281441->0.8463777 ( 41-> 61, 43.7%) *
## 5 0.8463777->0.8351547 ( 61-> 51, 57.7%)
## 6 0.8463777->0.8449634 ( 61-> 58, 25.3%)
## 7 0.8463777->0.8466321 ( 61-> 53, 18.8%) *
## 8 0.8466321->0.834707 ( 53-> 47, 49.3%)
## 9 0.8466321->0.8354294 ( 53-> 61, 23.9%)
## 10 0.8466321->0.8435287 ( 53-> 49, 70.0%)
## + final model##################################
# Reporting the cross-validation results
# for the train set
##################################
LDA_GA_Tune##
## Genetic Algorithm Feature Selection
##
## 267 samples
## 127 predictors
## 2 classes: 'Impaired', 'Control'
##
## Maximum generations: 10
## Population per generation: 50
## Crossover probability: 0.8
## Mutation probability: 0.1
## Elitism: 0
##
## Internal performance values: Accuracy, Kappa
## Subset selection driven to maximize internal Accuracy
##
## External performance values: Accuracy, Kappa
## Best iteration chose by maximizing external Accuracy
## External resampling method: Cross-Validated (10 fold)
##
## During resampling:
## * the top 5 selected variables (out of a possible 127):
## Cystatin_C (90%), MMP10 (90%), Apolipoprotein_A1 (80%), Cortisol (80%), VEGF (80%)
## * on average, 46.7 variables were selected (min = 30, max = 62)
##
## In the final search using the entire training set:
## * 61 features selected at iteration 4 including:
## Alpha_1_Microglobulin, Alpha_2_Macroglobulin, Angiotensinogen, Apolipoprotein_CIII, Apolipoprotein_D ...
## * external performance at this iteration is
##
## Accuracy Kappa
## 0.7940 0.4894LDA_GA_Tune$fit## Linear Discriminant Analysis
##
## 267 samples
## 61 predictor
## 2 classes: 'Impaired', 'Control'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 241, 240, 239, 241, 239, 241, ...
## Resampling results:
##
## Accuracy Kappa
## 0.8091372 0.5091527LDA_GA_Tune$averages## Iter Accuracy Kappa
## 1 1 0.7757530 0.4076982
## 2 2 0.7572446 0.3840816
## 3 3 0.7907509 0.4854290
## 4 4 0.7940273 0.4893657
## 5 5 0.7719170 0.4169970
## 6 6 0.7791921 0.4459888
## 7 7 0.7636956 0.3945538
## 8 8 0.7640924 0.4192004
## 9 9 0.7595543 0.3801691
## 10 10 0.7712556 0.4149006(LDA_GA_Train_Accuracy <- LDA_GA_Tune$averages[LDA_GA_Tune$averages$Accuracy==max(LDA_GA_Tune$averages$Accuracy),
c("Accuracy")])## [1] 0.7940273##################################
# Independently evaluating the model and
# reporting the independent evaluation results
# on the test set
##################################
LDA_GA_Test <- data.frame(LDA_GA_Observed = PMA_PreModelling_Test$Class,
LDA_GA_Predicted = predict(LDA_GA_Tune,
PMA_PreModelling_Test[,!names(PMA_PreModelling_Test) %in% c("Class")],
type = "raw"))
LDA_GA_Test## LDA_GA_Observed LDA_GA_Predicted.pred LDA_GA_Predicted.Impaired
## 4 Control Control 1.344467e-03
## 10 Impaired Impaired 9.648635e-01
## 13 Impaired Impaired 9.945636e-01
## 15 Control Control 4.525513e-01
## 27 Impaired Control 2.383854e-03
## 32 Impaired Control 2.210414e-03
## 33 Impaired Impaired 9.188461e-01
## 49 Control Control 2.158310e-02
## 52 Impaired Impaired 8.944029e-01
## 54 Control Control 8.452680e-02
## 58 Control Control 4.582054e-01
## 66 Control Control 1.274641e-03
## 79 Control Impaired 7.553738e-01
## 87 Impaired Control 1.587294e-01
## 89 Control Control 1.703803e-02
## 91 Control Control 7.594765e-02
## 92 Control Control 1.265478e-02
## 101 Impaired Impaired 9.949380e-01
## 102 Control Control 8.502519e-02
## 106 Control Control 2.760468e-02
## 116 Control Control 2.425436e-05
## 119 Control Control 3.278133e-03
## 120 Control Control 7.913202e-04
## 122 Control Control 2.953061e-02
## 125 Control Control 1.815725e-04
## 127 Control Control 7.718520e-03
## 138 Control Control 3.352697e-03
## 142 Control Control 2.496666e-01
## 150 Control Control 8.810881e-03
## 151 Control Control 1.563173e-02
## 164 Impaired Impaired 9.710313e-01
## 173 Control Control 3.017419e-03
## 187 Control Control 1.139955e-02
## 188 Control Control 1.834751e-03
## 196 Control Impaired 6.068846e-01
## 199 Control Impaired 9.969451e-01
## 203 Control Control 5.481570e-02
## 204 Control Control 1.022203e-01
## 206 Impaired Control 1.005856e-02
## 207 Control Control 2.813131e-03
## 209 Control Control 5.077507e-03
## 211 Control Control 3.200174e-01
## 217 Control Control 2.912975e-02
## 221 Impaired Impaired 9.800391e-01
## 222 Control Control 1.122470e-02
## 235 Control Control 1.666724e-03
## 238 Control Control 1.849200e-05
## 248 Impaired Impaired 5.587321e-01
## 252 Control Control 1.352342e-03
## 259 Impaired Impaired 9.741620e-01
## 266 Control Control 2.499570e-01
## 276 Impaired Impaired 9.458447e-01
## 280 Impaired Control 4.462540e-01
## 284 Control Control 2.577057e-03
## 285 Control Control 2.565497e-04
## 286 Control Control 3.899414e-02
## 288 Control Control 3.638500e-02
## 293 Impaired Control 1.139168e-03
## 295 Control Control 1.681312e-03
## 296 Impaired Impaired 5.191660e-01
## 300 Control Control 1.324779e-01
## 309 Control Control 1.717021e-02
## 310 Impaired Control 1.449930e-01
## 318 Control Control 9.490306e-03
## 319 Control Control 6.748458e-02
## 328 Control Control 5.151371e-03
## LDA_GA_Predicted.Control
## 4 0.998655533
## 10 0.035136540
## 13 0.005436385
## 15 0.547448712
## 27 0.997616146
## 32 0.997789586
## 33 0.081153927
## 49 0.978416897
## 52 0.105597076
## 54 0.915473198
## 58 0.541794577
## 66 0.998725359
## 79 0.244626204
## 87 0.841270595
## 89 0.982961973
## 91 0.924052348
## 92 0.987345220
## 101 0.005061995
## 102 0.914974810
## 106 0.972395320
## 116 0.999975746
## 119 0.996721867
## 120 0.999208680
## 122 0.970469390
## 125 0.999818428
## 127 0.992281480
## 138 0.996647303
## 142 0.750333399
## 150 0.991189119
## 151 0.984368275
## 164 0.028968735
## 173 0.996982581
## 187 0.988600451
## 188 0.998165249
## 196 0.393115388
## 199 0.003054864
## 203 0.945184300
## 204 0.897779666
## 206 0.989941442
## 207 0.997186869
## 209 0.994922493
## 211 0.679982577
## 217 0.970870254
## 221 0.019960885
## 222 0.988775300
## 235 0.998333276
## 238 0.999981508
## 248 0.441267869
## 252 0.998647658
## 259 0.025837998
## 266 0.750042957
## 276 0.054155258
## 280 0.553745988
## 284 0.997422943
## 285 0.999743450
## 286 0.961005863
## 288 0.963614996
## 293 0.998860832
## 295 0.998318688
## 296 0.480833989
## 300 0.867522101
## 309 0.982829787
## 310 0.855007037
## 318 0.990509694
## 319 0.932515416
## 328 0.994848629##################################
# Reporting the independent evaluation results
# for the test set
##################################
(LDA_GA_Test_Accuracy <- Accuracy(y_pred = LDA_GA_Test$LDA_GA_Predicted.pred,
y_true = LDA_GA_Test$LDA_GA_Observed))## [1] 0.84848481.6 Consolidated Findings
[A] The simulated annealing and genetic algorithms to select a subset of informative predictors performed better for models without an inherent variable selection feature (i.e. linear discriminant analysis as compared to random forest).
[A.1] RF: Random Forest (randomForest package)
[A.1.1] RF_FULL (Random Forest Without Simulated Annealing and Genetic Algorithms)
[A.1.1.1] Cross-Validation Accuracy = 0.77975
[A.1.1.2] Test Accuracy = 0.80303
[A.1.2] RF_SA (Random Forest With Simulated Annealing)
[A.1.2.1] Cross-Validation Accuracy = 0.77618
[A.1.2.2] Test Accuracy = 0.77272
[A.1.3] RF_GA (Random Forest With Genetic Algorithms)
[A.1.3.1] Cross-Validation Accuracy = 0.79842
[A.1.3.2] Test Accuracy = 0.78787
[A.2] LDA: Linear Discriminant Analysis (MASS package)
[A.2.1] LDA_FULL (Linear Discriminant Analysis Without Simulated Annealing and Genetic Algorithms)
[A.2.1.1] Cross-Validation Accuracy = 0.76754
[A.2.1.2]Test Accuracy = 0.75757
[A.2.2] LDA_SA (Linear Discriminant Analysis With Simulated Annealing)
[A.2.2.1] Cross-Validation Accuracy = 0.80941
[A.2.2.2] Test Accuracy = 0.81818
[A.2.3] LDA_GA (Linear Discriminant Analysis With Genetic Algorithms)
[A.2.3.1] Cross-Validation Accuracy = 0.79402
[A.2.3.2] Test Accuracy = 0.84848
Code Chunk | Output
##################################
# Consolidating all evaluation results
# for the train and test sets
# using the accuracy metric
##################################
Model <- c('RF_FULL','RF_SA','RF_GA','LDA_FULL','LDA_SA','LDA_GA',
'RF_FULL','RF_SA','RF_GA','LDA_FULL','LDA_SA','LDA_GA')
Set <- c(rep('Cross-Validation',6),rep('Test',6))
Accuracy <- c(RF_FULL_Train_Accuracy,
RF_SA_Train_Accuracy,
RF_GA_Train_Accuracy,
LDA_FULL_Train_Accuracy,
LDA_SA_Train_Accuracy,
LDA_GA_Train_Accuracy,
RF_FULL_Test_Accuracy,
RF_SA_Test_Accuracy,
RF_GA_Test_Accuracy,
LDA_FULL_Test_Accuracy,
LDA_SA_Test_Accuracy,
LDA_GA_Test_Accuracy)
Accuracy_Summary <- as.data.frame(cbind(Model,Set,Accuracy))
Accuracy_Summary$Accuracy <- as.numeric(as.character(Accuracy_Summary$Accuracy))
Accuracy_Summary$Set <- factor(Accuracy_Summary$Set,
levels = c("Cross-Validation",
"Test"))
Accuracy_Summary$Model <- factor(Accuracy_Summary$Model,
levels = c('RF_FULL',
'RF_SA',
'RF_GA',
'LDA_FULL',
'LDA_SA',
'LDA_GA'))
print(Accuracy_Summary, row.names=FALSE)## Model Set Accuracy
## RF_FULL Cross-Validation 0.7797517
## RF_SA Cross-Validation 0.7761803
## RF_GA Cross-Validation 0.7984229
## LDA_FULL Cross-Validation 0.7675417
## LDA_SA Cross-Validation 0.8094119
## LDA_GA Cross-Validation 0.7940273
## RF_FULL Test 0.8030303
## RF_SA Test 0.7727273
## RF_GA Test 0.7878788
## LDA_FULL Test 0.7575758
## LDA_SA Test 0.8181818
## LDA_GA Test 0.8484848(Accuracy_Plot <- dotplot(Model ~ Accuracy,
data = Accuracy_Summary,
groups = Set,
main = "Classification Model Performance Comparison",
ylab = "Model",
xlab = "Accuracy",
auto.key = list(adj=1, space="top", columns=2),
type=c("p", "h"),
origin = 0,
alpha = 0.45,
pch = 16,
cex = 2))
3. References
[Book] Applied Predictive Modeling by Max Kuhn and Kjell Johnson
[Book] An Introduction to Statistical Learning by Gareth James, Daniela Witten, Trevor Hastie and Rob Tibshirani
[Book] Multivariate Data Visualization with R by Deepayan Sarkar
[Book] Machine Learning by Samuel Jackson
[Book] Data Modeling Methods by Jacob Larget
[Book] Feature Engineering and Selection: A Practical Approach for Predictive Models by Max Kuhn and Kjell Johnson
[R Package] AppliedPredictiveModeling by Max Kuhn
[R Package] caret by Max Kuhn
[R Package] rpart by Terry Therneau and Beth Atkinson
[R Package] lattice by Deepayan Sarkar
[R Package] dplyr by Hadley Wickham
[R Package] moments by Lukasz Komsta and Frederick
[R Package] skimr by Elin Waring
[R Package] RANN by Sunil Arya, David Mount, Samuel Kemp and Gregory Jefferis
[R Package] corrplot by Taiyun Wei
[R Package] tidyverse by Hadley Wickham
[R Package] lares by Bernardo Lares
[R Package] DMwR2 by Luis Torgo
[R Package] gridExtra by Baptiste Auguie and Anton Antonov
[R Package] rattle by Graham Williams
[R Package] rpart.plot by Stephen Milborrow
[R Package] RColorBrewer by Erich Neuwirth
[R Package] stats by R Core Team
[R Package] pls by Kristian Hovde Liland
[R Package] nnet by Brian Ripley
[R Package] elasticnet by Hui Zou
[R Package] earth by Stephen Milborrow
[R Package] party by Torsten Hothorn
[R Package] kernlab by Alexandros Karatzoglou
[R Package] randomForest by Andy Liaw
[R Package] pROC by Xavier Robin
[R Package] mda by Trevor Hastie
[R Package] klaR by Christian Roever, Nils Raabe, Karsten Luebke, Uwe Ligges, Gero Szepannek, Marc Zentgraf and David Meyer
[R Package] pamr by Trevor Hastie, Rob Tibshirani, Balasubramanian Narasimhan and Gil Chu
[Article] The caret Package by Max Kuhn
[Article] A Short Introduction to the caret Package by Max Kuhn
[Article] Caret Package – A Practical Guide to Machine Learning in R by Selva Prabhakaran
[Article] Tuning Machine Learning Models Using the Caret R Package by Jason Brownlee
[Article] Lattice Graphs by Alboukadel Kassambara
[Article] A Tour of Machine Learning Algorithms by Jason Brownlee
[Article] How to Choose a Feature Selection Method For Machine Learning by Jason Brownlee
[Article] Simulated Annealing Feature Selection by Max Kuhn
[Article] Simulated Annealing Algorithm Explained from Scratch (Python) by Naveen James
[Article] Simulated Annealing: A Simple Overview in 5 Points by Ajay Ohri
[Article] Simulated Annealing From Scratch in Python by Jason Brownlee
[Article] Simulated Annealing for Beginners by Lee Jacobson
[Article] Genetic Algorithms for Feature Selection by By Fernando Gomez, Alberto Quesada, Pedro Ángel Fraile Manzano and Roberto Lopez
[Article] Feature Selection Using Genetic Algorithm by Let The Data Confess Team
[Article] Feature Selection using Genetic Algorithms in R by Pablo Casas
[Article] What is Genetic Algorithm? by Priya Pedamkar
[Article] Genetic Algorithms by Geeks For Geeks Team
[Article] Decision Tree Algorithm Examples In Data Mining by Software Testing Help Team
[Article] 4 Types of Classification Tasks in Machine Learning by Jason Brownlee
[Article] Spot-Check Classification Machine Learning Algorithms in Python with scikit-learn by Jason Brownlee
[Article] An Introduction to Naive Bayes Algorithm for Beginners by Turing Team
[Article] Machine Learning Tutorial: A Step-by-Step Guide for Beginners by Mayank Banoula
[Article] Discriminant Analysis Essentials in R by Alboukadel Kassambara
[Article] Linear Discriminant Analysis, Explained by Xiaozhou Yang
[Article] Classification Tree by BCCVL Team
[Article] Random Forest by BCCVL Team
[Article] What is a Random Forest? by Thomas Wood
[Article] Random Forest Algorithm - How It Works & Why It’s So Effective by Turing Team
[Article] Generalized Linear Model by BCCVL Team
[Article] Linear Discriminant Analysis for Machine Learning by Jason Brownlee
[Article] An Illustrative Introduction to Fisher’s Linear Discriminant by Free Code Camp Team
[Article] ML | Linear Discriminant Analysis by Geeks For Geeks Team
[Publication] Optimization by Simulated Annealing by S Kirkpatrick, C Gelatt and M Vecchi (Science)
[Publication] Simulated Annealing Algorithms: An Overview by R Rutenbar (IEEE Circuits and Devices Magazine)
[Publication] An Introduction to Genetic Algorithms by Melanie Mitchell (Complex Adaptive Systems)
[Publication] Bagging Predictors by Leo Breiman (Machine Learning)
[Publication] Random Forest by Leo Breiman (Machine Learning)
[Publication] The Use of Multiple Measurements in Taxonomic Problems by Ronald Fisher (Annals of Human Genetics)
[Course] Applied Data Mining and Statistical Learning by Penn State Eberly College of Science
[Course] Regression Methods by Penn State Eberly College of Science
[Course] Applied Regression Analysis by Penn State Eberly College of Science
[Course] Applied Data Mining and Statistical Learning by Penn State Eberly College of Science