Data Preprocessing : Missing Data Pattern Analysis, Imputation Method Evaluation and Post-Imputation Diagnostics
John Pauline Pineda
August 16, 2022
1. Table of Contents
This project explores various analysis and imputation procedures for incomplete data using various helpful packages in R. Missing data patterns were visualized using matrix, cluster and correlation plots, with the missing data mechanism evaluated using a Regression-Based Test. Methods applied in the analysis to replace missing data points with substituted values included Random Replacement, Median Imputation, Mean Imputation, Mutivariate Data Analysis Imputation (Regularized, Expectation-Maximization), Principal Component Analysis Imputation (Probabilistic, Bayesian, Support Vector Machine-Based, Non-Linear Iterative Partial Least Squares, Non-Linear Principal Component Analysis), Multivariate Imputation by Chained Equations, Bayesian Multiple Imputation, Expectation-Maximization with Bootstrapping, Random Forest Imputation, Multiple Imputation Using Additive Regression, Bootstrapping and Predictive Mean Matching and K-Nearest Neighbors Imputation. Performance of the missing data imputation methods was evaluated using the processing time, root mean squared error, mean absolute error and Kolmogorov-Smirnov test statistic metrics. Post-imputation diagnostics was performed to assess the plausibility of the substituted values in comparison to the complete data. All results were consolidated in a Summary presented at the end of the document.
Missing data refer to instances of observations intended to be collected but did not, which reduce the representativeness of the sample. Depending on how missing data occurred, it introduces bias into the statistical estimates and leads to inefficient data analysis. Imputation refers to the replacement of missing data with another value based on a reasonable estimate. Imputation algorithms applied in this study (mostly contained in the missCompare, mi, mice, missForest, missMDA and pcaMethods packages) attempt to perform a valid analysis for different missingness mechanisms with the objective of completing the dataset while maintaining its true underlying distribution and multivariate associations.
1.1 Sample Data
The Traumatic Brain Injury dataset from the book Clinical Prediction Models was used for this illustrated example.
Preliminary dataset assessment:
[A] 2159 rows (observations)
[B] 16 columns (variables)
[B.1] 2/16 response = unfav and mort variables (factor)
[B.2] 14/16 predictors = All remaining variables (4/14 numeric + 10/14 factor)
Code Chunk | Output
##################################
# Loading R libraries
##################################
library(datasets)
library(caret)
library(moments)
library(missCompare)
library(mi)
library(missMDA)
library(pcaMethods)
library(missForest)
library(rms)
library(mice)
library(VIM)
library(misty)
library(Hmisc)
library(Amelia)
library(foreign)
library(RBtest)
##################################
# Defining file paths
##################################
DATASETS_PATH <- file.path("datasets")
##################################
# Loading source and
# formulating the analysis set
##################################
TBI <- read.spss(file.path("..", DATASETS_PATH, "TBI.sav"),
use.value.labels=F,
to.data.frame=T)
##################################
# Performing a general exploration of the dataset
##################################
dim(TBI)## [1] 2159 24summary(TBI)## trial d.gos d.mort d.unfav
## Length:2159 Min. :1.000 Min. :0.000 Min. :0.0000
## Class :character 1st Qu.:2.000 1st Qu.:0.000 1st Qu.:0.0000
## Mode :character Median :4.000 Median :0.000 Median :0.0000
## Mean :3.543 Mean :0.233 Mean :0.3942
## 3rd Qu.:5.000 3rd Qu.:0.000 3rd Qu.:1.0000
## Max. :5.000 Max. :1.000 Max. :1.0000
##
## cause age d.motor d.pupil
## Min. :3.000 Min. :14.00 Min. :1.000 Min. :1.000
## 1st Qu.:3.000 1st Qu.:22.00 1st Qu.:3.000 1st Qu.:1.000
## Median :4.000 Median :30.00 Median :4.000 Median :1.000
## Mean :4.908 Mean :33.21 Mean :3.991 Mean :1.458
## 3rd Qu.:6.000 3rd Qu.:43.00 3rd Qu.:5.000 3rd Qu.:2.000
## Max. :9.000 Max. :79.00 Max. :6.000 Max. :3.000
## NA's :123
## pupil.i hypoxia hypotens ctclass
## Min. :1.000 Min. :0.0000 Min. :0.0000 Min. :1.000
## 1st Qu.:1.000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:2.000
## Median :1.000 Median :0.0000 Median :0.0000 Median :3.000
## Mean :1.462 Mean :0.2167 Mean :0.1795 Mean :3.281
## 3rd Qu.:2.000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:5.000
## Max. :3.000 Max. :1.0000 Max. :1.0000 Max. :6.000
## NA's :249 NA's :59 NA's :25
## tsah edh cisterns shift
## Min. :0.0000 Min. :0.0000 Min. :1.000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:1.000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :1.000 Median :0.0000
## Mean :0.4779 Mean :0.1268 Mean :1.455 Mean :0.1987
## 3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:2.000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :3.000 Max. :1.0000
## NA's :96 NA's :38 NA's :257 NA's :252
## d.sysbpt glucose glucoset ph
## Min. : 60.0 Min. : 0.5556 Min. : 3.000 Min. :6.790
## 1st Qu.:121.1 1st Qu.: 6.7000 1st Qu.: 6.700 1st Qu.:7.320
## Median :131.3 Median : 8.2000 Median : 8.200 Median :7.380
## Mean :131.4 Mean : 8.9078 Mean : 8.863 Mean :7.376
## 3rd Qu.:142.1 3rd Qu.:10.4000 3rd Qu.:10.400 3rd Qu.:7.450
## Max. :207.4 Max. :41.4000 Max. :20.000 Max. :7.660
## NA's :64 NA's :64 NA's :457
## sodium sodiumt hb hbt
## Min. :114.0 Min. :125.0 Min. : 2.50 Min. : 6.00
## 1st Qu.:137.0 1st Qu.:137.0 1st Qu.:10.90 1st Qu.:10.90
## Median :140.0 Median :140.0 Median :12.90 Median :12.90
## Mean :139.3 Mean :139.3 Mean :12.45 Mean :12.47
## 3rd Qu.:142.0 3rd Qu.:142.0 3rd Qu.:14.30 3rd Qu.:14.30
## Max. :154.0 Max. :154.0 Max. :18.60 Max. :17.00
## NA's :62 NA's :62 NA's :24 NA's :24describe(TBI)## TBI
##
## 24 Variables 2159 Observations
## --------------------------------------------------------------------------------
## trial
## n missing distinct
## 2159 0 2
##
## Value 74 75
## Frequency 1118 1041
## Proportion 0.518 0.482
## --------------------------------------------------------------------------------
## d.gos
## n missing distinct Info Mean Gmd
## 2159 0 5 0.894 3.543 1.726
##
## Value 1 2 3 4 5
## Frequency 503 86 262 351 957
## Proportion 0.233 0.040 0.121 0.163 0.443
##
## For the frequency table, variable is rounded to the nearest 0
## --------------------------------------------------------------------------------
## d.mort
## n missing distinct Info Sum Mean Gmd
## 2159 0 2 0.536 503 0.233 0.3576
##
## --------------------------------------------------------------------------------
## d.unfav
## n missing distinct Info Sum Mean Gmd
## 2159 0 2 0.716 851 0.3942 0.4778
##
## --------------------------------------------------------------------------------
## cause
## n missing distinct Info Mean Gmd
## 2159 0 5 0.921 4.908 2.301
##
## Value 3 4 5 6 9
## Frequency 848 420 134 370 387
## Proportion 0.393 0.195 0.062 0.171 0.179
##
## For the frequency table, variable is rounded to the nearest 0
## --------------------------------------------------------------------------------
## age
## n missing distinct Info Mean Gmd .05 .10
## 2159 0 64 0.999 33.21 15.17 17 18
## .25 .50 .75 .90 .95
## 22 30 43 54 59
##
## lowest : 14 15 16 17 18, highest: 74 75 76 77 79
## --------------------------------------------------------------------------------
## d.motor
## n missing distinct Info Mean Gmd
## 2159 0 6 0.919 3.991 1.226
##
## Value 1 2 3 4 5 6
## Frequency 14 279 369 627 790 80
## Proportion 0.006 0.129 0.171 0.290 0.366 0.037
##
## For the frequency table, variable is rounded to the nearest 0
## --------------------------------------------------------------------------------
## d.pupil
## n missing distinct Info Mean Gmd
## 2036 123 3 0.647 1.458 0.6881
##
## Value 1 2 3
## Frequency 1430 279 327
## Proportion 0.702 0.137 0.161
##
## For the frequency table, variable is rounded to the nearest 0
## --------------------------------------------------------------------------------
## pupil.i
## n missing distinct Info Mean Gmd
## 2159 0 3 0.65 1.462 0.6915
##
## Value 1 2 3
## Frequency 1511 299 349
## Proportion 0.700 0.138 0.162
##
## For the frequency table, variable is rounded to the nearest 0
## --------------------------------------------------------------------------------
## hypoxia
## n missing distinct Info Sum Mean Gmd
## 1910 249 2 0.509 414 0.2168 0.3397
##
## --------------------------------------------------------------------------------
## hypotens
## n missing distinct Info Sum Mean Gmd
## 2100 59 2 0.442 377 0.1795 0.2947
##
## --------------------------------------------------------------------------------
## ctclass
## n missing distinct Info Mean Gmd
## 2134 25 6 0.928 3.281 1.689
##
## Value 1 2 3 4 5 6
## Frequency 149 781 414 85 521 184
## Proportion 0.070 0.366 0.194 0.040 0.244 0.086
##
## For the frequency table, variable is rounded to the nearest 0
## --------------------------------------------------------------------------------
## tsah
## n missing distinct Info Sum Mean Gmd
## 2063 96 2 0.749 986 0.4779 0.4993
##
## --------------------------------------------------------------------------------
## edh
## n missing distinct Info Sum Mean Gmd
## 2121 38 2 0.332 269 0.1268 0.2216
##
## --------------------------------------------------------------------------------
## cisterns
## n missing distinct Info Mean Gmd
## 1902 257 3 0.716 1.455 0.6367
##
## Value 1 2 3
## Frequency 1223 492 187
## Proportion 0.643 0.259 0.098
##
## For the frequency table, variable is rounded to the nearest 0
## --------------------------------------------------------------------------------
## shift
## n missing distinct Info Sum Mean Gmd
## 1907 252 2 0.478 379 0.1987 0.3187
##
## --------------------------------------------------------------------------------
## d.sysbpt
## n missing distinct Info Mean Gmd .05 .10
## 2159 0 1566 1 131.4 17.61 107.0 112.2
## .25 .50 .75 .90 .95
## 121.1 131.3 142.1 151.1 156.2
##
## lowest : 60 64.19 65.6 71.33 73.71 , highest: 182.92 184.16 184.7 188.29 207.4
## --------------------------------------------------------------------------------
## glucose
## n missing distinct Info Mean Gmd .05 .10
## 2095 64 431 1 8.908 3.56 5.000 5.633
## .25 .50 .75 .90 .95
## 6.700 8.200 10.400 13.056 15.350
##
## lowest : 0.555556 1 1.03 1.04 1.22
## highest: 29.2222 30.8889 31.1111 32.5556 41.4
## --------------------------------------------------------------------------------
## glucoset
## n missing distinct Info Mean Gmd .05 .10
## 2095 64 381 1 8.863 3.405 5.000 5.633
## .25 .50 .75 .90 .95
## 6.700 8.200 10.400 13.056 15.350
##
## lowest : 3 3.03 3.05556 3.2 3.44444
## highest: 19.5 19.5556 19.7778 19.8 20
## --------------------------------------------------------------------------------
## ph
## n missing distinct Info Mean Gmd .05 .10
## 1702 457 112 0.999 7.376 0.1183 7.19 7.24
## .25 .50 .75 .90 .95
## 7.32 7.38 7.45 7.50 7.54
##
## lowest : 6.79 6.83 6.87 6.9 6.91, highest: 7.62 7.63 7.64 7.65 7.66
## --------------------------------------------------------------------------------
## sodium
## n missing distinct Info Mean Gmd .05 .10
## 2097 62 62 0.993 139.3 4.448 132 134
## .25 .50 .75 .90 .95
## 137 140 142 144 145
##
## lowest : 114 117 118 121 123 , highest: 150 151 151.7 153 154
## --------------------------------------------------------------------------------
## sodiumt
## n missing distinct Info Mean Gmd .05 .10
## 2097 62 55 0.993 139.3 4.408 132 134
## .25 .50 .75 .90 .95
## 137 140 142 144 145
##
## lowest : 125 126 126.5 127 127.4, highest: 150 151 151.7 153 154
## --------------------------------------------------------------------------------
## hb
## n missing distinct Info Mean Gmd .05 .10
## 2135 24 156 1 12.45 2.846 7.7 8.8
## .25 .50 .75 .90 .95
## 10.9 12.9 14.3 15.3 15.9
##
## lowest : 2.5 2.8 3.4 3.6 4 , highest: 17.3 17.4 17.6 17.7 18.6
## --------------------------------------------------------------------------------
## hbt
## n missing distinct Info Mean Gmd .05 .10
## 2135 24 130 1 12.47 2.809 7.7 8.8
## .25 .50 .75 .90 .95
## 10.9 12.9 14.3 15.3 15.9
##
## lowest : 6 6.1 6.2 6.3 6.4 , highest: 16.6 16.7 16.8 16.9 17
## --------------------------------------------------------------------------------##################################
# Performing re-categorization and re-grouping
# of factor variables
##################################
TBI$pupil <- ifelse(TBI$d.pupil==9,NA,TBI$d.pupil)
TBI$motor <- ifelse(is.na(TBI$d.motor),9,TBI$d.motor)
TBI$motor1 <- ifelse(TBI$motor==1,1,0)
TBI$motor2 <- ifelse(TBI$motor==2,1,0)
TBI$motor3 <- ifelse(TBI$motor==3,1,0)
TBI$motor4 <- ifelse(TBI$motor==4,1,0)
TBI$motor56 <- ifelse(TBI$motor==5 | TBI$motor==6,1,0)
TBI$motor9 <- ifelse(TBI$motor==9,1,0)
TBI$motorG <- ifelse(TBI$motor1==1,5,
ifelse(TBI$motor2==1,4,
ifelse(TBI$motor3==1,3,
ifelse(TBI$motor4==1,2,
ifelse(TBI$motor56==1,1,
ifelse(TBI$motor9==1,9,NA))))))
TBI$motorG <- as.factor(TBI$motorG)
TBI$mort <- ifelse(TBI$d.gos==1,1,ifelse(TBI$d.gos==6,NA,0))
TBI$deadveg <- ifelse(TBI$d.gos<3,1,ifelse(TBI$d.gos==6,NA,0))
TBI$unfav <- ifelse(TBI$d.gos<4,1,ifelse(TBI$d.gos==6,NA,0))
TBI$good <- ifelse(TBI$d.gos<5,1,ifelse(TBI$d.gos==6,NA,0))
TBI$ctclass2 <- ifelse(TBI$ctclass==2,1,0)
TBI$ctclass1 <- ifelse(TBI$ctclass==1,1,0)
TBI$ctclass34 <- ifelse(TBI$ctclass==3 | TBI$ctclass==4,1,0)
TBI$ctclass56 <- ifelse(TBI$ctclass==5 | TBI$ctclass==6,1,0)
TBI$ctclassr4 <- ifelse(TBI$ctclass1==1,2,
ifelse(TBI$ctclass2==1,1,
ifelse(TBI$ctclass34==1,3,
ifelse(TBI$ctclass56==1,4,NA))))
TBI$ctclassr4 <- as.factor(TBI$ctclassr4)
TBI$ctclassr3 <- ifelse(TBI$ctclass1==1 | TBI$ctclass2==1,1,
ifelse(TBI$ctclass34==1,2,
ifelse(TBI$ctclass56==1,3,NA)))
TBI$ctclassr3 <- as.factor(TBI$ctclassr3)
TBI.Analysis <- TBI[,Cs(trial,
age,
hypoxia,
hypotens,
cisterns,
shift,
tsah,
edh,
pupil,
motorG,
ctclassr3,
d.sysbpt,
hbt,
glucoset,
unfav,
mort)]
names(TBI.Analysis) <- Cs(trial,
age,
hypoxia,
hypotens,
cisterns,
shift,
tsah,
edh,
pupil,
motor,
ctclass,
d.sysbp,
hb,
glucose,
unfav,
mort )
TBI.Analysis$cisterns <- ifelse(TBI.Analysis$cisterns>1,1,0)
TBI.Analysis$trial <- as.factor(TBI.Analysis$trial)
TBI.Analysis$age <- as.numeric(TBI.Analysis$age)
TBI.Analysis$hypoxia <-as.factor(TBI.Analysis$hypoxia)
TBI.Analysis$hypotens <-as.factor(TBI.Analysis$hypotens)
TBI.Analysis$cisterns <-as.factor(TBI.Analysis$cisterns)
TBI.Analysis$shift <-as.factor(TBI.Analysis$shift)
TBI.Analysis$tsah <-as.factor(TBI.Analysis$tsah)
TBI.Analysis$edh <-as.factor(TBI.Analysis$edh)
TBI.Analysis$pupil <-as.factor(TBI.Analysis$pupil)
TBI.Analysis$motor <-as.factor(TBI.Analysis$motor)
TBI.Analysis$ctclass <-as.factor(TBI.Analysis$ctclass)
TBI.Analysis$d.sysbp <-as.numeric(TBI.Analysis$d.sysbp)
TBI.Analysis$hb <-as.numeric(TBI.Analysis$hb)
TBI.Analysis$glucose <-as.numeric(TBI.Analysis$glucose)
TBI.Analysis$unfav <-as.factor(TBI.Analysis$unfav)
TBI.Analysis$mort <-as.factor(TBI.Analysis$mort)
dim(TBI.Analysis)## [1] 2159 16describe(TBI.Analysis)## TBI.Analysis
##
## 16 Variables 2159 Observations
## --------------------------------------------------------------------------------
## trial
## n missing distinct
## 2159 0 2
##
## Value 74 75
## Frequency 1118 1041
## Proportion 0.518 0.482
## --------------------------------------------------------------------------------
## age
## n missing distinct Info Mean Gmd .05 .10
## 2159 0 64 0.999 33.21 15.17 17 18
## .25 .50 .75 .90 .95
## 22 30 43 54 59
##
## lowest : 14 15 16 17 18, highest: 74 75 76 77 79
## --------------------------------------------------------------------------------
## hypoxia
## n missing distinct
## 1910 249 2
##
## Value 0 1
## Frequency 1496 414
## Proportion 0.783 0.217
## --------------------------------------------------------------------------------
## hypotens
## n missing distinct
## 2100 59 2
##
## Value 0 1
## Frequency 1723 377
## Proportion 0.82 0.18
## --------------------------------------------------------------------------------
## cisterns
## n missing distinct
## 1902 257 2
##
## Value 0 1
## Frequency 1223 679
## Proportion 0.643 0.357
## --------------------------------------------------------------------------------
## shift
## n missing distinct
## 1907 252 2
##
## Value 0 1
## Frequency 1528 379
## Proportion 0.801 0.199
## --------------------------------------------------------------------------------
## tsah
## n missing distinct
## 2063 96 2
##
## Value 0 1
## Frequency 1077 986
## Proportion 0.522 0.478
## --------------------------------------------------------------------------------
## edh
## n missing distinct
## 2121 38 2
##
## Value 0 1
## Frequency 1852 269
## Proportion 0.873 0.127
## --------------------------------------------------------------------------------
## pupil
## n missing distinct
## 2036 123 3
##
## Value 1 2 3
## Frequency 1430 279 327
## Proportion 0.702 0.137 0.161
## --------------------------------------------------------------------------------
## motor
## n missing distinct
## 2159 0 5
##
## Value 1 2 3 4 5
## Frequency 870 627 369 279 14
## Proportion 0.403 0.290 0.171 0.129 0.006
## --------------------------------------------------------------------------------
## ctclass
## n missing distinct
## 2134 25 3
##
## Value 1 2 3
## Frequency 930 499 705
## Proportion 0.436 0.234 0.330
## --------------------------------------------------------------------------------
## d.sysbp
## n missing distinct Info Mean Gmd .05 .10
## 2159 0 1566 1 131.4 17.61 107.0 112.2
## .25 .50 .75 .90 .95
## 121.1 131.3 142.1 151.1 156.2
##
## lowest : 60 64.19 65.6 71.33 73.71 , highest: 182.92 184.16 184.7 188.29 207.4
## --------------------------------------------------------------------------------
## hb
## n missing distinct Info Mean Gmd .05 .10
## 2135 24 130 1 12.47 2.809 7.7 8.8
## .25 .50 .75 .90 .95
## 10.9 12.9 14.3 15.3 15.9
##
## lowest : 6 6.1 6.2 6.3 6.4 , highest: 16.6 16.7 16.8 16.9 17
## --------------------------------------------------------------------------------
## glucose
## n missing distinct Info Mean Gmd .05 .10
## 2095 64 381 1 8.863 3.405 5.000 5.633
## .25 .50 .75 .90 .95
## 6.700 8.200 10.400 13.056 15.350
##
## lowest : 3 3.03 3.05556 3.2 3.44444
## highest: 19.5 19.5556 19.7778 19.8 20
## --------------------------------------------------------------------------------
## unfav
## n missing distinct
## 2159 0 2
##
## Value 0 1
## Frequency 1308 851
## Proportion 0.606 0.394
## --------------------------------------------------------------------------------
## mort
## n missing distinct
## 2159 0 2
##
## Value 0 1
## Frequency 1656 503
## Proportion 0.767 0.233
## --------------------------------------------------------------------------------summary(TBI.Analysis)## trial age hypoxia hypotens cisterns shift
## 74:1118 Min. :14.00 0 :1496 0 :1723 0 :1223 0 :1528
## 75:1041 1st Qu.:22.00 1 : 414 1 : 377 1 : 679 1 : 379
## Median :30.00 NA's: 249 NA's: 59 NA's: 257 NA's: 252
## Mean :33.21
## 3rd Qu.:43.00
## Max. :79.00
##
## tsah edh pupil motor ctclass d.sysbp
## 0 :1077 0 :1852 1 :1430 1:870 1 :930 Min. : 60.0
## 1 : 986 1 : 269 2 : 279 2:627 2 :499 1st Qu.:121.1
## NA's: 96 NA's: 38 3 : 327 3:369 3 :705 Median :131.3
## NA's: 123 4:279 NA's: 25 Mean :131.4
## 5: 14 3rd Qu.:142.1
## Max. :207.4
##
## hb glucose unfav mort
## Min. : 6.00 Min. : 3.000 0:1308 0:1656
## 1st Qu.:10.90 1st Qu.: 6.700 1: 851 1: 503
## Median :12.90 Median : 8.200
## Mean :12.47 Mean : 8.863
## 3rd Qu.:14.30 3rd Qu.:10.400
## Max. :17.00 Max. :20.000
## NA's :24 NA's :64##################################
# Formulating a data type assessment summary
##################################
PDA <- TBI.Analysis
(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 trial factor
## 2 2 age numeric
## 3 3 hypoxia factor
## 4 4 hypotens factor
## 5 5 cisterns factor
## 6 6 shift factor
## 7 7 tsah factor
## 8 8 edh factor
## 9 9 pupil factor
## 10 10 motor factor
## 11 11 ctclass factor
## 12 12 d.sysbp numeric
## 13 13 hb numeric
## 14 14 glucose numeric
## 15 15 unfav factor
## 16 16 mort factor1.2 Data Quality Assessment
[A] Missing observations noted for 10 variables with NA.Count>0 and Fill.Rate<1.0.
[A.1] hypoxia variable (factor) with NA.Count=249 and Fill.Rate=0.885
[A.2] hypotens variable (factor) with NA.Count=59 and Fill.Rate=0.973
[A.3] cisterns variable (factor) with NA.Count=257 and Fill.Rate=0.881
[A.4] shift variable (factor) with NA.Count=252 and Fill.Rate=0.883
[A.5] tsah variable (factor) with NA.Count=96 and Fill.Rate=0.956
[A.6] edh variable (factor) with NA.Count=38 and Fill.Rate=0.982
[A.7] pupil variable (factor) with NA.Count=123 and Fill.Rate=0.943
[A.8] ctclass variable (factor) with NA.Count=25 and Fill.Rate=0.988
[A.9] hb variable (numeric) with NA.Count=24 and Fill.Rate=0.989
[A.10] glucose variable (numeric) with NA.Count=64 and Fill.Rate=0.970
[B] Low variance noted for 1 variable with First.Second.Mode.Ratio>5 or Unique.Count.Ratio<0.01.
[B.1] edh variable (factor) with First.Second.Mode.Ratio=6.885
[C] No high skewness (Skewness>3 or Skewness<(-3)) noted for any variable.
Code Chunk | Output
##################################
# Loading dataset
##################################
DQA <- TBI.Analysis
##################################
# Listing all predictors
##################################
DQA.Predictors <- DQA[,names(DQA)]
##################################
# 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 NA.Count Fill.Rate
## 1 1 trial factor 2159 0 1.000
## 2 2 age numeric 2159 0 1.000
## 3 3 hypoxia factor 2159 249 0.885
## 4 4 hypotens factor 2159 59 0.973
## 5 5 cisterns factor 2159 257 0.881
## 6 6 shift factor 2159 252 0.883
## 7 7 tsah factor 2159 96 0.956
## 8 8 edh factor 2159 38 0.982
## 9 9 pupil factor 2159 123 0.943
## 10 10 motor factor 2159 0 1.000
## 11 11 ctclass factor 2159 25 0.988
## 12 12 d.sysbp numeric 2159 0 1.000
## 13 13 hb numeric 2159 24 0.989
## 14 14 glucose numeric 2159 64 0.970
## 15 15 unfav factor 2159 0 1.000
## 16 16 mort factor 2159 0 1.000##################################
# Listing all numeric predictors
##################################
DQA.Predictors.Numeric <- DQA.Predictors[,sapply(DQA.Predictors, is.numeric)]
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 4 numeric predictor variable(s)."##################################
# Listing all factor predictors
##################################
DQA.Predictors.Factor <- DQA.Predictors[,sapply(DQA.Predictors, is.factor)]
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 12 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))
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 trial factor 2 74 75
## 2 hypoxia factor 3 0 1
## 3 hypotens factor 3 0 1
## 4 cisterns factor 3 0 1
## 5 shift factor 3 0 1
## 6 tsah factor 3 0 1
## 7 edh factor 3 0 1
## 8 pupil factor 4 1 3
## 9 motor factor 5 1 2
## 10 ctclass factor 4 1 3
## 11 unfav factor 2 0 1
## 12 mort factor 2 0 1
## First.Mode.Count Second.Mode.Count Unique.Count.Ratio
## 1 1118 1041 0.001
## 2 1496 414 0.001
## 3 1723 377 0.001
## 4 1223 679 0.001
## 5 1528 379 0.001
## 6 1077 986 0.001
## 7 1852 269 0.001
## 8 1430 327 0.002
## 9 870 627 0.002
## 10 930 705 0.002
## 11 1308 851 0.001
## 12 1656 503 0.001
## First.Second.Mode.Ratio
## 1 1.074
## 2 3.614
## 3 4.570
## 4 1.801
## 5 4.032
## 6 1.092
## 7 6.885
## 8 4.373
## 9 1.388
## 10 1.319
## 11 1.537
## 12 3.292##################################
# 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))
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(moments::skewness(x,na.rm = TRUE),3), nsmall=3)),
Kurtosis=sapply(DQA.Predictors.Numeric, function(x) format(round(moments::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 Unique.Count.Ratio First.Mode.Value
## 1 age numeric 64 0.030 21.000
## 2 d.sysbp numeric 1566 0.725 130.000
## 3 hb numeric 131 0.061 13.900
## 4 glucose numeric 382 0.177 20.000
## Second.Mode.Value First.Mode.Count Second.Mode.Count First.Second.Mode.Ratio
## 1 19.000 104 100 1.040
## 2 120.000 9 8 1.125
## 3 13.600 47 43 1.093
## 4 6.500 29 27 1.074
## Minimum Mean Median Maximum Skewness Kurtosis Percentile25th
## 1 14.000 33.211 30.000 79.000 0.721 2.585 22.000
## 2 60.000 131.430 131.280 207.400 -0.022 3.982 121.085
## 3 6.000 12.468 12.900 17.000 -0.619 2.786 10.900
## 4 3.000 8.863 8.200 20.000 1.192 4.727 6.700
## Percentile75th
## 1 43.000
## 2 142.060
## 3 14.300
## 4 10.400##################################
# 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$NA.Count>0,]
} else {
print("No missing observations noted.")
}## [1] "Missing observations noted for 10 variable(s) with NA.Count>0 and Fill.Rate<1.0."## Column.Index Column.Name Column.Type Row.Count NA.Count Fill.Rate
## 3 3 hypoxia factor 2159 249 0.885
## 4 4 hypotens factor 2159 59 0.973
## 5 5 cisterns factor 2159 257 0.881
## 6 6 shift factor 2159 252 0.883
## 7 7 tsah factor 2159 96 0.956
## 8 8 edh factor 2159 38 0.982
## 9 9 pupil factor 2159 123 0.943
## 11 11 ctclass factor 2159 25 0.988
## 13 13 hb numeric 2159 24 0.989
## 14 14 glucose numeric 2159 64 0.970##################################
# Checking for zero or near-zero variance predictors
##################################
if (length(names(DQA.Predictors.Factor))==0) {
print("No factor predictors noted.")
} else if (nrow(DQA.Predictors.Factor.Summary[as.numeric(as.character(DQA.Predictors.Factor.Summary$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 1 factor variable(s) with First.Second.Mode.Ratio>5."## Column.Name Column.Type Unique.Count First.Mode.Value Second.Mode.Value
## 7 edh factor 3 0 1
## First.Mode.Count Second.Mode.Count Unique.Count.Ratio First.Second.Mode.Ratio
## 7 1852 269 0.001 6.885if (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 Missing Data Pattern Analysis Summary
1.3.1 Assessment using MISSCOMPARE
[A] The original dataset was reconstructed using the clean method from the missCompare package.
[A.1] All observations and variables retained.
[A.1.1] All variables were within the defined 50% observation fill rate or missingness ratio criterion.
[A.1.2] All observation were within the defined 80% variable fill rate or missingness ratio criterion.
[A.2] All 12 factor variables were converted to numeric variables.
[A.3] All NA labels retained. No NA labels were re-coded.
[B] The missing data patterns were summarized using the get_data method from the missCompare package.
[B.1] There were 1431/2159 (0.663) observations assessed as complete.
[B.2] There were 1187/34544 (0.034) instances assessed as missing.
[B.3] The cisterns variable (factor), shift variable (factor) and hypoxia variable (factor) contributed the most missing data.
[B.4] There are 59 missing data patterns observed employing various combinations of the 16 variables.
[B.5] The missing data patterns are clustered between the following variables:
[B.5.1] cisterns variable (factor) and shift variable (factor) variables.
[B.5.2] hb variable (numeric) and glucose variable (numeric) variables.
[B.5.3] trash variable (factor) and edh variable (factor) variables.
[B.5.4] hypoxia variable (factor) and hypotens (factor) variables.
[B.5.5] pupil variable (factor) and ctclass variable (factor) variables.
[B.6] Thresholding the minimum number of observations per distinct missing data pattern showed different percentages of observations retained:
[B.6.1] With the minimum number of observations per distinct missing data pattern set to 5, 89% of observations are retained.
[B.6.2] With the minimum number of observations per distinct missing data pattern set to 10, 81% of observations are retained.
[B.6.3] With the minimum number of observations per distinct missing data pattern set to 20, 74% of observations are retained.
Code Chunk | Output
##################################
# Loading dataset
##################################
MDPA <- TBI.Analysis
##################################
# Reconstructing the dataset by :
# removing variables with fill rate > 0.50
# removing observations with NA ratio > 0.80
# converting factor variables to numeric variables
##################################
MDPA.Cleaned <- missCompare::clean(MDPA,
var_removal_threshold=0.50,
ind_removal_threshold=0.80)
##################################
# Gathering the metadata using the reconstructed dataset
##################################
MDPA.Cleaned.Metadata <- missCompare::get_data(MDPA.Cleaned,
matrixplot_sort = T,
plot_transform = T)
##################################
# Gathering the number of complete cases
##################################
MDPA.Cleaned.Metadata$Complete_cases## [1] 1431MDPA.Cleaned.Metadata$Rows## [1] 2159MDPA.Cleaned.Metadata$Columns## [1] 16MDPA.Cleaned.Metadata$Complete_cases/MDPA.Cleaned.Metadata$Rows## [1] 0.6628069##################################
# Gathering the number of incomplete cases
##################################
MDPA.Cleaned.Metadata$Total_NA## [1] 1187MDPA.Cleaned.Metadata$NA_per_variable## trial age hypoxia hypotens cisterns shift tsah edh
## 0 0 249 59 257 252 96 38
## pupil motor ctclass d.sysbp hb glucose unfav mort
## 123 0 25 0 24 64 0 0MDPA.Cleaned.Metadata$Fraction_missingness## [1] 0.03436197MDPA.Cleaned.Metadata$Fraction_missingness_per_variable## trial age hypoxia hypotens cisterns shift tsah
## 0.00000000 0.00000000 0.11533117 0.02732747 0.11903659 0.11672070 0.04446503
## edh pupil motor ctclass d.sysbp hb glucose
## 0.01760074 0.05697082 0.00000000 0.01157943 0.00000000 0.01111626 0.02964335
## unfav mort
## 0.00000000 0.00000000##################################
# Gathering the missing data patterns
##################################
MDPA.Cleaned.Metadata$Matrix_plot
MDPA.Cleaned.Metadata$Cluster_plot
MDPA.Cleaned.Metadata$Corr_matrix## trial age hypoxia hypotens cisterns
## trial 1.000000000 -0.030651416 1.656750e-01 0.1050912318 0.0090874012
## age -0.030651416 1.000000000 1.031147e-03 0.0797683643 0.0513284240
## hypoxia 0.165675039 0.001031147 1.000000e+00 0.2323622569 0.0460174467
## hypotens 0.105091232 0.079768364 2.323623e-01 1.0000000000 0.0004308286
## cisterns 0.009087401 0.051328424 4.601745e-02 0.0004308286 1.0000000000
## shift -0.065358546 0.104812735 4.487131e-20 -0.0549581210 0.4585598379
## tsah -0.097721950 0.174014741 1.627862e-02 -0.0075673746 0.0329649255
## edh -0.119425686 0.002670862 -4.682238e-02 -0.0770647036 0.0237954129
## pupil 0.088381902 0.016622292 1.438070e-01 0.1137020246 0.1464712963
## motor -0.051699973 -0.008694701 1.885604e-01 0.0656417934 0.1168144834
## ctclass -0.015770576 0.153012007 1.850571e-02 -0.0194182715 0.2788307306
## d.sysbp 0.087643656 0.012554957 -1.094494e-01 -0.2634324171 -0.0114882127
## hb 0.227845969 -0.031832004 -5.386741e-02 -0.2705358063 -0.0417687110
## glucose 0.090165100 0.069076332 1.619970e-01 0.1994708499 0.0498702817
## unfav -0.029068950 0.208375143 1.742552e-01 0.1776370570 0.1396093897
## mort -0.038439923 0.153665440 1.414791e-01 0.1666659119 0.1424181948
## shift tsah edh pupil motor
## trial -6.535855e-02 -0.097721950 -0.119425686 0.08838190 -0.051699973
## age 1.048127e-01 0.174014741 0.002670862 0.01662229 -0.008694701
## hypoxia 4.487131e-20 0.016278621 -0.046822378 0.14380701 0.188560393
## hypotens -5.495812e-02 -0.007567375 -0.077064704 0.11370202 0.065641793
## cisterns 4.585598e-01 0.032964926 0.023795413 0.14647130 0.116814483
## shift 1.000000e+00 0.090218463 0.041278708 0.09772835 0.088389352
## tsah 9.021846e-02 1.000000000 -0.010786454 0.14788861 0.116778650
## edh 4.127871e-02 -0.010786454 1.000000000 -0.02558442 -0.046758976
## pupil 9.772835e-02 0.147888607 -0.025584420 1.00000000 0.381055618
## motor 8.838935e-02 0.116778650 -0.046758976 0.38105562 1.000000000
## ctclass 2.793684e-01 0.191225179 0.296787667 0.21786366 0.167952008
## d.sysbp 9.615297e-03 -0.022296366 -0.015739545 -0.08779228 -0.123171876
## hb -3.378804e-02 0.030632398 -0.019653199 -0.08586573 -0.064731488
## glucose 2.573764e-02 0.102781495 -0.001029329 0.18136723 0.128402858
## unfav 1.340827e-01 0.249226529 -0.065700956 0.31905926 0.353979268
## mort 1.612055e-01 0.229655718 -0.061375715 0.25297999 0.267972519
## ctclass d.sysbp hb glucose unfav
## trial -0.015770576 0.087643656 0.227845969 0.090165100 -0.02906895
## age 0.153012007 0.012554957 -0.031832004 0.069076332 0.20837514
## hypoxia 0.018505712 -0.109449414 -0.053867408 0.161996976 0.17425522
## hypotens -0.019418271 -0.263432417 -0.270535806 0.199470850 0.17763706
## cisterns 0.278830731 -0.011488213 -0.041768711 0.049870282 0.13960939
## shift 0.279368362 0.009615297 -0.033788043 0.025737640 0.13408269
## tsah 0.191225179 -0.022296366 0.030632398 0.102781495 0.24922653
## edh 0.296787667 -0.015739545 -0.019653199 -0.001029329 -0.06570096
## pupil 0.217863665 -0.087792278 -0.085865732 0.181367225 0.31905926
## motor 0.167952008 -0.123171876 -0.064731488 0.128402858 0.35397927
## ctclass 1.000000000 -0.015114873 -0.000441974 0.123201094 0.24639544
## d.sysbp -0.015114873 1.000000000 0.195736194 -0.125362570 -0.09119451
## hb -0.000441974 0.195736194 1.000000000 -0.134613174 -0.15508193
## glucose 0.123201094 -0.125362570 -0.134613174 1.000000000 0.22878822
## unfav 0.246395438 -0.091194506 -0.155081925 0.228788217 1.00000000
## mort 0.222675184 -0.178138387 -0.162844394 0.229159186 0.68327089
## mort
## trial -0.03843992
## age 0.15366544
## hypoxia 0.14147910
## hypotens 0.16666591
## cisterns 0.14241819
## shift 0.16120554
## tsah 0.22965572
## edh -0.06137571
## pupil 0.25297999
## motor 0.26797252
## ctclass 0.22267518
## d.sysbp -0.17813839
## hb -0.16284439
## glucose 0.22915919
## unfav 0.68327089
## mort 1.00000000MDPA.Cleaned.Metadata$MD_Pattern## trial age hypoxia hypotens cisterns shift tsah edh pupil motor ctclass
## 1431 1 1 1 1 1 1 1 1 1 1 1
## 5 1 1 1 1 0 1 1 1 1 1 1
## 1 1 1 1 1 1 0 1 1 1 1 1
## 200 1 1 1 1 0 0 1 1 1 1 1
## 157 1 1 0 1 1 1 1 1 1 1 1
## 12 1 1 0 1 0 0 1 1 1 1 1
## 82 1 1 1 1 1 1 1 1 0 1 1
## 12 1 1 1 1 0 0 1 1 0 1 1
## 10 1 1 0 1 1 1 1 1 0 1 1
## 1 1 1 0 1 0 1 1 1 0 1 1
## 42 1 1 1 1 1 1 0 1 1 1 1
## 9 1 1 1 1 0 0 0 1 1 1 1
## 11 1 1 0 1 1 1 0 1 1 1 1
## 5 1 1 1 1 1 1 0 1 0 1 1
## 34 1 1 1 1 1 1 1 1 1 1 1
## 8 1 1 0 1 1 1 1 1 1 1 1
## 2 1 1 1 1 1 1 1 1 0 1 1
## 2 1 1 1 1 1 1 0 1 1 1 1
## 10 1 1 1 0 1 1 1 1 1 1 1
## 27 1 1 0 0 1 1 1 1 1 1 1
## 2 1 1 0 0 0 0 1 1 1 1 1
## 3 1 1 0 0 1 1 1 1 0 1 1
## 2 1 1 1 0 1 1 0 1 1 1 1
## 2 1 1 0 0 1 1 0 1 1 1 1
## 3 1 1 1 0 1 1 1 1 1 1 1
## 1 1 1 0 0 1 1 1 1 1 1 1
## 1 1 1 0 0 1 1 0 1 1 1 1
## 7 1 1 1 1 1 1 1 0 1 1 1
## 3 1 1 1 1 0 0 1 0 1 1 1
## 3 1 1 0 1 1 1 1 0 1 1 1
## 1 1 1 1 1 1 1 1 0 0 1 1
## 1 1 1 0 1 1 1 1 0 0 1 1
## 10 1 1 1 1 1 1 0 0 1 1 1
## 4 1 1 1 1 0 0 0 0 1 1 1
## 1 1 1 0 1 1 1 0 0 1 1 1
## 1 1 1 1 1 1 1 0 0 0 1 1
## 1 1 1 0 1 1 1 0 0 1 1 1
## 1 1 1 1 0 1 1 1 0 1 1 1
## 1 1 1 0 0 1 1 1 0 1 1 1
## 1 1 1 1 0 1 1 0 0 1 1 1
## 11 1 1 1 1 1 1 1 1 1 1 0
## 2 1 1 1 1 0 0 1 1 1 1 0
## 4 1 1 0 1 1 1 1 1 1 1 0
## 3 1 1 1 1 1 1 1 1 0 1 0
## 1 1 1 1 0 1 1 1 1 1 1 0
## 1 1 1 1 0 0 0 1 1 1 1 0
## 1 1 1 1 1 1 1 1 0 1 1 0
## 2 1 1 1 1 1 1 0 0 1 1 0
## 5 1 1 1 1 1 1 1 1 1 1 1
## 4 1 1 1 1 0 0 1 1 1 1 1
## 1 1 1 1 1 1 1 1 1 0 1 1
## 7 1 1 1 1 1 1 1 1 1 1 1
## 1 1 1 1 1 0 0 1 1 1 1 1
## 1 1 1 0 1 1 1 1 1 1 1 1
## 1 1 1 1 1 0 0 1 1 0 1 1
## 1 1 1 1 1 1 1 0 1 1 1 1
## 2 1 1 0 0 1 1 1 1 1 1 1
## 1 1 1 1 0 1 1 0 1 1 1 1
## 0 0 249 59 257 252 96 38 123 0 25
## d.sysbp hb glucose unfav mort
## 1431 1 1 1 1 1
## 5 1 1 1 1 1
## 1 1 1 1 1 1
## 200 1 1 1 1 1
## 157 1 1 1 1 1
## 12 1 1 1 1 1
## 82 1 1 1 1 1
## 12 1 1 1 1 1
## 10 1 1 1 1 1
## 1 1 1 1 1 1
## 42 1 1 1 1 1
## 9 1 1 1 1 1
## 11 1 1 1 1 1
## 5 1 1 1 1 1
## 34 1 1 0 1 1
## 8 1 1 0 1 1
## 2 1 1 0 1 1
## 2 1 1 0 1 1
## 10 1 1 1 1 1
## 27 1 1 1 1 1
## 2 1 1 1 1 1
## 3 1 1 1 1 1
## 2 1 1 1 1 1
## 2 1 1 1 1 1
## 3 1 1 0 1 1
## 1 1 1 0 1 1
## 1 1 1 0 1 1
## 7 1 1 1 1 1
## 3 1 1 1 1 1
## 3 1 1 1 1 1
## 1 1 1 1 1 1
## 1 1 1 1 1 1
## 10 1 1 1 1 1
## 4 1 1 1 1 1
## 1 1 1 1 1 1
## 1 1 1 1 1 1
## 1 1 1 0 1 1
## 1 1 1 1 1 1
## 1 1 1 1 1 1
## 1 1 1 1 1 1
## 11 1 1 1 1 1
## 2 1 1 1 1 1
## 4 1 1 1 1 1
## 3 1 1 1 1 1
## 1 1 1 1 1 1
## 1 1 1 1 1 1
## 1 1 1 1 1 1
## 2 1 1 1 1 1
## 5 1 0 1 1 1
## 4 1 0 1 1 1
## 1 1 0 1 1 1
## 7 1 0 0 1 1
## 1 1 0 0 1 1
## 1 1 0 0 1 1
## 1 1 0 0 1 1
## 1 1 0 0 1 1
## 2 1 0 1 1 1
## 1 1 0 0 1 1
## 0 24 64 0 0dim(MDPA.Cleaned.Metadata$MD_Pattern)## [1] 59 16MDPA.Cleaned.Metadata$NA_Correlations## trial age hypoxia hypotens
## trial_is.na NaN NaN NaN NaN
## age_is.na NaN NaN NaN NaN
## hypoxia_is.na 0.003075342 -1.991261e-02 NaN -0.050871031
## hypotens_is.na -0.003139022 9.723747e-03 -0.070715627 NaN
## cisterns_is.na -0.020274316 5.403308e-03 -0.036463860 0.021305289
## shift_is.na -0.012972969 2.893106e-03 -0.040060700 0.018044005
## tsah_is.na -0.048171238 1.924787e-02 -0.067614722 -0.098680649
## edh_is.na 0.023420299 5.196470e-03 -0.043045790 -0.065097712
## pupil_is.na 0.037218347 -4.342998e-02 -0.030756342 -0.018479920
## motor_is.na NaN NaN NaN NaN
## ctclass_is.na -0.008194874 -8.522036e-03 -0.005461126 -0.046146806
## d.sysbp_is.na NaN NaN NaN NaN
## hb_is.na -0.039147773 2.245985e-05 -0.029832037 -0.002868117
## glucose_is.na 0.092140222 1.110012e-03 -0.005690478 0.003122214
## unfav_is.na NaN NaN NaN NaN
## mort_is.na NaN NaN NaN NaN
## cisterns shift tsah edh
## trial_is.na NaN NaN NaN NaN
## age_is.na NaN NaN NaN NaN
## hypoxia_is.na 0.005132467 -0.037162241 -8.090368e-03 0.0209094526
## hypotens_is.na 0.019420226 -0.014558767 -9.092611e-04 0.0009040846
## cisterns_is.na NaN 0.027979664 5.895326e-02 -0.0364386527
## shift_is.na -0.030781323 NaN 4.920710e-02 -0.0351378312
## tsah_is.na 0.035616071 -0.016129896 NaN 0.0201143139
## edh_is.na 0.017911716 0.012064215 3.759542e-02 NaN
## pupil_is.na 0.032634364 -0.017689375 -2.970642e-02 0.0320063995
## motor_is.na NaN NaN NaN NaN
## ctclass_is.na 0.008762896 0.004581525 -6.719949e-05 0.0390176196
## d.sysbp_is.na NaN NaN NaN NaN
## hb_is.na -0.029175385 0.007846099 4.863460e-03 -0.0128075625
## glucose_is.na -0.042431688 -0.027251502 -1.925087e-02 -0.0167735791
## unfav_is.na NaN NaN NaN NaN
## mort_is.na NaN NaN NaN NaN
## pupil motor ctclass d.sysbp hb
## trial_is.na NaN NaN NaN NaN NaN
## age_is.na NaN NaN NaN NaN NaN
## hypoxia_is.na -0.0383020501 -0.077961939 -0.018323675 0.06582073 0.02059243
## hypotens_is.na -0.0252221782 -0.029960226 -0.013411691 0.02261856 -0.02056744
## cisterns_is.na 0.0268112302 0.111893054 -0.006296335 -0.06654302 0.11436064
## shift_is.na 0.0192540664 0.105806117 -0.017223821 -0.06403836 0.12099795
## tsah_is.na -0.0308960246 -0.041118410 0.002862034 0.07287370 0.06924227
## edh_is.na -0.0298496078 -0.023869160 0.018298843 0.04278551 0.06563305
## pupil_is.na NaN -0.028658751 -0.020254575 0.02318343 0.03887609
## motor_is.na NaN NaN NaN NaN NaN
## ctclass_is.na -0.0750312122 -0.023662963 NaN 0.01626310 0.06052439
## d.sysbp_is.na NaN NaN NaN NaN NaN
## hb_is.na 0.0005132771 -0.003710246 -0.012940904 0.02107206 NaN
## glucose_is.na 0.0150930949 -0.020565988 -0.049791976 0.04466416 0.01725871
## unfav_is.na NaN NaN NaN NaN NaN
## mort_is.na NaN NaN NaN NaN NaN
## glucose unfav mort
## trial_is.na NaN NaN NaN
## age_is.na NaN NaN NaN
## hypoxia_is.na -0.004860708 -0.002531656 -0.02054161
## hypotens_is.na 0.011223556 0.013113682 0.01173212
## cisterns_is.na -0.046590315 0.033074703 0.03341347
## shift_is.na -0.045520597 0.024587698 0.02631154
## tsah_is.na -0.088678630 -0.055916708 -0.04589547
## edh_is.na -0.036218129 -0.021781268 -0.02622100
## pupil_is.na 0.010353762 -0.018474498 -0.02998735
## motor_is.na NaN NaN NaN
## ctclass_is.na -0.074101567 -0.063310212 -0.07348964
## d.sysbp_is.na NaN NaN NaN
## hb_is.na -0.008761202 -0.022962768 -0.03562051
## glucose_is.na NaN -0.015499980 -0.01349823
## unfav_is.na NaN NaN NaN
## mort_is.na NaN NaN NaNMDPA.Cleaned.Metadata$NA_Correlation_plot
MDPA.Cleaned.Metadata$min_PDM_thresholds## min_PDM_threshold perc_obs_retained
## 1 5 89
## 2 10 81
## 3 20 74
## 4 50 60
## 5 100 49
## 6 200 0
## 7 500 0
## 8 1000 0MDPA.Cleaned.Metadata$Vars_above_half## character(0)1.3.2 Assessment using RBTEST
[A] The missing data mechanisms were summarized using the RBtest method from the RBtest package.
[A.1] Variables assessed with Missing at Random (MAR) mechanism as evaluated against the trial variable (factor), age variable (numeric), motor variable (factor), d.sysbp variable (numeric), unfav variable (factor) and mort variable (factor) with complete observations :
[A.1.1] hypoxia variable (factor)
[A.1.2] cisterns variable (factor)
[A.1.3] ctclass variable (factor)
[A.2] Variables assessed with Missing Completely at Random (MCAR) mechanism as evaluated against the trial variable (factor), age variable (numeric), motor variable (factor), d.sysbp variable (numeric), unfav variable (factor) and mort variable (factor) with complete observations :
[A.2.1] hypotens variable (factor)
[A.2.2] shift variable (factor)
[A.2.3] tsah variable (factor)
[A.2.4] edh variable (factor)
[A.2.5] pupil variable (factor)
[A.2.6] hb variable (numeric)
[A.2.7] glucose variable (numeric)
Code Chunk | Output
##################################
# Loading dataset
##################################
MDPA <- TBI.Analysis
##################################
# Testing the missingness mechanism using a regression-based approach
# MCAR (Missing Completely at Random) versus MAR (Missing at Random)
# for variables with missing data as evaluated against variables with complete observations
##################################
RBtest(TBI.Analysis)## $abs.nbrMD
## trial age hypoxia hypotens cisterns shift tsah edh
## 0 0 249 59 257 252 96 38
## pupil motor ctclass d.sysbp hb glucose unfav mort
## 123 0 25 0 24 64 0 0
##
## $rel.nbrMD
## trial age hypoxia hypotens cisterns shift tsah edh
## 0.00 0.00 0.12 0.03 0.12 0.12 0.04 0.02
## pupil motor ctclass d.sysbp hb glucose unfav mort
## 0.06 0.00 0.01 0.00 0.01 0.03 0.00 0.00
##
## $type
## trial age hypoxia hypotens cisterns shift tsah edh
## -1 -1 1 0 1 0 0 0
## pupil motor ctclass d.sysbp hb glucose unfav mort
## 0 -1 1 -1 0 0 -1 -11.4 Imputation Method Performance Comparison Summary
1.4.1 Evaluation using MISSCOMPARE
Random Replacement imputes missing values with random instances of the data. This method is typically used as a baseline method to which other imputations methods are compared from, but may not be appropriate to be applied in practice due to its inability to take into account any patterns or relationships in the data that may exist between the variable with missing values and other variables in the dataset. This can lead to imputed values that do not reflect reasonably plausible values for the missing data, potentially driving unstable and inaccurate estimates of relationships between variables.
Median / Mean Imptutation replaces missing value with the sample median / mean depending on the distribution of the data. This method is a fast and simple fix for the missing data. However, it will change the distributional shape, underestimate the variance, disturb the relations between variables, bias almost any estimate other than the median / mean and bias the estimate of the median / mean when data are not missing completely at random, especially when the missing values are large in number. This method can be slightly improved by stratifying data into subgroups.
Expectation-Maximization Principal Component Imputation is also referred to as iterative principal component method serving as a data matrix completion framework by generating a fixed structure having a low rank representation in a number of dimensions corrupted by noise which converge to a possible local maximum. The algorithm provides a good estimation of the principal component parameters when there are very strong correlations between variables and the number of missing values is very small. However, it may very rapidly suffers from overfitting problems when data are noisy and/or there are many missing values.
Regularized Iterative Principal Component Imputation applies regularization methods to the iterative principal component analysis algorithm to address the potential issue of overfitting. The imputation is carried out by simultaneously taking into account the similarities among individuals and relationships between variables. The algorithm involves setting the missing elements at initial values, conducting principal component methods on the imputed data set and filling in the missing values with the reconstruction formula using a predefined number of dimensions. All parameter estimation steps via principal components and missing value imputation using the fitted matrix are then iterated until convergence.
PPCA : Probabilistic Principal Component Analysis Imputation combines an expectation-maximization (EM) approach for principal component analysis (PCA) with a probabilistic model. The EM approach is based on the assumption that the latent variables as well as the noise are normally distributed. In standard PCA, data which is far from the training set but close to the principal subspace may have the same reconstruction error. The algorithm defines a likelihood function such that the likelihood for data far from the training set is much lower, even if they are close to the principal subspace. This allows to improve the estimation accuracy.
SVD : Singular Value Decomposition Imputation estimates the missing values as a linear combination of a number of most significant eigengenes. As SVD can only be performed on complete matrices, all missing values are initially replaced by 0. The algorithm works iteratively until the change in the estimated solution falls below a certain threshold. For each step, the eigengenes of the current estimate are calculated and used to determine a new estimate. Eigengenes denote the loadings if principal is performed considering variable as observations. An optimal linear combination is found by regressing the incomplete variable against the number of most significant eigengenes. If the value at a certain position is missing, the corresponding value of the eigengenes is not used when determining the regression coefficients.
BPCA : Bayesian Principal Component Analysis Imputation combines an expectation-maximization (EM) approach for principal component analysis (PCA) with a Bayesian model. In standard PCA, data far from the training set but close to the principal subspace may have the same reconstruction error. The algorithm defines a likelihood function such that the likelihood for data far from the training set is much lower, even if they are close to the principal subspace. Scores and loadings obtained with Bayesian PCA slightly differ from those obtained with conventional PCA. The algorithm does not force orthogonality between factor loadings, as a result factor loadings are not necessarily orthogonal. The difference between real and predicted Eigenvalues becomes larger when the number of observation is smaller, because it reflects the lack of information to accurately determine true factor loadings from the limited and noisy data. As a result, weights of factors to predict missing values are not the same as with conventional PCA, but the missing value estimation is improved. BPCA works iteratively requiring several matrix inversions. The size of the matrices to invert depends on the number of components used for re-estimation
NIPALS : Non-Linear Iterative Partial Least Squares computes PCA on a numeric matrix using the non-linear iterative partial least squares (NIPALS) algorithm which is an iterative approach for estimating the principal components, extracting them one at a time.
NLPCA : Non-Linear Principal Component Analysis Imputation implements artificial neural network (MLP) for performing non-linear principal component analysis (PCA). Non-linear PCA is conceptually similar to classical PCA but theoretically quite different. Instead of simply decomposing the matrix to scores, loadings and an error, a neural network is trained to find a curve through the multidimensional space that describes a much variance as possible. Classical ways of interpreting PCA results are thus not applicable to NLPCA since the loadings are hidden in the network. However, the scores of components that lead to low cross-validation errors can still be interpreted via the score plot.
MICE : Multivariate Imputation by Chained Equations as an imputation method is based on fully conditional specification, where each incomplete variable is imputed by a separate model. As a sequential regression imputation technique, the algorithm imputes an incomplete column (target column) by generating plausible synthetic values given other columns in the data. Each incomplete column must act as a target column, and has its own specific set of predictors. For predictors that are incomplete themselves, the most recently generated imputations are used to complete the predictors prior to prior to imputation of the target columns.
Iterative Multiple Imputation from Conditional Distributions performs multiple imputation for data with missing values by iteratively drawing imputed values from the conditional distribution for each variable given the observed and imputed values of the other variables in the data. The process approximates a Bayesian framework where multiple chains are run and convergence is assessed after a pre-specified number of iterations within each chain.
AMELIA : Multiple Imputation of Incomplete Multivariate Data creates a bootstrapped version of the original data, estimates the sufficient statistics (with priors if specified) by expectation-maximization on this bootstrapped sample, and then imputes the missing values of the original data using the estimated sufficient statistics. The algorithm repeats this process several times to produce the multiple complete datasets where the observed values are the same and the unobserved values are drawn from their posterior distributions.
Non-Parametric Missing Value Imputation Using Random Forest imputes missing values particularly in the case of mixed-type data such as continuous and/or categorical data including complex interactions and nonlinear relations. The algorithm yields an out-of-bag (OOB) imputation error estimate. After each iteration the difference between the previous and the new imputed data matrix is assessed for the continuous and categorical parts. The stopping criterion is defined such that the imputation process is stopped as soon as both differences have become larger once. In case of only one type of variable the computation stops as soon as the corresponding difference goes up for the first time.
AREG : Multiple Imputation using Additive Regression, Bootstrapping, and Predictive Mean Matching creates flexible additive imputation models by taking all aspects of uncertainty in the imputations into account by using the bootstrap to approximate the process of drawing predicted values from a full Bayesian predictive distribution. Different bootstrap resamples are used for each of the multiple imputations, a flexible additive model is fitted on a sample with replacement from the original data and this model is used to predict all of the original missing and non-missing values for the target variable.
K-Nearest Neighbors Imputation applies the variation of the Gower Distance for the imputation of numerical, categorical, ordered and semi-continuous variables.
Missing data imputation method evaluation:
[A] The performance of 16 missing data imputation methods were evaluated on the simulated dataset using the impute_simulated method from the missCompare package.
[A.1] Method 1: Random replacement
[A.2] Method 2: Median imputation
[A.3] Method 3: Mean imputation
[A.4] Method 4: missMDA Regularized
[A.5] Method 5: missMDA EM
[A.6] Method 6: pcaMethods PPCA
[A.7] Method 7: pcaMethods svdImpute
[A.8] Method 8: pcaMethods BPCA
[A.9] Method 9: pcaMethods NIPALS
[A.10] Method 10: pcaMethods NLPCA
[A.11] Method 11: mice mixed
[A.12] Method 12: mi Bayesian
[A.13] Method 13: Amelia II
[A.14] Method 14: missForest
[A.15] Method 15: Hmisc aregImpute
[A.16] Method 16: VIM kNN
[B] The missing data imputation methods from the missMDA and pcaMethods packages had the best MAE and RMSE performance.
[C] The missing data imputation methods from the mice, mi, Amelia, missForest, Hmisc and VIM packages had the best KS test performance.
[D] Due to the nature of the dataset containing both numeric and factor variables, the missing data imputation methods from the mice, Hmisc and VIM packages which offer more flexibility for mixed data types were chosen for the subsequent process.
Code Chunk | Output
##################################
# Loading dataset
##################################
MDIE <- TBI.Analysis
##################################
# Reconstructing the dataset by :
# removing variables with fill rate > 0.50
# removing observations with NA ratio > 0.80
# converting factor variables to numeric variables
##################################
MDIE.Cleaned <- missCompare::clean(MDIE,
var_removal_threshold=0.50,
ind_removal_threshold=0.80)
##################################
# Gathering the metadata using the reconstructed dataset
##################################
MDIE.Cleaned.Metadata <- missCompare::get_data(MDIE.Cleaned,
matrixplot_sort = T,
plot_transform = T)
##################################
# Simulating a dataset using the metadata characteristics
# applying MCAR, MAR and MNAR mechanisms
##################################
MDIE.Simulated <- missCompare::simulate(rownum=MDIE.Cleaned.Metadata$Rows,
colnum=MDIE.Cleaned.Metadata$Columns,
cormat=MDIE.Cleaned.Metadata$Corr_matrix,
meanval=0,
sdval=1)
##################################
# Performing 16 imputation methods
# on the simulated dataset
# Method 1 : random replacement
# Method 2 : median imputation
# Method 3 : mean imputation
# Method 4 : missMDA Regularized
# Method 5 : missMDA EM
# Method 6 : pcaMethods PPCA
# Method 7 : pcaMethods svdImpute
# Method 8 : pcaMethods BPCA
# Method 9 : pcaMethods NIPALS
# Method 10 : pcaMethods NLPCA
# Method 11 : mice mixed
# Method 12 : mi Bayesian
# Method 13 : Amelia II
# Method 14 : missForest
# Method 15 : Hmisc aregImpute
# Method 16 : VIM kNN
##################################
##################################
# Process parameters defined as follows :
# Minimum number of observations per distinct missing data pattern = 10
# Number of iterations = 1 (for illustration only, actual number should be set high in real applications)
##################################
MDIE.Simulated.Imputed <- missCompare::impute_simulated(rownum=MDIE.Cleaned.Metadata$Rows,
colnum=MDIE.Cleaned.Metadata$Columns,
cormat=MDIE.Cleaned.Metadata$Corr_matrix,
MD_pattern=MDIE.Cleaned.Metadata$MD_Pattern,
NA_fraction=MDIE.Cleaned.Metadata$Fraction_missingness,
min_PDM=10,
n.iter=1,
assumed_pattern=NA)## [1] "ITERATION 1 OF TOTAL 1 - IN PROGRESS"## [1] "random replacement imputation - in progress"
## [1] "Median imputation - in progress"
## [1] "Mean imputation - in progress"
## [1] "missMDA regularized imputation - in progress"
## [1] "missMDA EM imputation - in progress"
## [1] "pcaMethods PPCA imputation - in progress"
## [1] "pcaMethods svdImpute imputation - in progress"
## [1] "pcaMethods BPCA imputation - in progress"
## [1] "pcaMethods NIPALS imputation - in progress"
## [1] "pcaMethods NLPCA imputation - in progress"
## [1] "mice mixed imputation - in progress"
## [1] "mi imputation - in progress"## [1] "Amelia II imputation - in progress"
## [1] "missForest imputation - in progress"
## [1] "Hmisc aregImpute imputation - in progress"
## [1] "VIM kNN imputation - in progress"##################################
# Comparing the performance of the 16 imputation methods
# in terms of the process execution time
# per missing data mechanism
##################################
MDIE.Simulated.Imputed$Plot_TIME
##################################
# Comparing the performance of the 16 imputation methods
# in terms of the root mean square error
# per missing data mechanism
##################################
MDIE.Simulated.Imputed$Plot_RMSE
##################################
# Comparing the performance of the 16 imputation methods
# in terms of the mean absolute error
# per missing data mechanism
##################################
MDIE.Simulated.Imputed$Plot_MAE
##################################
# Comparing the performance of the 16 imputation methods
# in terms of the kolmogorov smirnov statistic
# per missing data mechanism
##################################
MDIE.Simulated.Imputed$Plot_KS
1.5 Missing Data Imputation and Post-Imputation Diagnostics
1.5.1 Imputation using MICE MIXED
Multivariate Imputation by Chained Equations as an imputation method is based on fully conditional specification, where each incomplete variable is imputed by a separate model. As a sequential regression imputation technique, the algorithm imputes an incomplete column (target column) by generating plausible synthetic values given other columns in the data. Each incomplete column must act as a target column, and has its own specific set of predictors. For predictors that are incomplete themselves, the most recently generated imputations are used to complete the predictors prior to prior to imputation of the target columns.
[A] The Multivariate Imputation by Chained Equations method from the mice package as implemented in the missCompare package showed:
[A.1] Relatively poor data plausibility for the numeric variables in the imputed dataset as compared to the original dataset.
[A.2] Relatively good data plausibility for the categorical variables in the imputed dataset as compared to the original dataset.
[A.3] Consistent numeric variable clustering in the imputed dataset as compared to the original dataset.
Code Chunk | Output
##################################
# Loading dataset
##################################
MDIPID <- TBI.Analysis
##################################
# Performing missing data imputation
# on the original dataset using
# Method 11 : mice mixed
##################################
##################################
# Process parameters defined as follows :
# Number of iterations = 3 (for illustration only, actual number should be set high in real applications)
##################################
MDIPID.Imputed.MiceMixed <- missCompare::impute_data(MDIPID,
scale=F,
n.iter=3,
sel_method=c(11))## [1] "mice mixed imputation - in progress"##################################
# Performing post-imputation diagnostics
# using Method 11 : mice mixed
##################################
##################################
# Process parameters defined as follows :
# Number of bootstrap cycles = 5 (for illustration only, actual number should be set high in real applications)
##################################
MDIPID.Imputed.MiceMixed.Diagnostics <- missCompare::post_imp_diag(MDIPID,
MDIPID.Imputed.MiceMixed$mice_mixed_imputation[[1]],
scale=F,
n.boot=5)
##################################
# Comparing the histograms of the numeric variables
# between the imputed and original datasets
# from Method 11 : mice mixed
##################################
MDIPID.Imputed.MiceMixed.Diagnostics$Histograms## $age
##
## $d.sysbp
##
## $hb
##
## $glucose
##################################
# Comparing the box plots of the numeric variables
# between the imputed and original datasets
# from Method 11 : mice mixed
##################################
MDIPID.Imputed.MiceMixed.Diagnostics$Boxplots## $age
##
## $d.sysbp
##
## $hb
##
## $glucose
##################################
# Comparing the summary statistics of the numeric variables
# between the imputed and original datasets
# from Method 11 : mice mixed
##################################
MDIPID.Imputed.MiceMixed.Diagnostics$Statistics## $age
## Mean_original SD_original Mean_imputed SD_imputed Welch_ttest_P
## 33.21121 13.57760 NA NA NA
## KS_test
## NA
##
## $d.sysbp
## Mean_original SD_original Mean_imputed SD_imputed Welch_ttest_P
## 131.42962 15.85943 NA NA NA
## KS_test
## NA
##
## $hb
## Mean_original SD_original Mean_imputed SD_imputed Welch_ttest_P
## 12.46761124 2.50332935 13.32916667 1.77040383 0.02686154
## KS_test.D
## 0.19814598
##
## $glucose
## Mean_original SD_original Mean_imputed SD_imputed Welch_ttest_P
## 8.86326120 3.19075643 8.98048611 3.16849310 0.77157338
## KS_test.D
## 0.06303699##################################
# Comparing the correlation plots of the numeric variables
# between the imputed and original datasets
# from Method 11 : mice mixed
##################################
MDIPID.Imputed.MiceMixed.Diagnostics$Correlation_plot
##################################
# Comparing the bar charts of the numeric variables
# between the imputed and original datasets
# from Method 11 : mice mixed
##################################
MDIPID.Imputed.MiceMixed.Diagnostics$Barcharts## $trial
##
## $hypoxia
##
## $hypotens
##
## $cisterns
##
## $shift
##
## $tsah
##
## $edh
##
## $pupil
##
## $motor
##
## $ctclass
##
## $unfav
##
## $mort
##################################
# Comparing the cluster plot of the variables
# between the imputed and original datasets
# from Method 11 : mice mixed
###############################
MDIPID.Imputed.MiceMixed.Diagnostics$Variable_clusters_imp
MDIPID.Imputed.MiceMixed.Diagnostics$Variable_clusters_orig
1.5.2 Imputation using HMISC AREGIMPUTE
AREG : Multiple Imputation using Additive Regression, Bootstrapping, and Predictive Mean Matching creates flexible additive imputation models by taking all aspects of uncertainty in the imputations into account by using the bootstrap to approximate the process of drawing predicted values from a full Bayesian predictive distribution. Different bootstrap resamples are used for each of the multiple imputations, a flexible additive model is fitted on a sample with replacement from the original data and this model is used to predict all of the original missing and non-missing values for the target variable.
[A] The Multiple Imputation Using Additive Regression method from the Hmisc package as implemented in the missCompare package showed:
[A.1] Relatively poor data plausibility for the numeric variables in the imputed dataset as compared to the original dataset.
[A.2] Relatively good data plausibility for the categorical variables in the imputed dataset as compared to the original dataset.
[A.3] Consistent numeric variable clustering in the imputed dataset as compared to the original dataset.
Code Chunk | Output
##################################
# Loading dataset
##################################
MDIPID <- TBI.Analysis
##################################
# Performing missing data imputation
# on the original dataset using
# Method 15 : Hmisc aregImpute
##################################
##################################
# Process parameters defined as follows :
# Number of iterations = 3 (for illustration only, actual number should be set high in real applications)
##################################
MDIPID.Imputed.HmiscAregImpute <- missCompare::impute_data(MDIPID,
scale=F,
n.iter=3,
sel_method=c(15))## [1] "Hmisc aregImpute imputation - in progress"##################################
# Performing post-imputation diagnostics
# Method 15 : Hmisc aregImpute
##################################
##################################
# Process parameters defined as follows :
# Number of bootstrap cycles = 5 (for illustration only, actual number should be set high in real applications)
##################################
MDIPID.Imputed.HmiscAregImpute.Diagnostics <- missCompare::post_imp_diag(MDIPID,
MDIPID.Imputed.HmiscAregImpute$Hmisc_aregImpute_imputation[[1]],
scale=F,
n.boot=5)
##################################
# Comparing the histograms of the numeric variables
# between the imputed and original datasets
# from Method 15 : Hmisc aregImpute
##################################
MDIPID.Imputed.HmiscAregImpute.Diagnostics$Histograms## $age
##
## $d.sysbp
##
## $hb
##
## $glucose
##################################
# Comparing the box plots of the numeric variables
# between the imputed and original datasets
# from Method 15 : Hmisc aregImpute
##################################
MDIPID.Imputed.HmiscAregImpute.Diagnostics$Boxplots## $age
##
## $d.sysbp
##
## $hb
##
## $glucose
##################################
# Comparing the summary statistics of the numeric variables
# between the imputed and original datasets
# from Method 15 : Hmisc aregImpute
##################################
MDIPID.Imputed.HmiscAregImpute.Diagnostics$Statistics## $age
## Mean_original SD_original Mean_imputed SD_imputed Welch_ttest_P
## 33.21121 13.57760 NA NA NA
## KS_test
## NA
##
## $d.sysbp
## Mean_original SD_original Mean_imputed SD_imputed Welch_ttest_P
## 131.42962 15.85943 NA NA NA
## KS_test
## NA
##
## $hb
## Mean_original SD_original Mean_imputed SD_imputed Welch_ttest_P
## 12.4676112 2.5033293 12.8291667 2.1772498 0.4273850
## KS_test.D
## 0.1156909
##
## $glucose
## Mean_original SD_original Mean_imputed SD_imputed Welch_ttest_P
## 8.86326120 3.19075643 8.76217014 3.27316496 0.80831262
## KS_test.D
## 0.06581891##################################
# Comparing the correlation plots of the numeric variables
# between the imputed and original datasets
# from Method 15 : Hmisc aregImpute
##################################
MDIPID.Imputed.HmiscAregImpute.Diagnostics$Correlation_plot
##################################
# Comparing the bar charts of the numeric variables
# between the imputed and original datasets
# from Method 15 : Hmisc aregImpute
##################################
MDIPID.Imputed.HmiscAregImpute.Diagnostics$Barcharts## $trial
##
## $hypoxia
##
## $hypotens
##
## $cisterns
##
## $shift
##
## $tsah
##
## $edh
##
## $pupil
##
## $motor
##
## $ctclass
##
## $unfav
##
## $mort
##################################
# Comparing the cluster plot of the variables
# between the imputed and original datasets
# from Method 15 : Hmisc aregImpute
###############################
MDIPID.Imputed.HmiscAregImpute.Diagnostics$Variable_clusters_imp
MDIPID.Imputed.HmiscAregImpute.Diagnostics$Variable_clusters_orig
1.5.3 Imputation using VIM KNN
K-Nearest Neighbors Imputation applies the variation of the Gower Distance for the imputation of numerical, categorical, ordered and semi-continuous variables.
[A] The K-Nearest Neighbors Imputation method from the VIM package as implemented in the missCompare package showed:
[A.1] Relatively good data plausibility for the numeric variables in the imputed dataset as compared to the original dataset.
[A.2] Relatively poor data plausibility for the categorical variables in the imputed dataset as compared to the original dataset.
[A.3] Consistent numeric variable clustering in the imputed dataset as compared to the original dataset.
Code Chunk | Output
##################################
# Loading dataset
##################################
MDIPID <- TBI.Analysis
##################################
# Performing missing data imputation
# on the original dataset using
# Method 16 : VIM kNN
##################################
##################################
# Process parameters defined as follows :
# Number of iterations = 3 (for illustration only, actual number should be set high in real applications)
##################################
MDIPID.Imputed.VIMkNN <- missCompare::impute_data(MDIPID,
scale=F,
n.iter=3,
sel_method=c(16))## [1] "VIM kNN imputation - in progress"##################################
# Performing post-imputation diagnostics
# using Method 16 : VIM kNN
##################################
##################################
# Process parameters defined as follows :
# Number of bootstrap cycles = 5 (for illustration only, actual number should be set high in real applications)
##################################
MDIPID.Imputed.VIMkNN.Diagnostics <- missCompare::post_imp_diag(MDIPID,
MDIPID.Imputed.VIMkNN$VIM_kNN_imputation[[1]],
scale=F,
n.boot=5)
##################################
# Comparing the histograms of the numeric variables
# between the imputed and original datasets
# from Method 16 : VIM kNN
##################################
MDIPID.Imputed.VIMkNN.Diagnostics$Histograms## $age
##
## $d.sysbp
##
## $hb
##
## $glucose
##################################
# Comparing the box plots of the numeric variables
# between the imputed and original datasets
# from Method 16 : VIM kNN
##################################
MDIPID.Imputed.VIMkNN.Diagnostics$Boxplots## $age
##
## $d.sysbp
##
## $hb
##
## $glucose
##################################
# Comparing the summary statistics of the numeric variables
# between the imputed and original datasets
# from Method 16 : VIM kNN
##################################
MDIPID.Imputed.VIMkNN.Diagnostics$Statistics## $age
## Mean_original SD_original Mean_imputed SD_imputed Welch_ttest_P
## 33.21121 13.57760 NA NA NA
## KS_test
## NA
##
## $d.sysbp
## Mean_original SD_original Mean_imputed SD_imputed Welch_ttest_P
## 131.42962 15.85943 NA NA NA
## KS_test
## NA
##
## $hb
## Mean_original SD_original Mean_imputed SD_imputed Welch_ttest_P
## 12.46761124 2.50332935 12.98958333 1.22669396 0.05223604
## KS_test.D
## 0.22775176
##
## $glucose
## Mean_original SD_original Mean_imputed SD_imputed Welch_ttest_P
## 8.8632612039 3.1907564349 8.1860677083 1.2654165421 0.0001742062
## KS_test.D
## 0.2199806086##################################
# Comparing the correlation plots of the numeric variables
# between the imputed and original datasets
# from Method 12 : VIM kNN
##################################
MDIPID.Imputed.VIMkNN.Diagnostics$Correlation_plot
##################################
# Comparing the bar charts of the numeric variables
# between the imputed and original datasets
# from Method 16 : VIM kNN
##################################
MDIPID.Imputed.VIMkNN.Diagnostics$Barcharts## $trial
##
## $hypoxia
##
## $hypotens
##
## $cisterns
##
## $shift
##
## $tsah
##
## $edh
##
## $pupil
##
## $motor
##
## $ctclass
##
## $unfav
##
## $mort
##################################
# Comparing the cluster plot of the variables
# between the imputed and original datasets
# from Method 16 : VIM kNN
###############################
MDIPID.Imputed.VIMkNN.Diagnostics$Variable_clusters_imp
MDIPID.Imputed.VIMkNN.Diagnostics$Variable_clusters_orig
1.6 Consolidated Findings
[A] Post-imputation diagnostics showed more plausible estimates for the following algorithms in imputing missing categorical data:
[A.1] Multivariate Imputation by Chained Equations (missCompare package)
[A.2] Multiple Imputation using Additive Regression, Bootstrapping, and Predictive Mean Matching (missCompare package)
[B] Post-imputation diagnostics showed more plausible estimates for the following algorithm in imputing missing numeric data:
[B.1] K-Nearest Neighbors Imputation (VIM package)
3. References
[Book] Clinical Prediction Models by Ewout Steyerberg
[Book] Flexible Imputation of Missing Data by Stef van Buuren
[Book] Introduction to Regression Methods for Public Health Using R by Ramzi Nahhas
[R Package] missCompare by Tibor Varga
[R Package] mice by Gerko Vink and Stef van Buuren
[R Package] miceRanger by Sam Wilson
[R Package] missMDA by Vincent Audigier
[R Package] VIM by Matthias Templ
[R Package] Amelia by James Honaker, Gary King and Matthew Blackwell
[R Package] pcaMethods by Wolfram Stacklies, Henning Redestig and Kevin Wright
[R Package] mi by Jon Kropko
[R Package] missForest by Daniel Stekhoven
[R Package] Hmisc by Frank Harrell
[R Package] RBtest by Serguei Rouzinov and Andre Berchtold
[R Package] Caret by Max Kuhn
[Article] Imputing Missing Data with R; MICE package by Michy Alice
[Article] A Complete Tutorial to missCompare by Tibor Varga
[Article] How Do I Perform Multiple Imputation Using Predictive Mean Matching In R? by UCLA Advanced Research Computing Group
[Article] A Solution to Missing Data: Imputation Using R by Chaitanya Sagar
[Article] Predictive Mean Matching Imputation (Theory & Example in R) by Joachim Schork
[Article] Imputation of Missing Values by Scikit-Learn Team
[Article] Imputation in R: Top 3 Ways for Imputing Missing Data by Dario Radecic
[Article] Data Imputation Techniques – An Introduction by Suraj RP
[Article] Missing Data Imputation Techniques in Machine Learning by Ajitesh Kumar
[Article] Types of Missing Data : MCAR, MAR, MNAR by Nayan
[Article] The NIPALS Algorithm by Kevin Wright
[Article] Missing Values by mixOmics Team
[Article] The MICE Algorithm by Sam Wilson
[Article] Nonlinear PCA Algorithm by Matthias Scholz
[Article] MICE Algorithm to Impute Missing Values in a Dataset by Bhuvaneswari Gopalan
[Article] Multivariate Imputation by Chained Equations by AMICES Team
[Article] Amelia II: A Program for Missing Data by James Honaker, Gary King and Matthew Blackwell
[Article] Using Amelia by James Honaker, Gary King and Matthew Blackwell
[Article] Missing Data | Types, Explanation, & Imputation by Pritha Bhandari
[Article] Estimating Missing Data with aregImpute() by R-Bloggers Team
[Article] Multiple Imputation using Additive Regression, Bootstrapping, and Predictive Mean Matching by Frank Harrell
[Article] The KNN Algorithm – Explanation, Opportunities, Limitations by Aymane Hachcham
[Article] A Guide To KNN Imputation For Handling Missing Values by Start-Tech Academy Team
[Article] KNN Imputation for Missing Values in Machine Learning by Charles Durfee
[Article] All About Random Forests And Handling Missing Values In Them by Manju Hariashok
[Article] How to Use Python and MissForest Algorithm to Impute Missing Data by Better Data Science Team
[Article] Bayesian PCA Missing Value Estimator for MATLAB by Shigeyuki Oba
[Article] Imputing Missing Values with SVD by CMDLineTips Team
[Article] EM Imputation and Missing Data: Is Mean Imputation Really So Terrible? by Karen Grace-Martin
[Publication] Handling Missing Values in Exploratory Multivariate Data Analysis Methods by François Husson and Julie Josse (Computer Science)
[Publication] EM Algorithms for PCA and SPCA by Sam Roweis (Computer Science)
[Publication] Missing Value Estimation Methods for DNA Microarrays by Olga Troyanskaya, Michael Cantor, Gavin Sherlock, Pat Brown, Trevor Hastie, Robert Tibshirani, David Botstein and Russ Altman (Bioinformatics)
[Publication] A Bayesian Missing Value Estimation Method for Gene Expression Profile Data by Shigeyuki Oba, Masa-aki Sato, Ichiro Takemasa, Morito Monden, Ken-ichi Matsubara and Shin Ishii (Bioinformatics)
[Publication] Soft Modelling by Latent Variables: The Non-Linear Iterative Partial Least Squares (NIPALS) Approach by Herman Wold (Journal of Applied Probability)
[Publication] Non-Linear PCA: A Missing Data Approach by Matthias Scholz, Fatma Kaplan, Charles Guy, Joachim Kopka, Joachim Selbig (Bioinformatics)
[Publication] Multiple Imputation of Discrete and Continuous Data by Fully Conditional Specification by Stef van Buuren (Statistical Methods in Medical Research)
[Publication] Amelia II: A Program for Missing Data by James Honaker, Gary King, and Matthew Blackwell (Journal of Statistical Software)
[Publication] MissForest — Non-Parametric Missing Value Imputation for Mixed-Type Data by Daniel Stekhoven and Peter Bühlmann (Bioinformatics)
[Publication] Random Forest Missing Data Algorithms by Fei Tang and Hemant Ishwaran (ASA Data Science Journal)
[Publication] Robust Likelihood-Based Analysis of Multivariate Data with Missing Values by Roderick Little and Hyonggin An (Statistica Sinica)
[Publication] Imputation with the R Package VIM by Alexander Kowarik and Matthias Templ (Journal of Statistical Software)