Supervised Learning : Clinical Research Prediction Model Development and Evaluation for Prognosis
John Pauline Pineda
2022-09-14
1. Table of Contents
This project explores the best practices when developing and evaluating prognostic models for clinical research using various helpful packages in R. The methods and results presented in the chapter entitled Case Study on Survival Analysis: Prediction of Cardiovascular Events using the Second Manifestations of Arterial Diseases (SMART) dataset from the book Clinical Prediction Models were replicated. The general requirements for the clinical study were defined including the formulation of the research question, intended application, outcome, predictors, study design, statistical model and sample size computation. The individual steps involved in model development were presented including the data quality assessment, predictor coding, data preprocessing, as well as the specification, selection, performance estimation, performance validation and presentation of the model used in the study. Additional details on model validity evaluation was also provided. All results were consolidated in a Summary presented at the end of the document.
Clinical Prediction Models estimate the risk of existing disease (diagnostic prediction model) or future outcome (prognostic prediction model) for an individual, which is conditional on the values of multiple predictors (prognostic or risk factors) such as clinicopathological characteristics and biomarkers. As an explicit and empirical approach to estimating probabilities or outcomes of a disease, these models relate to evidence-based medicine which aims to use the current best evidence in making decisions about the care of individual patients. Evidence-based medicine applies the scientific method to medical practice. Its laudable intentions are to make clinical practice more scientific and empirically grounded and thereby achieving safer, more consistent, and more cost-effective care.
Various guidelines such as the TRIPOD (Transparent Reporting of a Multivariable Prediction Model for Individual Prognosis Or Diagnosis), STARD (Standards for Reporting Diagnostic Accuracy Studies) and PROBAST (Prediction Model Risk of Bias Assessment Tool) have been formulated which aim to improve the transparency in the reporting of clinical research studies developing, validating, or updating multivariable prediction models, whether for diagnostic or prognostic purposes.
Multivariable prediction models fall into two broad categories: diagnostic and prognostic prediction models. In both the diagnostic and prognostic setting, probability estimates are commonly based on combining information from multiple predictors observed or measured from an individual. In a diagnostic model, multiple predictors (often referred to as diagnostic test results) are combined to estimate the probability that a certain condition or disease is present (or absent) at the moment of prediction. In a prognostic model, multiple predictors are combined to estimate the probability of a particular outcome or event (for example, mortality, disease recurrence, complication, or therapy response) occurring in a certain period in the future. In virtually all medical domains, diagnostic and prognostic multivariable (risk) prediction models are being developed, validated, updated, and implemented with the aim to assist doctors and individuals in estimating probabilities and potentially influence their decision making.
1.1 General Considerations
1.1.1 Research Question
The aim of the study was to develop a prediction model for long term outcome. Given the available follow-up, the yearly risks could be assessed reliably. Achieving adequate predictions was more prominent than insight in the predictor effects.
1.1.2 Intended Application
The intended application of the study was more toward clinical practice rather than experimental research - particularly on inpatient counseling where a high absolute risk might motivate patients to change inappropriate lifestyles and to comply with their medication regimens.
1.1.3 Outcome
The primary outcome was any cardiovascular event, comprised of cardiovascular death, non-fatal stroke, and non-fatal myocardial infarction. Combining different events was made to increase statistical power (which is a common approach for vascular research).
1.1.4 Predictors
The selection of predictors was motivated by characteristics included in the Framingham and SCORE models. The relationship with future events has also been established for several traditional risk factors, including hyperhomocysteinemia, intima-media thickness (IMT) and creatinine. Other candidate predictors were demographics (sex and age) and risk factors for vascular events in the general population (smoking, alcohol use, body mass index, diastolic and systolic blood pressure, lipids and diabetes). In addition, indicators of atherosclerosis were added as relevant predictors in the study including location of symptomatic vascular disease (cerebral, coronary, peripheral arterial disease or abdominal aortic aneurysm (AAA)) and markers of the extent of atherosclerosis (homocysteine, creatinine, albumin, intima-media thickness (IMT) and presence of carotid artery stenosis).
1.1.5 Study Design
The study was designed as a prospective dynamic cohort study. Patients were enrolled when presenting at the hospital with follow-up starting from study inclusion.
1.1.6 Statistical Model
The default statistical model for survival outcomes - Cox proportional hazard regression model was used which was deemed appropriate for such a relatively short-term study as 5-year cumulative incidence of cardiovascular events.
1.1.7 Sample Size
With the minimum events per variable (EPV) generally targeted at 10 and having identified 29 candidate predictors, the study required at least 290 events gathered prospectively during the course of the study follow-up period.
1.2 Modelling Steps
1.2.1 Sample Data
The Second Manifestations of Arterial Diseases (SMART) dataset contained:
[A] 3873 rows (observations)
[B] 29 columns (variables)
[B.1] 2/29 response = TEVENT variable (numeric) and EVENT variable (factor)
[B.2] 27/29 predictors = All remaining variables (18/27 numeric + 9/27 factor)
[C] 460 recorded events resulting to an 11.88% event rate (460/3873). With 29 candidate predictors, the estimated events per variable (EPV) was equal to 16 which was sufficiently more than the minimum EPV requirement of 10.
Code Chunk | Output
##################################
# Loading R libraries
##################################
library("survival")
library("survminer")
library("mice")
library("foreign")
library("rms")
library("Hmisc")
library("VIM")
library("gridExtra")
library("finalfit")
library("knitr")
library("dplyr")
library("gtsummary")
library("tidyr")
library("purrr")
library("moments")
library("lattice")
##################################
# Defining file paths
##################################
DATASETS_PATH <- file.path("datasets")
##################################
# Loading dataset
##################################
SMART <- read.spss(file.path("..", DATASETS_PATH, "SMARTst.sav"),
use.value.labels=F,
to.data.frame=T)
##################################
# Performing a general exploration of the dataset
##################################
dim(SMART)## [1] 3873 29summary(SMART)## TEVENT EVENT SEX AGE
## Min. : 0.1 Min. :0.0000 Min. :1.000 Min. :19.00
## 1st Qu.: 555.0 1st Qu.:0.0000 1st Qu.:1.000 1st Qu.:52.00
## Median :1213.0 Median :0.0000 Median :1.000 Median :60.00
## Mean :1370.3 Mean :0.1188 Mean :1.252 Mean :59.56
## 3rd Qu.:2165.0 3rd Qu.:0.0000 3rd Qu.:2.000 3rd Qu.:68.00
## Max. :3466.0 Max. :1.0000 Max. :2.000 Max. :82.00
##
## DIABETES CEREBRAL CARDIAC AAA
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :1.0000 Median :0.0000
## Mean :0.2207 Mean :0.2962 Mean :0.5577 Mean :0.1074
## 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## NA's :40
## PERIPH STENOSIS SYSTBP DIASTBP
## Min. :0.0000 Min. :0.000 Min. : 96.0 Min. : 46.0
## 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:127.0 1st Qu.: 73.0
## Median :0.0000 Median :0.000 Median :139.0 Median : 79.0
## Mean :0.2427 Mean :0.191 Mean :141.3 Mean : 79.7
## 3rd Qu.:0.0000 3rd Qu.:0.000 3rd Qu.:154.0 3rd Qu.: 86.0
## Max. :1.0000 Max. :1.000 Max. :216.0 Max. :127.0
## NA's :93 NA's :1223 NA's :1221
## SYSTH DIASTH LENGTH WEIGHT BMI
## Min. : 79.0 Min. : 45.00 Min. :1.53 Min. : 50 Min. :18.70
## 1st Qu.:126.0 1st Qu.: 75.00 1st Qu.:1.68 1st Qu.: 72 1st Qu.:24.11
## Median :140.0 Median : 82.00 Median :1.75 Median : 80 Median :26.30
## Mean :142.2 Mean : 82.44 Mean :1.74 Mean : 81 Mean :26.70
## 3rd Qu.:156.0 3rd Qu.: 90.00 3rd Qu.:1.80 3rd Qu.: 89 3rd Qu.:28.73
## Max. :244.0 Max. :136.00 Max. :1.94 Max. :124 Max. :39.80
## NA's :1498 NA's :1499 NA's :1 NA's :2 NA's :3
## CHOL HDL LDL TRIG HOMOC
## Min. :2.800 Min. :0.58 Min. :1.100 Min. :0.560 Min. : 6.10
## 1st Qu.:4.400 1st Qu.:0.96 1st Qu.:2.390 1st Qu.:1.120 1st Qu.:10.32
## Median :5.100 Median :1.17 Median :3.060 Median :1.540 Median :12.80
## Mean :5.191 Mean :1.23 Mean :3.144 Mean :1.854 Mean :13.84
## 3rd Qu.:5.900 3rd Qu.:1.42 3rd Qu.:3.830 3rd Qu.:2.230 3rd Qu.:15.70
## Max. :9.400 Max. :2.51 Max. :6.600 Max. :8.960 Max. :38.30
## NA's :18 NA's :30 NA's :216 NA's :28 NA's :463
## GLUT CREAT IMT albumin
## Min. : 4.300 Min. : 54.00 Min. :0.4700 Min. :1.000
## 1st Qu.: 5.300 1st Qu.: 78.00 1st Qu.:0.7500 1st Qu.:1.000
## Median : 5.700 Median : 89.00 Median :0.8800 Median :1.000
## Mean : 6.333 Mean : 98.39 Mean :0.9346 Mean :1.241
## 3rd Qu.: 6.500 3rd Qu.:101.00 3rd Qu.:1.0700 3rd Qu.:1.000
## Max. :18.700 Max. :825.00 Max. :1.8300 Max. :3.000
## NA's :19 NA's :17 NA's :98 NA's :207
## SMOKING packyrs alcohol
## Min. :1.000 Min. : 0.00 Min. :1.000
## 1st Qu.:2.000 1st Qu.: 5.90 1st Qu.:2.000
## Median :2.000 Median : 19.50 Median :3.000
## Mean :1.935 Mean : 22.62 Mean :2.504
## 3rd Qu.:2.000 3rd Qu.: 34.20 3rd Qu.:3.000
## Max. :3.000 Max. :120.00 Max. :3.000
## NA's :25 NA's :21 NA's :25describe(SMART)## SMART
##
## 29 Variables 3873 Observations
## --------------------------------------------------------------------------------
## TEVENT
## n missing distinct Info Mean Gmd .05 .10
## 3873 0 1934 1 1370 1078 98.6 197.0
## .25 .50 .75 .90 .95
## 555.0 1213.0 2165.0 2762.4 3017.4
##
## lowest : 0.1 1 2 3 4 , highest: 3451 3452 3463 3465 3466
## --------------------------------------------------------------------------------
## EVENT
## n missing distinct Info Sum Mean Gmd
## 3873 0 2 0.314 460 0.1188 0.2094
##
## --------------------------------------------------------------------------------
## SEX
## n missing distinct Info Mean Gmd
## 3873 0 2 0.565 1.252 0.3771
##
## Value 1 2
## Frequency 2897 976
## Proportion 0.748 0.252
## --------------------------------------------------------------------------------
## AGE
## n missing distinct Info Mean Gmd .05 .10
## 3873 0 62 0.999 59.56 11.94 41 46
## .25 .50 .75 .90 .95
## 52 60 68 73 76
##
## lowest : 19 20 23 24 25, highest: 78 79 80 81 82
## --------------------------------------------------------------------------------
## DIABETES
## n missing distinct Info Sum Mean Gmd
## 3833 40 2 0.516 846 0.2207 0.3441
##
## --------------------------------------------------------------------------------
## CEREBRAL
## n missing distinct Info Sum Mean Gmd
## 3873 0 2 0.625 1147 0.2962 0.417
##
## --------------------------------------------------------------------------------
## CARDIAC
## n missing distinct Info Sum Mean Gmd
## 3873 0 2 0.74 2160 0.5577 0.4935
##
## --------------------------------------------------------------------------------
## AAA
## n missing distinct Info Sum Mean Gmd
## 3873 0 2 0.288 416 0.1074 0.1918
##
## --------------------------------------------------------------------------------
## PERIPH
## n missing distinct Info Sum Mean Gmd
## 3873 0 2 0.551 940 0.2427 0.3677
##
## --------------------------------------------------------------------------------
## STENOSIS
## n missing distinct Info Sum Mean Gmd
## 3780 93 2 0.464 722 0.191 0.3091
##
## --------------------------------------------------------------------------------
## SYSTBP
## n missing distinct Info Mean Gmd .05 .10
## 2650 1223 114 1 141.3 22.41 112 117
## .25 .50 .75 .90 .95
## 127 139 154 169 178
##
## lowest : 96 97 98 99 100, highest: 206 209 211 212 216
## --------------------------------------------------------------------------------
## DIASTBP
## n missing distinct Info Mean Gmd .05 .10
## 2652 1221 70 0.999 79.7 11.03 65 68
## .25 .50 .75 .90 .95
## 73 79 86 93 97
##
## lowest : 46 48 52 53 54, highest: 117 118 120 124 127
## --------------------------------------------------------------------------------
## SYSTH
## n missing distinct Info Mean Gmd .05 .10
## 2375 1498 132 1 142.2 24.91 110.0 116.0
## .25 .50 .75 .90 .95
## 126.0 140.0 156.0 172.0 182.3
##
## lowest : 79 88 91 93 94, highest: 222 223 228 242 244
## --------------------------------------------------------------------------------
## DIASTH
## n missing distinct Info Mean Gmd .05 .10
## 2374 1499 77 0.999 82.44 13.22 64 68
## .25 .50 .75 .90 .95
## 75 82 90 98 103
##
## lowest : 45 49 50 52 53, highest: 123 125 126 130 136
## --------------------------------------------------------------------------------
## LENGTH
## n missing distinct Info Mean Gmd .05 .10
## 3872 1 42 0.999 1.74 0.09863 1.59 1.62
## .25 .50 .75 .90 .95
## 1.68 1.75 1.80 1.85 1.88
##
## lowest : 1.53 1.54 1.55 1.56 1.57, highest: 1.9 1.91 1.92 1.93 1.94
## --------------------------------------------------------------------------------
## WEIGHT
## n missing distinct Info Mean Gmd .05 .10
## 3871 2 75 0.999 81 15.41 59 64
## .25 .50 .75 .90 .95
## 72 80 89 99 104
##
## lowest : 50 51 52 53 54, highest: 120 121 122 123 124
## --------------------------------------------------------------------------------
## BMI
## n missing distinct Info Mean Gmd .05 .10
## 3870 3 995 1 26.7 4.258 20.96 22.16
## .25 .50 .75 .90 .95
## 24.11 26.30 28.73 31.86 33.90
##
## lowest : 18.7 18.71 18.73 18.78 18.81, highest: 39.25 39.43 39.45 39.64 39.8
## --------------------------------------------------------------------------------
## CHOL
## n missing distinct Info Mean Gmd .05 .10
## 3855 18 65 0.999 5.191 1.283 3.5 3.8
## .25 .50 .75 .90 .95
## 4.4 5.1 5.9 6.7 7.2
##
## lowest : 2.8 2.9 3 3.1 3.2, highest: 8.8 8.9 9.1 9.2 9.4
## --------------------------------------------------------------------------------
## HDL
## n missing distinct Info Mean Gmd .05 .10
## 3843 30 188 1 1.23 0.4025 0.74 0.82
## .25 .50 .75 .90 .95
## 0.96 1.17 1.42 1.73 1.94
##
## lowest : 0.58 0.59 0.6 0.61 0.62, highest: 2.46 2.47 2.48 2.49 2.51
## --------------------------------------------------------------------------------
## LDL
## n missing distinct Info Mean Gmd .05 .10
## 3657 216 478 1 3.144 1.17 1.580 1.860
## .25 .50 .75 .90 .95
## 2.390 3.060 3.830 4.550 4.982
##
## lowest : 1.1 1.11 1.12 1.14 1.15, highest: 6.34 6.37 6.41 6.47 6.6
## --------------------------------------------------------------------------------
## TRIG
## n missing distinct Info Mean Gmd .05 .10
## 3845 28 461 1 1.854 1.095 0.760 0.880
## .25 .50 .75 .90 .95
## 1.120 1.540 2.230 3.130 3.918
##
## lowest : 0.56 0.57 0.58 0.59 0.6 , highest: 8.28 8.61 8.68 8.91 8.96
## --------------------------------------------------------------------------------
## HOMOC
## n missing distinct Info Mean Gmd .05 .10
## 3410 463 255 1 13.84 5.359 7.90 8.70
## .25 .50 .75 .90 .95
## 10.33 12.80 15.70 19.90 23.85
##
## lowest : 6.1 6.2 6.3 6.4 6.5 , highest: 35.5 35.9 36.1 37.1 38.3
## --------------------------------------------------------------------------------
## GLUT
## n missing distinct Info Mean Gmd .05 .10
## 3854 19 125 0.998 6.333 1.701 4.8 5.0
## .25 .50 .75 .90 .95
## 5.3 5.7 6.5 8.4 10.4
##
## lowest : 4.3 4.4 4.5 4.6 4.7 , highest: 17.6 17.7 17.9 18 18.7
## --------------------------------------------------------------------------------
## CREAT
## n missing distinct Info Mean Gmd .05 .10
## 3856 17 194 1 98.39 34.63 64.75 69.00
## .25 .50 .75 .90 .95
## 78.00 89.00 101.00 118.00 138.25
##
## lowest : 54 55 56 57 58, highest: 784 799 809 813 825
## --------------------------------------------------------------------------------
## IMT
## n missing distinct Info Mean Gmd .05 .10
## 3775 98 99 0.999 0.9346 0.2879 0.600 0.650
## .25 .50 .75 .90 .95
## 0.750 0.880 1.070 1.292 1.450
##
## lowest : 0.47 0.48 0.5 0.52 0.53, highest: 1.77 1.78 1.8 1.82 1.83
## --------------------------------------------------------------------------------
## albumin
## n missing distinct Info Mean Gmd
## 3666 207 3 0.501 1.241 0.3919
##
## Value 1 2 3
## Frequency 2897 655 114
## Proportion 0.790 0.179 0.031
##
## For the frequency table, variable is rounded to the nearest 0
## --------------------------------------------------------------------------------
## SMOKING
## n missing distinct Info Mean Gmd
## 3848 25 3 0.643 1.935 0.4996
##
## Value 1 2 3
## Frequency 693 2711 444
## Proportion 0.180 0.705 0.115
##
## For the frequency table, variable is rounded to the nearest 0
## --------------------------------------------------------------------------------
## packyrs
## n missing distinct Info Mean Gmd .05 .10
## 3852 21 263 0.994 22.62 22.26 0.0 0.0
## .25 .50 .75 .90 .95
## 5.9 19.5 34.2 50.4 62.0
##
## lowest : 0 0.3 0.6 0.7 0.8, highest: 100 102 104 110 120
## --------------------------------------------------------------------------------
## alcohol
## n missing distinct Info Mean Gmd
## 3848 25 3 0.65 2.504 0.7353
##
## Value 1 2 3
## Frequency 751 408 2689
## Proportion 0.195 0.106 0.699
##
## For the frequency table, variable is rounded to the nearest 0
## --------------------------------------------------------------------------------##################################
# Performing re-categorization and re-grouping
# of factor variables
##################################
SMART$EVENT <- as.factor(SMART$EVENT)
SMART$SEX <- as.factor(SMART$SEX)
SMART$DIABETES <- as.factor(SMART$DIABETES)
SMART$CEREBRAL <- as.factor(SMART$CEREBRAL)
SMART$CARDIAC <- as.factor(SMART$CARDIAC)
SMART$AAA <- as.factor(SMART$AAA)
SMART$PERIPH <- as.factor(SMART$PERIPH)
SMART$STENOSIS <- as.factor(SMART$STENOSIS)
SMART$albumin <- as.factor(SMART$albumin)
SMART$SMOKING <- as.factor(SMART$SMOKING)
SMART$alcohol <- as.factor(SMART$alcohol)
##################################
# Formulating a data type assessment summary
##################################
PDA <- SMART
(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 TEVENT numeric
## 2 2 EVENT factor
## 3 3 SEX factor
## 4 4 AGE numeric
## 5 5 DIABETES factor
## 6 6 CEREBRAL factor
## 7 7 CARDIAC factor
## 8 8 AAA factor
## 9 9 PERIPH factor
## 10 10 STENOSIS factor
## 11 11 SYSTBP numeric
## 12 12 DIASTBP numeric
## 13 13 SYSTH numeric
## 14 14 DIASTH numeric
## 15 15 LENGTH numeric
## 16 16 WEIGHT numeric
## 17 17 BMI numeric
## 18 18 CHOL numeric
## 19 19 HDL numeric
## 20 20 LDL numeric
## 21 21 TRIG numeric
## 22 22 HOMOC numeric
## 23 23 GLUT numeric
## 24 24 CREAT numeric
## 25 25 IMT numeric
## 26 26 albumin factor
## 27 27 SMOKING factor
## 28 28 packyrs numeric
## 29 29 alcohol factor1.2.2 Data Quality Assessment
[A] Missing observations noted for 21 variables with NA.Count>0 and Fill.Rate<1.0.
[A.1] DIABETES variable (factor) with NA.Count=40 and Fill.Rate=0.990
[A.2] STENOSIS variable (factor) with NA.Count=93 and Fill.Rate=0.976
[A.3] SYSTBP variable (numeric) with NA.Count=1223 and Fill.Rate=0.684
[A.4] DIASTBP variable (numeric) with NA.Count=1221 and Fill.Rate=0.685
[A.5] SYSTH variable (numeric) with NA.Count=1498 and Fill.Rate=0.613
[A.6] DIASTH variable (numeric) with NA.Count=1499 and Fill.Rate=0.613
[A.7] LENGTH variable (numeric) with NA.Count=1 and Fill.Rate=1.000
[A.8] WEIGHT variable (numeric) with NA.Count=2 and Fill.Rate=0.999
[A.9] BMI variable (numeric) with NA.Count=3 and Fill.Rate=0.999
[A.10] CHOL variable (numeric) with NA.Count=18 and Fill.Rate=0.995
[A.11] HDL variable (numeric) with NA.Count=30 and Fill.Rate=0.992
[A.12] LDL variable (numeric) with NA.Count=216 and Fill.Rate=0.944
[A.13] TRIG variable (numeric) with NA.Count=28 and Fill.Rate=0.993
[A.14] HOMOC variable (numeric) with NA.Count=463 and Fill.Rate=0.880
[A.15] GLUT variable (numeric) with NA.Count=19 and Fill.Rate=0.995
[A.16] CREAT variable (numeric) with NA.Count=17 and Fill.Rate=0.996
[A.17] IMT variable (numeric) with NA.Count=98 and Fill.Rate=0.975
[A.18] albumin variable (factor) with NA.Count=207 and Fill.Rate=0.947
[A.19] SMOKING variable (factor) with NA.Count=25 and Fill.Rate=0.994
[A.20] packyrs variable (numeric) with NA.Count=21 and Fill.Rate=0.995
[A.21] alcohol variable (factor) with NA.Count=25 and Fill.Rate=0.994
[B] Low variance noted for 2 variables with First.Second.Mode.Ratio>5 or Unique.Count.Ratio<0.01.
[B.1] AAA variable (factor) with First.Second.Mode.Ratio=8.310
[B.2] packyrs variable (numeric) with First.Second.Mode.Ratio=16.595
[C] High skewness noted for 4 variables with Skewness>3 or Skewness<(-3).
[C.1] TRIG variable (numeric) with Skewness=14.074
[C.2] HOMOC variable (numeric) with Skewness=19.387
[C.3] GLUT variable (numeric) with Skewness=3.251
[C.4] CREAT variable (numeric) with Skewness=9.927
Code Chunk | Output
##################################
# Loading dataset
##################################
DQA <- SMART
##################################
# Listing all predictors
##################################
DQA.Predictors <- DQA[,!names(DQA) %in% c("TEVENT","EVENT")]
##################################
# 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 TEVENT numeric 3873 0 1.000
## 2 2 EVENT factor 3873 0 1.000
## 3 3 SEX factor 3873 0 1.000
## 4 4 AGE numeric 3873 0 1.000
## 5 5 DIABETES factor 3873 40 0.990
## 6 6 CEREBRAL factor 3873 0 1.000
## 7 7 CARDIAC factor 3873 0 1.000
## 8 8 AAA factor 3873 0 1.000
## 9 9 PERIPH factor 3873 0 1.000
## 10 10 STENOSIS factor 3873 93 0.976
## 11 11 SYSTBP numeric 3873 1223 0.684
## 12 12 DIASTBP numeric 3873 1221 0.685
## 13 13 SYSTH numeric 3873 1498 0.613
## 14 14 DIASTH numeric 3873 1499 0.613
## 15 15 LENGTH numeric 3873 1 1.000
## 16 16 WEIGHT numeric 3873 2 0.999
## 17 17 BMI numeric 3873 3 0.999
## 18 18 CHOL numeric 3873 18 0.995
## 19 19 HDL numeric 3873 30 0.992
## 20 20 LDL numeric 3873 216 0.944
## 21 21 TRIG numeric 3873 28 0.993
## 22 22 HOMOC numeric 3873 463 0.880
## 23 23 GLUT numeric 3873 19 0.995
## 24 24 CREAT numeric 3873 17 0.996
## 25 25 IMT numeric 3873 98 0.975
## 26 26 albumin factor 3873 207 0.947
## 27 27 SMOKING factor 3873 25 0.994
## 28 28 packyrs numeric 3873 21 0.995
## 29 29 alcohol factor 3873 25 0.994##################################
# 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 17 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 10 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 SEX factor 2 1 2
## 2 DIABETES factor 3 0 1
## 3 CEREBRAL factor 2 0 1
## 4 CARDIAC factor 2 1 0
## 5 AAA factor 2 0 1
## 6 PERIPH factor 2 0 1
## 7 STENOSIS factor 3 0 1
## 8 albumin factor 4 1 2
## 9 SMOKING factor 4 2 1
## 10 alcohol factor 4 3 1
## First.Mode.Count Second.Mode.Count Unique.Count.Ratio
## 1 2897 976 0.001
## 2 2987 846 0.001
## 3 2726 1147 0.001
## 4 2160 1713 0.001
## 5 3457 416 0.001
## 6 2933 940 0.001
## 7 3058 722 0.001
## 8 2897 655 0.001
## 9 2711 693 0.001
## 10 2689 751 0.001
## First.Second.Mode.Ratio
## 1 2.968
## 2 3.531
## 3 2.377
## 4 1.261
## 5 8.310
## 6 3.120
## 7 4.235
## 8 4.423
## 9 3.912
## 10 3.581##################################
# 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 62 0.016 58.000
## 2 SYSTBP numeric 115 0.030 127.000
## 3 DIASTBP numeric 71 0.018 77.000
## 4 SYSTH numeric 133 0.034 140.000
## 5 DIASTH numeric 78 0.020 80.000
## 6 LENGTH numeric 43 0.011 1.780
## 7 WEIGHT numeric 76 0.020 80.000
## 8 BMI numeric 996 0.257 28.090
## 9 CHOL numeric 66 0.017 4.800
## 10 HDL numeric 189 0.049 1.160
## 11 LDL numeric 479 0.124 1.100
## 12 TRIG numeric 462 0.119 1.100
## 13 HOMOC numeric 256 0.066 11.600
## 14 GLUT numeric 126 0.033 5.400
## 15 CREAT numeric 195 0.050 86.000
## 16 IMT numeric 100 0.026 0.870
## 17 packyrs numeric 264 0.068 0.000
## Second.Mode.Value First.Mode.Count Second.Mode.Count First.Second.Mode.Ratio
## 1 63.000 147 140 1.050
## 2 133.000 66 62 1.065
## 3 75.000 122 118 1.034
## 4 130.000 66 60 1.100
## 5 84.000 132 94 1.404
## 6 1.760 223 208 1.072
## 7 78.000 148 137 1.080
## 8 28.730 35 32 1.094
## 9 4.500 156 146 1.068
## 10 1.020 61 58 1.052
## 11 2.790 41 24 1.708
## 12 1.460 34 33 1.030
## 13 11.700 49 48 1.021
## 14 5.500 224 220 1.018
## 15 93.000 99 93 1.065
## 16 0.780 126 121 1.041
## 17 30.600 697 42 16.595
## Minimum Mean Median Maximum Skewness Kurtosis Percentile25th
## 1 19.000 59.557 60.000 82.000 -0.388 2.839 52.000
## 2 96.000 141.322 139.000 216.000 0.531 3.151 127.000
## 3 46.000 79.698 79.000 127.000 0.475 3.693 73.000
## 4 79.000 142.163 140.000 244.000 0.684 3.735 126.000
## 5 45.000 82.442 82.000 136.000 0.347 3.396 75.000
## 6 1.530 1.740 1.750 1.940 -0.195 2.662 1.680
## 7 50.000 81.001 80.000 124.000 0.366 3.292 72.000
## 8 18.700 26.696 26.300 39.800 0.647 3.648 24.110
## 9 2.800 5.191 5.100 9.400 0.457 3.238 4.400
## 10 0.580 1.230 1.170 2.510 0.927 3.934 0.960
## 11 1.100 3.144 3.060 6.600 0.392 2.857 2.390
## 12 0.560 1.854 1.540 8.960 2.618 13.156 1.120
## 13 6.100 13.843 12.800 38.300 1.845 7.874 10.325
## 14 4.300 6.333 5.700 18.700 2.929 13.442 5.300
## 15 54.000 98.394 89.000 825.000 8.636 88.940 78.000
## 16 0.470 0.935 0.880 1.830 1.099 4.398 0.750
## 17 0.000 22.623 19.500 120.000 0.965 3.650 5.900
## Percentile75th
## 1 68.000
## 2 154.000
## 3 86.000
## 4 156.000
## 5 90.000
## 6 1.800
## 7 89.000
## 8 28.730
## 9 5.900
## 10 1.420
## 11 3.830
## 12 2.230
## 13 15.700
## 14 6.500
## 15 101.000
## 16 1.070
## 17 34.200##################################
# 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$NA.Count>0,]
} else {
print("No missing observations noted.")
}## [1] "Missing observations noted for 21 variable(s) with NA.Count>0 and Fill.Rate<1.0."## Column.Index Column.Name Column.Type Row.Count NA.Count Fill.Rate
## 5 5 DIABETES factor 3873 40 0.990
## 10 10 STENOSIS factor 3873 93 0.976
## 11 11 SYSTBP numeric 3873 1223 0.684
## 12 12 DIASTBP numeric 3873 1221 0.685
## 13 13 SYSTH numeric 3873 1498 0.613
## 14 14 DIASTH numeric 3873 1499 0.613
## 15 15 LENGTH numeric 3873 1 1.000
## 16 16 WEIGHT numeric 3873 2 0.999
## 17 17 BMI numeric 3873 3 0.999
## 18 18 CHOL numeric 3873 18 0.995
## 19 19 HDL numeric 3873 30 0.992
## 20 20 LDL numeric 3873 216 0.944
## 21 21 TRIG numeric 3873 28 0.993
## 22 22 HOMOC numeric 3873 463 0.880
## 23 23 GLUT numeric 3873 19 0.995
## 24 24 CREAT numeric 3873 17 0.996
## 25 25 IMT numeric 3873 98 0.975
## 26 26 albumin factor 3873 207 0.947
## 27 27 SMOKING factor 3873 25 0.994
## 28 28 packyrs numeric 3873 21 0.995
## 29 29 alcohol factor 3873 25 0.994##################################
# Checking for zero or near-zero variance predictors
##################################
if (length(names(DQA.Predictors.Factor))==0) {
print("No factor predictors noted.")
} else if (nrow(DQA.Predictors.Factor.Summary[as.numeric(as.character(DQA.Predictors.Factor.Summary$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
## 5 AAA factor 2 0 1
## First.Mode.Count Second.Mode.Count Unique.Count.Ratio First.Second.Mode.Ratio
## 5 3457 416 0.001 8.310if (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$First.Second.Mode.Ratio))>5,]
} else {
print("No low variance numeric predictors due to high first-second mode ratio noted.")
}## [1] "Low variance observed for 1 numeric variable(s) with First.Second.Mode.Ratio>5."## Column.Name Column.Type Unique.Count Unique.Count.Ratio First.Mode.Value
## 17 packyrs numeric 264 0.068 0.000
## Second.Mode.Value First.Mode.Count Second.Mode.Count First.Second.Mode.Ratio
## 17 30.600 697 42 16.595
## Minimum Mean Median Maximum Skewness Kurtosis Percentile25th
## 17 0.000 22.623 19.500 120.000 0.965 3.650 5.900
## Percentile75th
## 17 34.200if (length(names(DQA.Predictors.Numeric))==0) {
print("No numeric predictors noted.")
} else if (nrow(DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$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] "High skewness observed for 1 numeric variable(s) with Skewness>3 or Skewness<(-3)."## Column.Name Column.Type Unique.Count Unique.Count.Ratio First.Mode.Value
## 15 CREAT numeric 195 0.050 86.000
## Second.Mode.Value First.Mode.Count Second.Mode.Count First.Second.Mode.Ratio
## 15 93.000 99 93 1.065
## Minimum Mean Median Maximum Skewness Kurtosis Percentile25th
## 15 54.000 98.394 89.000 825.000 8.636 88.940 78.000
## Percentile75th
## 15 101.0001.2.3 Predictor Coding
[A] Considering prognostic significance (determined using the Wald Chi-squared value from the formulated Cox regression models) as a criterion while maintaining model parsimony (minimal variable transformation), most predictors can be coded linearly during model development except for the following variables where a transformation might improve their performance:
[A.1] The AGE variable (numeric) was coded using its squared value after 50 years [if (AGE>50) then (AGE-50)^2 else 0] since this demonstrated a better Wald Chi-squared value as compared to other transformation types.
[A.2] The CREAT variable (numeric) was coded using its logarithm [log(CREAT)] since this demonstrated a better Wald Chi-squared value as compared to other transformation types.
[A.3] The CEREBRAL variable (numeric), CARDIAC variable (numeric), AAA variable (numeric) and PERIPH variable (numeric) were coded using their linear combination [CEREBRAL + CARDIAC + (2*AAA) + PERIPH] since this demonstrated a better Wald Chi-squared value as compared to other transformation types.
Code Chunk | Output
##################################
# Loading dataset
##################################
PC <- SMART
PC$EVENT <- as.numeric(PC$EVENT)
##################################
# Evaluating the impact of predictor coding
# for AGE as applied in a univariate Cox regression model
#################################
##################################
# Relationship of AGE with prognostic outcome = Linear
# (TEVENT,EVENT) ~ AGE
#################################
AGE_CoxPHFit_Linear <- cph(Surv(TEVENT,EVENT) ~ AGE, data=PC)
anova(AGE_CoxPHFit_Linear)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## AGE 97.17 1 <.0001
## TOTAL 97.17 1 <.0001(AGE_CoxPHFit_Linear_WaldX2 <- anova(AGE_CoxPHFit_Linear)[1])## [1] 97.17258##################################
# Relationship of AGE with prognostic outcome = Squared
# (TEVENT,EVENT) ~ AGE +AGE^2
#################################
AGE_CoxPHFit_Squared <- cph(Surv(TEVENT,EVENT) ~ pol(AGE,2), data=PC)
anova(AGE_CoxPHFit_Squared)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## AGE 124.99 2 <.0001
## Nonlinear 15.00 1 1e-04
## TOTAL 124.99 2 <.0001(AGE_CoxPHFit_Squared_WaldX2 <- anova(AGE_CoxPHFit_Squared)[1])## [1] 124.9852##################################
# Relationship of AGE with prognostic outcome = Linear after 55
# (TEVENT,EVENT) ~ if (AGE>55) then (AGE-55) else 0
#################################
AGE_CoxPHFit_LinearAfter55 <- cph(Surv(TEVENT,EVENT) ~ ifelse(AGE>55, (AGE-55),0), data=PC)
anova(AGE_CoxPHFit_LinearAfter55)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## AGE 118.59 1 <.0001
## TOTAL 118.59 1 <.0001(AGE_CoxPHFit_LinearAfter55_WaldX2 <- anova(AGE_CoxPHFit_LinearAfter55)[1])## [1] 118.591##################################
# Relationship of AGE with prognostic outcome = Squared after 50
# (TEVENT,EVENT) ~ if (AGE>50) then (AGE-50)^2 else 0
#################################
AGE_CoxPHFit_SquaredAfter50 <- cph(Surv(TEVENT,EVENT) ~ ifelse(AGE>50, (AGE-50)^2,0), data=PC)
anova(AGE_CoxPHFit_SquaredAfter50)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## AGE 129.64 1 <.0001
## TOTAL 129.64 1 <.0001(AGE_CoxPHFit_SquaredAfter50_WaldX2 <- anova(AGE_CoxPHFit_SquaredAfter50)[1])## [1] 129.6405##################################
# Relationship of AGE with prognostic outcome = Restricted cubic spline (4 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(AGE,4)
#################################
AGE_CoxPHFit_RCS4Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(AGE,4), data=PC)
anova(AGE_CoxPHFit_RCS4Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## AGE 125.30 3 <.0001
## Nonlinear 13.77 2 0.001
## TOTAL 125.30 3 <.0001(AGE_CoxPHFit_RCS4Knots_WaldX2 <- anova(AGE_CoxPHFit_RCS4Knots)[1])## [1] 125.3017##################################
# Relationship of AGE with prognostic outcome = Quartiles
# (TEVENT,EVENT) ~ AGE(Quartile1, Quartile2, Quartile3, Quartile4)
#################################
tapply(PC$AGE, ifelse(PC$AGE<50,1,
ifelse(PC$AGE<60,2,
ifelse(PC$AGE<70,3,4))),mean)## 1 2 3 4
## 43.20362 54.78531 64.53566 73.59654PC$AGEQuartile <- as.factor(ifelse(PC$AGE<50,43,
ifelse(PC$AGE<60,55,
ifelse(PC$AGE<70,65,74))))
PC$AGEQuartile <- as.factor(PC$AGEQuartile)
AGE_CoxPHFit_Quartile <- cph(Surv(TEVENT,EVENT) ~ AGEQuartile, data=PC)
anova(AGE_CoxPHFit_Quartile)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## AGEQuartile 93.22 3 <.0001
## TOTAL 93.22 3 <.0001(AGE_CoxPHFit_Quartile_WaldX2 <- anova(AGE_CoxPHFit_Quartile)[1])## [1] 93.22204##################################
# Relationship of AGE with prognostic outcome = Quartiles
# (TEVENT,EVENT) ~ AGE(Half1, Half2)
#################################
tapply(PC$AGE, cut2(PC$AGE,g=2), mean)## [19,61) [61,82]
## 51.29891 68.50350AGE_CoxPHFit_Dichotomized <- cph(Surv(TEVENT,EVENT) ~ ifelse(SMART$AGE<61,51,69), data=PC)
anova(AGE_CoxPHFit_Dichotomized)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## SMART 72.47 1 <.0001
## TOTAL 72.47 1 <.0001(AGE_CoxPHFit_Dichotomized_WaldX2 <- anova(AGE_CoxPHFit_Dichotomized)[1])## [1] 72.46705##################################
# Evaluating the impact of predictor coding
# for CREAT as applied in a univariate Cox regression model
#################################
##################################
# Relationship of CREAT with prognostic outcome = Linear
# (TEVENT,EVENT) ~ CREAT
#################################
CREAT_CoxPHFit_Linear <- cph(Surv(TEVENT,EVENT) ~ CREAT, data=PC)
anova(CREAT_CoxPHFit_Linear)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## CREAT 93.42 1 <.0001
## TOTAL 93.42 1 <.0001(CREAT_CoxPHFit_Linear_WaldX2 <- anova(CREAT_CoxPHFit_Linear)[1])## [1] 93.42011##################################
# Relationship of CREAT with prognostic outcome = Restricted cubic spline (4 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(CREAT,4)
#################################
CREAT_CoxPHFit_RCS4Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(CREAT,4), data=PC)
anova(CREAT_CoxPHFit_RCS4Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## CREAT 116.1 3 <.0001
## Nonlinear 42.6 2 <.0001
## TOTAL 116.1 3 <.0001(CREAT_CoxPHFit_RCS4Knots_WaldX2 <- anova(CREAT_CoxPHFit_RCS4Knots)[1])## [1] 116.102##################################
# Relationship of CREAT with prognostic outcome = Restricted cubic spline (3 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(CREAT,3)
#################################
CREAT_CoxPHFit_RCS3Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(CREAT,3), data=PC)
anova(CREAT_CoxPHFit_RCS3Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## CREAT 99.03 2 <.0001
## Nonlinear 20.32 1 <.0001
## TOTAL 99.03 2 <.0001(CREAT_CoxPHFit_RCS3Knots_WaldX2 <- anova(CREAT_CoxPHFit_RCS3Knots)[1])## [1] 99.02755##################################
# Relationship of CREAT with prognostic outcome = Logarithm
# (TEVENT,EVENT) ~ Logarithm(CREAT)
#################################
CREAT_CoxPHFit_Log <- cph(Surv(TEVENT,EVENT) ~ log(CREAT), data=PC)
anova(CREAT_CoxPHFit_Log)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## CREAT 131.01 1 <.0001
## TOTAL 131.01 1 <.0001(CREAT_CoxPHFit_Log_WaldX2 <- anova(CREAT_CoxPHFit_Log)[1])## [1] 131.0105##################################
# Evaluating the impact of predictor coding
# for SYSTH as applied in a univariate Cox regression model
#################################
##################################
# Relationship of SYSTH with prognostic outcome = Linear
# (TEVENT,EVENT) ~ SYSTH
#################################
SYSTH_CoxPHFit_Linear <- cph(Surv(TEVENT,EVENT) ~ SYSTH, data=PC)
anova(SYSTH_CoxPHFit_Linear)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## SYSTH 15.49 1 1e-04
## TOTAL 15.49 1 1e-04(SYSTH_CoxPHFit_Linear_WaldX2 <- anova(SYSTH_CoxPHFit_Linear)[1])## [1] 15.49085##################################
# Relationship of SYSTH with prognostic outcome = Restricted cubic spline (4 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(SYSTH,4)
#################################
SYSTH_CoxPHFit_RCS4Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(SYSTH,4), data=PC)
anova(SYSTH_CoxPHFit_RCS4Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## SYSTH 15.60 3 0.0014
## Nonlinear 0.25 2 0.8841
## TOTAL 15.60 3 0.0014(SYSTH_CoxPHFit_RCS4Knots_WaldX2 <- anova(SYSTH_CoxPHFit_RCS4Knots)[1])## [1] 15.5989##################################
# Relationship of SYSTH with prognostic outcome = Restricted cubic spline (3 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(SYSTH,3)
#################################
SYSTH_CoxPHFit_RCS3Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(SYSTH,3), data=PC)
anova(SYSTH_CoxPHFit_RCS3Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## SYSTH 15.17 2 0.0005
## Nonlinear 0.05 1 0.8261
## TOTAL 15.17 2 0.0005(SYSTH_CoxPHFit_RCS3Knots_WaldX2 <- anova(SYSTH_CoxPHFit_RCS3Knots)[1])## [1] 15.16692##################################
# Relationship of SYSTH with prognostic outcome = Logarithm
# (TEVENT,EVENT) ~ Logarithm(SYSTH)
#################################
SYSTH_CoxPHFit_Log <- cph(Surv(TEVENT,EVENT) ~ log(SYSTH), data=PC)
anova(SYSTH_CoxPHFit_Log)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## SYSTH 14.39 1 1e-04
## TOTAL 14.39 1 1e-04(SYSTH_CoxPHFit_Log_WaldX2 <- anova(SYSTH_CoxPHFit_Log)[1])## [1] 14.39016##################################
# Evaluating the impact of predictor coding
# for DIASTH as applied in a univariate Cox regression model
#################################
##################################
# Relationship of DIASTH with prognostic outcome = Linear
# (TEVENT,EVENT) ~ DIASTH
#################################
DIASTH_CoxPHFit_Linear <- cph(Surv(TEVENT,EVENT) ~ DIASTH, data=PC)
anova(DIASTH_CoxPHFit_Linear)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## DIASTH 0.73 1 0.3916
## TOTAL 0.73 1 0.3916(DIASTH_CoxPHFit_Linear_WaldX2 <- anova(DIASTH_CoxPHFit_Linear)[1])## [1] 0.7339729##################################
# Relationship of DIASTH with prognostic outcome = Restricted cubic spline (4 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(DIASTH,4)
#################################
DIASTH_CoxPHFit_RCS4Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(DIASTH,4), data=PC)
anova(DIASTH_CoxPHFit_RCS4Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## DIASTH 2.62 3 0.4540
## Nonlinear 1.91 2 0.3851
## TOTAL 2.62 3 0.4540(DIASTH_CoxPHFit_RCS4Knots_WaldX2 <- anova(DIASTH_CoxPHFit_RCS4Knots)[1])## [1] 2.620047##################################
# Relationship of DIASTH with prognostic outcome = Restricted cubic spline (3 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(DIASTH,3)
#################################
DIASTH_CoxPHFit_RCS3Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(DIASTH,3), data=PC)
anova(DIASTH_CoxPHFit_RCS3Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## DIASTH 2.08 2 0.3528
## Nonlinear 1.24 1 0.2659
## TOTAL 2.08 2 0.3528(DIASTH_CoxPHFit_RCS3Knots_WaldX2 <- anova(DIASTH_CoxPHFit_RCS3Knots)[1])## [1] 2.083467##################################
# Relationship of DIASTH with prognostic outcome = Logarithm
# (TEVENT,EVENT) ~ Logarithm(DIASTH)
#################################
DIASTH_CoxPHFit_Log <- cph(Surv(TEVENT,EVENT) ~ log(DIASTH), data=PC)
anova(DIASTH_CoxPHFit_Log)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## DIASTH 0.47 1 0.492
## TOTAL 0.47 1 0.492(DIASTH_CoxPHFit_Log_WaldX2 <- anova(DIASTH_CoxPHFit_Log)[1])## [1] 0.4721145##################################
# Evaluating the impact of predictor coding
# for SYSTBP as applied in a univariate Cox regression model
#################################
##################################
# Relationship of SYSTBP with prognostic outcome = Linear
# (TEVENT,EVENT) ~ SYSTBP
#################################
SYSTBP_CoxPHFit_Linear <- cph(Surv(TEVENT,EVENT) ~ SYSTBP, data=PC)
anova(SYSTBP_CoxPHFit_Linear)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## SYSTBP 23.22 1 <.0001
## TOTAL 23.22 1 <.0001(SYSTBP_CoxPHFit_Linear_WaldX2 <- anova(SYSTBP_CoxPHFit_Linear)[1])## [1] 23.22008##################################
# Relationship of SYSTBP with prognostic outcome = Restricted cubic spline (4 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(SYSTBP,4)
#################################
SYSTBP_CoxPHFit_RCS4Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(SYSTBP,4), data=PC)
anova(SYSTBP_CoxPHFit_RCS4Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## SYSTBP 26.27 3 <.0001
## Nonlinear 1.73 2 0.4219
## TOTAL 26.27 3 <.0001(SYSTBP_CoxPHFit_RCS4Knots_WaldX2 <- anova(SYSTBP_CoxPHFit_RCS4Knots)[1])## [1] 26.27116##################################
# Relationship of SYSTBP with prognostic outcome = Restricted cubic spline (3 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(SYSTBP,3)
#################################
SYSTBP_CoxPHFit_RCS3Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(SYSTBP,3), data=PC)
anova(SYSTBP_CoxPHFit_RCS3Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## SYSTBP 26.26 2 <.0001
## Nonlinear 1.37 1 0.2422
## TOTAL 26.26 2 <.0001(SYSTBP_CoxPHFit_RCS3Knots_WaldX2 <- anova(SYSTBP_CoxPHFit_RCS3Knots)[1])## [1] 26.26421##################################
# Relationship of SYSTBP with prognostic outcome = Logarithm
# (TEVENT,EVENT) ~ Logarithm(SYSTBP)
#################################
SYSTBP_CoxPHFit_Log <- cph(Surv(TEVENT,EVENT) ~ log(SYSTBP), data=PC)
anova(SYSTBP_CoxPHFit_Log)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## SYSTBP 21.2 1 <.0001
## TOTAL 21.2 1 <.0001(SYSTBP_CoxPHFit_Log_WaldX2 <- anova(SYSTBP_CoxPHFit_Log)[1])## [1] 21.20011##################################
# Evaluating the impact of predictor coding
# for DIASTBP as applied in a univariate Cox regression model
#################################
##################################
# Relationship of DIASTBP with prognostic outcome = Linear
# (TEVENT,EVENT) ~ DIASTBP
#################################
DIASTBP_CoxPHFit_Linear <- cph(Surv(TEVENT,EVENT) ~ DIASTBP, data=PC)
anova(DIASTBP_CoxPHFit_Linear)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## DIASTBP 1.67 1 0.1962
## TOTAL 1.67 1 0.1962(DIASTBP_CoxPHFit_Linear_WaldX2 <- anova(DIASTBP_CoxPHFit_Linear)[1])## [1] 1.670766##################################
# Relationship of DIASTBP with prognostic outcome = Restricted cubic spline (4 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(DIASTBP,4)
#################################
DIASTBP_CoxPHFit_RCS4Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(DIASTBP,4), data=PC)
anova(DIASTBP_CoxPHFit_RCS4Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## DIASTBP 25.15 3 <.0001
## Nonlinear 23.22 2 <.0001
## TOTAL 25.15 3 <.0001(DIASTBP_CoxPHFit_RCS4Knots_WaldX2 <- anova(DIASTBP_CoxPHFit_RCS4Knots)[1])## [1] 25.14634##################################
# Relationship of DIASTBP with prognostic outcome = Restricted cubic spline (3 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(DIASTBP,3)
#################################
DIASTBP_CoxPHFit_RCS3Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(DIASTBP,3), data=PC)
anova(DIASTBP_CoxPHFit_RCS3Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## DIASTBP 24.84 2 <.0001
## Nonlinear 22.29 1 <.0001
## TOTAL 24.84 2 <.0001(DIASTBP_CoxPHFit_RCS3Knots_WaldX2 <- anova(DIASTBP_CoxPHFit_RCS3Knots)[1])## [1] 24.84403##################################
# Relationship of DIASTBP with prognostic outcome = Logarithm
# (TEVENT,EVENT) ~ Logarithm(DIASTBP)
#################################
DIASTBP_CoxPHFit_Log <- cph(Surv(TEVENT,EVENT) ~ log(DIASTBP), data=PC)
anova(DIASTBP_CoxPHFit_Log)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## DIASTBP 0.68 1 0.4092
## TOTAL 0.68 1 0.4092(DIASTBP_CoxPHFit_Log_WaldX2 <- anova(DIASTBP_CoxPHFit_Log)[1])## [1] 0.6810459##################################
# Evaluating the impact of predictor coding
# for CHOL as applied in a univariate Cox regression model
#################################
##################################
# Relationship of CHOL with prognostic outcome = Linear
# (TEVENT,EVENT) ~ CHOL
#################################
CHOL_CoxPHFit_Linear <- cph(Surv(TEVENT,EVENT) ~ CHOL, data=PC)
anova(CHOL_CoxPHFit_Linear)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## CHOL 0.32 1 0.5717
## TOTAL 0.32 1 0.5717(CHOL_CoxPHFit_Linear_WaldX2 <- anova(CHOL_CoxPHFit_Linear)[1])## [1] 0.3199142##################################
# Relationship of CHOL with prognostic outcome = Restricted cubic spline (4 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(CHOL,4)
#################################
CHOL_CoxPHFit_RCS4Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(CHOL,4), data=PC)
anova(CHOL_CoxPHFit_RCS4Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## CHOL 0.60 3 0.8964
## Nonlinear 0.27 2 0.8720
## TOTAL 0.60 3 0.8964(CHOL_CoxPHFit_RCS4Knots_WaldX2 <- anova(CHOL_CoxPHFit_RCS4Knots)[1])## [1] 0.5999714##################################
# Relationship of CHOL with prognostic outcome = Restricted cubic spline (3 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(CHOL,3)
#################################
CHOL_CoxPHFit_RCS3Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(CHOL,3), data=PC)
anova(CHOL_CoxPHFit_RCS3Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## CHOL 0.60 2 0.7399
## Nonlinear 0.25 1 0.6161
## TOTAL 0.60 2 0.7399(CHOL_CoxPHFit_RCS3Knots_WaldX2 <- anova(CHOL_CoxPHFit_RCS3Knots)[1])## [1] 0.6024457##################################
# Relationship of CHOL with prognostic outcome = Logarithm
# (TEVENT,EVENT) ~ Logarithm(CHOL)
#################################
CHOL_CoxPHFit_Log <- cph(Surv(TEVENT,EVENT) ~ log(CHOL), data=PC)
anova(CHOL_CoxPHFit_Log)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## CHOL 0.25 1 0.6171
## TOTAL 0.25 1 0.6171(CHOL_CoxPHFit_Log_WaldX2 <- anova(CHOL_CoxPHFit_Log)[1])## [1] 0.2499827##################################
# Evaluating the impact of predictor coding
# for HDL as applied in a univariate Cox regression model
#################################
##################################
# Relationship of HDL with prognostic outcome = Linear
# (TEVENT,EVENT) ~ HDL
#################################
HDL_CoxPHFit_Linear <- cph(Surv(TEVENT,EVENT) ~ HDL, data=PC)
anova(HDL_CoxPHFit_Linear)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## HDL 11.83 1 6e-04
## TOTAL 11.83 1 6e-04(HDL_CoxPHFit_Linear_WaldX2 <- anova(HDL_CoxPHFit_Linear)[1])## [1] 11.83362##################################
# Relationship of HDL with prognostic outcome = Restricted cubic spline (4 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(HDL,4)
#################################
HDL_CoxPHFit_RCS4Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(HDL,4), data=PC)
anova(HDL_CoxPHFit_RCS4Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## HDL 11.94 3 0.0076
## Nonlinear 0.63 2 0.7302
## TOTAL 11.94 3 0.0076(HDL_CoxPHFit_RCS4Knots_WaldX2 <- anova(HDL_CoxPHFit_RCS4Knots)[1])## [1] 11.93661##################################
# Relationship of HDL with prognostic outcome = Restricted cubic spline (3 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(HDL,3)
#################################
HDL_CoxPHFit_RCS3Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(HDL,3), data=PC)
anova(HDL_CoxPHFit_RCS3Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## HDL 11.61 2 0.0030
## Nonlinear 0.08 1 0.7741
## TOTAL 11.61 2 0.0030(HDL_CoxPHFit_RCS3Knots_WaldX2 <- anova(HDL_CoxPHFit_RCS3Knots)[1])## [1] 11.60599##################################
# Relationship of HDL with prognostic outcome = Logarithm
# (TEVENT,EVENT) ~ Logarithm(HDL)
#################################
HDL_CoxPHFit_Log <- cph(Surv(TEVENT,EVENT) ~ log(HDL), data=PC)
anova(HDL_CoxPHFit_Log)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## HDL 11.8 1 6e-04
## TOTAL 11.8 1 6e-04(HDL_CoxPHFit_Log_WaldX2 <- anova(HDL_CoxPHFit_Log)[1])## [1] 11.79606##################################
# Evaluating the impact of predictor coding
# for LDL as applied in a univariate Cox regression model
#################################
##################################
# Relationship of LDL with prognostic outcome = Linear
# (TEVENT,EVENT) ~ LDL
#################################
LDL_CoxPHFit_Linear <- cph(Surv(TEVENT,EVENT) ~ LDL, data=PC)
anova(LDL_CoxPHFit_Linear)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## LDL 1.28 1 0.2584
## TOTAL 1.28 1 0.2584(LDL_CoxPHFit_Linear_WaldX2 <- anova(LDL_CoxPHFit_Linear)[1])## [1] 1.2771##################################
# Relationship of LDL with prognostic outcome = Restricted cubic spline (4 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(LDL,4)
#################################
LDL_CoxPHFit_RCS4Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(LDL,4), data=PC)
anova(LDL_CoxPHFit_RCS4Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## LDL 1.52 3 0.6777
## Nonlinear 0.25 2 0.8812
## TOTAL 1.52 3 0.6777(LDL_CoxPHFit_RCS4Knots_WaldX2 <- anova(LDL_CoxPHFit_RCS4Knots)[1])## [1] 1.519874##################################
# Relationship of LDL with prognostic outcome = Restricted cubic spline (3 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(LDL,3)
#################################
LDL_CoxPHFit_RCS3Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(LDL,3), data=PC)
anova(LDL_CoxPHFit_RCS3Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## LDL 1.28 2 0.5260
## Nonlinear 0.00 1 0.9537
## TOTAL 1.28 2 0.5260(LDL_CoxPHFit_RCS3Knots_WaldX2 <- anova(LDL_CoxPHFit_RCS3Knots)[1])## [1] 1.284805##################################
# Relationship of LDL with prognostic outcome = Logarithm
# (TEVENT,EVENT) ~ Logarithm(LDL)
#################################
LDL_CoxPHFit_Log <- cph(Surv(TEVENT,EVENT) ~ log(LDL), data=PC)
anova(LDL_CoxPHFit_Log)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## LDL 1.15 1 0.2839
## TOTAL 1.15 1 0.2839(LDL_CoxPHFit_Log_WaldX2 <- anova(LDL_CoxPHFit_Log)[1])## [1] 1.148225##################################
# Evaluating the impact of predictor coding
# for TRIG as applied in a univariate Cox regression model
#################################
##################################
# Relationship of TRIG with prognostic outcome = Linear
# (TEVENT,EVENT) ~ TRIG
#################################
TRIG_CoxPHFit_Linear <- cph(Surv(TEVENT,EVENT) ~ TRIG, data=PC)
anova(TRIG_CoxPHFit_Linear)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## TRIG 1.4 1 0.2366
## TOTAL 1.4 1 0.2366(TRIG_CoxPHFit_Linear_WaldX2 <- anova(TRIG_CoxPHFit_Linear)[1])## [1] 1.400792##################################
# Relationship of TRIG with prognostic outcome = Restricted cubic spline (4 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(TRIG,4)
#################################
TRIG_CoxPHFit_RCS4Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(TRIG,4), data=PC)
anova(TRIG_CoxPHFit_RCS4Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## TRIG 3.51 3 0.3192
## Nonlinear 2.12 2 0.3456
## TOTAL 3.51 3 0.3192(TRIG_CoxPHFit_RCS4Knots_WaldX2 <- anova(TRIG_CoxPHFit_RCS4Knots)[1])## [1] 3.512266##################################
# Relationship of TRIG with prognostic outcome = Restricted cubic spline (3 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(TRIG,3)
#################################
TRIG_CoxPHFit_RCS3Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(TRIG,3), data=PC)
anova(TRIG_CoxPHFit_RCS3Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## TRIG 3.25 2 0.1965
## Nonlinear 1.94 1 0.1642
## TOTAL 3.25 2 0.1965(TRIG_CoxPHFit_RCS3Knots_WaldX2 <- anova(TRIG_CoxPHFit_RCS3Knots)[1])## [1] 3.253776##################################
# Relationship of TRIG with prognostic outcome = Logarithm
# (TEVENT,EVENT) ~ Logarithm(TRIG)
#################################
TRIG_CoxPHFit_Log <- cph(Surv(TEVENT,EVENT) ~ log(TRIG), data=PC)
anova(TRIG_CoxPHFit_Log)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## TRIG 2.47 1 0.1164
## TOTAL 2.47 1 0.1164(TRIG_CoxPHFit_Log_WaldX2 <- anova(TRIG_CoxPHFit_Log)[1])## [1] 2.46539##################################
# Evaluating the impact of predictor coding
# for HOMOC as applied in a univariate Cox regression model
#################################
##################################
# Relationship of HOMOC with prognostic outcome = Linear
# (TEVENT,EVENT) ~ HOMOC
#################################
HOMOC_CoxPHFit_Linear <- cph(Surv(TEVENT,EVENT) ~ HOMOC, data=PC)
anova(HOMOC_CoxPHFit_Linear)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## HOMOC 49.59 1 <.0001
## TOTAL 49.59 1 <.0001(HOMOC_CoxPHFit_Linear_WaldX2 <- anova(HOMOC_CoxPHFit_Linear)[1])## [1] 49.59385##################################
# Relationship of HOMOC with prognostic outcome = Restricted cubic spline (4 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(HOMOC,4)
#################################
HOMOC_CoxPHFit_RCS4Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(HOMOC,4), data=PC)
anova(HOMOC_CoxPHFit_RCS4Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## HOMOC 50.68 3 <.0001
## Nonlinear 7.97 2 0.0186
## TOTAL 50.68 3 <.0001(HOMOC_CoxPHFit_RCS4Knots_WaldX2 <- anova(HOMOC_CoxPHFit_RCS4Knots)[1])## [1] 50.67529##################################
# Relationship of HOMOC with prognostic outcome = Restricted cubic spline (3 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(HOMOC,3)
#################################
HOMOC_CoxPHFit_RCS3Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(HOMOC,3), data=PC)
anova(HOMOC_CoxPHFit_RCS3Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## HOMOC 47.32 2 <.0001
## Nonlinear 3.64 1 0.0563
## TOTAL 47.32 2 <.0001(HOMOC_CoxPHFit_RCS3Knots_WaldX2 <- anova(HOMOC_CoxPHFit_RCS3Knots)[1])## [1] 47.32265##################################
# Relationship of HOMOC with prognostic outcome = Logarithm
# (TEVENT,EVENT) ~ Logarithm(HOMOC)
#################################
HOMOC_CoxPHFit_Log <- cph(Surv(TEVENT,EVENT) ~ log(HOMOC), data=PC)
anova(HOMOC_CoxPHFit_Log)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## HOMOC 52.46 1 <.0001
## TOTAL 52.46 1 <.0001(HOMOC_CoxPHFit_Log_WaldX2 <- anova(HOMOC_CoxPHFit_Log)[1])## [1] 52.46239##################################
# Evaluating the impact of predictor coding
# for GLUT as applied in a univariate Cox regression model
#################################
##################################
# Relationship of GLUT with prognostic outcome = Linear
# (TEVENT,EVENT) ~ GLUT
#################################
GLUT_CoxPHFit_Linear <- cph(Surv(TEVENT,EVENT) ~ GLUT, data=PC)
anova(GLUT_CoxPHFit_Linear)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## GLUT 12.69 1 4e-04
## TOTAL 12.69 1 4e-04(GLUT_CoxPHFit_Linear_WaldX2 <- anova(GLUT_CoxPHFit_Linear)[1])## [1] 12.68661##################################
# Relationship of GLUT with prognostic outcome = Restricted cubic spline (4 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(GLUT,4)
#################################
GLUT_CoxPHFit_RCS4Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(GLUT,4), data=PC)
anova(GLUT_CoxPHFit_RCS4Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## GLUT 15.43 3 0.0015
## Nonlinear 3.16 2 0.2059
## TOTAL 15.43 3 0.0015(GLUT_CoxPHFit_RCS4Knots_WaldX2 <- anova(GLUT_CoxPHFit_RCS4Knots)[1])## [1] 15.42745##################################
# Relationship of GLUT with prognostic outcome = Restricted cubic spline (3 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(GLUT,3)
#################################
GLUT_CoxPHFit_RCS3Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(GLUT,3), data=PC)
anova(GLUT_CoxPHFit_RCS3Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## GLUT 13.03 2 0.0015
## Nonlinear 0.11 1 0.7407
## TOTAL 13.03 2 0.0015(GLUT_CoxPHFit_RCS3Knots_WaldX2 <- anova(GLUT_CoxPHFit_RCS3Knots)[1])## [1] 13.03222##################################
# Relationship of GLUT with prognostic outcome = Logarithm
# (TEVENT,EVENT) ~ Logarithm(GLUT)
#################################
GLUT_CoxPHFit_Log <- cph(Surv(TEVENT,EVENT) ~ log(GLUT), data=PC)
anova(GLUT_CoxPHFit_Log)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## GLUT 12.08 1 5e-04
## TOTAL 12.08 1 5e-04(GLUT_CoxPHFit_Log_WaldX2 <- anova(GLUT_CoxPHFit_Log)[1])## [1] 12.08488##################################
# Evaluating the impact of predictor coding
# for LENGTH as applied in a univariate Cox regression model
#################################
##################################
# Relationship of LENGTH with prognostic outcome = Linear
# (TEVENT,EVENT) ~ LENGTH
#################################
LENGTH_CoxPHFit_Linear <- cph(Surv(TEVENT,EVENT) ~ LENGTH, data=PC)
anova(LENGTH_CoxPHFit_Linear)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## LENGTH 0.01 1 0.9284
## TOTAL 0.01 1 0.9284(LENGTH_CoxPHFit_Linear_WaldX2 <- anova(LENGTH_CoxPHFit_Linear)[1])## [1] 0.008063822##################################
# Relationship of LENGTH with prognostic outcome = Restricted cubic spline (4 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(LENGTH,4)
#################################
LENGTH_CoxPHFit_RCS4Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(LENGTH,4), data=PC)
anova(LENGTH_CoxPHFit_RCS4Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## LENGTH 4.19 3 0.2417
## Nonlinear 4.17 2 0.1243
## TOTAL 4.19 3 0.2417(LENGTH_CoxPHFit_RCS4Knots_WaldX2 <- anova(LENGTH_CoxPHFit_RCS4Knots)[1])## [1] 4.189518##################################
# Relationship of LENGTH with prognostic outcome = Restricted cubic spline (3 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(LENGTH,3)
#################################
LENGTH_CoxPHFit_RCS3Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(LENGTH,3), data=PC)
anova(LENGTH_CoxPHFit_RCS3Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## LENGTH 4.11 2 0.1280
## Nonlinear 4.11 1 0.0427
## TOTAL 4.11 2 0.1280(LENGTH_CoxPHFit_RCS3Knots_WaldX2 <- anova(LENGTH_CoxPHFit_RCS3Knots)[1])## [1] 4.111306##################################
# Relationship of LENGTH with prognostic outcome = Logarithm
# (TEVENT,EVENT) ~ Logarithm(LENGTH)
#################################
LENGTH_CoxPHFit_Log <- cph(Surv(TEVENT,EVENT) ~ log(LENGTH), data=PC)
anova(LENGTH_CoxPHFit_Log)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## LENGTH 0 1 0.9751
## TOTAL 0 1 0.9751(LENGTH_CoxPHFit_Log_WaldX2 <- anova(LENGTH_CoxPHFit_Log)[1])## [1] 0.0009703188##################################
# Evaluating the impact of predictor coding
# for WEIGHT as applied in a univariate Cox regression model
#################################
##################################
# Relationship of WEIGHT with prognostic outcome = Linear
# (TEVENT,EVENT) ~ WEIGHT
#################################
WEIGHT_CoxPHFit_Linear <- cph(Surv(TEVENT,EVENT) ~ WEIGHT, data=PC)
anova(WEIGHT_CoxPHFit_Linear)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## WEIGHT 3.21 1 0.073
## TOTAL 3.21 1 0.073(WEIGHT_CoxPHFit_Linear_WaldX2 <- anova(WEIGHT_CoxPHFit_Linear)[1])## [1] 3.213383##################################
# Relationship of WEIGHT with prognostic outcome = Restricted cubic spline (4 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(WEIGHT,4)
#################################
WEIGHT_CoxPHFit_RCS4Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(WEIGHT,4), data=PC)
anova(WEIGHT_CoxPHFit_RCS4Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## WEIGHT 4.55 3 0.2080
## Nonlinear 1.85 2 0.3966
## TOTAL 4.55 3 0.2080(WEIGHT_CoxPHFit_RCS4Knots_WaldX2 <- anova(WEIGHT_CoxPHFit_RCS4Knots)[1])## [1] 4.548998##################################
# Relationship of WEIGHT with prognostic outcome = Restricted cubic spline (3 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(WEIGHT,3)
#################################
WEIGHT_CoxPHFit_RCS3Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(WEIGHT,3), data=PC)
anova(WEIGHT_CoxPHFit_RCS3Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## WEIGHT 4.08 2 0.1300
## Nonlinear 1.14 1 0.2847
## TOTAL 4.08 2 0.1300(WEIGHT_CoxPHFit_RCS3Knots_WaldX2 <- anova(WEIGHT_CoxPHFit_RCS3Knots)[1])## [1] 4.080816##################################
# Relationship of WEIGHT with prognostic outcome = Logarithm
# (TEVENT,EVENT) ~ Logarithm(WEIGHT)
#################################
WEIGHT_CoxPHFit_Log <- cph(Surv(TEVENT,EVENT) ~ log(WEIGHT), data=PC)
anova(WEIGHT_CoxPHFit_Log)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## WEIGHT 2.73 1 0.0982
## TOTAL 2.73 1 0.0982(WEIGHT_CoxPHFit_Log_WaldX2 <- anova(WEIGHT_CoxPHFit_Log)[1])## [1] 2.734381##################################
# Evaluating the impact of predictor coding
# for BMI as applied in a univariate Cox regression model
#################################
##################################
# Relationship of BMI with prognostic outcome = Linear
# (TEVENT,EVENT) ~ BMI
#################################
BMI_CoxPHFit_Linear <- cph(Surv(TEVENT,EVENT) ~ BMI, data=PC)
anova(BMI_CoxPHFit_Linear)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## BMI 3.87 1 0.0492
## TOTAL 3.87 1 0.0492(BMI_CoxPHFit_Linear_WaldX2 <- anova(BMI_CoxPHFit_Linear)[1])## [1] 3.867475##################################
# Relationship of BMI with prognostic outcome = Restricted cubic spline (4 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(BMI,4)
#################################
BMI_CoxPHFit_RCS4Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(BMI,4), data=PC)
anova(BMI_CoxPHFit_RCS4Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## BMI 7.64 3 0.0542
## Nonlinear 3.77 2 0.1516
## TOTAL 7.64 3 0.0542(BMI_CoxPHFit_RCS4Knots_WaldX2 <- anova(BMI_CoxPHFit_RCS4Knots)[1])## [1] 7.635769##################################
# Relationship of BMI with prognostic outcome = Restricted cubic spline (3 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(BMI,3)
#################################
BMI_CoxPHFit_RCS3Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(BMI,3), data=PC)
anova(BMI_CoxPHFit_RCS3Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## BMI 4.02 2 0.1342
## Nonlinear 0.08 1 0.7811
## TOTAL 4.02 2 0.1342(BMI_CoxPHFit_RCS3Knots_WaldX2 <- anova(BMI_CoxPHFit_RCS3Knots)[1])## [1] 4.01637##################################
# Relationship of BMI with prognostic outcome = Logarithm
# (TEVENT,EVENT) ~ Logarithm(BMI)
#################################
BMI_CoxPHFit_Log <- cph(Surv(TEVENT,EVENT) ~ log(BMI), data=PC)
anova(BMI_CoxPHFit_Log)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## BMI 3.9 1 0.0482
## TOTAL 3.9 1 0.0482(BMI_CoxPHFit_Log_WaldX2 <- anova(BMI_CoxPHFit_Log)[1])## [1] 3.902606##################################
# Evaluating the impact of predictor coding
# for PACKYRS as applied in a univariate Cox regression model
#################################
##################################
# Relationship of PACKYRS with prognostic outcome = Linear
# (TEVENT,EVENT) ~ PACKYRS
#################################
PACKYRS_CoxPHFit_Linear <- cph(Surv(TEVENT,EVENT) ~ packyrs, data=PC)
anova(PACKYRS_CoxPHFit_Linear)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## packyrs 12.95 1 3e-04
## TOTAL 12.95 1 3e-04(PACKYRS_CoxPHFit_Linear_WaldX2 <- anova(PACKYRS_CoxPHFit_Linear)[1])## [1] 12.95089##################################
# Relationship of PACKYRS with prognostic outcome = Restricted cubic spline (4 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(PACKYRS,4)
#################################
PACKYRS_CoxPHFit_RCS4Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(packyrs,4), data=PC)
anova(PACKYRS_CoxPHFit_RCS4Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## packyrs 14.85 3 0.0019
## Nonlinear 1.54 2 0.4640
## TOTAL 14.85 3 0.0019(PACKYRS_CoxPHFit_RCS4Knots_WaldX2 <- anova(PACKYRS_CoxPHFit_RCS4Knots)[1])## [1] 14.85005##################################
# Relationship of PACKYRS with prognostic outcome = Restricted cubic spline (3 knots)
# (TEVENT,EVENT) ~ Restricted Cubic Spline(PACKYRS,3)
#################################
PACKYRS_CoxPHFit_RCS3Knots <- cph(Surv(TEVENT,EVENT) ~ rcs(packyrs,3), data=PC)
anova(PACKYRS_CoxPHFit_RCS3Knots)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## packyrs 13.48 2 0.0012
## Nonlinear 0.13 1 0.7152
## TOTAL 13.48 2 0.0012(PACKYRS_CoxPHFit_RCS3Knots_WaldX2 <- anova(PACKYRS_CoxPHFit_RCS3Knots)[1])## [1] 13.47873##################################
# Evaluating the impact of predictor coding
# for CEREBRAL, CARDIAC, AAA and PERIPH
# as applied in a univariate and multivariate Cox regression model
#################################
PC$CEREBRAL <- as.numeric(as.character(PC$CEREBRAL))
PC$CARDIAC <- as.numeric(as.character(PC$CARDIAC))
PC$AAA <- as.numeric(as.character(PC$AAA))
PC$PERIPH <- as.numeric(as.character(PC$PERIPH))
##################################
# Relationship of CEREBRAL, CARDIAC, AAA and PERIPH
# with prognostic outcome = Linear
# (TEVENT,EVENT) ~ CEREBRAL + CARDIAC + AAA + PERIPH
#################################
COMBINED_CoxPHFit_Linear <- cph(Surv(TEVENT,EVENT) ~ CEREBRAL + CARDIAC + AAA + PERIPH, data=PC)
anova(COMBINED_CoxPHFit_Linear)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## CEREBRAL 35.73 1 <.0001
## CARDIAC 19.11 1 <.0001
## AAA 96.62 1 <.0001
## PERIPH 23.13 1 <.0001
## TOTAL 122.61 4 <.0001(CEREBRAL_CoxPHFit_Linear_WaldX2 <- anova(COMBINED_CoxPHFit_Linear)[1])## [1] 35.72751(CARDIAC_CoxPHFit_Linear_WaldX2 <- anova(COMBINED_CoxPHFit_Linear)[2])## [1] 19.11319(AAA_CoxPHFit_Linear_WaldX2 <- anova(COMBINED_CoxPHFit_Linear)[3])## [1] 96.62462(PERIPH_CoxPHFit_Linear_WaldX2 <- anova(COMBINED_CoxPHFit_Linear)[4])## [1] 23.12629(COMBINED_CoxPHFit_Linear_WaldX2 <- anova(COMBINED_CoxPHFit_Linear)[5])## [1] 122.6137##################################
# Relationship of (CEREBRAL + CARDIAC + AAA + PERIPH)
# with prognostic outcome = Linear
# (TEVENT,EVENT) ~ (CEREBRAL + CARDIAC + AAA + PERIPH)
#################################
PC$SUMSCORE_4LEVELS <- PC$CEREBRAL + PC$CARDIAC + PC$AAA + PC$PERIPH
SUMSCORE_4LEVELS_CoxPHFit_Linear <- cph(Surv(TEVENT,EVENT) ~ SUMSCORE_4LEVELS, data=PC)
(SUMSCORE_4LEVELS_CoxPHFit_Linear_WaldX2 <- anova(SUMSCORE_4LEVELS_CoxPHFit_Linear)[1])## [1] 95.98494##################################
# Relationship of (CEREBRAL + CARDIAC + 2*AAA + PERIPH)
# with prognostic outcome = Linear
# (TEVENT,EVENT) ~ (CEREBRAL + CARDIAC + 2*AAA + PERIPH)
#################################
PC$SUMSCORE_5LEVELS <- PC$CEREBRAL + PC$CARDIAC + (2*PC$AAA) + PC$PERIPH
SUMSCORE_5LEVELS_CoxPHFit_Linear <- cph(Surv(TEVENT,EVENT) ~ SUMSCORE_5LEVELS, data=PC)
(SUMSCORE_5LEVELS_CoxPHFit_Linear_WaldX2 <- anova(SUMSCORE_5LEVELS_CoxPHFit_Linear)[1])## [1] 119.3857##################################
# Consolidating all results
# of predictor coding evaluation
#################################
PredictorInformation <- c(rep("AGE",7),
rep("CREAT",4),
rep("SYSTH",4),
rep("DIASTH",4),
rep("SYSTBP",4),
rep("DIASTBP",4),
rep("CHOL",4),
rep("HDL",4),
rep("LDL",4),
rep("TRIG",4),
rep("HOMOC",4),
rep("GLUT",4),
rep("LENGTH",4),
rep("WEIGHT",4),
rep("BMI",4),
rep("PACKYRS",3),
rep("A-CEREBRAL",1),
rep("B-CARDIAC",1),
rep("C-AAA",1),
rep("D-PERIPH",1),
rep("(A,B,C,D)",1),
rep("(A+B+C+D)",1),
rep("[A+B+(2*C)+D]",1))
CodingInformation <- c("Linear",
"Squared",
"Linear Effect After 55",
"Squared Effect After 50",
"Restricted Cubic Spline (4 knots)",
"Quartiles",
"Dichotomized",
"Linear",
"Restricted Cubic Spline (4 knots)",
"Restricted Cubic Spline (3 knots)",
"Logarithm",
"Linear",
"Restricted Cubic Spline (4 knots)",
"Restricted Cubic Spline (3 knots)",
"Logarithm",
"Linear",
"Restricted Cubic Spline (4 knots)",
"Restricted Cubic Spline (3 knots)",
"Logarithm",
"Linear",
"Restricted Cubic Spline (4 knots)",
"Restricted Cubic Spline (3 knots)",
"Logarithm",
"Linear",
"Restricted Cubic Spline (4 knots)",
"Restricted Cubic Spline (3 knots)",
"Logarithm",
"Linear",
"Restricted Cubic Spline (4 knots)",
"Restricted Cubic Spline (3 knots)",
"Logarithm",
"Linear",
"Restricted Cubic Spline (4 knots)",
"Restricted Cubic Spline (3 knots)",
"Logarithm",
"Linear",
"Restricted Cubic Spline (4 knots)",
"Restricted Cubic Spline (3 knots)",
"Logarithm",
"Linear",
"Restricted Cubic Spline (4 knots)",
"Restricted Cubic Spline (3 knots)",
"Logarithm",
"Linear",
"Restricted Cubic Spline (4 knots)",
"Restricted Cubic Spline (3 knots)",
"Logarithm",
"Linear",
"Restricted Cubic Spline (4 knots)",
"Restricted Cubic Spline (3 knots)",
"Logarithm",
"Linear",
"Restricted Cubic Spline (4 knots)",
"Restricted Cubic Spline (3 knots)",
"Logarithm",
"Linear",
"Restricted Cubic Spline (4 knots)",
"Restricted Cubic Spline (3 knots)",
"Logarithm",
"Linear",
"Restricted Cubic Spline (4 knots)",
"Restricted Cubic Spline (3 knots)",
"Logarithm",
"Linear",
"Restricted Cubic Spline (4 knots)",
"Restricted Cubic Spline (3 knots)",
"Linear",
"Linear",
"Linear",
"Linear",
"Linear",
"Linear",
"Linear")
WaldX2Information <- c(AGE_CoxPHFit_Linear_WaldX2,
AGE_CoxPHFit_Squared_WaldX2,
AGE_CoxPHFit_LinearAfter55_WaldX2,
AGE_CoxPHFit_SquaredAfter50_WaldX2,
AGE_CoxPHFit_RCS4Knots_WaldX2,
AGE_CoxPHFit_Quartile_WaldX2,
AGE_CoxPHFit_Dichotomized_WaldX2,
CREAT_CoxPHFit_Linear_WaldX2,
CREAT_CoxPHFit_RCS4Knots_WaldX2,
CREAT_CoxPHFit_RCS3Knots_WaldX2,
CREAT_CoxPHFit_Log_WaldX2,
SYSTH_CoxPHFit_Linear_WaldX2,
SYSTH_CoxPHFit_RCS4Knots_WaldX2,
SYSTH_CoxPHFit_RCS3Knots_WaldX2,
SYSTH_CoxPHFit_Log_WaldX2,
DIASTH_CoxPHFit_Linear_WaldX2,
DIASTH_CoxPHFit_RCS4Knots_WaldX2,
DIASTH_CoxPHFit_RCS3Knots_WaldX2,
DIASTH_CoxPHFit_Log_WaldX2,
SYSTBP_CoxPHFit_Linear_WaldX2,
SYSTBP_CoxPHFit_RCS4Knots_WaldX2,
SYSTBP_CoxPHFit_RCS3Knots_WaldX2,
SYSTBP_CoxPHFit_Log_WaldX2,
DIASTBP_CoxPHFit_Linear_WaldX2,
DIASTBP_CoxPHFit_RCS4Knots_WaldX2,
DIASTBP_CoxPHFit_RCS3Knots_WaldX2,
DIASTBP_CoxPHFit_Log_WaldX2,
CHOL_CoxPHFit_Linear_WaldX2,
CHOL_CoxPHFit_RCS4Knots_WaldX2,
CHOL_CoxPHFit_RCS3Knots_WaldX2,
CHOL_CoxPHFit_Log_WaldX2,
HDL_CoxPHFit_Linear_WaldX2,
HDL_CoxPHFit_RCS4Knots_WaldX2,
HDL_CoxPHFit_RCS3Knots_WaldX2,
HDL_CoxPHFit_Log_WaldX2,
LDL_CoxPHFit_Linear_WaldX2,
LDL_CoxPHFit_RCS4Knots_WaldX2,
LDL_CoxPHFit_RCS3Knots_WaldX2,
LDL_CoxPHFit_Log_WaldX2,
TRIG_CoxPHFit_Linear_WaldX2,
TRIG_CoxPHFit_RCS4Knots_WaldX2,
TRIG_CoxPHFit_RCS3Knots_WaldX2,
TRIG_CoxPHFit_Log_WaldX2,
HOMOC_CoxPHFit_Linear_WaldX2,
HOMOC_CoxPHFit_RCS4Knots_WaldX2,
HOMOC_CoxPHFit_RCS3Knots_WaldX2,
HOMOC_CoxPHFit_Log_WaldX2,
GLUT_CoxPHFit_Linear_WaldX2,
GLUT_CoxPHFit_RCS4Knots_WaldX2,
GLUT_CoxPHFit_RCS3Knots_WaldX2,
GLUT_CoxPHFit_Log_WaldX2,
LENGTH_CoxPHFit_Linear_WaldX2,
LENGTH_CoxPHFit_RCS4Knots_WaldX2,
LENGTH_CoxPHFit_RCS3Knots_WaldX2,
LENGTH_CoxPHFit_Log_WaldX2,
WEIGHT_CoxPHFit_Linear_WaldX2,
WEIGHT_CoxPHFit_RCS4Knots_WaldX2,
WEIGHT_CoxPHFit_RCS3Knots_WaldX2,
WEIGHT_CoxPHFit_Log_WaldX2,
BMI_CoxPHFit_Linear_WaldX2,
BMI_CoxPHFit_RCS4Knots_WaldX2,
BMI_CoxPHFit_RCS3Knots_WaldX2,
BMI_CoxPHFit_Log_WaldX2,
PACKYRS_CoxPHFit_Linear_WaldX2,
PACKYRS_CoxPHFit_RCS4Knots_WaldX2,
PACKYRS_CoxPHFit_RCS3Knots_WaldX2,
CEREBRAL_CoxPHFit_Linear_WaldX2,
CARDIAC_CoxPHFit_Linear_WaldX2,
AAA_CoxPHFit_Linear_WaldX2,
PERIPH_CoxPHFit_Linear_WaldX2,
COMBINED_CoxPHFit_Linear_WaldX2,
SUMSCORE_4LEVELS_CoxPHFit_Linear_WaldX2,
SUMSCORE_5LEVELS_CoxPHFit_Linear_WaldX2)
PredictorCodingSummary <- as.data.frame(cbind(PredictorInformation,
CodingInformation,
WaldX2Information))
PredictorCodingSummary$WaldX2Information <- round(as.numeric(as.character(PredictorCodingSummary$WaldX2Information)),2)
colnames(PredictorCodingSummary)<- c("Predictor",
"Coding",
"Wald Chi-Squared")
##################################
# Summarizing all results
# of predictor coding evaluation
#################################
(PredictorCodingSummary)## Predictor Coding Wald Chi-Squared
## 1 AGE Linear 97.17
## 2 AGE Squared 124.99
## 3 AGE Linear Effect After 55 118.59
## 4 AGE Squared Effect After 50 129.64
## 5 AGE Restricted Cubic Spline (4 knots) 125.30
## 6 AGE Quartiles 93.22
## 7 AGE Dichotomized 72.47
## 8 CREAT Linear 93.42
## 9 CREAT Restricted Cubic Spline (4 knots) 116.10
## 10 CREAT Restricted Cubic Spline (3 knots) 99.03
## 11 CREAT Logarithm 131.01
## 12 SYSTH Linear 15.49
## 13 SYSTH Restricted Cubic Spline (4 knots) 15.60
## 14 SYSTH Restricted Cubic Spline (3 knots) 15.17
## 15 SYSTH Logarithm 14.39
## 16 DIASTH Linear 0.73
## 17 DIASTH Restricted Cubic Spline (4 knots) 2.62
## 18 DIASTH Restricted Cubic Spline (3 knots) 2.08
## 19 DIASTH Logarithm 0.47
## 20 SYSTBP Linear 23.22
## 21 SYSTBP Restricted Cubic Spline (4 knots) 26.27
## 22 SYSTBP Restricted Cubic Spline (3 knots) 26.26
## 23 SYSTBP Logarithm 21.20
## 24 DIASTBP Linear 1.67
## 25 DIASTBP Restricted Cubic Spline (4 knots) 25.15
## 26 DIASTBP Restricted Cubic Spline (3 knots) 24.84
## 27 DIASTBP Logarithm 0.68
## 28 CHOL Linear 0.32
## 29 CHOL Restricted Cubic Spline (4 knots) 0.60
## 30 CHOL Restricted Cubic Spline (3 knots) 0.60
## 31 CHOL Logarithm 0.25
## 32 HDL Linear 11.83
## 33 HDL Restricted Cubic Spline (4 knots) 11.94
## 34 HDL Restricted Cubic Spline (3 knots) 11.61
## 35 HDL Logarithm 11.80
## 36 LDL Linear 1.28
## 37 LDL Restricted Cubic Spline (4 knots) 1.52
## 38 LDL Restricted Cubic Spline (3 knots) 1.28
## 39 LDL Logarithm 1.15
## 40 TRIG Linear 1.40
## 41 TRIG Restricted Cubic Spline (4 knots) 3.51
## 42 TRIG Restricted Cubic Spline (3 knots) 3.25
## 43 TRIG Logarithm 2.47
## 44 HOMOC Linear 49.59
## 45 HOMOC Restricted Cubic Spline (4 knots) 50.68
## 46 HOMOC Restricted Cubic Spline (3 knots) 47.32
## 47 HOMOC Logarithm 52.46
## 48 GLUT Linear 12.69
## 49 GLUT Restricted Cubic Spline (4 knots) 15.43
## 50 GLUT Restricted Cubic Spline (3 knots) 13.03
## 51 GLUT Logarithm 12.08
## 52 LENGTH Linear 0.01
## 53 LENGTH Restricted Cubic Spline (4 knots) 4.19
## 54 LENGTH Restricted Cubic Spline (3 knots) 4.11
## 55 LENGTH Logarithm 0.00
## 56 WEIGHT Linear 3.21
## 57 WEIGHT Restricted Cubic Spline (4 knots) 4.55
## 58 WEIGHT Restricted Cubic Spline (3 knots) 4.08
## 59 WEIGHT Logarithm 2.73
## 60 BMI Linear 3.87
## 61 BMI Restricted Cubic Spline (4 knots) 7.64
## 62 BMI Restricted Cubic Spline (3 knots) 4.02
## 63 BMI Logarithm 3.90
## 64 PACKYRS Linear 12.95
## 65 PACKYRS Restricted Cubic Spline (4 knots) 14.85
## 66 PACKYRS Restricted Cubic Spline (3 knots) 13.48
## 67 A-CEREBRAL Linear 35.73
## 68 B-CARDIAC Linear 19.11
## 69 C-AAA Linear 96.62
## 70 D-PERIPH Linear 23.13
## 71 (A,B,C,D) Linear 122.61
## 72 (A+B+C+D) Linear 95.98
## 73 [A+B+(2*C)+D] Linear 119.391.2.4 Data Preprocessing
Missing data pattern assessment:
[A] The missing data patterns were summarized using the aggr method from the VIM package and the naclus method from the Hmisc package.
[A.1] There were 924/3873 (0.236) observations assessed as complete.
[A.2] The DIASTH variable (numeric), SYSTH variable (numeric), SYSTBP variable (numeric) and DIASTBP variable (numeric) contributed the most missing data.
[A.3] There were 105 missing data patterns observed employing various combinations of the 21 variables. The most prevalent pattern consists of two variables with missing data as noted from 1975/3873 (0.510) observations.
[A.4] The missing data patterns were predominantly clustered between the following variables:
[A.4.1] DIASTH (numeric) and SYSTH (numeric) variables.
[A.4.2] DIASTBP (numeric) and SYSTBP (numeric) variables.
Missing data imputation method implementation and plausibility evaluation:
[A] The missing data imputation method aregImpute (multiple imputation using additive regression, bootstrapping, and predictive mean matching) from the Hmisc package was applied using 5 iterations. The imputed values for each iteration were collectively compared to the original data by individual variable and showed:
[A.1] Relatively good data plausibility for the numeric variables in the imputed dataset as compared to the original dataset for all 5 iterations.
[A.2] Relatively good data plausibility for the categorical variables in the imputed dataset as compared to the original dataset for all 5 iterations.
Code Chunk | Output
##################################
# Loading dataset
##################################
DPP <- SMART
##################################
# Exploring the missing data patterns
##################################
DPP.Profile <- aggr(DPP,
plot = FALSE)
DPP.Profile.Summary <- summary(DPP.Profile)
nrow(DPP.Profile.Summary)## NULLplot(DPP.Profile,
numbers = TRUE,
prop = TRUE,
sortVars = TRUE,
col=c("green","red"))
##
## Variables sorted by number of missings:
## Variable Count
## DIASTH 0.3870384715
## SYSTH 0.3867802737
## SYSTBP 0.3157758843
## DIASTBP 0.3152594888
## HOMOC 0.1195455719
## LDL 0.0557707204
## albumin 0.0534469404
## IMT 0.0253033824
## STENOSIS 0.0240123935
## DIABETES 0.0103279112
## HDL 0.0077459334
## TRIG 0.0072295378
## SMOKING 0.0064549445
## alcohol 0.0064549445
## packyrs 0.0054221534
## GLUT 0.0049057578
## CHOL 0.0046475600
## CREAT 0.0043893623
## BMI 0.0007745933
## WEIGHT 0.0005163956
## LENGTH 0.0002581978
## TEVENT 0.0000000000
## EVENT 0.0000000000
## SEX 0.0000000000
## AGE 0.0000000000
## CEREBRAL 0.0000000000
## CARDIAC 0.0000000000
## AAA 0.0000000000
## PERIPH 0.0000000000par(mfrow=c(1,1))
DPP.Patterns <- naclus(DPP)
plot(DPP.Patterns,
ylab="Fraction of NAs in common",
col="red")
par(mfrow=c(1,2))
naplot(DPP.Patterns, which=c('na per var'),col="red")
naplot(DPP.Patterns, which=c('na per obs'),col="red")
##################################
# Conducting missing data imputation
# using AREGIMPUTE
# (Multiple Imputation using Additive Regression, Bootstrapping, and Predictive Mean Matching)
##################################
DPP$CEREBRAL <- as.numeric(as.character(DPP$CEREBRAL))
DPP$CARDIAC <- as.numeric(as.character(DPP$CARDIAC))
DPP$AAA <- as.numeric(as.character(DPP$AAA))
DPP$PERIPH <- as.numeric(as.character(DPP$PERIPH))
DPP$SUMSCORE_5LEVELS <- DPP$CEREBRAL +
DPP$CARDIAC +
(2*DPP$AAA) +
DPP$PERIPH
set.seed(123456789)
DPP.AREGIMPUTED <-aregImpute(~I(TEVENT)+EVENT+SEX+I(AGE)+
SYSTBP+DIASTBP+SYSTH+DIASTH+
DIABETES+CEREBRAL+CARDIAC+AAA+PERIPH+I(SUMSCORE_5LEVELS)+STENOSIS+
I(LENGTH)+I(WEIGHT)+I(BMI)+
I(CHOL)+I(HDL)+I(LDL)+I(TRIG)+I(HOMOC)+I(GLUT)+I(CREAT)+I(IMT)+
as.factor(albumin) +as.factor(SMOKING) + I(packyrs) + as.factor(alcohol),
n.impute=5,data=DPP)## Iteration 1 Iteration 2 Iteration 3 Iteration 4 Iteration 5 Iteration 6 Iteration 7 Iteration 8 ##################################
# Evaluating the plausibility of the
# AREG-imputed values for the
# numerical variables
##################################
SYSTBP_complete <- (DPP$SYSTBP[complete.cases(DPP$SYSTBP)])
DPP.AREGIMPUTED_aregImpute_SYSTBP <- as.data.frame(DPP.AREGIMPUTED$imputed$SYSTBP)
SYSTBP_aregImpute_1 <- DPP.AREGIMPUTED_aregImpute_SYSTBP$V1
SYSTBP_aregImpute_2 <- DPP.AREGIMPUTED_aregImpute_SYSTBP$V2
SYSTBP_aregImpute_3 <- DPP.AREGIMPUTED_aregImpute_SYSTBP$V3
SYSTBP_aregImpute_4 <- DPP.AREGIMPUTED_aregImpute_SYSTBP$V4
SYSTBP_aregImpute_5 <- DPP.AREGIMPUTED_aregImpute_SYSTBP$V5
SYSTBP_values <- c(SYSTBP_complete,
SYSTBP_aregImpute_1,
SYSTBP_aregImpute_2,
SYSTBP_aregImpute_3,
SYSTBP_aregImpute_4,
SYSTBP_aregImpute_5)
SYSTBP_labels <- c(rep("Original",length(SYSTBP_complete)),
rep("aregImputed_1",length(SYSTBP_aregImpute_1)),
rep("aregImputed_2",length(SYSTBP_aregImpute_2)),
rep("aregImputed_3",length(SYSTBP_aregImpute_3)),
rep("aregImputed_4",length(SYSTBP_aregImpute_4)),
rep("aregImputed_5",length(SYSTBP_aregImpute_5)))
DIASTBP_complete <- (DPP$DIASTBP[complete.cases(DPP$DIASTBP)])
DPP.AREGIMPUTED_aregImpute_DIASTBP <- as.data.frame(DPP.AREGIMPUTED$imputed$DIASTBP)
DIASTBP_aregImpute_1 <- DPP.AREGIMPUTED_aregImpute_DIASTBP$V1
DIASTBP_aregImpute_2 <- DPP.AREGIMPUTED_aregImpute_DIASTBP$V2
DIASTBP_aregImpute_3 <- DPP.AREGIMPUTED_aregImpute_DIASTBP$V3
DIASTBP_aregImpute_4 <- DPP.AREGIMPUTED_aregImpute_DIASTBP$V4
DIASTBP_aregImpute_5 <- DPP.AREGIMPUTED_aregImpute_DIASTBP$V5
DIASTBP_values <- c(DIASTBP_complete,
DIASTBP_aregImpute_1,
DIASTBP_aregImpute_2,
DIASTBP_aregImpute_3,
DIASTBP_aregImpute_4,
DIASTBP_aregImpute_5)
DIASTBP_labels <- c(rep("Original",length(DIASTBP_complete)),
rep("aregImputed_1",length(DIASTBP_aregImpute_1)),
rep("aregImputed_2",length(DIASTBP_aregImpute_2)),
rep("aregImputed_3",length(DIASTBP_aregImpute_3)),
rep("aregImputed_4",length(DIASTBP_aregImpute_4)),
rep("aregImputed_5",length(DIASTBP_aregImpute_5)))
SYSTH_complete <- (DPP$SYSTH[complete.cases(DPP$SYSTH)])
DPP.AREGIMPUTED_aregImpute_SYSTH <- as.data.frame(DPP.AREGIMPUTED$imputed$SYSTH)
SYSTH_aregImpute_1 <- DPP.AREGIMPUTED_aregImpute_SYSTH$V1
SYSTH_aregImpute_2 <- DPP.AREGIMPUTED_aregImpute_SYSTH$V2
SYSTH_aregImpute_3 <- DPP.AREGIMPUTED_aregImpute_SYSTH$V3
SYSTH_aregImpute_4 <- DPP.AREGIMPUTED_aregImpute_SYSTH$V4
SYSTH_aregImpute_5 <- DPP.AREGIMPUTED_aregImpute_SYSTH$V5
SYSTH_values <- c(SYSTH_complete,
SYSTH_aregImpute_1,
SYSTH_aregImpute_2,
SYSTH_aregImpute_3,
SYSTH_aregImpute_4,
SYSTH_aregImpute_5)
SYSTH_labels <- c(rep("Original",length(SYSTH_complete)),
rep("aregImputed_1",length(SYSTH_aregImpute_1)),
rep("aregImputed_2",length(SYSTH_aregImpute_2)),
rep("aregImputed_3",length(SYSTH_aregImpute_3)),
rep("aregImputed_4",length(SYSTH_aregImpute_4)),
rep("aregImputed_5",length(SYSTH_aregImpute_5)))
DIASTH_complete <- (DPP$DIASTH[complete.cases(DPP$DIASTH)])
DPP.AREGIMPUTED_aregImpute_DIASTH <- as.data.frame(DPP.AREGIMPUTED$imputed$DIASTH)
DIASTH_aregImpute_1 <- DPP.AREGIMPUTED_aregImpute_DIASTH$V1
DIASTH_aregImpute_2 <- DPP.AREGIMPUTED_aregImpute_DIASTH$V2
DIASTH_aregImpute_3 <- DPP.AREGIMPUTED_aregImpute_DIASTH$V3
DIASTH_aregImpute_4 <- DPP.AREGIMPUTED_aregImpute_DIASTH$V4
DIASTH_aregImpute_5 <- DPP.AREGIMPUTED_aregImpute_DIASTH$V5
DIASTH_values <- c(DIASTH_complete,
DIASTH_aregImpute_1,
DIASTH_aregImpute_2,
DIASTH_aregImpute_3,
DIASTH_aregImpute_4,
DIASTH_aregImpute_5)
DIASTH_labels <- c(rep("Original",length(DIASTH_complete)),
rep("aregImputed_1",length(DIASTH_aregImpute_1)),
rep("aregImputed_2",length(DIASTH_aregImpute_2)),
rep("aregImputed_3",length(DIASTH_aregImpute_3)),
rep("aregImputed_4",length(DIASTH_aregImpute_4)),
rep("aregImputed_5",length(DIASTH_aregImpute_5)))
LENGTH_complete <- (DPP$LENGTH[complete.cases(DPP$LENGTH)])
DPP.AREGIMPUTED_aregImpute_LENGTH <- as.data.frame(DPP.AREGIMPUTED$imputed$LENGTH)
LENGTH_aregImpute_1 <- DPP.AREGIMPUTED_aregImpute_LENGTH$V1
LENGTH_aregImpute_2 <- DPP.AREGIMPUTED_aregImpute_LENGTH$V2
LENGTH_aregImpute_3 <- DPP.AREGIMPUTED_aregImpute_LENGTH$V3
LENGTH_aregImpute_4 <- DPP.AREGIMPUTED_aregImpute_LENGTH$V4
LENGTH_aregImpute_5 <- DPP.AREGIMPUTED_aregImpute_LENGTH$V5
LENGTH_values <- c(LENGTH_complete,
LENGTH_aregImpute_1,
LENGTH_aregImpute_2,
LENGTH_aregImpute_3,
LENGTH_aregImpute_4,
LENGTH_aregImpute_5)
LENGTH_labels <- c(rep("Original",length(LENGTH_complete)),
rep("aregImputed_1",length(LENGTH_aregImpute_1)),
rep("aregImputed_2",length(LENGTH_aregImpute_2)),
rep("aregImputed_3",length(LENGTH_aregImpute_3)),
rep("aregImputed_4",length(LENGTH_aregImpute_4)),
rep("aregImputed_5",length(LENGTH_aregImpute_5)))
WEIGHT_complete <- (DPP$WEIGHT[complete.cases(DPP$WEIGHT)])
DPP.AREGIMPUTED_aregImpute_WEIGHT <- as.data.frame(DPP.AREGIMPUTED$imputed$WEIGHT)
WEIGHT_aregImpute_1 <- DPP.AREGIMPUTED_aregImpute_WEIGHT$V1
WEIGHT_aregImpute_2 <- DPP.AREGIMPUTED_aregImpute_WEIGHT$V2
WEIGHT_aregImpute_3 <- DPP.AREGIMPUTED_aregImpute_WEIGHT$V3
WEIGHT_aregImpute_4 <- DPP.AREGIMPUTED_aregImpute_WEIGHT$V4
WEIGHT_aregImpute_5 <- DPP.AREGIMPUTED_aregImpute_WEIGHT$V5
WEIGHT_values <- c(WEIGHT_complete,
WEIGHT_aregImpute_1,
WEIGHT_aregImpute_2,
WEIGHT_aregImpute_3,
WEIGHT_aregImpute_4,
WEIGHT_aregImpute_5)
WEIGHT_labels <- c(rep("Original",length(WEIGHT_complete)),
rep("aregImputed_1",length(WEIGHT_aregImpute_1)),
rep("aregImputed_2",length(WEIGHT_aregImpute_2)),
rep("aregImputed_3",length(WEIGHT_aregImpute_3)),
rep("aregImputed_4",length(WEIGHT_aregImpute_4)),
rep("aregImputed_5",length(WEIGHT_aregImpute_5)))
BMI_complete <- (DPP$BMI[complete.cases(DPP$BMI)])
DPP.AREGIMPUTED_aregImpute_BMI <- as.data.frame(DPP.AREGIMPUTED$imputed$BMI)
BMI_aregImpute_1 <- DPP.AREGIMPUTED_aregImpute_BMI$V1
BMI_aregImpute_2 <- DPP.AREGIMPUTED_aregImpute_BMI$V2
BMI_aregImpute_3 <- DPP.AREGIMPUTED_aregImpute_BMI$V3
BMI_aregImpute_4 <- DPP.AREGIMPUTED_aregImpute_BMI$V4
BMI_aregImpute_5 <- DPP.AREGIMPUTED_aregImpute_BMI$V5
BMI_values <- c(BMI_complete,
BMI_aregImpute_1,
BMI_aregImpute_2,
BMI_aregImpute_3,
BMI_aregImpute_4,
BMI_aregImpute_5)
BMI_labels <- c(rep("Original",length(BMI_complete)),
rep("aregImputed_1",length(BMI_aregImpute_1)),
rep("aregImputed_2",length(BMI_aregImpute_2)),
rep("aregImputed_3",length(BMI_aregImpute_3)),
rep("aregImputed_4",length(BMI_aregImpute_4)),
rep("aregImputed_5",length(BMI_aregImpute_5)))
CHOL_complete <- (DPP$CHOL[complete.cases(DPP$CHOL)])
DPP.AREGIMPUTED_aregImpute_CHOL <- as.data.frame(DPP.AREGIMPUTED$imputed$CHOL)
CHOL_aregImpute_1 <- DPP.AREGIMPUTED_aregImpute_CHOL$V1
CHOL_aregImpute_2 <- DPP.AREGIMPUTED_aregImpute_CHOL$V2
CHOL_aregImpute_3 <- DPP.AREGIMPUTED_aregImpute_CHOL$V3
CHOL_aregImpute_4 <- DPP.AREGIMPUTED_aregImpute_CHOL$V4
CHOL_aregImpute_5 <- DPP.AREGIMPUTED_aregImpute_CHOL$V5
CHOL_values <- c(CHOL_complete,
CHOL_aregImpute_1,
CHOL_aregImpute_2,
CHOL_aregImpute_3,
CHOL_aregImpute_4,
CHOL_aregImpute_5)
CHOL_labels <- c(rep("Original",length(CHOL_complete)),
rep("aregImputed_1",length(CHOL_aregImpute_1)),
rep("aregImputed_2",length(CHOL_aregImpute_2)),
rep("aregImputed_3",length(CHOL_aregImpute_3)),
rep("aregImputed_4",length(CHOL_aregImpute_4)),
rep("aregImputed_5",length(CHOL_aregImpute_5)))
HDL_complete <- (DPP$HDL[complete.cases(DPP$HDL)])
DPP.AREGIMPUTED_aregImpute_HDL <- as.data.frame(DPP.AREGIMPUTED$imputed$HDL)
HDL_aregImpute_1 <- DPP.AREGIMPUTED_aregImpute_HDL$V1
HDL_aregImpute_2 <- DPP.AREGIMPUTED_aregImpute_HDL$V2
HDL_aregImpute_3 <- DPP.AREGIMPUTED_aregImpute_HDL$V3
HDL_aregImpute_4 <- DPP.AREGIMPUTED_aregImpute_HDL$V4
HDL_aregImpute_5 <- DPP.AREGIMPUTED_aregImpute_HDL$V5
HDL_values <- c(HDL_complete,
HDL_aregImpute_1,
HDL_aregImpute_2,
HDL_aregImpute_3,
HDL_aregImpute_4,
HDL_aregImpute_5)
HDL_labels <- c(rep("Original",length(HDL_complete)),
rep("aregImputed_1",length(HDL_aregImpute_1)),
rep("aregImputed_2",length(HDL_aregImpute_2)),
rep("aregImputed_3",length(HDL_aregImpute_3)),
rep("aregImputed_4",length(HDL_aregImpute_4)),
rep("aregImputed_5",length(HDL_aregImpute_5)))
LDL_complete <- (DPP$LDL[complete.cases(DPP$LDL)])
DPP.AREGIMPUTED_aregImpute_LDL <- as.data.frame(DPP.AREGIMPUTED$imputed$LDL)
LDL_aregImpute_1 <- DPP.AREGIMPUTED_aregImpute_LDL$V1
LDL_aregImpute_2 <- DPP.AREGIMPUTED_aregImpute_LDL$V2
LDL_aregImpute_3 <- DPP.AREGIMPUTED_aregImpute_LDL$V3
LDL_aregImpute_4 <- DPP.AREGIMPUTED_aregImpute_LDL$V4
LDL_aregImpute_5 <- DPP.AREGIMPUTED_aregImpute_LDL$V5
LDL_values <- c(LDL_complete,
LDL_aregImpute_1,
LDL_aregImpute_2,
LDL_aregImpute_3,
LDL_aregImpute_4,
LDL_aregImpute_5)
LDL_labels <- c(rep("Original",length(LDL_complete)),
rep("aregImputed_1",length(LDL_aregImpute_1)),
rep("aregImputed_2",length(LDL_aregImpute_2)),
rep("aregImputed_3",length(LDL_aregImpute_3)),
rep("aregImputed_4",length(LDL_aregImpute_4)),
rep("aregImputed_5",length(LDL_aregImpute_5)))
TRIG_complete <- (DPP$TRIG[complete.cases(DPP$TRIG)])
DPP.AREGIMPUTED_aregImpute_TRIG <- as.data.frame(DPP.AREGIMPUTED$imputed$TRIG)
TRIG_aregImpute_1 <- DPP.AREGIMPUTED_aregImpute_TRIG$V1
TRIG_aregImpute_2 <- DPP.AREGIMPUTED_aregImpute_TRIG$V2
TRIG_aregImpute_3 <- DPP.AREGIMPUTED_aregImpute_TRIG$V3
TRIG_aregImpute_4 <- DPP.AREGIMPUTED_aregImpute_TRIG$V4
TRIG_aregImpute_5 <- DPP.AREGIMPUTED_aregImpute_TRIG$V5
TRIG_values <- c(TRIG_complete,
TRIG_aregImpute_1,
TRIG_aregImpute_2,
TRIG_aregImpute_3,
TRIG_aregImpute_4,
TRIG_aregImpute_5)
TRIG_labels <- c(rep("Original",length(TRIG_complete)),
rep("aregImputed_1",length(TRIG_aregImpute_1)),
rep("aregImputed_2",length(TRIG_aregImpute_2)),
rep("aregImputed_3",length(TRIG_aregImpute_3)),
rep("aregImputed_4",length(TRIG_aregImpute_4)),
rep("aregImputed_5",length(TRIG_aregImpute_5)))
HOMOC_complete <- (DPP$HOMOC[complete.cases(DPP$HOMOC)])
DPP.AREGIMPUTED_aregImpute_HOMOC <- as.data.frame(DPP.AREGIMPUTED$imputed$HOMOC)
HOMOC_aregImpute_1 <- DPP.AREGIMPUTED_aregImpute_HOMOC$V1
HOMOC_aregImpute_2 <- DPP.AREGIMPUTED_aregImpute_HOMOC$V2
HOMOC_aregImpute_3 <- DPP.AREGIMPUTED_aregImpute_HOMOC$V3
HOMOC_aregImpute_4 <- DPP.AREGIMPUTED_aregImpute_HOMOC$V4
HOMOC_aregImpute_5 <- DPP.AREGIMPUTED_aregImpute_HOMOC$V5
HOMOC_values <- c(HOMOC_complete,
HOMOC_aregImpute_1,
HOMOC_aregImpute_2,
HOMOC_aregImpute_3,
HOMOC_aregImpute_4,
HOMOC_aregImpute_5)
HOMOC_labels <- c(rep("Original",length(HOMOC_complete)),
rep("aregImputed_1",length(HOMOC_aregImpute_1)),
rep("aregImputed_2",length(HOMOC_aregImpute_2)),
rep("aregImputed_3",length(HOMOC_aregImpute_3)),
rep("aregImputed_4",length(HOMOC_aregImpute_4)),
rep("aregImputed_5",length(HOMOC_aregImpute_5)))
GLUT_complete <- (DPP$GLUT[complete.cases(DPP$GLUT)])
DPP.AREGIMPUTED_aregImpute_GLUT <- as.data.frame(DPP.AREGIMPUTED$imputed$GLUT)
GLUT_aregImpute_1 <- DPP.AREGIMPUTED_aregImpute_GLUT$V1
GLUT_aregImpute_2 <- DPP.AREGIMPUTED_aregImpute_GLUT$V2
GLUT_aregImpute_3 <- DPP.AREGIMPUTED_aregImpute_GLUT$V3
GLUT_aregImpute_4 <- DPP.AREGIMPUTED_aregImpute_GLUT$V4
GLUT_aregImpute_5 <- DPP.AREGIMPUTED_aregImpute_GLUT$V5
GLUT_values <- c(GLUT_complete,
GLUT_aregImpute_1,
GLUT_aregImpute_2,
GLUT_aregImpute_3,
GLUT_aregImpute_4,
GLUT_aregImpute_5)
GLUT_labels <- c(rep("Original",length(GLUT_complete)),
rep("aregImputed_1",length(GLUT_aregImpute_1)),
rep("aregImputed_2",length(GLUT_aregImpute_2)),
rep("aregImputed_3",length(GLUT_aregImpute_3)),
rep("aregImputed_4",length(GLUT_aregImpute_4)),
rep("aregImputed_5",length(GLUT_aregImpute_5)))
CREAT_complete <- (DPP$CREAT[complete.cases(DPP$CREAT)])
DPP.AREGIMPUTED_aregImpute_CREAT <- as.data.frame(DPP.AREGIMPUTED$imputed$CREAT)
CREAT_aregImpute_1 <- DPP.AREGIMPUTED_aregImpute_CREAT$V1
CREAT_aregImpute_2 <- DPP.AREGIMPUTED_aregImpute_CREAT$V2
CREAT_aregImpute_3 <- DPP.AREGIMPUTED_aregImpute_CREAT$V3
CREAT_aregImpute_4 <- DPP.AREGIMPUTED_aregImpute_CREAT$V4
CREAT_aregImpute_5 <- DPP.AREGIMPUTED_aregImpute_CREAT$V5
CREAT_values <- c(CREAT_complete,
CREAT_aregImpute_1,
CREAT_aregImpute_2,
CREAT_aregImpute_3,
CREAT_aregImpute_4,
CREAT_aregImpute_5)
CREAT_labels <- c(rep("Original",length(CREAT_complete)),
rep("aregImputed_1",length(CREAT_aregImpute_1)),
rep("aregImputed_2",length(CREAT_aregImpute_2)),
rep("aregImputed_3",length(CREAT_aregImpute_3)),
rep("aregImputed_4",length(CREAT_aregImpute_4)),
rep("aregImputed_5",length(CREAT_aregImpute_5)))
IMT_complete <- (DPP$IMT[complete.cases(DPP$IMT)])
DPP.AREGIMPUTED_aregImpute_IMT <- as.data.frame(DPP.AREGIMPUTED$imputed$IMT)
IMT_aregImpute_1 <- DPP.AREGIMPUTED_aregImpute_IMT$V1
IMT_aregImpute_2 <- DPP.AREGIMPUTED_aregImpute_IMT$V2
IMT_aregImpute_3 <- DPP.AREGIMPUTED_aregImpute_IMT$V3
IMT_aregImpute_4 <- DPP.AREGIMPUTED_aregImpute_IMT$V4
IMT_aregImpute_5 <- DPP.AREGIMPUTED_aregImpute_IMT$V5
IMT_values <- c(IMT_complete,
IMT_aregImpute_1,
IMT_aregImpute_2,
IMT_aregImpute_3,
IMT_aregImpute_4,
IMT_aregImpute_5)
IMT_labels <- c(rep("Original",length(IMT_complete)),
rep("aregImputed_1",length(IMT_aregImpute_1)),
rep("aregImputed_2",length(IMT_aregImpute_2)),
rep("aregImputed_3",length(IMT_aregImpute_3)),
rep("aregImputed_4",length(IMT_aregImpute_4)),
rep("aregImputed_5",length(IMT_aregImpute_5)))
PACKYRS_complete <- (DPP$packyrs[complete.cases(DPP$packyrs)])
DPP.AREGIMPUTED_aregImpute_PACKYRS <- as.data.frame(DPP.AREGIMPUTED$imputed$packyrs)
PACKYRS_aregImpute_1 <- DPP.AREGIMPUTED_aregImpute_PACKYRS$V1
PACKYRS_aregImpute_2 <- DPP.AREGIMPUTED_aregImpute_PACKYRS$V2
PACKYRS_aregImpute_3 <- DPP.AREGIMPUTED_aregImpute_PACKYRS$V3
PACKYRS_aregImpute_4 <- DPP.AREGIMPUTED_aregImpute_PACKYRS$V4
PACKYRS_aregImpute_5 <- DPP.AREGIMPUTED_aregImpute_PACKYRS$V5
PACKYRS_values <- c(PACKYRS_complete,
PACKYRS_aregImpute_1,
PACKYRS_aregImpute_2,
PACKYRS_aregImpute_3,
PACKYRS_aregImpute_4,
PACKYRS_aregImpute_5)
PACKYRS_labels <- c(rep("Original",length(PACKYRS_complete)),
rep("aregImputed_1",length(PACKYRS_aregImpute_1)),
rep("aregImputed_2",length(PACKYRS_aregImpute_2)),
rep("aregImputed_3",length(PACKYRS_aregImpute_3)),
rep("aregImputed_4",length(PACKYRS_aregImpute_4)),
rep("aregImputed_5",length(PACKYRS_aregImpute_5)))
VARIABLE_labels <- c(rep("SYSTBP",length(SYSTBP_labels)),
rep("DIASTBP",length(DIASTBP_labels)),
rep("SYSTH",length(SYSTH_labels)),
rep("DIASTH",length(DIASTH_labels)),
rep("LENGTH",length(LENGTH_labels)),
rep("WEIGHT",length(WEIGHT_labels)),
rep("BMI",length(BMI_labels)),
rep("CHOL",length(CHOL_labels)),
rep("HDL",length(HDL_labels)),
rep("LDL",length(LDL_labels)),
rep("TRIG",length(TRIG_labels)),
rep("HOMOC",length(HOMOC_labels)),
rep("GLUT",length(GLUT_labels)),
rep("CREAT",length(CREAT_labels)),
rep("IMT",length(IMT_labels)),
rep("PACKYRS",length(PACKYRS_labels)))
NUMERIC_VARIABLES_postimputation <- cbind(VARIABLE_labels,
c(SYSTBP_labels,
DIASTBP_labels,
SYSTH_labels,
DIASTH_labels,
LENGTH_labels,
WEIGHT_labels,
BMI_labels,
CHOL_labels,
HDL_labels,
LDL_labels,
TRIG_labels,
HOMOC_labels,
GLUT_labels,
CREAT_labels,
IMT_labels,
PACKYRS_labels),
c(SYSTBP_values,
DIASTBP_values,
SYSTH_values,
DIASTH_values,
LENGTH_values,
WEIGHT_values,
BMI_values,
CHOL_values,
HDL_values,
LDL_values,
TRIG_values,
HOMOC_values,
GLUT_values,
CREAT_values,
IMT_values,
PACKYRS_values))
NUMERIC_VARIABLES_postimputation <- as.data.frame(NUMERIC_VARIABLES_postimputation)
colnames(NUMERIC_VARIABLES_postimputation) <- c("Variable",
"Category",
"Value")
NUMERIC_VARIABLES_postimputation$Variable <- factor(NUMERIC_VARIABLES_postimputation$Variable,
levels=c("PACKYRS",
"IMT",
"CREAT",
"GLUT",
"HOMOC",
"TRIG",
"LDL",
"HDL",
"CHOL",
"BMI",
"WEIGHT",
"LENGTH",
"DIASTH",
"SYSTH",
"DIASTBP",
"SYSTBP"))
NUMERIC_VARIABLES_postimputation$Category <- factor(NUMERIC_VARIABLES_postimputation$Category,
levels=c("Original",
"aregImputed_1",
"aregImputed_2",
"aregImputed_3",
"aregImputed_4",
"aregImputed_5"))
NUMERIC_VARIABLES_postimputation_SYSTBP <- NUMERIC_VARIABLES_postimputation[NUMERIC_VARIABLES_postimputation$Variable=="SYSTBP",]
NUMERIC_VARIABLES_postimputation_SYSTH <- NUMERIC_VARIABLES_postimputation[NUMERIC_VARIABLES_postimputation$Variable=="SYSTH",]
NUMERIC_VARIABLES_postimputation_DIASTBP <- NUMERIC_VARIABLES_postimputation[NUMERIC_VARIABLES_postimputation$Variable=="DIASTBP",]
NUMERIC_VARIABLES_postimputation_DIASTH <- NUMERIC_VARIABLES_postimputation[NUMERIC_VARIABLES_postimputation$Variable=="DIASTH",]
NUMERIC_VARIABLES_postimputation_LENGTH <- NUMERIC_VARIABLES_postimputation[NUMERIC_VARIABLES_postimputation$Variable=="LENGTH",]
NUMERIC_VARIABLES_postimputation_WEIGHT <- NUMERIC_VARIABLES_postimputation[NUMERIC_VARIABLES_postimputation$Variable=="WEIGHT",]
NUMERIC_VARIABLES_postimputation_BMI <- NUMERIC_VARIABLES_postimputation[NUMERIC_VARIABLES_postimputation$Variable=="BMI",]
NUMERIC_VARIABLES_postimputation_CHOL <- NUMERIC_VARIABLES_postimputation[NUMERIC_VARIABLES_postimputation$Variable=="CHOL",]
NUMERIC_VARIABLES_postimputation_HDL <- NUMERIC_VARIABLES_postimputation[NUMERIC_VARIABLES_postimputation$Variable=="HDL",]
NUMERIC_VARIABLES_postimputation_LDL <- NUMERIC_VARIABLES_postimputation[NUMERIC_VARIABLES_postimputation$Variable=="LDL",]
NUMERIC_VARIABLES_postimputation_TRIG <- NUMERIC_VARIABLES_postimputation[NUMERIC_VARIABLES_postimputation$Variable=="TRIG",]
NUMERIC_VARIABLES_postimputation_HOMOC <- NUMERIC_VARIABLES_postimputation[NUMERIC_VARIABLES_postimputation$Variable=="HOMOC",]
NUMERIC_VARIABLES_postimputation_GLUT <- NUMERIC_VARIABLES_postimputation[NUMERIC_VARIABLES_postimputation$Variable=="GLUT",]
NUMERIC_VARIABLES_postimputation_CREAT <- NUMERIC_VARIABLES_postimputation[NUMERIC_VARIABLES_postimputation$Variable=="CREAT",]
NUMERIC_VARIABLES_postimputation_IMT <- NUMERIC_VARIABLES_postimputation[NUMERIC_VARIABLES_postimputation$Variable=="IMT",]
NUMERIC_VARIABLES_postimputation_PACKYRS <- NUMERIC_VARIABLES_postimputation[NUMERIC_VARIABLES_postimputation$Variable=="PACKYRS",]
DENSITY_SYSTBP <- densityplot(~ Value | Variable,
data = NUMERIC_VARIABLES_postimputation_SYSTBP,
groups = Category,
plot.points = FALSE,
ref = TRUE,
scales=list(relation="free"),
auto.key = list(adj=1, space="top", columns=1),
par.settings = list(superpose.line = list(lwd=2)))
DENSITY_SYSTH <- densityplot(~ Value | Variable,
data = NUMERIC_VARIABLES_postimputation_SYSTH,
groups = Category,
plot.points = FALSE,
ref = TRUE,
scales=list(relation="free"),
auto.key = list(adj=1, space="top", columns=1),
par.settings = list(superpose.line = list(lwd=2)))
DENSITY_DIASTBP <- densityplot(~ Value | Variable,
data = NUMERIC_VARIABLES_postimputation_DIASTBP,
groups = Category,
plot.points = FALSE,
ref = TRUE,
scales=list(relation="free"),
auto.key = list(adj=1, space="top", columns=1),
par.settings = list(superpose.line = list(lwd=2)))
DENSITY_DIASTH <- densityplot(~ Value | Variable,
data = NUMERIC_VARIABLES_postimputation_DIASTH,
groups = Category,
plot.points = FALSE,
ref = TRUE,
scales=list(relation="free"),
auto.key = list(adj=1, space="top", columns=1),
par.settings = list(superpose.line = list(lwd=2)))
DENSITY_LENGTH <- densityplot(~ Value | Variable,
data = NUMERIC_VARIABLES_postimputation_LENGTH,
groups = Category,
plot.points = FALSE,
ref = TRUE,
scales=list(relation="free"),
auto.key = list(adj=1, space="top", columns=1),
par.settings = list(superpose.line = list(lwd=2)))
DENSITY_WEIGHT <- densityplot(~ Value | Variable,
data = NUMERIC_VARIABLES_postimputation_WEIGHT,
groups = Category,
plot.points = FALSE,
ref = TRUE,
scales=list(relation="free"),
auto.key = list(adj=1, space="top", columns=1),
par.settings = list(superpose.line = list(lwd=2)))
DENSITY_BMI <- densityplot(~ Value | Variable,
data = NUMERIC_VARIABLES_postimputation_BMI,
groups = Category,
plot.points = FALSE,
ref = TRUE,
scales=list(relation="free"),
auto.key = list(adj=1, space="top", columns=1),
par.settings = list(superpose.line = list(lwd=2)))
DENSITY_CHOL <- densityplot(~ Value | Variable,
data = NUMERIC_VARIABLES_postimputation_CHOL,
groups = Category,
plot.points = FALSE,
ref = TRUE,
scales=list(relation="free"),
auto.key = list(adj=1, space="top", columns=1),
par.settings = list(superpose.line = list(lwd=2)))
DENSITY_HDL <- densityplot(~ Value | Variable,
data = NUMERIC_VARIABLES_postimputation_HDL,
groups = Category,
plot.points = FALSE,
ref = TRUE,
scales=list(relation="free"),
auto.key = list(adj=1, space="top", columns=1),
par.settings = list(superpose.line = list(lwd=2)))
DENSITY_LDL <- densityplot(~ Value | Variable,
data = NUMERIC_VARIABLES_postimputation_LDL,
groups = Category,
plot.points = FALSE,
ref = TRUE,
scales=list(relation="free"),
auto.key = list(adj=1, space="top", columns=1),
par.settings = list(superpose.line = list(lwd=2)))
DENSITY_TRIG <- densityplot(~ Value | Variable,
data = NUMERIC_VARIABLES_postimputation_TRIG,
groups = Category,
plot.points = FALSE,
ref = TRUE,
scales=list(relation="free"),
auto.key = list(adj=1, space="top", columns=1),
par.settings = list(superpose.line = list(lwd=2)))
DENSITY_HOMOC <- densityplot(~ Value | Variable,
data = NUMERIC_VARIABLES_postimputation_HOMOC,
groups = Category,
plot.points = FALSE,
ref = TRUE,
scales=list(relation="free"),
auto.key = list(adj=1, space="top", columns=1),
par.settings = list(superpose.line = list(lwd=2)))
DENSITY_GLUT <- densityplot(~ Value | Variable,
data = NUMERIC_VARIABLES_postimputation_GLUT,
groups = Category,
plot.points = FALSE,
ref = TRUE,
scales=list(relation="free"),
auto.key = list(adj=1, space="top", columns=1),
par.settings = list(superpose.line = list(lwd=2)))
DENSITY_CREAT <- densityplot(~ Value | Variable,
data = NUMERIC_VARIABLES_postimputation_CREAT,
groups = Category,
plot.points = FALSE,
ref = TRUE,
scales=list(relation="free"),
auto.key = list(adj=1, space="top", columns=1),
par.settings = list(superpose.line = list(lwd=2)))
DENSITY_IMT <- densityplot(~ Value | Variable,
data = NUMERIC_VARIABLES_postimputation_IMT,
groups = Category,
plot.points = FALSE,
ref = TRUE,
scales=list(relation="free"),
auto.key = list(adj=1, space="top", columns=1),
par.settings = list(superpose.line = list(lwd=2)))
DENSITY_PACKYRS <- densityplot(~ Value | Variable,
data = NUMERIC_VARIABLES_postimputation_PACKYRS,
groups = Category,
plot.points = FALSE,
ref = TRUE,
scales=list(relation="free"),
auto.key = list(adj=1, space="top", columns=1),
par.settings = list(superpose.line = list(lwd=2)))
grid.arrange(DENSITY_SYSTBP,
DENSITY_SYSTH,
DENSITY_DIASTBP,
DENSITY_DIASTH,
DENSITY_LENGTH,
DENSITY_WEIGHT,
DENSITY_BMI,
DENSITY_CHOL,
DENSITY_HDL,
DENSITY_LDL,
DENSITY_TRIG,
DENSITY_HOMOC,
DENSITY_GLUT,
DENSITY_CREAT,
DENSITY_IMT,
DENSITY_PACKYRS,
ncol = 4) 
##################################
# Evaluating the plausibility of the
# AREG-imputed values for the
# numerical variables
##################################
DIABETES_complete <- (DPP$DIABETES[complete.cases(DPP$DIABETES)])
DPP.AREGIMPUTED_aregImpute_DIABETES <- as.data.frame(DPP.AREGIMPUTED$imputed$DIABETES)
DIABETES_aregImpute_1 <- DPP.AREGIMPUTED_aregImpute_DIABETES$V1
DIABETES_aregImpute_2 <- DPP.AREGIMPUTED_aregImpute_DIABETES$V2
DIABETES_aregImpute_3 <- DPP.AREGIMPUTED_aregImpute_DIABETES$V3
DIABETES_aregImpute_4 <- DPP.AREGIMPUTED_aregImpute_DIABETES$V4
DIABETES_aregImpute_5 <- DPP.AREGIMPUTED_aregImpute_DIABETES$V5
DIABETES_values <- c(DIABETES_complete,
DIABETES_aregImpute_1,
DIABETES_aregImpute_2,
DIABETES_aregImpute_3,
DIABETES_aregImpute_4,
DIABETES_aregImpute_5)
DIABETES_labels <- c(rep("Original",length(DIABETES_complete)),
rep("aregImputed_1",length(DIABETES_aregImpute_1)),
rep("aregImputed_2",length(DIABETES_aregImpute_2)),
rep("aregImputed_3",length(DIABETES_aregImpute_3)),
rep("aregImputed_4",length(DIABETES_aregImpute_4)),
rep("aregImputed_5",length(DIABETES_aregImpute_5)))
DIABETES_postimputation <- cbind(DIABETES_values,
DIABETES_labels)
DIABETES_postimputation <- as.data.frame(DIABETES_postimputation)
colnames(DIABETES_postimputation) <- c("Value",
"Category")
DIABETES_postimputation_proportion <- as.data.frame(prop.table(table(DIABETES_postimputation), 2))
DIABETES_postimputation_proportion$Category <- factor(DIABETES_postimputation_proportion$Category,
levels=c("Original",
"aregImputed_1",
"aregImputed_2",
"aregImputed_3",
"aregImputed_4",
"aregImputed_5"))
DIABETES_postimputation_proportion$Variable <- rep("DIABETES",nrow(DIABETES_postimputation_proportion))
BAR_DIABETES <- barchart(Freq ~ Category | Variable,
data=DIABETES_postimputation_proportion,
groups = Value,
stack=TRUE,
ylab = "Proportion",
auto.key = list(adj=1, space="top", columns=2))
STENOSIS_complete <- (DPP$STENOSIS[complete.cases(DPP$STENOSIS)])
DPP.AREGIMPUTED_aregImpute_STENOSIS <- as.data.frame(DPP.AREGIMPUTED$imputed$STENOSIS)
STENOSIS_aregImpute_1 <- DPP.AREGIMPUTED_aregImpute_STENOSIS$V1
STENOSIS_aregImpute_2 <- DPP.AREGIMPUTED_aregImpute_STENOSIS$V2
STENOSIS_aregImpute_3 <- DPP.AREGIMPUTED_aregImpute_STENOSIS$V3
STENOSIS_aregImpute_4 <- DPP.AREGIMPUTED_aregImpute_STENOSIS$V4
STENOSIS_aregImpute_5 <- DPP.AREGIMPUTED_aregImpute_STENOSIS$V5
STENOSIS_values <- c(STENOSIS_complete,
STENOSIS_aregImpute_1,
STENOSIS_aregImpute_2,
STENOSIS_aregImpute_3,
STENOSIS_aregImpute_4,
STENOSIS_aregImpute_5)
STENOSIS_labels <- c(rep("Original",length(STENOSIS_complete)),
rep("aregImputed_1",length(STENOSIS_aregImpute_1)),
rep("aregImputed_2",length(STENOSIS_aregImpute_2)),
rep("aregImputed_3",length(STENOSIS_aregImpute_3)),
rep("aregImputed_4",length(STENOSIS_aregImpute_4)),
rep("aregImputed_5",length(STENOSIS_aregImpute_5)))
STENOSIS_postimputation <- cbind(STENOSIS_values,
STENOSIS_labels)
STENOSIS_postimputation <- as.data.frame(STENOSIS_postimputation)
colnames(STENOSIS_postimputation) <- c("Value",
"Category")
STENOSIS_postimputation_proportion <- as.data.frame(prop.table(table(STENOSIS_postimputation), 2))
STENOSIS_postimputation_proportion$Category <- factor(STENOSIS_postimputation_proportion$Category,
levels=c("Original",
"aregImputed_1",
"aregImputed_2",
"aregImputed_3",
"aregImputed_4",
"aregImputed_5"))
STENOSIS_postimputation_proportion$Variable <- rep("STENOSIS",nrow(STENOSIS_postimputation_proportion))
BAR_STENOSIS <- barchart(Freq ~ Category | Variable,
data=STENOSIS_postimputation_proportion,
groups = Value,
stack=TRUE,
ylab = "Proportion",
auto.key = list(adj=1, space="top", columns=2))
ALBUMIN_complete <- (DPP$ albumin [complete.cases(DPP$albumin)])
DPP.AREGIMPUTED_aregImpute_ALBUMIN <- as.data.frame(DPP.AREGIMPUTED$imputed$ albumin)
ALBUMIN_aregImpute_1 <- DPP.AREGIMPUTED_aregImpute_ALBUMIN$V1
ALBUMIN_aregImpute_2 <- DPP.AREGIMPUTED_aregImpute_ALBUMIN$V2
ALBUMIN_aregImpute_3 <- DPP.AREGIMPUTED_aregImpute_ALBUMIN$V3
ALBUMIN_aregImpute_4 <- DPP.AREGIMPUTED_aregImpute_ALBUMIN$V4
ALBUMIN_aregImpute_5 <- DPP.AREGIMPUTED_aregImpute_ALBUMIN$V5
ALBUMIN_values <- c(ALBUMIN_complete,
ALBUMIN_aregImpute_1,
ALBUMIN_aregImpute_2,
ALBUMIN_aregImpute_3,
ALBUMIN_aregImpute_4,
ALBUMIN_aregImpute_5)
ALBUMIN_labels <- c(rep("Original",length(ALBUMIN_complete)),
rep("aregImputed_1",length(ALBUMIN_aregImpute_1)),
rep("aregImputed_2",length(ALBUMIN_aregImpute_2)),
rep("aregImputed_3",length(ALBUMIN_aregImpute_3)),
rep("aregImputed_4",length(ALBUMIN_aregImpute_4)),
rep("aregImputed_5",length(ALBUMIN_aregImpute_5)))
ALBUMIN_postimputation <- cbind(ALBUMIN_values,
ALBUMIN_labels)
ALBUMIN_postimputation <- as.data.frame(ALBUMIN_postimputation)
colnames(ALBUMIN_postimputation) <- c("Value",
"Category")
ALBUMIN_postimputation_proportion <- as.data.frame(prop.table(table(ALBUMIN_postimputation), 2))
ALBUMIN_postimputation_proportion$Category <- factor(ALBUMIN_postimputation_proportion$Category,
levels=c("Original",
"aregImputed_1",
"aregImputed_2",
"aregImputed_3",
"aregImputed_4",
"aregImputed_5"))
ALBUMIN_postimputation_proportion$Variable <- rep("ALBUMIN",nrow(ALBUMIN_postimputation_proportion))
BAR_ALBUMIN <- barchart(Freq ~ Category | Variable,
data=ALBUMIN_postimputation_proportion,
groups = Value,
stack=TRUE,
ylab = "Proportion",
auto.key = list(adj=1, space="top", columns=3))
SMOKING_complete <- (DPP$ SMOKING [complete.cases(DPP$SMOKING)])
DPP.AREGIMPUTED_aregImpute_SMOKING <- as.data.frame(DPP.AREGIMPUTED$imputed$SMOKING)
SMOKING_aregImpute_1 <- DPP.AREGIMPUTED_aregImpute_SMOKING$V1
SMOKING_aregImpute_2 <- DPP.AREGIMPUTED_aregImpute_SMOKING$V2
SMOKING_aregImpute_3 <- DPP.AREGIMPUTED_aregImpute_SMOKING$V3
SMOKING_aregImpute_4 <- DPP.AREGIMPUTED_aregImpute_SMOKING$V4
SMOKING_aregImpute_5 <- DPP.AREGIMPUTED_aregImpute_SMOKING$V5
SMOKING_values <- c(SMOKING_complete,
SMOKING_aregImpute_1,
SMOKING_aregImpute_2,
SMOKING_aregImpute_3,
SMOKING_aregImpute_4,
SMOKING_aregImpute_5)
SMOKING_labels <- c(rep("Original",length(SMOKING_complete)),
rep("aregImputed_1",length(SMOKING_aregImpute_1)),
rep("aregImputed_2",length(SMOKING_aregImpute_2)),
rep("aregImputed_3",length(SMOKING_aregImpute_3)),
rep("aregImputed_4",length(SMOKING_aregImpute_4)),
rep("aregImputed_5",length(SMOKING_aregImpute_5)))
SMOKING_postimputation <- cbind(SMOKING_values,
SMOKING_labels)
SMOKING_postimputation <- as.data.frame(SMOKING_postimputation)
colnames(SMOKING_postimputation) <- c("Value",
"Category")
SMOKING_postimputation_proportion <- as.data.frame(prop.table(table(SMOKING_postimputation), 2))
SMOKING_postimputation_proportion$Category <- factor(SMOKING_postimputation_proportion$Category,
levels=c("Original",
"aregImputed_1",
"aregImputed_2",
"aregImputed_3",
"aregImputed_4",
"aregImputed_5"))
SMOKING_postimputation_proportion$Variable <- rep("SMOKING",nrow(SMOKING_postimputation_proportion))
BAR_SMOKING <- barchart(Freq ~ Category | Variable,
data=SMOKING_postimputation_proportion,
groups = Value,
stack=TRUE,
ylab = "Proportion",
auto.key = list(adj=1, space="top", columns=3))
ALCOHOL_complete <- (DPP$ alcohol [complete.cases(DPP$alcohol)])
DPP.AREGIMPUTED_aregImpute_ALCOHOL <- as.data.frame(DPP.AREGIMPUTED$imputed$alcohol)
ALCOHOL_aregImpute_1 <- DPP.AREGIMPUTED_aregImpute_ALCOHOL$V1
ALCOHOL_aregImpute_2 <- DPP.AREGIMPUTED_aregImpute_ALCOHOL$V2
ALCOHOL_aregImpute_3 <- DPP.AREGIMPUTED_aregImpute_ALCOHOL$V3
ALCOHOL_aregImpute_4 <- DPP.AREGIMPUTED_aregImpute_ALCOHOL$V4
ALCOHOL_aregImpute_5 <- DPP.AREGIMPUTED_aregImpute_ALCOHOL$V5
ALCOHOL_values <- c(ALCOHOL_complete,
ALCOHOL_aregImpute_1,
ALCOHOL_aregImpute_2,
ALCOHOL_aregImpute_3,
ALCOHOL_aregImpute_4,
ALCOHOL_aregImpute_5)
ALCOHOL_labels <- c(rep("Original",length(ALCOHOL_complete)),
rep("aregImputed_1",length(ALCOHOL_aregImpute_1)),
rep("aregImputed_2",length(ALCOHOL_aregImpute_2)),
rep("aregImputed_3",length(ALCOHOL_aregImpute_3)),
rep("aregImputed_4",length(ALCOHOL_aregImpute_4)),
rep("aregImputed_5",length(ALCOHOL_aregImpute_5)))
ALCOHOL_postimputation <- cbind(ALCOHOL_values,
ALCOHOL_labels)
ALCOHOL_postimputation <- as.data.frame(ALCOHOL_postimputation)
colnames(ALCOHOL_postimputation) <- c("Value",
"Category")
ALCOHOL_postimputation_proportion <- as.data.frame(prop.table(table(ALCOHOL_postimputation), 2))
ALCOHOL_postimputation_proportion$Category <- factor(ALCOHOL_postimputation_proportion$Category,
levels=c("Original",
"aregImputed_1",
"aregImputed_2",
"aregImputed_3",
"aregImputed_4",
"aregImputed_5"))
ALCOHOL_postimputation_proportion$Variable <- rep("ALCOHOL",nrow(ALCOHOL_postimputation_proportion))
BAR_ALCOHOL <- barchart(Freq ~ Category | Variable,
data=ALCOHOL_postimputation_proportion,
groups = Value,
stack=TRUE,
ylab = "Proportion",
auto.key = list(adj=1, space="top", columns=3))
grid.arrange(BAR_DIABETES,
BAR_STENOSIS,
BAR_ALBUMIN,
BAR_SMOKING,
BAR_ALCOHOL,
ncol = 2)
1.2.5 Model Specification
Missing data imputation evaluation using full model specification:
[A] Certain variables were initially excluded for modelling in order to (1) reduce potential multicollinearity among predictors (those which reported high variance inflation factor values); (2) remove variables which were minimally associated to the outcome based from initial data exploration (those which reported low Wald chi-squared values); and (3) only retain important and standard risk factors (those which have been previously shown as significant clinical survival predictors based from expert recommendations and/or literature review) :
[A.1] DIASTH variable (numeric)
[A.2] DIASBP variable (numeric)
[A.3] SYSTBP variable (numeric)
[A.4] LENGTH variable (numeric)
[A.5] WEIGHT variable (numeric)
[A.6] CHOL variable (numeric)
[A.7] LDL variable (numeric)
[A.8] TRIG variable (numeric)
[A.9] GLUT variable (numeric)
[A.10] PACKYRS variable (numeric)
[B] The variables selected to be a part of the full model comprised of the following:
[B.1] AGE variable (numeric) coded using its squared value after 50 years [if (AGE>50) then (AGE-50)^2 else 0]
[B.2] SEX variable (factor)
[B.3] SMOKING variable (factor)
[B.4] ALCOHOL variable (factor)
[B.5] BMI variable (numeric)
[B.6] SYSTH variable (numeric)
[B.7] HDL variable (numeric)
[B.8] DIABETES variable (factor)
[B.9] CEREBRAL variable (numeric), CARDIAC variable (numeric), AAA variable (numeric) and PERIPH variable (numeric) coded using their linear combination [CEREBRAL + CARDIAC + (2*AAA) + PERIPH] called SUMSCORE_5LEVELS variable (numeric)
[B.10] HOMOC variable (numeric)
[B.11] CREAT variable (numeric) coded using its logarithm [log(CREAT)]
[B.12] ALBUMIN variable (factor)
[B.13] STENOSIS variable (factor)
[B.14] IMT variable (numeric)
[B.15] HOMOC variable (numeric)
[C] The five imputed datasets (aregImputed_1, aregImputed_2, aregImputed_3, aregImputed_4 and aregImputed_5) demonstrated generally stable estimated coefficients for the full cox proportional hazards model. The imputed data from iteration 3 (aregImputed_3) was assigned for the subsequent model selection process.
Code Chunk | Output
##################################
# Loading the modelling dataset
# by combining the complete and imputed values
##################################
##################################
# Combining the complete and
# 1ST imputation results from AREG
##################################
DPP.AREGIMPUTED_1 <- impute.transcan(DPP.AREGIMPUTED,
imputation=1,
data=DPP,
list.out=TRUE,
pr=FALSE,
check=FALSE)
SMART.AREGIMPUTED_1 <- SMART
SMART.AREGIMPUTED_1[names(DPP.AREGIMPUTED_1)] <- DPP.AREGIMPUTED_1
SMART.AREGIMPUTED_1$CEREBRAL <- as.numeric(as.character(SMART.AREGIMPUTED_1$CEREBRAL))
SMART.AREGIMPUTED_1$CARDIAC <- as.numeric(as.character(SMART.AREGIMPUTED_1$CARDIAC))
SMART.AREGIMPUTED_1$AAA <- as.numeric(as.character(SMART.AREGIMPUTED_1$AAA))
SMART.AREGIMPUTED_1$PERIPH <- as.numeric(as.character(SMART.AREGIMPUTED_1$PERIPH))
SMART.AREGIMPUTED_1$SUMSCORE_5LEVELS <- SMART.AREGIMPUTED_1$CEREBRAL +
SMART.AREGIMPUTED_1$CARDIAC +
(2*SMART.AREGIMPUTED_1$AAA) +
SMART.AREGIMPUTED_1$PERIPH
##################################
# Combining the complete and
# 2ND imputation results from AREG
##################################
DPP.AREGIMPUTED_2 <- impute.transcan(DPP.AREGIMPUTED,
imputation=2,
data=DPP,
list.out=TRUE,
pr=FALSE,
check=FALSE)
SMART.AREGIMPUTED_2 <- SMART
SMART.AREGIMPUTED_2[names(DPP.AREGIMPUTED_2)] <- DPP.AREGIMPUTED_2
SMART.AREGIMPUTED_2$CEREBRAL <- as.numeric(as.character(SMART.AREGIMPUTED_2$CEREBRAL))
SMART.AREGIMPUTED_2$CARDIAC <- as.numeric(as.character(SMART.AREGIMPUTED_2$CARDIAC))
SMART.AREGIMPUTED_2$AAA <- as.numeric(as.character(SMART.AREGIMPUTED_2$AAA))
SMART.AREGIMPUTED_2$PERIPH <- as.numeric(as.character(SMART.AREGIMPUTED_2$PERIPH))
SMART.AREGIMPUTED_2$SUMSCORE_5LEVELS <- SMART.AREGIMPUTED_2$CEREBRAL +
SMART.AREGIMPUTED_2$CARDIAC +
(2*SMART.AREGIMPUTED_2$AAA) +
SMART.AREGIMPUTED_2$PERIPH
##################################
# Combining the complete and
# 3RD imputation results from AREG
##################################
DPP.AREGIMPUTED_3 <- impute.transcan(DPP.AREGIMPUTED,
imputation=3,
data=DPP,
list.out=TRUE,
pr=FALSE,
check=FALSE)
SMART.AREGIMPUTED_3 <- SMART
SMART.AREGIMPUTED_3[names(DPP.AREGIMPUTED_3)] <- DPP.AREGIMPUTED_3
SMART.AREGIMPUTED_3$CEREBRAL <- as.numeric(as.character(SMART.AREGIMPUTED_3$CEREBRAL))
SMART.AREGIMPUTED_3$CARDIAC <- as.numeric(as.character(SMART.AREGIMPUTED_3$CARDIAC))
SMART.AREGIMPUTED_3$AAA <- as.numeric(as.character(SMART.AREGIMPUTED_3$AAA))
SMART.AREGIMPUTED_3$PERIPH <- as.numeric(as.character(SMART.AREGIMPUTED_3$PERIPH))
SMART.AREGIMPUTED_3$SUMSCORE_5LEVELS <- SMART.AREGIMPUTED_3$CEREBRAL +
SMART.AREGIMPUTED_3$CARDIAC +
(2*SMART.AREGIMPUTED_3$AAA) +
SMART.AREGIMPUTED_3$PERIPH
##################################
# Combining the complete and
# 4TH imputation results from AREG
##################################
DPP.AREGIMPUTED_4 <- impute.transcan(DPP.AREGIMPUTED,
imputation=4,
data=DPP,
list.out=TRUE,
pr=FALSE,
check=FALSE)
SMART.AREGIMPUTED_4 <- SMART
SMART.AREGIMPUTED_4[names(DPP.AREGIMPUTED_4)] <- DPP.AREGIMPUTED_4
SMART.AREGIMPUTED_4$CEREBRAL <- as.numeric(as.character(SMART.AREGIMPUTED_4$CEREBRAL))
SMART.AREGIMPUTED_4$CARDIAC <- as.numeric(as.character(SMART.AREGIMPUTED_4$CARDIAC))
SMART.AREGIMPUTED_4$AAA <- as.numeric(as.character(SMART.AREGIMPUTED_4$AAA))
SMART.AREGIMPUTED_4$PERIPH <- as.numeric(as.character(SMART.AREGIMPUTED_4$PERIPH))
SMART.AREGIMPUTED_4$SUMSCORE_5LEVELS <- SMART.AREGIMPUTED_4$CEREBRAL +
SMART.AREGIMPUTED_4$CARDIAC +
(2*SMART.AREGIMPUTED_4$AAA) +
SMART.AREGIMPUTED_4$PERIPH
##################################
# Combining the complete and
# 5TH imputation results from AREG
##################################
DPP.AREGIMPUTED_5 <- impute.transcan(DPP.AREGIMPUTED,
imputation=5,
data=DPP,
list.out=TRUE,
pr=FALSE,
check=FALSE)
SMART.AREGIMPUTED_5 <- SMART
SMART.AREGIMPUTED_5[names(DPP.AREGIMPUTED_5)] <- DPP.AREGIMPUTED_5
SMART.AREGIMPUTED_5$CEREBRAL <- as.numeric(as.character(SMART.AREGIMPUTED_5$CEREBRAL))
SMART.AREGIMPUTED_5$CARDIAC <- as.numeric(as.character(SMART.AREGIMPUTED_5$CARDIAC))
SMART.AREGIMPUTED_5$AAA <- as.numeric(as.character(SMART.AREGIMPUTED_5$AAA))
SMART.AREGIMPUTED_5$PERIPH <- as.numeric(as.character(SMART.AREGIMPUTED_5$PERIPH))
SMART.AREGIMPUTED_5$SUMSCORE_5LEVELS <- SMART.AREGIMPUTED_5$CEREBRAL +
SMART.AREGIMPUTED_5$CARDIAC +
(2*SMART.AREGIMPUTED_5$AAA) +
SMART.AREGIMPUTED_5$PERIPH
##################################
# Exploring the single imputation
# results using AREG
##################################
describe(SMART.AREGIMPUTED_1)## SMART.AREGIMPUTED_1
##
## 30 Variables 3873 Observations
## --------------------------------------------------------------------------------
## TEVENT
## n missing distinct Info Mean Gmd .05 .10
## 3873 0 1934 1 1370 1078 98.6 197.0
## .25 .50 .75 .90 .95
## 555.0 1213.0 2165.0 2762.4 3017.4
##
## lowest : 0.1 1 2 3 4 , highest: 3451 3452 3463 3465 3466
## --------------------------------------------------------------------------------
## EVENT
## n missing distinct
## 3873 0 2
##
## Value 0 1
## Frequency 3413 460
## Proportion 0.881 0.119
## --------------------------------------------------------------------------------
## SEX
## n missing distinct
## 3873 0 2
##
## Value 1 2
## Frequency 2897 976
## Proportion 0.748 0.252
## --------------------------------------------------------------------------------
## AGE
## n missing distinct Info Mean Gmd .05 .10
## 3873 0 62 0.999 59.56 11.94 41 46
## .25 .50 .75 .90 .95
## 52 60 68 73 76
##
## lowest : 19 20 23 24 25, highest: 78 79 80 81 82
## --------------------------------------------------------------------------------
## DIABETES
## n missing imputed distinct
## 3873 0 40 2
##
## Value 0 1
## Frequency 3024 849
## Proportion 0.781 0.219
## --------------------------------------------------------------------------------
## CEREBRAL
## n missing distinct Info Sum Mean Gmd
## 3873 0 2 0.625 1147 0.2962 0.417
##
## --------------------------------------------------------------------------------
## CARDIAC
## n missing distinct Info Sum Mean Gmd
## 3873 0 2 0.74 2160 0.5577 0.4935
##
## --------------------------------------------------------------------------------
## AAA
## n missing distinct Info Sum Mean Gmd
## 3873 0 2 0.288 416 0.1074 0.1918
##
## --------------------------------------------------------------------------------
## PERIPH
## n missing distinct Info Sum Mean Gmd
## 3873 0 2 0.551 940 0.2427 0.3677
##
## --------------------------------------------------------------------------------
## STENOSIS
## n missing imputed distinct
## 3873 0 93 2
##
## Value 0 1
## Frequency 3131 742
## Proportion 0.808 0.192
## --------------------------------------------------------------------------------
## SYSTBP
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 1223 114 1 140.8 22.31 112
## .10 .25 .50 .75 .90 .95
## 117 126 139 153 168 178
##
## lowest : 96 97 98 99 100, highest: 206 209 211 212 216
## --------------------------------------------------------------------------------
## DIASTBP
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 1221 70 0.999 79.72 10.94 65
## .10 .25 .50 .75 .90 .95
## 68 73 79 86 93 97
##
## lowest : 46 48 52 53 54, highest: 117 118 120 124 127
## --------------------------------------------------------------------------------
## SYSTH
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 1498 132 1 143.1 24.73 111
## .10 .25 .50 .75 .90 .95
## 117 127 140 157 173 183
##
## lowest : 79 88 91 93 94, highest: 222 223 228 242 244
## --------------------------------------------------------------------------------
## DIASTH
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 1499 77 0.999 81.93 12.92 64
## .10 .25 .50 .75 .90 .95
## 68 74 81 89 97 102
##
## lowest : 45 49 50 52 53, highest: 123 125 126 130 136
## --------------------------------------------------------------------------------
## LENGTH
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 1 42 0.999 1.74 0.09862 1.59
## .10 .25 .50 .75 .90 .95
## 1.62 1.68 1.75 1.80 1.85 1.88
##
## lowest : 1.53 1.54 1.55 1.56 1.57, highest: 1.9 1.91 1.92 1.93 1.94
## --------------------------------------------------------------------------------
## WEIGHT
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 2 75 0.999 80.99 15.41 59
## .10 .25 .50 .75 .90 .95
## 64 72 80 89 99 104
##
## lowest : 50 51 52 53 54, highest: 120 121 122 123 124
## --------------------------------------------------------------------------------
## BMI
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 3 995 1 26.69 4.259 20.96
## .10 .25 .50 .75 .90 .95
## 22.16 24.11 26.30 28.73 31.86 33.90
##
## lowest : 18.7 18.71 18.73 18.78 18.81, highest: 39.25 39.43 39.45 39.64 39.8
## --------------------------------------------------------------------------------
## CHOL
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 18 65 0.999 5.191 1.283 3.5
## .10 .25 .50 .75 .90 .95
## 3.8 4.4 5.1 5.9 6.7 7.2
##
## lowest : 2.8 2.9 3 3.1 3.2, highest: 8.8 8.9 9.1 9.2 9.4
## --------------------------------------------------------------------------------
## HDL
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 30 188 1 1.23 0.4031 0.74
## .10 .25 .50 .75 .90 .95
## 0.82 0.96 1.17 1.42 1.73 1.94
##
## lowest : 0.58 0.59 0.6 0.61 0.62, highest: 2.46 2.47 2.48 2.49 2.51
## --------------------------------------------------------------------------------
## LDL
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 216 478 1 3.129 1.184 1.52
## .10 .25 .50 .75 .90 .95
## 1.82 2.37 3.05 3.83 4.55 4.98
##
## lowest : 1.1 1.11 1.12 1.14 1.15, highest: 6.34 6.37 6.41 6.47 6.6
## --------------------------------------------------------------------------------
## TRIG
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 28 461 1 1.852 1.093 0.760
## .10 .25 .50 .75 .90 .95
## 0.880 1.120 1.530 2.230 3.120 3.904
##
## lowest : 0.56 0.57 0.58 0.59 0.6 , highest: 8.28 8.61 8.68 8.91 8.96
## --------------------------------------------------------------------------------
## HOMOC
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 463 255 1 14.17 5.609 8.0
## .10 .25 .50 .75 .90 .95
## 8.8 10.5 13.0 16.2 20.6 24.8
##
## lowest : 6.1 6.2 6.3 6.4 6.5 , highest: 35.5 35.9 36.1 37.1 38.3
## --------------------------------------------------------------------------------
## GLUT
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 19 125 0.998 6.333 1.702 4.8
## .10 .25 .50 .75 .90 .95
## 5.0 5.3 5.7 6.5 8.4 10.4
##
## lowest : 4.3 4.4 4.5 4.6 4.7 , highest: 17.6 17.7 17.9 18 18.7
## --------------------------------------------------------------------------------
## CREAT
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 17 194 1 98.35 34.53 65
## .10 .25 .50 .75 .90 .95
## 69 78 89 101 118 138
##
## lowest : 54 55 56 57 58, highest: 784 799 809 813 825
## --------------------------------------------------------------------------------
## IMT
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 98 99 0.999 0.936 0.2883 0.60
## .10 .25 .50 .75 .90 .95
## 0.65 0.75 0.88 1.07 1.30 1.45
##
## lowest : 0.47 0.48 0.5 0.52 0.53, highest: 1.77 1.78 1.8 1.82 1.83
## --------------------------------------------------------------------------------
## albumin
## n missing imputed distinct
## 3873 0 207 3
##
## Value 1 2 3
## Frequency 3045 696 132
## Proportion 0.786 0.180 0.034
## --------------------------------------------------------------------------------
## SMOKING
## n missing imputed distinct
## 3873 0 25 3
##
## Value 1 2 3
## Frequency 694 2733 446
## Proportion 0.179 0.706 0.115
## --------------------------------------------------------------------------------
## packyrs
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 21 263 0.994 22.64 22.26 0.0
## .10 .25 .50 .75 .90 .95
## 0.0 5.9 19.5 34.2 50.4 62.0
##
## lowest : 0 0.3 0.6 0.7 0.8, highest: 100 102 104 110 120
## --------------------------------------------------------------------------------
## alcohol
## n missing imputed distinct
## 3873 0 25 3
##
## Value 1 2 3
## Frequency 756 412 2705
## Proportion 0.195 0.106 0.698
## --------------------------------------------------------------------------------
## SUMSCORE_5LEVELS
## n missing distinct Info Mean Gmd
## 3873 0 5 0.532 1.311 0.511
##
## Value 1 2 3 4 5
## Frequency 2999 605 211 53 5
## Proportion 0.774 0.156 0.054 0.014 0.001
##
## For the frequency table, variable is rounded to the nearest 0
## --------------------------------------------------------------------------------describe(SMART.AREGIMPUTED_2)## SMART.AREGIMPUTED_2
##
## 30 Variables 3873 Observations
## --------------------------------------------------------------------------------
## TEVENT
## n missing distinct Info Mean Gmd .05 .10
## 3873 0 1934 1 1370 1078 98.6 197.0
## .25 .50 .75 .90 .95
## 555.0 1213.0 2165.0 2762.4 3017.4
##
## lowest : 0.1 1 2 3 4 , highest: 3451 3452 3463 3465 3466
## --------------------------------------------------------------------------------
## EVENT
## n missing distinct
## 3873 0 2
##
## Value 0 1
## Frequency 3413 460
## Proportion 0.881 0.119
## --------------------------------------------------------------------------------
## SEX
## n missing distinct
## 3873 0 2
##
## Value 1 2
## Frequency 2897 976
## Proportion 0.748 0.252
## --------------------------------------------------------------------------------
## AGE
## n missing distinct Info Mean Gmd .05 .10
## 3873 0 62 0.999 59.56 11.94 41 46
## .25 .50 .75 .90 .95
## 52 60 68 73 76
##
## lowest : 19 20 23 24 25, highest: 78 79 80 81 82
## --------------------------------------------------------------------------------
## DIABETES
## n missing imputed distinct
## 3873 0 40 2
##
## Value 0 1
## Frequency 3024 849
## Proportion 0.781 0.219
## --------------------------------------------------------------------------------
## CEREBRAL
## n missing distinct Info Sum Mean Gmd
## 3873 0 2 0.625 1147 0.2962 0.417
##
## --------------------------------------------------------------------------------
## CARDIAC
## n missing distinct Info Sum Mean Gmd
## 3873 0 2 0.74 2160 0.5577 0.4935
##
## --------------------------------------------------------------------------------
## AAA
## n missing distinct Info Sum Mean Gmd
## 3873 0 2 0.288 416 0.1074 0.1918
##
## --------------------------------------------------------------------------------
## PERIPH
## n missing distinct Info Sum Mean Gmd
## 3873 0 2 0.551 940 0.2427 0.3677
##
## --------------------------------------------------------------------------------
## STENOSIS
## n missing imputed distinct
## 3873 0 93 2
##
## Value 0 1
## Frequency 3130 743
## Proportion 0.808 0.192
## --------------------------------------------------------------------------------
## SYSTBP
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 1223 114 1 140.7 21.96 112
## .10 .25 .50 .75 .90 .95
## 117 126 138 153 167 177
##
## lowest : 96 97 98 99 100, highest: 206 209 211 212 216
## --------------------------------------------------------------------------------
## DIASTBP
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 1221 70 0.999 79.85 10.89 65
## .10 .25 .50 .75 .90 .95
## 68 73 79 86 93 97
##
## lowest : 46 48 52 53 54, highest: 117 118 120 124 127
## --------------------------------------------------------------------------------
## SYSTH
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 1498 132 1 143.1 24.78 111
## .10 .25 .50 .75 .90 .95
## 117 127 140 157 173 183
##
## lowest : 79 88 91 93 94, highest: 222 223 228 242 244
## --------------------------------------------------------------------------------
## DIASTH
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 1499 77 0.999 82.13 12.95 64
## .10 .25 .50 .75 .90 .95
## 68 74 81 90 97 102
##
## lowest : 45 49 50 52 53, highest: 123 125 126 130 136
## --------------------------------------------------------------------------------
## LENGTH
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 1 42 0.999 1.74 0.09862 1.59
## .10 .25 .50 .75 .90 .95
## 1.62 1.68 1.75 1.80 1.85 1.88
##
## lowest : 1.53 1.54 1.55 1.56 1.57, highest: 1.9 1.91 1.92 1.93 1.94
## --------------------------------------------------------------------------------
## WEIGHT
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 2 75 0.999 80.99 15.41 59
## .10 .25 .50 .75 .90 .95
## 64 72 80 89 99 104
##
## lowest : 50 51 52 53 54, highest: 120 121 122 123 124
## --------------------------------------------------------------------------------
## BMI
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 3 995 1 26.69 4.258 20.96
## .10 .25 .50 .75 .90 .95
## 22.16 24.11 26.30 28.73 31.86 33.90
##
## lowest : 18.7 18.71 18.73 18.78 18.81, highest: 39.25 39.43 39.45 39.64 39.8
## --------------------------------------------------------------------------------
## CHOL
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 18 65 0.999 5.191 1.283 3.5
## .10 .25 .50 .75 .90 .95
## 3.8 4.4 5.1 5.9 6.7 7.2
##
## lowest : 2.8 2.9 3 3.1 3.2, highest: 8.8 8.9 9.1 9.2 9.4
## --------------------------------------------------------------------------------
## HDL
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 30 188 1 1.23 0.4031 0.74
## .10 .25 .50 .75 .90 .95
## 0.82 0.96 1.17 1.42 1.73 1.94
##
## lowest : 0.58 0.59 0.6 0.61 0.62, highest: 2.46 2.47 2.48 2.49 2.51
## --------------------------------------------------------------------------------
## LDL
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 216 478 1 3.129 1.186 1.52
## .10 .25 .50 .75 .90 .95
## 1.82 2.37 3.05 3.83 4.55 4.97
##
## lowest : 1.1 1.11 1.12 1.14 1.15, highest: 6.34 6.37 6.41 6.47 6.6
## --------------------------------------------------------------------------------
## TRIG
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 28 461 1 1.852 1.093 0.760
## .10 .25 .50 .75 .90 .95
## 0.880 1.120 1.530 2.230 3.120 3.904
##
## lowest : 0.56 0.57 0.58 0.59 0.6 , highest: 8.28 8.61 8.68 8.91 8.96
## --------------------------------------------------------------------------------
## HOMOC
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 463 255 1 14.1 5.525 8.00
## .10 .25 .50 .75 .90 .95
## 8.80 10.50 12.90 16.00 20.48 24.60
##
## lowest : 6.1 6.2 6.3 6.4 6.5 , highest: 35.5 35.9 36.1 37.1 38.3
## --------------------------------------------------------------------------------
## GLUT
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 19 125 0.998 6.335 1.704 4.8
## .10 .25 .50 .75 .90 .95
## 5.0 5.3 5.7 6.5 8.4 10.4
##
## lowest : 4.3 4.4 4.5 4.6 4.7 , highest: 17.6 17.7 17.9 18 18.7
## --------------------------------------------------------------------------------
## CREAT
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 17 194 1 98.34 34.54 65.0
## .10 .25 .50 .75 .90 .95
## 69.2 78.0 89.0 101.0 118.0 138.0
##
## lowest : 54 55 56 57 58, highest: 784 799 809 813 825
## --------------------------------------------------------------------------------
## IMT
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 98 99 0.999 0.9359 0.2887 0.60
## .10 .25 .50 .75 .90 .95
## 0.65 0.75 0.88 1.07 1.30 1.47
##
## lowest : 0.47 0.48 0.5 0.52 0.53, highest: 1.77 1.78 1.8 1.82 1.83
## --------------------------------------------------------------------------------
## albumin
## n missing imputed distinct
## 3873 0 207 3
##
## Value 1 2 3
## Frequency 3040 695 138
## Proportion 0.785 0.179 0.036
## --------------------------------------------------------------------------------
## SMOKING
## n missing imputed distinct
## 3873 0 25 3
##
## Value 1 2 3
## Frequency 696 2731 446
## Proportion 0.180 0.705 0.115
## --------------------------------------------------------------------------------
## packyrs
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 21 263 0.994 22.7 22.32 0.0
## .10 .25 .50 .75 .90 .95
## 0.0 5.9 19.5 34.2 51.3 62.0
##
## lowest : 0 0.3 0.6 0.7 0.8, highest: 100 102 104 110 120
## --------------------------------------------------------------------------------
## alcohol
## n missing imputed distinct
## 3873 0 25 3
##
## Value 1 2 3
## Frequency 754 408 2711
## Proportion 0.195 0.105 0.700
## --------------------------------------------------------------------------------
## SUMSCORE_5LEVELS
## n missing distinct Info Mean Gmd
## 3873 0 5 0.532 1.311 0.511
##
## Value 1 2 3 4 5
## Frequency 2999 605 211 53 5
## Proportion 0.774 0.156 0.054 0.014 0.001
##
## For the frequency table, variable is rounded to the nearest 0
## --------------------------------------------------------------------------------describe(SMART.AREGIMPUTED_3)## SMART.AREGIMPUTED_3
##
## 30 Variables 3873 Observations
## --------------------------------------------------------------------------------
## TEVENT
## n missing distinct Info Mean Gmd .05 .10
## 3873 0 1934 1 1370 1078 98.6 197.0
## .25 .50 .75 .90 .95
## 555.0 1213.0 2165.0 2762.4 3017.4
##
## lowest : 0.1 1 2 3 4 , highest: 3451 3452 3463 3465 3466
## --------------------------------------------------------------------------------
## EVENT
## n missing distinct
## 3873 0 2
##
## Value 0 1
## Frequency 3413 460
## Proportion 0.881 0.119
## --------------------------------------------------------------------------------
## SEX
## n missing distinct
## 3873 0 2
##
## Value 1 2
## Frequency 2897 976
## Proportion 0.748 0.252
## --------------------------------------------------------------------------------
## AGE
## n missing distinct Info Mean Gmd .05 .10
## 3873 0 62 0.999 59.56 11.94 41 46
## .25 .50 .75 .90 .95
## 52 60 68 73 76
##
## lowest : 19 20 23 24 25, highest: 78 79 80 81 82
## --------------------------------------------------------------------------------
## DIABETES
## n missing imputed distinct
## 3873 0 40 2
##
## Value 0 1
## Frequency 3024 849
## Proportion 0.781 0.219
## --------------------------------------------------------------------------------
## CEREBRAL
## n missing distinct Info Sum Mean Gmd
## 3873 0 2 0.625 1147 0.2962 0.417
##
## --------------------------------------------------------------------------------
## CARDIAC
## n missing distinct Info Sum Mean Gmd
## 3873 0 2 0.74 2160 0.5577 0.4935
##
## --------------------------------------------------------------------------------
## AAA
## n missing distinct Info Sum Mean Gmd
## 3873 0 2 0.288 416 0.1074 0.1918
##
## --------------------------------------------------------------------------------
## PERIPH
## n missing distinct Info Sum Mean Gmd
## 3873 0 2 0.551 940 0.2427 0.3677
##
## --------------------------------------------------------------------------------
## STENOSIS
## n missing imputed distinct
## 3873 0 93 2
##
## Value 0 1
## Frequency 3136 737
## Proportion 0.81 0.19
## --------------------------------------------------------------------------------
## SYSTBP
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 1223 114 1 140.7 22.07 112
## .10 .25 .50 .75 .90 .95
## 117 126 139 153 167 177
##
## lowest : 96 97 98 99 100, highest: 206 209 211 212 216
## --------------------------------------------------------------------------------
## DIASTBP
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 1221 70 0.999 79.71 10.75 65
## .10 .25 .50 .75 .90 .95
## 68 73 79 86 92 97
##
## lowest : 46 48 52 53 54, highest: 117 118 120 124 127
## --------------------------------------------------------------------------------
## SYSTH
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 1498 132 1 143 24.67 111
## .10 .25 .50 .75 .90 .95
## 117 127 141 156 172 182
##
## lowest : 79 88 91 93 94, highest: 222 223 228 242 244
## --------------------------------------------------------------------------------
## DIASTH
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 1499 77 0.999 82.15 13 64
## .10 .25 .50 .75 .90 .95
## 68 74 81 90 97 102
##
## lowest : 45 49 50 52 53, highest: 123 125 126 130 136
## --------------------------------------------------------------------------------
## LENGTH
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 1 42 0.999 1.74 0.09862 1.59
## .10 .25 .50 .75 .90 .95
## 1.62 1.68 1.75 1.80 1.85 1.88
##
## lowest : 1.53 1.54 1.55 1.56 1.57, highest: 1.9 1.91 1.92 1.93 1.94
## --------------------------------------------------------------------------------
## WEIGHT
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 2 75 0.999 80.99 15.41 59
## .10 .25 .50 .75 .90 .95
## 64 72 80 89 99 104
##
## lowest : 50 51 52 53 54, highest: 120 121 122 123 124
## --------------------------------------------------------------------------------
## BMI
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 3 995 1 26.69 4.257 20.96
## .10 .25 .50 .75 .90 .95
## 22.16 24.11 26.30 28.73 31.86 33.90
##
## lowest : 18.7 18.71 18.73 18.78 18.81, highest: 39.25 39.43 39.45 39.64 39.8
## --------------------------------------------------------------------------------
## CHOL
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 18 65 0.999 5.191 1.283 3.5
## .10 .25 .50 .75 .90 .95
## 3.8 4.4 5.1 5.9 6.7 7.2
##
## lowest : 2.8 2.9 3 3.1 3.2, highest: 8.8 8.9 9.1 9.2 9.4
## --------------------------------------------------------------------------------
## HDL
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 30 188 1 1.23 0.4028 0.74
## .10 .25 .50 .75 .90 .95
## 0.82 0.96 1.17 1.42 1.73 1.94
##
## lowest : 0.58 0.59 0.6 0.61 0.62, highest: 2.46 2.47 2.48 2.49 2.51
## --------------------------------------------------------------------------------
## LDL
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 216 478 1 3.128 1.186 1.520
## .10 .25 .50 .75 .90 .95
## 1.820 2.370 3.050 3.830 4.550 4.984
##
## lowest : 1.1 1.11 1.12 1.14 1.15, highest: 6.34 6.37 6.41 6.47 6.6
## --------------------------------------------------------------------------------
## TRIG
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 28 461 1 1.853 1.093 0.760
## .10 .25 .50 .75 .90 .95
## 0.880 1.130 1.540 2.230 3.120 3.914
##
## lowest : 0.56 0.57 0.58 0.59 0.6 , highest: 8.28 8.61 8.68 8.91 8.96
## --------------------------------------------------------------------------------
## HOMOC
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 463 255 1 14.12 5.548 8.00
## .10 .25 .50 .75 .90 .95
## 8.80 10.50 13.00 16.00 20.50 24.64
##
## lowest : 6.1 6.2 6.3 6.4 6.5 , highest: 35.5 35.9 36.1 37.1 38.3
## --------------------------------------------------------------------------------
## GLUT
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 19 125 0.998 6.33 1.698 4.8
## .10 .25 .50 .75 .90 .95
## 5.0 5.3 5.7 6.5 8.4 10.4
##
## lowest : 4.3 4.4 4.5 4.6 4.7 , highest: 17.6 17.7 17.9 18 18.7
## --------------------------------------------------------------------------------
## CREAT
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 17 194 1 98.34 34.56 64
## .10 .25 .50 .75 .90 .95
## 69 78 89 101 118 138
##
## lowest : 54 55 56 57 58, highest: 784 799 809 813 825
## --------------------------------------------------------------------------------
## IMT
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 98 99 0.999 0.9368 0.2895 0.60
## .10 .25 .50 .75 .90 .95
## 0.65 0.75 0.88 1.07 1.30 1.47
##
## lowest : 0.47 0.48 0.5 0.52 0.53, highest: 1.77 1.78 1.8 1.82 1.83
## --------------------------------------------------------------------------------
## albumin
## n missing imputed distinct
## 3873 0 207 3
##
## Value 1 2 3
## Frequency 3040 696 137
## Proportion 0.785 0.180 0.035
## --------------------------------------------------------------------------------
## SMOKING
## n missing imputed distinct
## 3873 0 25 3
##
## Value 1 2 3
## Frequency 695 2731 447
## Proportion 0.179 0.705 0.115
## --------------------------------------------------------------------------------
## packyrs
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 21 263 0.994 22.62 22.24 0.0
## .10 .25 .50 .75 .90 .95
## 0.0 5.9 19.5 34.2 50.4 62.0
##
## lowest : 0 0.3 0.6 0.7 0.8, highest: 100 102 104 110 120
## --------------------------------------------------------------------------------
## alcohol
## n missing imputed distinct
## 3873 0 25 3
##
## Value 1 2 3
## Frequency 759 410 2704
## Proportion 0.196 0.106 0.698
## --------------------------------------------------------------------------------
## SUMSCORE_5LEVELS
## n missing distinct Info Mean Gmd
## 3873 0 5 0.532 1.311 0.511
##
## Value 1 2 3 4 5
## Frequency 2999 605 211 53 5
## Proportion 0.774 0.156 0.054 0.014 0.001
##
## For the frequency table, variable is rounded to the nearest 0
## --------------------------------------------------------------------------------describe(SMART.AREGIMPUTED_4)## SMART.AREGIMPUTED_4
##
## 30 Variables 3873 Observations
## --------------------------------------------------------------------------------
## TEVENT
## n missing distinct Info Mean Gmd .05 .10
## 3873 0 1934 1 1370 1078 98.6 197.0
## .25 .50 .75 .90 .95
## 555.0 1213.0 2165.0 2762.4 3017.4
##
## lowest : 0.1 1 2 3 4 , highest: 3451 3452 3463 3465 3466
## --------------------------------------------------------------------------------
## EVENT
## n missing distinct
## 3873 0 2
##
## Value 0 1
## Frequency 3413 460
## Proportion 0.881 0.119
## --------------------------------------------------------------------------------
## SEX
## n missing distinct
## 3873 0 2
##
## Value 1 2
## Frequency 2897 976
## Proportion 0.748 0.252
## --------------------------------------------------------------------------------
## AGE
## n missing distinct Info Mean Gmd .05 .10
## 3873 0 62 0.999 59.56 11.94 41 46
## .25 .50 .75 .90 .95
## 52 60 68 73 76
##
## lowest : 19 20 23 24 25, highest: 78 79 80 81 82
## --------------------------------------------------------------------------------
## DIABETES
## n missing imputed distinct
## 3873 0 40 2
##
## Value 0 1
## Frequency 3022 851
## Proportion 0.78 0.22
## --------------------------------------------------------------------------------
## CEREBRAL
## n missing distinct Info Sum Mean Gmd
## 3873 0 2 0.625 1147 0.2962 0.417
##
## --------------------------------------------------------------------------------
## CARDIAC
## n missing distinct Info Sum Mean Gmd
## 3873 0 2 0.74 2160 0.5577 0.4935
##
## --------------------------------------------------------------------------------
## AAA
## n missing distinct Info Sum Mean Gmd
## 3873 0 2 0.288 416 0.1074 0.1918
##
## --------------------------------------------------------------------------------
## PERIPH
## n missing distinct Info Sum Mean Gmd
## 3873 0 2 0.551 940 0.2427 0.3677
##
## --------------------------------------------------------------------------------
## STENOSIS
## n missing imputed distinct
## 3873 0 93 2
##
## Value 0 1
## Frequency 3135 738
## Proportion 0.809 0.191
## --------------------------------------------------------------------------------
## SYSTBP
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 1223 114 1 140.4 21.93 112.0
## .10 .25 .50 .75 .90 .95
## 117.0 126.0 138.0 152.0 167.0 176.4
##
## lowest : 96 97 98 99 100, highest: 206 209 211 212 216
## --------------------------------------------------------------------------------
## DIASTBP
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 1221 70 0.999 79.66 10.82 65
## .10 .25 .50 .75 .90 .95
## 68 73 79 86 92 97
##
## lowest : 46 48 52 53 54, highest: 117 118 120 124 127
## --------------------------------------------------------------------------------
## SYSTH
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 1498 132 1 143.2 24.87 111
## .10 .25 .50 .75 .90 .95
## 117 127 141 157 173 183
##
## lowest : 79 88 91 93 94, highest: 222 223 228 242 244
## --------------------------------------------------------------------------------
## DIASTH
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 1499 77 0.999 82.17 13.01 64
## .10 .25 .50 .75 .90 .95
## 68 74 81 90 97 102
##
## lowest : 45 49 50 52 53, highest: 123 125 126 130 136
## --------------------------------------------------------------------------------
## LENGTH
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 1 42 0.999 1.74 0.09862 1.59
## .10 .25 .50 .75 .90 .95
## 1.62 1.68 1.75 1.80 1.85 1.88
##
## lowest : 1.53 1.54 1.55 1.56 1.57, highest: 1.9 1.91 1.92 1.93 1.94
## --------------------------------------------------------------------------------
## WEIGHT
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 2 75 0.999 80.99 15.41 59
## .10 .25 .50 .75 .90 .95
## 64 72 80 89 99 104
##
## lowest : 50 51 52 53 54, highest: 120 121 122 123 124
## --------------------------------------------------------------------------------
## BMI
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 3 995 1 26.69 4.257 20.96
## .10 .25 .50 .75 .90 .95
## 22.17 24.11 26.30 28.73 31.86 33.90
##
## lowest : 18.7 18.71 18.73 18.78 18.81, highest: 39.25 39.43 39.45 39.64 39.8
## --------------------------------------------------------------------------------
## CHOL
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 18 65 0.999 5.191 1.283 3.5
## .10 .25 .50 .75 .90 .95
## 3.8 4.4 5.1 5.9 6.7 7.2
##
## lowest : 2.8 2.9 3 3.1 3.2, highest: 8.8 8.9 9.1 9.2 9.4
## --------------------------------------------------------------------------------
## HDL
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 30 188 1 1.23 0.4029 0.74
## .10 .25 .50 .75 .90 .95
## 0.82 0.96 1.17 1.42 1.73 1.94
##
## lowest : 0.58 0.59 0.6 0.61 0.62, highest: 2.46 2.47 2.48 2.49 2.51
## --------------------------------------------------------------------------------
## LDL
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 216 478 1 3.128 1.187 1.51
## .10 .25 .50 .75 .90 .95
## 1.82 2.37 3.05 3.83 4.55 4.98
##
## lowest : 1.1 1.11 1.12 1.14 1.15, highest: 6.34 6.37 6.41 6.47 6.6
## --------------------------------------------------------------------------------
## TRIG
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 28 461 1 1.853 1.093 0.760
## .10 .25 .50 .75 .90 .95
## 0.880 1.130 1.540 2.230 3.120 3.914
##
## lowest : 0.56 0.57 0.58 0.59 0.6 , highest: 8.28 8.61 8.68 8.91 8.96
## --------------------------------------------------------------------------------
## HOMOC
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 463 255 1 14.07 5.533 8.0
## .10 .25 .50 .75 .90 .95
## 8.8 10.5 12.9 16.0 20.4 24.8
##
## lowest : 6.1 6.2 6.3 6.4 6.5 , highest: 35.5 35.9 36.1 37.1 38.3
## --------------------------------------------------------------------------------
## GLUT
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 19 125 0.998 6.333 1.702 4.8
## .10 .25 .50 .75 .90 .95
## 5.0 5.3 5.7 6.5 8.4 10.4
##
## lowest : 4.3 4.4 4.5 4.6 4.7 , highest: 17.6 17.7 17.9 18 18.7
## --------------------------------------------------------------------------------
## CREAT
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 17 194 1 98.4 34.6 65.0
## .10 .25 .50 .75 .90 .95
## 69.2 78.0 89.0 101.0 118.0 138.4
##
## lowest : 54 55 56 57 58, highest: 784 799 809 813 825
## --------------------------------------------------------------------------------
## IMT
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 98 99 0.999 0.9366 0.2889 0.60
## .10 .25 .50 .75 .90 .95
## 0.65 0.75 0.88 1.07 1.30 1.47
##
## lowest : 0.47 0.48 0.5 0.52 0.53, highest: 1.77 1.78 1.8 1.82 1.83
## --------------------------------------------------------------------------------
## albumin
## n missing imputed distinct
## 3873 0 207 3
##
## Value 1 2 3
## Frequency 3046 689 138
## Proportion 0.786 0.178 0.036
## --------------------------------------------------------------------------------
## SMOKING
## n missing imputed distinct
## 3873 0 25 3
##
## Value 1 2 3
## Frequency 696 2731 446
## Proportion 0.180 0.705 0.115
## --------------------------------------------------------------------------------
## packyrs
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 21 263 0.994 22.64 22.26 0.00
## .10 .25 .50 .75 .90 .95
## 0.00 5.90 19.50 34.20 51.12 62.00
##
## lowest : 0 0.3 0.6 0.7 0.8, highest: 100 102 104 110 120
## --------------------------------------------------------------------------------
## alcohol
## n missing imputed distinct
## 3873 0 25 3
##
## Value 1 2 3
## Frequency 755 411 2707
## Proportion 0.195 0.106 0.699
## --------------------------------------------------------------------------------
## SUMSCORE_5LEVELS
## n missing distinct Info Mean Gmd
## 3873 0 5 0.532 1.311 0.511
##
## Value 1 2 3 4 5
## Frequency 2999 605 211 53 5
## Proportion 0.774 0.156 0.054 0.014 0.001
##
## For the frequency table, variable is rounded to the nearest 0
## --------------------------------------------------------------------------------describe(SMART.AREGIMPUTED_5)## SMART.AREGIMPUTED_5
##
## 30 Variables 3873 Observations
## --------------------------------------------------------------------------------
## TEVENT
## n missing distinct Info Mean Gmd .05 .10
## 3873 0 1934 1 1370 1078 98.6 197.0
## .25 .50 .75 .90 .95
## 555.0 1213.0 2165.0 2762.4 3017.4
##
## lowest : 0.1 1 2 3 4 , highest: 3451 3452 3463 3465 3466
## --------------------------------------------------------------------------------
## EVENT
## n missing distinct
## 3873 0 2
##
## Value 0 1
## Frequency 3413 460
## Proportion 0.881 0.119
## --------------------------------------------------------------------------------
## SEX
## n missing distinct
## 3873 0 2
##
## Value 1 2
## Frequency 2897 976
## Proportion 0.748 0.252
## --------------------------------------------------------------------------------
## AGE
## n missing distinct Info Mean Gmd .05 .10
## 3873 0 62 0.999 59.56 11.94 41 46
## .25 .50 .75 .90 .95
## 52 60 68 73 76
##
## lowest : 19 20 23 24 25, highest: 78 79 80 81 82
## --------------------------------------------------------------------------------
## DIABETES
## n missing imputed distinct
## 3873 0 40 2
##
## Value 0 1
## Frequency 3023 850
## Proportion 0.781 0.219
## --------------------------------------------------------------------------------
## CEREBRAL
## n missing distinct Info Sum Mean Gmd
## 3873 0 2 0.625 1147 0.2962 0.417
##
## --------------------------------------------------------------------------------
## CARDIAC
## n missing distinct Info Sum Mean Gmd
## 3873 0 2 0.74 2160 0.5577 0.4935
##
## --------------------------------------------------------------------------------
## AAA
## n missing distinct Info Sum Mean Gmd
## 3873 0 2 0.288 416 0.1074 0.1918
##
## --------------------------------------------------------------------------------
## PERIPH
## n missing distinct Info Sum Mean Gmd
## 3873 0 2 0.551 940 0.2427 0.3677
##
## --------------------------------------------------------------------------------
## STENOSIS
## n missing imputed distinct
## 3873 0 93 2
##
## Value 0 1
## Frequency 3127 746
## Proportion 0.807 0.193
## --------------------------------------------------------------------------------
## SYSTBP
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 1223 114 1 140.3 21.97 112
## .10 .25 .50 .75 .90 .95
## 116 126 138 152 167 176
##
## lowest : 96 97 98 99 100, highest: 206 209 211 212 216
## --------------------------------------------------------------------------------
## DIASTBP
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 1221 70 0.999 79.78 10.93 65
## .10 .25 .50 .75 .90 .95
## 68 73 79 86 93 97
##
## lowest : 46 48 52 53 54, highest: 117 118 120 124 127
## --------------------------------------------------------------------------------
## SYSTH
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 1498 132 1 142.9 24.88 110
## .10 .25 .50 .75 .90 .95
## 117 127 140 156 172 183
##
## lowest : 79 88 91 93 94, highest: 222 223 228 242 244
## --------------------------------------------------------------------------------
## DIASTH
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 1499 77 0.999 82.12 12.93 64
## .10 .25 .50 .75 .90 .95
## 68 74 81 89 97 102
##
## lowest : 45 49 50 52 53, highest: 123 125 126 130 136
## --------------------------------------------------------------------------------
## LENGTH
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 1 42 0.999 1.74 0.09862 1.59
## .10 .25 .50 .75 .90 .95
## 1.62 1.68 1.75 1.80 1.85 1.88
##
## lowest : 1.53 1.54 1.55 1.56 1.57, highest: 1.9 1.91 1.92 1.93 1.94
## --------------------------------------------------------------------------------
## WEIGHT
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 2 75 0.999 81 15.41 59
## .10 .25 .50 .75 .90 .95
## 64 72 80 89 99 104
##
## lowest : 50 51 52 53 54, highest: 120 121 122 123 124
## --------------------------------------------------------------------------------
## BMI
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 3 995 1 26.69 4.257 20.96
## .10 .25 .50 .75 .90 .95
## 22.17 24.11 26.30 28.73 31.86 33.90
##
## lowest : 18.7 18.71 18.73 18.78 18.81, highest: 39.25 39.43 39.45 39.64 39.8
## --------------------------------------------------------------------------------
## CHOL
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 18 65 0.999 5.191 1.283 3.5
## .10 .25 .50 .75 .90 .95
## 3.8 4.4 5.1 5.9 6.7 7.2
##
## lowest : 2.8 2.9 3 3.1 3.2, highest: 8.8 8.9 9.1 9.2 9.4
## --------------------------------------------------------------------------------
## HDL
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 30 188 1 1.229 0.4026 0.74
## .10 .25 .50 .75 .90 .95
## 0.82 0.96 1.17 1.42 1.73 1.94
##
## lowest : 0.58 0.59 0.6 0.61 0.62, highest: 2.46 2.47 2.48 2.49 2.51
## --------------------------------------------------------------------------------
## LDL
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 216 478 1 3.129 1.185 1.52
## .10 .25 .50 .75 .90 .95
## 1.82 2.37 3.05 3.83 4.55 4.98
##
## lowest : 1.1 1.11 1.12 1.14 1.15, highest: 6.34 6.37 6.41 6.47 6.6
## --------------------------------------------------------------------------------
## TRIG
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 28 461 1 1.853 1.092 0.760
## .10 .25 .50 .75 .90 .95
## 0.880 1.130 1.540 2.230 3.120 3.914
##
## lowest : 0.56 0.57 0.58 0.59 0.6 , highest: 8.28 8.61 8.68 8.91 8.96
## --------------------------------------------------------------------------------
## HOMOC
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 463 255 1 14.19 5.641 8.0
## .10 .25 .50 .75 .90 .95
## 8.8 10.5 13.0 16.1 20.7 25.5
##
## lowest : 6.1 6.2 6.3 6.4 6.5 , highest: 35.5 35.9 36.1 37.1 38.3
## --------------------------------------------------------------------------------
## GLUT
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 19 125 0.998 6.334 1.701 4.80
## .10 .25 .50 .75 .90 .95
## 5.00 5.30 5.70 6.50 8.48 10.40
##
## lowest : 4.3 4.4 4.5 4.6 4.7 , highest: 17.6 17.7 17.9 18 18.7
## --------------------------------------------------------------------------------
## CREAT
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 17 194 1 98.38 34.6 64.0
## .10 .25 .50 .75 .90 .95
## 69.0 78.0 89.0 101.0 118.0 138.4
##
## lowest : 54 55 56 57 58, highest: 784 799 809 813 825
## --------------------------------------------------------------------------------
## IMT
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 98 99 0.999 0.9361 0.2889 0.60
## .10 .25 .50 .75 .90 .95
## 0.65 0.75 0.88 1.07 1.30 1.47
##
## lowest : 0.47 0.48 0.5 0.52 0.53, highest: 1.77 1.78 1.8 1.82 1.83
## --------------------------------------------------------------------------------
## albumin
## n missing imputed distinct
## 3873 0 207 3
##
## Value 1 2 3
## Frequency 3040 692 141
## Proportion 0.785 0.179 0.036
## --------------------------------------------------------------------------------
## SMOKING
## n missing imputed distinct
## 3873 0 25 3
##
## Value 1 2 3
## Frequency 694 2730 449
## Proportion 0.179 0.705 0.116
## --------------------------------------------------------------------------------
## packyrs
## n missing imputed distinct Info Mean Gmd .05
## 3873 0 21 263 0.994 22.65 22.28 0.00
## .10 .25 .50 .75 .90 .95
## 0.00 5.90 19.50 34.20 51.12 62.00
##
## lowest : 0 0.3 0.6 0.7 0.8, highest: 100 102 104 110 120
## --------------------------------------------------------------------------------
## alcohol
## n missing imputed distinct
## 3873 0 25 3
##
## Value 1 2 3
## Frequency 757 411 2705
## Proportion 0.195 0.106 0.698
## --------------------------------------------------------------------------------
## SUMSCORE_5LEVELS
## n missing distinct Info Mean Gmd
## 3873 0 5 0.532 1.311 0.511
##
## Value 1 2 3 4 5
## Frequency 2999 605 211 53 5
## Proportion 0.774 0.156 0.054 0.014 0.001
##
## For the frequency table, variable is rounded to the nearest 0
## --------------------------------------------------------------------------------##################################
# Formulating the FULL
# Cox Proportional Hazards Model
# Using the combined complete and
# 1ST imputation results from AREG
##################################
SMART.AREGIMPUTED_1$EVENT <- as.numeric(SMART.AREGIMPUTED_1$EVENT)
SMART.AREGIMPUTED_1$SMOKING <- as.factor(SMART.AREGIMPUTED_1$SMOKING)
SMART.AREGIMPUTED_1$alcohol <- as.factor(SMART.AREGIMPUTED_1$alcohol)
SMART.AREGIMPUTED_1$albumin <- as.factor(SMART.AREGIMPUTED_1$albumin)
dd <- datadist(SMART.AREGIMPUTED_1)
options(datadist="dd")
##################################
# FULL COMPLETE
##################################
COXPH.FULL.COMPLETE.AREGIMPUTED_1 <-cph(Surv(TEVENT,EVENT) ~ ifelse(AGE>50, (AGE-50)^2,0) +
SEX +
SMOKING +
alcohol +
BMI +
SYSTH +
SYSTBP +
DIASTH +
DIASTBP +
WEIGHT +
LENGTH +
CHOL +
LDL +
HDL+
DIABETES +
SUMSCORE_5LEVELS +
HOMOC +
log(CREAT) +
albumin +
STENOSIS +
IMT +
TRIG +
GLUT +
packyrs,
data = SMART.AREGIMPUTED_1,
x=T,
y=T,
surv=T)
anova(COXPH.FULL.COMPLETE.AREGIMPUTED_1)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## AGE 36.78 1 <.0001
## SEX 0.88 1 0.3477
## SMOKING 0.13 2 0.9381
## alcohol 1.83 2 0.4004
## BMI 0.70 1 0.4029
## SYSTH 0.27 1 0.6059
## SYSTBP 0.01 1 0.9269
## DIASTH 2.02 1 0.1556
## DIASTBP 0.18 1 0.6745
## WEIGHT 1.28 1 0.2575
## LENGTH 0.64 1 0.4242
## CHOL 0.14 1 0.7100
## LDL 0.19 1 0.6664
## HDL 0.00 1 0.9978
## DIABETES 0.17 1 0.6790
## SUMSCORE_5LEVELS 34.66 1 <.0001
## HOMOC 0.01 1 0.9157
## CREAT 18.21 1 <.0001
## albumin 9.55 2 0.0084
## STENOSIS 2.29 1 0.1302
## IMT 9.33 1 0.0023
## TRIG 0.14 1 0.7067
## GLUT 2.83 1 0.0922
## packyrs 5.29 1 0.0214
## TOTAL 328.92 27 <.0001summary(COXPH.FULL.COMPLETE.AREGIMPUTED_1)## Effects Response : Surv(TEVENT, EVENT)
##
## Factor Low High Diff. Effect S.E. Lower 0.95 Upper 0.95
## AGE 52.00 68.00 16.00 0.4359300 0.071877 0.2950500 0.576800
## Hazard Ratio 52.00 68.00 16.00 1.5464000 NA 1.3432000 1.780300
## BMI 24.11 28.73 4.62 0.4127800 0.493520 -0.5545000 1.380100
## Hazard Ratio 24.11 28.73 4.62 1.5110000 NA 0.5743600 3.975100
## SYSTH 127.00 157.00 30.00 -0.0614390 0.119090 -0.2948400 0.171960
## Hazard Ratio 127.00 157.00 30.00 0.9404100 NA 0.7446500 1.187600
## SYSTBP 126.00 153.00 27.00 -0.0105570 0.115110 -0.2361700 0.215050
## Hazard Ratio 126.00 153.00 27.00 0.9895000 NA 0.7896500 1.239900
## DIASTH 74.00 89.00 15.00 0.1512000 0.106460 -0.0574710 0.359860
## Hazard Ratio 74.00 89.00 15.00 1.1632000 NA 0.9441500 1.433100
## DIASTBP 73.00 86.00 13.00 -0.0410810 0.097805 -0.2327800 0.150610
## Hazard Ratio 73.00 86.00 13.00 0.9597500 NA 0.7923300 1.162500
## WEIGHT 72.00 89.00 17.00 -0.6868900 0.606660 -1.8759000 0.502160
## Hazard Ratio 72.00 89.00 17.00 0.5031400 NA 0.1532100 1.652300
## LENGTH 1.68 1.80 0.12 0.3213700 0.402110 -0.4667600 1.109500
## Hazard Ratio 1.68 1.80 0.12 1.3790000 NA 0.6270300 3.032800
## CHOL 4.40 5.90 1.50 -0.5446400 1.464600 -3.4152000 2.325900
## Hazard Ratio 4.40 5.90 1.50 0.5800500 NA 0.0328700 10.236000
## LDL 2.37 3.83 1.46 0.6199000 1.438000 -2.1985000 3.438300
## Hazard Ratio 2.37 3.83 1.46 1.8587000 NA 0.1109600 31.135000
## HDL 0.96 1.42 0.46 -0.0012456 0.455170 -0.8933600 0.890870
## Hazard Ratio 0.96 1.42 0.46 0.9987600 NA 0.4092800 2.437300
## SUMSCORE_5LEVELS 1.00 5.00 4.00 1.3307000 0.226020 0.8876800 1.773700
## Hazard Ratio 1.00 5.00 4.00 3.7836000 NA 2.4295000 5.892400
## HOMOC 10.50 16.20 5.70 -0.0052107 0.049239 -0.1017200 0.091297
## Hazard Ratio 10.50 16.20 5.70 0.9948000 NA 0.9032800 1.095600
## CREAT 78.00 101.00 23.00 0.1653600 0.038752 0.0894030 0.241310
## Hazard Ratio 78.00 101.00 23.00 1.1798000 NA 1.0935000 1.272900
## IMT 0.75 1.07 0.32 0.1772100 0.058007 0.0635150 0.290900
## Hazard Ratio 0.75 1.07 0.32 1.1939000 NA 1.0656000 1.337600
## TRIG 1.12 2.23 1.11 0.1800500 0.478510 -0.7578200 1.117900
## Hazard Ratio 1.12 2.23 1.11 1.1973000 NA 0.4686900 3.058500
## GLUT 5.30 6.50 1.20 0.0593030 0.035222 -0.0097303 0.128340
## Hazard Ratio 5.30 6.50 1.20 1.0611000 NA 0.9903200 1.136900
## packyrs 5.90 34.20 28.30 0.1585500 0.068926 0.0234600 0.293650
## Hazard Ratio 5.90 34.20 28.30 1.1718000 NA 1.0237000 1.341300
## SEX - 2:1 1.00 2.00 NA -0.1524500 0.162350 -0.4706500 0.165750
## Hazard Ratio 1.00 2.00 NA 0.8586000 NA 0.6246000 1.180300
## SMOKING - 1:2 2.00 1.00 NA -0.0262960 0.161320 -0.3424800 0.289890
## Hazard Ratio 2.00 1.00 NA 0.9740500 NA 0.7100000 1.336300
## SMOKING - 3:2 2.00 3.00 NA 0.0602720 0.201840 -0.3353300 0.455880
## Hazard Ratio 2.00 3.00 NA 1.0621000 NA 0.7151000 1.577600
## alcohol - 1:3 3.00 1.00 NA 0.1474700 0.121360 -0.0903840 0.385330
## Hazard Ratio 3.00 1.00 NA 1.1589000 NA 0.9135800 1.470100
## alcohol - 2:3 3.00 2.00 NA -0.0417340 0.148450 -0.3326900 0.249220
## Hazard Ratio 3.00 2.00 NA 0.9591200 NA 0.7169900 1.283000
## DIABETES - 1:0 1.00 2.00 NA 0.0645840 0.156090 -0.2413400 0.370510
## Hazard Ratio 1.00 2.00 NA 1.0667000 NA 0.7855700 1.448500
## albumin - 2:1 1.00 2.00 NA 0.2609800 0.117980 0.0297510 0.492210
## Hazard Ratio 1.00 2.00 NA 1.2982000 NA 1.0302000 1.635900
## albumin - 3:1 1.00 3.00 NA 0.5620000 0.208220 0.1538900 0.970110
## Hazard Ratio 1.00 3.00 NA 1.7542000 NA 1.1664000 2.638200
## STENOSIS - 1:0 1.00 2.00 NA 0.1637700 0.108210 -0.0483250 0.375870
## Hazard Ratio 1.00 2.00 NA 1.1779000 NA 0.9528200 1.456300vif(COXPH.FULL.COMPLETE.AREGIMPUTED_1)## AGE SEX=2 SMOKING=2 SMOKING=3
## 1.422223 1.839738 1.917030 1.535045
## alcohol=2 alcohol=3 BMI SYSTH
## 1.439301 1.576363 63.830100 3.778977
## SYSTBP DIASTH DIASTBP WEIGHT
## 3.466886 3.098436 2.731506 89.258836
## LENGTH CHOL LDL HDL
## 34.868141 499.517309 446.035588 46.254999
## DIABETES=1 SUMSCORE_5LEVELS HOMOC CREAT
## 2.268709 1.173653 1.521747 1.920921
## albumin=2 albumin=3 STENOSIS=1 IMT
## 1.194679 1.573030 1.206110 1.329620
## TRIG GLUT packyrs
## 117.623369 2.191857 1.355974COXPH.FULL.COMPLETE.AREGIMPUTED_1## Cox Proportional Hazards Model
##
## cph(formula = Surv(TEVENT, EVENT) ~ ifelse(AGE > 50, (AGE - 50)^2,
## 0) + SEX + SMOKING + alcohol + BMI + SYSTH + SYSTBP + DIASTH +
## DIASTBP + WEIGHT + LENGTH + CHOL + LDL + HDL + DIABETES +
## SUMSCORE_5LEVELS + HOMOC + log(CREAT) + albumin + STENOSIS +
## IMT + TRIG + GLUT + packyrs, data = SMART.AREGIMPUTED_1,
## x = T, y = T, surv = T)
##
## Model Tests Discrimination
## Indexes
## Obs 3873 LR chi2 291.65 R2 0.087
## Events 460 d.f. 27 R2(27,3873)0.066
## Center 8.2501 Pr(> chi2) 0.0000 R2(27,460)0.437
## Score chi2 362.97 Dxy 0.395
## Pr(> chi2) 0.0000
##
## Coef S.E. Wald Z Pr(>|Z|)
## AGE 0.0014 0.0002 6.06 <0.0001
## SEX=2 -0.1524 0.1623 -0.94 0.3477
## SMOKING=2 0.0263 0.1613 0.16 0.8705
## SMOKING=3 0.0866 0.2445 0.35 0.7232
## alcohol=2 -0.1892 0.1673 -1.13 0.2581
## alcohol=3 -0.1475 0.1214 -1.22 0.2243
## BMI 0.0893 0.1068 0.84 0.4029
## SYSTH -0.0020 0.0040 -0.52 0.6059
## SYSTBP -0.0004 0.0043 -0.09 0.9269
## DIASTH 0.0101 0.0071 1.42 0.1556
## DIASTBP -0.0032 0.0075 -0.42 0.6745
## WEIGHT -0.0404 0.0357 -1.13 0.2575
## LENGTH 2.6781 3.3509 0.80 0.4242
## CHOL -0.3631 0.9764 -0.37 0.7100
## LDL 0.4246 0.9849 0.43 0.6664
## HDL -0.0027 0.9895 0.00 0.9978
## DIABETES=1 0.0646 0.1561 0.41 0.6790
## SUMSCORE_5LEVELS 0.3327 0.0565 5.89 <0.0001
## HOMOC -0.0009 0.0086 -0.11 0.9157
## CREAT 0.6399 0.1500 4.27 <0.0001
## albumin=2 0.2610 0.1180 2.21 0.0270
## albumin=3 0.5620 0.2082 2.70 0.0070
## STENOSIS=1 0.1638 0.1082 1.51 0.1302
## IMT 0.5538 0.1813 3.05 0.0023
## TRIG 0.1622 0.4311 0.38 0.7067
## GLUT 0.0494 0.0294 1.68 0.0922
## packyrs 0.0056 0.0024 2.30 0.0214##################################
# FULL
# After removing variables which are:
# High multicollinearity contributors
# Non-standard risk factors
# Minimal predictors of survival outcome based from initial exploration
# Minimal predictors of survival outcome based from domain knowledge and literature
##################################
COXPH.FULL.AREGIMPUTED_1 <-cph(Surv(TEVENT,EVENT) ~ ifelse(AGE>50, (AGE-50)^2,0) +
SEX +
SMOKING +
alcohol +
BMI +
SYSTH +
HDL+
DIABETES +
SUMSCORE_5LEVELS +
HOMOC +
log(CREAT) +
albumin +
STENOSIS +
IMT,
data = SMART.AREGIMPUTED_1,
x=T,
y=T,
surv=T)
anova(COXPH.FULL.AREGIMPUTED_1)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## AGE 37.92 1 <.0001
## SEX 0.15 1 0.6941
## SMOKING 1.83 2 0.3998
## alcohol 1.31 2 0.5189
## BMI 3.06 1 0.0802
## SYSTH 0.24 1 0.6232
## HDL 5.61 1 0.0178
## DIABETES 3.62 1 0.0570
## SUMSCORE_5LEVELS 35.39 1 <.0001
## HOMOC 0.01 1 0.9047
## CREAT 16.77 1 <.0001
## albumin 9.89 2 0.0071
## STENOSIS 2.56 1 0.1099
## IMT 8.73 1 0.0031
## TOTAL 314.86 17 <.0001summary(COXPH.FULL.AREGIMPUTED_1)## Effects Response : Surv(TEVENT, EVENT)
##
## Factor Low High Diff. Effect S.E. Lower 0.95 Upper 0.95
## AGE 52.00 68.00 16.00 0.422220 0.068568 0.2878300 0.556610
## Hazard Ratio 52.00 68.00 16.00 1.525300 NA 1.3335000 1.744800
## BMI 24.11 28.73 4.62 -0.114360 0.065359 -0.2424600 0.013741
## Hazard Ratio 24.11 28.73 4.62 0.891940 NA 0.7846900 1.013800
## SYSTH 127.00 157.00 30.00 0.032049 0.065222 -0.0957840 0.159880
## Hazard Ratio 127.00 157.00 30.00 1.032600 NA 0.9086600 1.173400
## HDL 0.96 1.42 0.46 -0.173710 0.073314 -0.3174000 -0.030015
## Hazard Ratio 0.96 1.42 0.46 0.840540 NA 0.7280400 0.970430
## SUMSCORE_5LEVELS 1.00 5.00 4.00 1.327400 0.223150 0.8900700 1.764800
## Hazard Ratio 1.00 5.00 4.00 3.771400 NA 2.4353000 5.840500
## HOMOC 10.50 16.20 5.70 0.005793 0.048361 -0.0889930 0.100580
## Hazard Ratio 10.50 16.20 5.70 1.005800 NA 0.9148500 1.105800
## CREAT 78.00 101.00 23.00 0.155040 0.037857 0.0808410 0.229240
## Hazard Ratio 78.00 101.00 23.00 1.167700 NA 1.0842000 1.257600
## IMT 0.75 1.07 0.32 0.168820 0.057133 0.0568450 0.280800
## Hazard Ratio 0.75 1.07 0.32 1.183900 NA 1.0585000 1.324200
## SEX - 2:1 1.00 2.00 NA -0.053230 0.135340 -0.3184900 0.212030
## Hazard Ratio 1.00 2.00 NA 0.948160 NA 0.7272400 1.236200
## SMOKING - 1:2 2.00 1.00 NA -0.183620 0.144760 -0.4673500 0.100120
## Hazard Ratio 2.00 1.00 NA 0.832250 NA 0.6266600 1.105300
## SMOKING - 3:2 2.00 3.00 NA 0.066860 0.200970 -0.3270300 0.460750
## Hazard Ratio 2.00 3.00 NA 1.069100 NA 0.7210600 1.585300
## alcohol - 1:3 3.00 1.00 NA 0.126340 0.120810 -0.1104500 0.363130
## Hazard Ratio 3.00 1.00 NA 1.134700 NA 0.8954300 1.437800
## alcohol - 2:3 3.00 2.00 NA -0.029509 0.147220 -0.3180500 0.259030
## Hazard Ratio 3.00 2.00 NA 0.970920 NA 0.7275700 1.295700
## DIABETES - 1:0 1.00 2.00 NA 0.208900 0.109740 -0.0061847 0.423990
## Hazard Ratio 1.00 2.00 NA 1.232300 NA 0.9938300 1.528000
## albumin - 2:1 1.00 2.00 NA 0.264540 0.117310 0.0346040 0.494470
## Hazard Ratio 1.00 2.00 NA 1.302800 NA 1.0352000 1.639600
## albumin - 3:1 1.00 3.00 NA 0.562210 0.205920 0.1586100 0.965820
## Hazard Ratio 1.00 3.00 NA 1.754600 NA 1.1719000 2.626900
## STENOSIS - 1:0 1.00 2.00 NA 0.170850 0.106860 -0.0385980 0.380290
## Hazard Ratio 1.00 2.00 NA 1.186300 NA 0.9621400 1.462700vif(COXPH.FULL.AREGIMPUTED_1)## AGE SEX=2 SMOKING=2 SMOKING=3
## 1.299339 1.278601 1.543592 1.412798
## alcohol=2 alcohol=3 BMI SYSTH
## 1.422216 1.562523 1.108005 1.152175
## HDL DIABETES=1 SUMSCORE_5LEVELS HOMOC
## 1.209756 1.121312 1.156664 1.473997
## CREAT albumin=2 albumin=3 STENOSIS=1
## 1.847485 1.181861 1.539938 1.175423
## IMT
## 1.303815COXPH.FULL.AREGIMPUTED_1## Cox Proportional Hazards Model
##
## cph(formula = Surv(TEVENT, EVENT) ~ ifelse(AGE > 50, (AGE - 50)^2,
## 0) + SEX + SMOKING + alcohol + BMI + SYSTH + HDL + DIABETES +
## SUMSCORE_5LEVELS + HOMOC + log(CREAT) + albumin + STENOSIS +
## IMT, data = SMART.AREGIMPUTED_1, x = T, y = T, surv = T)
##
## Model Tests Discrimination
## Indexes
## Obs 3873 LR chi2 276.30 R2 0.082
## Events 460 d.f. 17 R2(17,3873)0.065
## Center 3.1178 Pr(> chi2) 0.0000 R2(17,460)0.431
## Score chi2 347.73 Dxy 0.392
## Pr(> chi2) 0.0000
##
## Coef S.E. Wald Z Pr(>|Z|)
## AGE 0.0013 0.0002 6.16 <0.0001
## SEX=2 -0.0532 0.1353 -0.39 0.6941
## SMOKING=2 0.1836 0.1448 1.27 0.2047
## SMOKING=3 0.2505 0.2345 1.07 0.2855
## alcohol=2 -0.1559 0.1663 -0.94 0.3488
## alcohol=3 -0.1263 0.1208 -1.05 0.2957
## BMI -0.0248 0.0141 -1.75 0.0802
## SYSTH 0.0011 0.0022 0.49 0.6232
## HDL -0.3776 0.1594 -2.37 0.0178
## DIABETES=1 0.2089 0.1097 1.90 0.0570
## SUMSCORE_5LEVELS 0.3319 0.0558 5.95 <0.0001
## HOMOC 0.0010 0.0085 0.12 0.9047
## CREAT 0.6000 0.1465 4.10 <0.0001
## albumin=2 0.2645 0.1173 2.25 0.0241
## albumin=3 0.5622 0.2059 2.73 0.0063
## STENOSIS=1 0.1708 0.1069 1.60 0.1099
## IMT 0.5276 0.1785 2.95 0.0031##################################
# Formulating the FULL
# Cox Proportional Hazards Model
# Using the combined complete and
# 2ND imputation results from AREG
##################################
SMART.AREGIMPUTED_2$EVENT <- as.numeric(SMART.AREGIMPUTED_2$EVENT)
SMART.AREGIMPUTED_2$SMOKING <- as.factor(SMART.AREGIMPUTED_2$SMOKING)
SMART.AREGIMPUTED_2$alcohol <- as.factor(SMART.AREGIMPUTED_2$alcohol)
SMART.AREGIMPUTED_2$albumin <- as.factor(SMART.AREGIMPUTED_2$albumin)
dd <- datadist(SMART.AREGIMPUTED_2)
options(datadist="dd")
##################################
# FULL COMPLETE
##################################
COXPH.FULL.COMPLETE.AREGIMPUTED_2 <-cph(Surv(TEVENT,EVENT) ~ ifelse(AGE>50, (AGE-50)^2,0) +
SEX +
SMOKING +
alcohol +
BMI +
SYSTH +
SYSTBP +
DIASTH +
DIASTBP +
WEIGHT +
LENGTH +
CHOL +
LDL +
HDL+
DIABETES +
SUMSCORE_5LEVELS +
HOMOC +
log(CREAT) +
albumin +
STENOSIS +
IMT +
TRIG +
GLUT +
packyrs,
data = SMART.AREGIMPUTED_2,
x=T,
y=T,
surv=T)
anova(COXPH.FULL.COMPLETE.AREGIMPUTED_2)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## AGE 35.47 1 <.0001
## SEX 0.46 1 0.4990
## SMOKING 0.06 2 0.9682
## alcohol 1.70 2 0.4283
## BMI 0.75 1 0.3850
## SYSTH 1.60 1 0.2055
## SYSTBP 3.89 1 0.0485
## DIASTH 0.04 1 0.8409
## DIASTBP 1.88 1 0.1708
## WEIGHT 1.34 1 0.2479
## LENGTH 0.69 1 0.4045
## CHOL 0.08 1 0.7736
## LDL 0.12 1 0.7307
## HDL 0.01 1 0.9305
## DIABETES 0.09 1 0.7655
## SUMSCORE_5LEVELS 36.02 1 <.0001
## HOMOC 0.09 1 0.7672
## CREAT 15.96 1 0.0001
## albumin 11.13 2 0.0038
## STENOSIS 2.17 1 0.1411
## IMT 10.54 1 0.0012
## TRIG 0.09 1 0.7673
## GLUT 3.16 1 0.0753
## packyrs 5.60 1 0.0180
## TOTAL 332.03 27 <.0001summary(COXPH.FULL.COMPLETE.AREGIMPUTED_2)## Effects Response : Surv(TEVENT, EVENT)
##
## Factor Low High Diff. Effect S.E. Lower 0.95 Upper 0.95
## AGE 52.00 68.00 16.00 0.427070 0.071709 0.28652000 0.5676200
## Hazard Ratio 52.00 68.00 16.00 1.532800 NA 1.33180000 1.7641000
## BMI 24.11 28.73 4.62 0.430730 0.495820 -0.54105000 1.4025000
## Hazard Ratio 24.11 28.73 4.62 1.538400 NA 0.58214000 4.0654000
## SYSTH 127.00 157.00 30.00 0.151300 0.119500 -0.08291300 0.3855200
## Hazard Ratio 127.00 157.00 30.00 1.163300 NA 0.92043000 1.4704000
## SYSTBP 126.00 153.00 27.00 -0.223730 0.113390 -0.44597000 -0.0014791
## Hazard Ratio 126.00 153.00 27.00 0.799530 NA 0.64020000 0.9985200
## DIASTH 74.00 90.00 16.00 -0.022334 0.111270 -0.24041000 0.1957500
## Hazard Ratio 74.00 90.00 16.00 0.977910 NA 0.78630000 1.2162000
## DIASTBP 73.00 86.00 13.00 0.128540 0.093857 -0.05542000 0.3124900
## Hazard Ratio 73.00 86.00 13.00 1.137200 NA 0.94609000 1.3668000
## WEIGHT 72.00 89.00 17.00 -0.704430 0.609600 -1.89920000 0.4903500
## Hazard Ratio 72.00 89.00 17.00 0.494390 NA 0.14968000 1.6329000
## LENGTH 1.68 1.80 0.12 0.336580 0.403770 -0.45478000 1.1279000
## Hazard Ratio 1.68 1.80 0.12 1.400200 NA 0.63458000 3.0893000
## CHOL 4.40 5.90 1.50 -0.422550 1.468700 -3.30110000 2.4560000
## Hazard Ratio 4.40 5.90 1.50 0.655370 NA 0.03684200 11.6580000
## LDL 2.37 3.83 1.46 0.495510 1.439800 -2.32650000 3.3175000
## Hazard Ratio 2.37 3.83 1.46 1.641300 NA 0.09763400 27.5930000
## HDL 0.96 1.42 0.46 -0.039806 0.456530 -0.93459000 0.8549800
## Hazard Ratio 0.96 1.42 0.46 0.960980 NA 0.39275000 2.3513000
## SUMSCORE_5LEVELS 1.00 5.00 4.00 1.357300 0.226150 0.91409000 1.8006000
## Hazard Ratio 1.00 5.00 4.00 3.885900 NA 2.49450000 6.0533000
## HOMOC 10.50 16.00 5.50 0.014223 0.048052 -0.07995600 0.1084000
## Hazard Ratio 10.50 16.00 5.50 1.014300 NA 0.92316000 1.1145000
## CREAT 78.00 101.00 23.00 0.155110 0.038821 0.07902000 0.2312000
## Hazard Ratio 78.00 101.00 23.00 1.167800 NA 1.08220000 1.2601000
## IMT 0.75 1.07 0.32 0.188340 0.058019 0.07462800 0.3020600
## Hazard Ratio 0.75 1.07 0.32 1.207200 NA 1.07750000 1.3526000
## TRIG 1.12 2.23 1.11 0.142450 0.481340 -0.80096000 1.0859000
## Hazard Ratio 1.12 2.23 1.11 1.153100 NA 0.44890000 2.9620000
## GLUT 5.30 6.50 1.20 0.061953 0.034827 -0.00630670 0.1302100
## Hazard Ratio 5.30 6.50 1.20 1.063900 NA 0.99371000 1.1391000
## packyrs 5.90 34.20 28.30 0.165940 0.070146 0.02845400 0.3034200
## Hazard Ratio 5.90 34.20 28.30 1.180500 NA 1.02890000 1.3545000
## SEX - 2:1 1.00 2.00 NA -0.109690 0.162250 -0.42770000 0.2083200
## Hazard Ratio 1.00 2.00 NA 0.896110 NA 0.65201000 1.2316000
## SMOKING - 1:2 2.00 1.00 NA -0.017550 0.161910 -0.33488000 0.2997800
## Hazard Ratio 2.00 1.00 NA 0.982600 NA 0.71542000 1.3496000
## SMOKING - 3:2 2.00 3.00 NA 0.043922 0.201980 -0.35195000 0.4397900
## Hazard Ratio 2.00 3.00 NA 1.044900 NA 0.70332000 1.5524000
## alcohol - 1:3 3.00 1.00 NA 0.147610 0.121350 -0.09023100 0.3854400
## Hazard Ratio 3.00 1.00 NA 1.159100 NA 0.91372000 1.4703000
## alcohol - 2:3 3.00 2.00 NA -0.024662 0.148250 -0.31522000 0.2658900
## Hazard Ratio 3.00 2.00 NA 0.975640 NA 0.72963000 1.3046000
## DIABETES - 1:0 1.00 2.00 NA 0.046684 0.156520 -0.26009000 0.3534600
## Hazard Ratio 1.00 2.00 NA 1.047800 NA 0.77098000 1.4240000
## albumin - 2:1 1.00 2.00 NA 0.234650 0.119250 0.00093568 0.4683700
## Hazard Ratio 1.00 2.00 NA 1.264500 NA 1.00090000 1.5974000
## albumin - 3:1 1.00 3.00 NA 0.637920 0.202230 0.24155000 1.0343000
## Hazard Ratio 1.00 3.00 NA 1.892500 NA 1.27320000 2.8131000
## STENOSIS - 1:0 1.00 2.00 NA 0.159590 0.108420 -0.05291900 0.3721000
## Hazard Ratio 1.00 2.00 NA 1.173000 NA 0.94846000 1.4508000vif(COXPH.FULL.COMPLETE.AREGIMPUTED_2)## AGE SEX=2 SMOKING=2 SMOKING=3
## 1.415309 1.837522 1.930927 1.547808
## alcohol=2 alcohol=3 BMI SYSTH
## 1.431119 1.572093 64.453293 3.876986
## SYSTBP DIASTH DIASTBP WEIGHT
## 3.362049 3.035763 2.601137 90.131708
## LENGTH CHOL LDL HDL
## 35.159350 502.529866 449.417395 46.213107
## DIABETES=1 SUMSCORE_5LEVELS HOMOC CREAT
## 2.271060 1.170919 1.542203 1.941807
## albumin=2 albumin=3 STENOSIS=1 IMT
## 1.184876 1.614102 1.209187 1.346155
## TRIG GLUT packyrs
## 119.680408 2.177683 1.362550COXPH.FULL.COMPLETE.AREGIMPUTED_2## Cox Proportional Hazards Model
##
## cph(formula = Surv(TEVENT, EVENT) ~ ifelse(AGE > 50, (AGE - 50)^2,
## 0) + SEX + SMOKING + alcohol + BMI + SYSTH + SYSTBP + DIASTH +
## DIASTBP + WEIGHT + LENGTH + CHOL + LDL + HDL + DIABETES +
## SUMSCORE_5LEVELS + HOMOC + log(CREAT) + albumin + STENOSIS +
## IMT + TRIG + GLUT + packyrs, data = SMART.AREGIMPUTED_2,
## x = T, y = T, surv = T)
##
## Model Tests Discrimination
## Indexes
## Obs 3873 LR chi2 298.32 R2 0.089
## Events 460 d.f. 27 R2(27,3873)0.068
## Center 8.4099 Pr(> chi2) 0.0000 R2(27,460)0.446
## Score chi2 372.48 Dxy 0.397
## Pr(> chi2) 0.0000
##
## Coef S.E. Wald Z Pr(>|Z|)
## AGE 0.0013 0.0002 5.96 <0.0001
## SEX=2 -0.1097 0.1623 -0.68 0.4990
## SMOKING=2 0.0175 0.1619 0.11 0.9137
## SMOKING=3 0.0615 0.2454 0.25 0.8022
## alcohol=2 -0.1723 0.1681 -1.02 0.3054
## alcohol=3 -0.1476 0.1213 -1.22 0.2238
## BMI 0.0932 0.1073 0.87 0.3850
## SYSTH 0.0050 0.0040 1.27 0.2055
## SYSTBP -0.0083 0.0042 -1.97 0.0485
## DIASTH -0.0014 0.0070 -0.20 0.8409
## DIASTBP 0.0099 0.0072 1.37 0.1708
## WEIGHT -0.0414 0.0359 -1.16 0.2479
## LENGTH 2.8049 3.3647 0.83 0.4045
## CHOL -0.2817 0.9791 -0.29 0.7736
## LDL 0.3394 0.9862 0.34 0.7307
## HDL -0.0865 0.9925 -0.09 0.9305
## DIABETES=1 0.0467 0.1565 0.30 0.7655
## SUMSCORE_5LEVELS 0.3393 0.0565 6.00 <0.0001
## HOMOC 0.0026 0.0087 0.30 0.7672
## CREAT 0.6002 0.1502 4.00 <0.0001
## albumin=2 0.2347 0.1192 1.97 0.0491
## albumin=3 0.6379 0.2022 3.15 0.0016
## STENOSIS=1 0.1596 0.1084 1.47 0.1411
## IMT 0.5886 0.1813 3.25 0.0012
## TRIG 0.1283 0.4336 0.30 0.7673
## GLUT 0.0516 0.0290 1.78 0.0753
## packyrs 0.0059 0.0025 2.37 0.0180##################################
# FULL
# After removing variables which are:
# High multicollinearity contributors
# Non-standard risk factors
# Minimal predictors of survival outcome based from initial exploration
# Minimal predictors of survival outcome based from domain knowledge and literature
##################################
COXPH.FULL.AREGIMPUTED_2 <-cph(Surv(TEVENT,EVENT) ~ ifelse(AGE>50, (AGE-50)^2,0) +
SEX +
SMOKING +
alcohol +
BMI +
SYSTH +
HDL+
DIABETES +
SUMSCORE_5LEVELS +
HOMOC +
log(CREAT) +
albumin +
STENOSIS +
IMT,
data = SMART.AREGIMPUTED_2,
x=T,
y=T,
surv=T)
anova(COXPH.FULL.AREGIMPUTED_2)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## AGE 36.20 1 <.0001
## SEX 0.15 1 0.6996
## SMOKING 1.81 2 0.4040
## alcohol 1.25 2 0.5347
## BMI 2.77 1 0.0959
## SYSTH 1.01 1 0.3157
## HDL 5.80 1 0.0161
## DIABETES 2.84 1 0.0919
## SUMSCORE_5LEVELS 35.74 1 <.0001
## HOMOC 0.18 1 0.6730
## CREAT 14.49 1 0.0001
## albumin 11.33 2 0.0035
## STENOSIS 2.63 1 0.1046
## IMT 9.41 1 0.0022
## TOTAL 318.65 17 <.0001summary(COXPH.FULL.AREGIMPUTED_2)## Effects Response : Surv(TEVENT, EVENT)
##
## Factor Low High Diff. Effect S.E. Lower 0.95 Upper 0.95
## AGE 52.00 68.00 16.00 0.412890 0.068624 0.2783900 0.547400
## Hazard Ratio 52.00 68.00 16.00 1.511200 NA 1.3210000 1.728700
## BMI 24.11 28.73 4.62 -0.109170 0.065571 -0.2376900 0.019344
## Hazard Ratio 24.11 28.73 4.62 0.896580 NA 0.7884500 1.019500
## SYSTH 127.00 157.00 30.00 0.066168 0.065951 -0.0630930 0.195430
## Hazard Ratio 127.00 157.00 30.00 1.068400 NA 0.9388600 1.215800
## HDL 0.96 1.42 0.46 -0.176910 0.073475 -0.3209200 -0.032900
## Hazard Ratio 0.96 1.42 0.46 0.837860 NA 0.7254800 0.967640
## SUMSCORE_5LEVELS 1.00 5.00 4.00 1.333000 0.222970 0.8959500 1.770000
## Hazard Ratio 1.00 5.00 4.00 3.792300 NA 2.4496000 5.870800
## HOMOC 10.50 16.00 5.50 0.020056 0.047525 -0.0730920 0.113200
## Hazard Ratio 10.50 16.00 5.50 1.020300 NA 0.9295200 1.119900
## CREAT 78.00 101.00 23.00 0.144220 0.037890 0.0699530 0.218480
## Hazard Ratio 78.00 101.00 23.00 1.155100 NA 1.0725000 1.244200
## IMT 0.75 1.07 0.32 0.174920 0.057034 0.0631390 0.286710
## Hazard Ratio 0.75 1.07 0.32 1.191200 NA 1.0652000 1.332000
## SEX - 2:1 1.00 2.00 NA -0.052169 0.135210 -0.3171800 0.212840
## Hazard Ratio 1.00 2.00 NA 0.949170 NA 0.7282000 1.237200
## SMOKING - 1:2 2.00 1.00 NA -0.184270 0.144830 -0.4681400 0.099591
## Hazard Ratio 2.00 1.00 NA 0.831710 NA 0.6261700 1.104700
## SMOKING - 3:2 2.00 3.00 NA 0.060750 0.201060 -0.3333200 0.454820
## Hazard Ratio 2.00 3.00 NA 1.062600 NA 0.7165400 1.575900
## alcohol - 1:3 3.00 1.00 NA 0.119670 0.120890 -0.1172600 0.356600
## Hazard Ratio 3.00 1.00 NA 1.127100 NA 0.8893500 1.428500
## alcohol - 2:3 3.00 2.00 NA -0.040309 0.147650 -0.3297000 0.249080
## Hazard Ratio 3.00 2.00 NA 0.960490 NA 0.7191400 1.282900
## DIABETES - 1:0 1.00 2.00 NA 0.185690 0.110160 -0.0302130 0.401600
## Hazard Ratio 1.00 2.00 NA 1.204100 NA 0.9702400 1.494200
## albumin - 2:1 1.00 2.00 NA 0.230480 0.118490 -0.0017567 0.462710
## Hazard Ratio 1.00 2.00 NA 1.259200 NA 0.9982400 1.588400
## albumin - 3:1 1.00 3.00 NA 0.636100 0.199770 0.2445500 1.027700
## Hazard Ratio 1.00 3.00 NA 1.889100 NA 1.2771000 2.794500
## STENOSIS - 1:0 1.00 2.00 NA 0.174090 0.107260 -0.0361370 0.384320
## Hazard Ratio 1.00 2.00 NA 1.190200 NA 0.9645100 1.468600vif(COXPH.FULL.AREGIMPUTED_2)## AGE SEX=2 SMOKING=2 SMOKING=3
## 1.299593 1.276089 1.544960 1.418226
## alcohol=2 alcohol=3 BMI SYSTH
## 1.417444 1.560499 1.109009 1.190620
## HDL DIABETES=1 SUMSCORE_5LEVELS HOMOC
## 1.209404 1.124695 1.158816 1.507124
## CREAT albumin=2 albumin=3 STENOSIS=1
## 1.869956 1.170582 1.576933 1.182581
## IMT
## 1.309736COXPH.FULL.AREGIMPUTED_2## Cox Proportional Hazards Model
##
## cph(formula = Surv(TEVENT, EVENT) ~ ifelse(AGE > 50, (AGE - 50)^2,
## 0) + SEX + SMOKING + alcohol + BMI + SYSTH + HDL + DIABETES +
## SUMSCORE_5LEVELS + HOMOC + log(CREAT) + albumin + STENOSIS +
## IMT, data = SMART.AREGIMPUTED_2, x = T, y = T, surv = T)
##
## Model Tests Discrimination
## Indexes
## Obs 3873 LR chi2 280.67 R2 0.084
## Events 460 d.f. 17 R2(17,3873)0.066
## Center 3.1607 Pr(> chi2) 0.0000 R2(17,460)0.436
## Score chi2 355.08 Dxy 0.393
## Pr(> chi2) 0.0000
##
## Coef S.E. Wald Z Pr(>|Z|)
## AGE 0.0013 0.0002 6.02 <0.0001
## SEX=2 -0.0522 0.1352 -0.39 0.6996
## SMOKING=2 0.1843 0.1448 1.27 0.2033
## SMOKING=3 0.2450 0.2349 1.04 0.2969
## alcohol=2 -0.1600 0.1673 -0.96 0.3389
## alcohol=3 -0.1197 0.1209 -0.99 0.3222
## BMI -0.0236 0.0142 -1.66 0.0959
## SYSTH 0.0022 0.0022 1.00 0.3157
## HDL -0.3846 0.1597 -2.41 0.0161
## DIABETES=1 0.1857 0.1102 1.69 0.0919
## SUMSCORE_5LEVELS 0.3332 0.0557 5.98 <0.0001
## HOMOC 0.0036 0.0086 0.42 0.6730
## CREAT 0.5581 0.1466 3.81 0.0001
## albumin=2 0.2305 0.1185 1.95 0.0518
## albumin=3 0.6361 0.1998 3.18 0.0015
## STENOSIS=1 0.1741 0.1073 1.62 0.1046
## IMT 0.5466 0.1782 3.07 0.0022##################################
# Formulating the FULL
# Cox Proportional Hazards Model
# Using the combined complete and
# 3RD imputation results from AREG
##################################
SMART.AREGIMPUTED_3$EVENT <- as.numeric(SMART.AREGIMPUTED_3$EVENT)
SMART.AREGIMPUTED_3$SMOKING <- as.factor(SMART.AREGIMPUTED_3$SMOKING)
SMART.AREGIMPUTED_3$alcohol <- as.factor(SMART.AREGIMPUTED_3$alcohol)
SMART.AREGIMPUTED_3$albumin <- as.factor(SMART.AREGIMPUTED_3$albumin)
dd <- datadist(SMART.AREGIMPUTED_3)
options(datadist="dd")
##################################
# FULL COMPLETE
##################################
COXPH.FULL.COMPLETE.AREGIMPUTED_3 <-cph(Surv(TEVENT,EVENT) ~ ifelse(AGE>50, (AGE-50)^2,0) +
SEX +
SMOKING +
alcohol +
BMI +
SYSTH +
SYSTBP +
DIASTH +
DIASTBP +
WEIGHT +
LENGTH +
CHOL +
LDL +
HDL+
DIABETES +
SUMSCORE_5LEVELS +
HOMOC +
log(CREAT) +
albumin +
STENOSIS +
IMT +
TRIG +
GLUT +
packyrs,
data = SMART.AREGIMPUTED_3,
x=T,
y=T,
surv=T)
anova(COXPH.FULL.COMPLETE.AREGIMPUTED_3)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## AGE 36.90 1 <.0001
## SEX 0.75 1 0.3869
## SMOKING 0.35 2 0.8388
## alcohol 1.46 2 0.4817
## BMI 0.68 1 0.4083
## SYSTH 0.15 1 0.6983
## SYSTBP 0.44 1 0.5070
## DIASTH 0.66 1 0.4168
## DIASTBP 0.19 1 0.6599
## WEIGHT 1.27 1 0.2590
## LENGTH 0.59 1 0.4439
## CHOL 0.55 1 0.4581
## LDL 0.65 1 0.4218
## HDL 0.09 1 0.7588
## DIABETES 0.19 1 0.6617
## SUMSCORE_5LEVELS 34.76 1 <.0001
## HOMOC 0.06 1 0.8014
## CREAT 17.68 1 <.0001
## albumin 7.20 2 0.0274
## STENOSIS 3.01 1 0.0825
## IMT 7.65 1 0.0057
## TRIG 0.56 1 0.4530
## GLUT 2.49 1 0.1143
## packyrs 5.86 1 0.0155
## TOTAL 320.20 27 <.0001summary(COXPH.FULL.COMPLETE.AREGIMPUTED_3)## Effects Response : Surv(TEVENT, EVENT)
##
## Factor Low High Diff. Effect S.E. Lower 0.95 Upper 0.95
## AGE 52.00 68.00 16.00 0.435920 0.071766 0.295260 0.57658
## Hazard Ratio 52.00 68.00 16.00 1.546400 NA 1.343500 1.77990
## BMI 24.11 28.73 4.62 0.406580 0.491680 -0.557090 1.37030
## Hazard Ratio 24.11 28.73 4.62 1.501700 NA 0.572870 3.93640
## SYSTH 127.00 156.00 29.00 0.045244 0.116720 -0.183520 0.27401
## Hazard Ratio 127.00 156.00 29.00 1.046300 NA 0.832330 1.31520
## SYSTBP 126.00 153.00 27.00 -0.074237 0.111870 -0.293510 0.14503
## Hazard Ratio 126.00 153.00 27.00 0.928450 NA 0.745640 1.15610
## DIASTH 74.00 90.00 16.00 0.088751 0.109310 -0.125490 0.30299
## Hazard Ratio 74.00 90.00 16.00 1.092800 NA 0.882060 1.35390
## DIASTBP 73.00 86.00 13.00 0.041562 0.094439 -0.143530 0.22666
## Hazard Ratio 73.00 86.00 13.00 1.042400 NA 0.866290 1.25440
## WEIGHT 72.00 89.00 17.00 -0.681140 0.603430 -1.863800 0.50155
## Hazard Ratio 72.00 89.00 17.00 0.506040 NA 0.155080 1.65130
## LENGTH 1.68 1.80 0.12 0.306690 0.400570 -0.478400 1.09180
## Hazard Ratio 1.68 1.80 0.12 1.358900 NA 0.619770 2.97960
## CHOL 4.40 5.90 1.50 -0.991960 1.336800 -3.612000 1.62810
## Hazard Ratio 4.40 5.90 1.50 0.370850 NA 0.026997 5.09420
## LDL 2.37 3.83 1.46 1.054400 1.312500 -1.518100 3.62690
## Hazard Ratio 2.37 3.83 1.46 2.870100 NA 0.219120 37.59400
## HDL 0.96 1.42 0.46 0.127730 0.416070 -0.687750 0.94322
## Hazard Ratio 0.96 1.42 0.46 1.136200 NA 0.502700 2.56820
## SUMSCORE_5LEVELS 1.00 5.00 4.00 1.337900 0.226920 0.893180 1.78270
## Hazard Ratio 1.00 5.00 4.00 3.811200 NA 2.442900 5.94580
## HOMOC 10.50 16.00 5.50 0.011972 0.047590 -0.081302 0.10525
## Hazard Ratio 10.50 16.00 5.50 1.012000 NA 0.921920 1.11100
## CREAT 78.00 101.00 23.00 0.162680 0.038689 0.086847 0.23850
## Hazard Ratio 78.00 101.00 23.00 1.176700 NA 1.090700 1.26930
## IMT 0.75 1.07 0.32 0.160880 0.058184 0.046842 0.27492
## Hazard Ratio 0.75 1.07 0.32 1.174500 NA 1.048000 1.31640
## TRIG 1.13 2.23 1.10 0.327860 0.436890 -0.528420 1.18410
## Hazard Ratio 1.13 2.23 1.10 1.388000 NA 0.589540 3.26790
## GLUT 5.30 6.50 1.20 0.055650 0.035244 -0.013426 0.12473
## Hazard Ratio 5.30 6.50 1.20 1.057200 NA 0.986660 1.13280
## packyrs 5.90 34.20 28.30 0.172410 0.071214 0.032828 0.31198
## Hazard Ratio 5.90 34.20 28.30 1.188200 NA 1.033400 1.36610
## SEX - 2:1 1.00 2.00 NA -0.141230 0.163230 -0.461150 0.17869
## Hazard Ratio 1.00 2.00 NA 0.868290 NA 0.630560 1.19570
## SMOKING - 1:2 2.00 1.00 NA -0.024508 0.161910 -0.341850 0.29283
## Hazard Ratio 2.00 1.00 NA 0.975790 NA 0.710460 1.34020
## SMOKING - 3:2 2.00 3.00 NA 0.110050 0.198790 -0.279580 0.49967
## Hazard Ratio 2.00 3.00 NA 1.116300 NA 0.756100 1.64820
## alcohol - 1:3 3.00 1.00 NA 0.133760 0.120890 -0.103180 0.37071
## Hazard Ratio 3.00 1.00 NA 1.143100 NA 0.901960 1.44880
## alcohol - 2:3 3.00 2.00 NA -0.029839 0.147830 -0.319570 0.25990
## Hazard Ratio 3.00 2.00 NA 0.970600 NA 0.726460 1.29680
## DIABETES - 1:0 1.00 2.00 NA 0.068163 0.155790 -0.237180 0.37351
## Hazard Ratio 1.00 2.00 NA 1.070500 NA 0.788850 1.45280
## albumin - 2:1 1.00 2.00 NA 0.188130 0.119630 -0.046335 0.42259
## Hazard Ratio 1.00 2.00 NA 1.207000 NA 0.954720 1.52590
## albumin - 3:1 1.00 3.00 NA 0.532280 0.209570 0.121520 0.94303
## Hazard Ratio 1.00 3.00 NA 1.702800 NA 1.129200 2.56770
## STENOSIS - 1:0 1.00 2.00 NA 0.187470 0.107970 -0.024146 0.39908
## Hazard Ratio 1.00 2.00 NA 1.206200 NA 0.976140 1.49050vif(COXPH.FULL.COMPLETE.AREGIMPUTED_3)## AGE SEX=2 SMOKING=2 SMOKING=3
## 1.420179 1.859980 1.945645 1.558441
## alcohol=2 alcohol=3 BMI SYSTH
## 1.426484 1.568374 63.258403 3.781325
## SYSTBP DIASTH DIASTBP WEIGHT
## 3.316955 3.055128 2.581655 88.682439
## LENGTH CHOL LDL HDL
## 34.592113 414.210018 374.656141 38.295659
## DIABETES=1 SUMSCORE_5LEVELS HOMOC CREAT
## 2.249795 1.180905 1.455960 1.929293
## albumin=2 albumin=3 STENOSIS=1 IMT
## 1.184010 1.626924 1.203558 1.339445
## TRIG GLUT packyrs
## 99.397839 2.164191 1.362993COXPH.FULL.COMPLETE.AREGIMPUTED_3## Cox Proportional Hazards Model
##
## cph(formula = Surv(TEVENT, EVENT) ~ ifelse(AGE > 50, (AGE - 50)^2,
## 0) + SEX + SMOKING + alcohol + BMI + SYSTH + SYSTBP + DIASTH +
## DIASTBP + WEIGHT + LENGTH + CHOL + LDL + HDL + DIABETES +
## SUMSCORE_5LEVELS + HOMOC + log(CREAT) + albumin + STENOSIS +
## IMT + TRIG + GLUT + packyrs, data = SMART.AREGIMPUTED_3,
## x = T, y = T, surv = T)
##
## Model Tests Discrimination
## Indexes
## Obs 3873 LR chi2 289.89 R2 0.086
## Events 460 d.f. 27 R2(27,3873)0.066
## Center 8.2833 Pr(> chi2) 0.0000 R2(27,460)0.435
## Score chi2 357.27 Dxy 0.393
## Pr(> chi2) 0.0000
##
## Coef S.E. Wald Z Pr(>|Z|)
## AGE 0.0014 0.0002 6.07 <0.0001
## SEX=2 -0.1412 0.1632 -0.87 0.3869
## SMOKING=2 0.0245 0.1619 0.15 0.8797
## SMOKING=3 0.1346 0.2424 0.56 0.5789
## alcohol=2 -0.1636 0.1666 -0.98 0.3260
## alcohol=3 -0.1338 0.1209 -1.11 0.2685
## BMI 0.0880 0.1064 0.83 0.4083
## SYSTH 0.0016 0.0040 0.39 0.6983
## SYSTBP -0.0027 0.0041 -0.66 0.5070
## DIASTH 0.0055 0.0068 0.81 0.4168
## DIASTBP 0.0032 0.0073 0.44 0.6599
## WEIGHT -0.0401 0.0355 -1.13 0.2590
## LENGTH 2.5558 3.3380 0.77 0.4439
## CHOL -0.6613 0.8912 -0.74 0.4581
## LDL 0.7222 0.8990 0.80 0.4218
## HDL 0.2777 0.9045 0.31 0.7588
## DIABETES=1 0.0682 0.1558 0.44 0.6617
## SUMSCORE_5LEVELS 0.3345 0.0567 5.90 <0.0001
## HOMOC 0.0022 0.0087 0.25 0.8014
## CREAT 0.6295 0.1497 4.20 <0.0001
## albumin=2 0.1881 0.1196 1.57 0.1158
## albumin=3 0.5323 0.2096 2.54 0.0111
## STENOSIS=1 0.1875 0.1080 1.74 0.0825
## IMT 0.5027 0.1818 2.77 0.0057
## TRIG 0.2981 0.3972 0.75 0.4530
## GLUT 0.0464 0.0294 1.58 0.1143
## packyrs 0.0061 0.0025 2.42 0.0155##################################
# FULL
# After removing variables which are:
# High multicollinearity contributors
# Non-standard risk factors
# Minimal predictors of survival outcome based from initial exploration
# Minimal predictors of survival outcome based from domain knowledge and literature
##################################
COXPH.FULL.AREGIMPUTED_3 <-cph(Surv(TEVENT,EVENT) ~ ifelse(AGE>50, (AGE-50)^2,0) +
SEX +
SMOKING +
alcohol +
BMI +
SYSTH +
HDL+
DIABETES +
SUMSCORE_5LEVELS +
HOMOC +
log(CREAT) +
albumin +
STENOSIS +
IMT,
data = SMART.AREGIMPUTED_3,
x=T,
y=T,
surv=T)
anova(COXPH.FULL.AREGIMPUTED_3)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## AGE 37.94 1 <.0001
## SEX 0.12 1 0.7269
## SMOKING 2.25 2 0.3250
## alcohol 1.11 2 0.5753
## BMI 2.88 1 0.0899
## SYSTH 1.69 1 0.1939
## HDL 6.08 1 0.0137
## DIABETES 3.15 1 0.0761
## SUMSCORE_5LEVELS 36.05 1 <.0001
## HOMOC 0.24 1 0.6207
## CREAT 15.67 1 0.0001
## albumin 7.32 2 0.0257
## STENOSIS 3.43 1 0.0642
## IMT 6.57 1 0.0103
## TOTAL 311.06 17 <.0001summary(COXPH.FULL.AREGIMPUTED_3)## Effects Response : Surv(TEVENT, EVENT)
##
## Factor Low High Diff. Effect S.E. Lower 0.95 Upper 0.95
## AGE 52.00 68.00 16.00 0.421290 0.068396 0.287240 0.555340
## Hazard Ratio 52.00 68.00 16.00 1.523900 NA 1.332700 1.742500
## BMI 24.11 28.73 4.62 -0.111310 0.065642 -0.239960 0.017347
## Hazard Ratio 24.11 28.73 4.62 0.894660 NA 0.786660 1.017500
## SYSTH 127.00 156.00 29.00 0.083927 0.064609 -0.042704 0.210560
## Hazard Ratio 127.00 156.00 29.00 1.087500 NA 0.958200 1.234400
## HDL 0.96 1.42 0.46 -0.181520 0.073610 -0.325790 -0.037244
## Hazard Ratio 0.96 1.42 0.46 0.834000 NA 0.721960 0.963440
## SUMSCORE_5LEVELS 1.00 5.00 4.00 1.338700 0.222960 0.901750 1.775700
## Hazard Ratio 1.00 5.00 4.00 3.814200 NA 2.463900 5.904600
## HOMOC 10.50 16.00 5.50 0.023263 0.047004 -0.068862 0.115390
## Hazard Ratio 10.50 16.00 5.50 1.023500 NA 0.933460 1.122300
## CREAT 78.00 101.00 23.00 0.150200 0.037942 0.075835 0.224570
## Hazard Ratio 78.00 101.00 23.00 1.162100 NA 1.078800 1.251800
## IMT 0.75 1.07 0.32 0.146240 0.057032 0.034457 0.258020
## Hazard Ratio 0.75 1.07 0.32 1.157500 NA 1.035100 1.294400
## SEX - 2:1 1.00 2.00 NA -0.047213 0.135210 -0.312210 0.217790
## Hazard Ratio 1.00 2.00 NA 0.953880 NA 0.731830 1.243300
## SMOKING - 1:2 2.00 1.00 NA -0.193240 0.144660 -0.476770 0.090286
## Hazard Ratio 2.00 1.00 NA 0.824280 NA 0.620780 1.094500
## SMOKING - 3:2 2.00 3.00 NA 0.105120 0.197840 -0.282640 0.492880
## Hazard Ratio 2.00 3.00 NA 1.110800 NA 0.753790 1.637000
## alcohol - 1:3 3.00 1.00 NA 0.114520 0.120600 -0.121850 0.350880
## Hazard Ratio 3.00 1.00 NA 1.121300 NA 0.885280 1.420300
## alcohol - 2:3 3.00 2.00 NA -0.030120 0.147370 -0.318970 0.258730
## Hazard Ratio 3.00 2.00 NA 0.970330 NA 0.726900 1.295300
## DIABETES - 1:0 1.00 2.00 NA 0.195840 0.110430 -0.020590 0.412270
## Hazard Ratio 1.00 2.00 NA 1.216300 NA 0.979620 1.510200
## albumin - 2:1 1.00 2.00 NA 0.194770 0.118990 -0.038447 0.427990
## Hazard Ratio 1.00 2.00 NA 1.215000 NA 0.962280 1.534200
## albumin - 3:1 1.00 3.00 NA 0.525450 0.207680 0.118400 0.932500
## Hazard Ratio 1.00 3.00 NA 1.691200 NA 1.125700 2.540900
## STENOSIS - 1:0 1.00 2.00 NA 0.197860 0.106910 -0.011678 0.407410
## Hazard Ratio 1.00 2.00 NA 1.218800 NA 0.988390 1.502900vif(COXPH.FULL.AREGIMPUTED_3)## AGE SEX=2 SMOKING=2 SMOKING=3
## 1.295338 1.276244 1.553076 1.428452
## alcohol=2 alcohol=3 BMI SYSTH
## 1.414689 1.560807 1.108995 1.175784
## HDL DIABETES=1 SUMSCORE_5LEVELS HOMOC
## 1.214632 1.130052 1.153692 1.418524
## CREAT albumin=2 albumin=3 STENOSIS=1
## 1.872846 1.172256 1.599649 1.179656
## IMT
## 1.303127COXPH.FULL.AREGIMPUTED_3## Cox Proportional Hazards Model
##
## cph(formula = Surv(TEVENT, EVENT) ~ ifelse(AGE > 50, (AGE - 50)^2,
## 0) + SEX + SMOKING + alcohol + BMI + SYSTH + HDL + DIABETES +
## SUMSCORE_5LEVELS + HOMOC + log(CREAT) + albumin + STENOSIS +
## IMT, data = SMART.AREGIMPUTED_3, x = T, y = T, surv = T)
##
## Model Tests Discrimination
## Indexes
## Obs 3873 LR chi2 274.70 R2 0.082
## Events 460 d.f. 17 R2(17,3873)0.064
## Center 3.2859 Pr(> chi2) 0.0000 R2(17,460)0.429
## Score chi2 344.55 Dxy 0.391
## Pr(> chi2) 0.0000
##
## Coef S.E. Wald Z Pr(>|Z|)
## AGE 0.0013 0.0002 6.16 <0.0001
## SEX=2 -0.0472 0.1352 -0.35 0.7269
## SMOKING=2 0.1932 0.1447 1.34 0.1816
## SMOKING=3 0.2984 0.2320 1.29 0.1985
## alcohol=2 -0.1446 0.1659 -0.87 0.3833
## alcohol=3 -0.1145 0.1206 -0.95 0.3423
## BMI -0.0241 0.0142 -1.70 0.0899
## SYSTH 0.0029 0.0022 1.30 0.1939
## HDL -0.3946 0.1600 -2.47 0.0137
## DIABETES=1 0.1958 0.1104 1.77 0.0761
## SUMSCORE_5LEVELS 0.3347 0.0557 6.00 <0.0001
## HOMOC 0.0042 0.0085 0.49 0.6207
## CREAT 0.5812 0.1468 3.96 <0.0001
## albumin=2 0.1948 0.1190 1.64 0.1017
## albumin=3 0.5255 0.2077 2.53 0.0114
## STENOSIS=1 0.1979 0.1069 1.85 0.0642
## IMT 0.4570 0.1782 2.56 0.0103##################################
# Formulating the FULL
# Cox Proportional Hazards Model
# Using the combined complete and
# 4TH imputation results from AREG
##################################
SMART.AREGIMPUTED_4$EVENT <- as.numeric(SMART.AREGIMPUTED_4$EVENT)
SMART.AREGIMPUTED_4$SMOKING <- as.factor(SMART.AREGIMPUTED_4$SMOKING)
SMART.AREGIMPUTED_4$alcohol <- as.factor(SMART.AREGIMPUTED_4$alcohol)
SMART.AREGIMPUTED_4$albumin <- as.factor(SMART.AREGIMPUTED_4$albumin)
dd <- datadist(SMART.AREGIMPUTED_4)
options(datadist="dd")
##################################
# FULL COMPLETE
##################################
COXPH.FULL.COMPLETE.AREGIMPUTED_4 <-cph(Surv(TEVENT,EVENT) ~ ifelse(AGE>50, (AGE-50)^2,0) +
SEX +
SMOKING +
alcohol +
BMI +
SYSTH +
SYSTBP +
DIASTH +
DIASTBP +
WEIGHT +
LENGTH +
CHOL +
LDL +
HDL+
DIABETES +
SUMSCORE_5LEVELS +
HOMOC +
log(CREAT) +
albumin +
STENOSIS +
IMT +
TRIG +
GLUT +
packyrs,
data = SMART.AREGIMPUTED_4,
x=T,
y=T,
surv=T)
anova(COXPH.FULL.COMPLETE.AREGIMPUTED_4)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## AGE 32.02 1 <.0001
## SEX 0.65 1 0.4189
## SMOKING 0.06 2 0.9706
## alcohol 1.76 2 0.4157
## BMI 1.03 1 0.3107
## SYSTH 0.14 1 0.7122
## SYSTBP 0.48 1 0.4866
## DIASTH 1.49 1 0.2221
## DIASTBP 0.01 1 0.9432
## WEIGHT 1.72 1 0.1892
## LENGTH 0.92 1 0.3388
## CHOL 0.00 1 0.9449
## LDL 0.00 1 0.9841
## HDL 0.17 1 0.6797
## DIABETES 0.19 1 0.6617
## SUMSCORE_5LEVELS 32.02 1 <.0001
## HOMOC 2.03 1 0.1541
## CREAT 16.44 1 0.0001
## albumin 8.32 2 0.0156
## STENOSIS 1.89 1 0.1693
## IMT 9.93 1 0.0016
## TRIG 0.01 1 0.9395
## GLUT 3.35 1 0.0673
## packyrs 5.40 1 0.0202
## TOTAL 326.89 27 <.0001summary(COXPH.FULL.COMPLETE.AREGIMPUTED_4)## Effects Response : Surv(TEVENT, EVENT)
##
## Factor Low High Diff. Effect S.E. Lower 0.95 Upper 0.95
## AGE 52.00 68.00 16.00 0.4076500 0.072045 0.2664400 0.54885
## Hazard Ratio 52.00 68.00 16.00 1.5033000 NA 1.3053000 1.73130
## BMI 24.11 28.73 4.62 0.5012000 0.494450 -0.4679000 1.47030
## Hazard Ratio 24.11 28.73 4.62 1.6507000 NA 0.6263100 4.35060
## SYSTH 127.00 157.00 30.00 0.0448550 0.121590 -0.1934600 0.28317
## Hazard Ratio 127.00 157.00 30.00 1.0459000 NA 0.8241100 1.32730
## SYSTBP 126.00 152.00 26.00 -0.0768050 0.110390 -0.2931600 0.13955
## Hazard Ratio 126.00 152.00 26.00 0.9260700 NA 0.7459000 1.14980
## DIASTH 74.00 90.00 16.00 0.1377800 0.112850 -0.0833960 0.35895
## Hazard Ratio 74.00 90.00 16.00 1.1477000 NA 0.9199900 1.43180
## DIASTBP 73.00 86.00 13.00 0.0068640 0.096422 -0.1821200 0.19585
## Hazard Ratio 73.00 86.00 13.00 1.0069000 NA 0.8335000 1.21630
## WEIGHT 72.00 89.00 17.00 -0.7990600 0.608650 -1.9920000 0.39387
## Hazard Ratio 72.00 89.00 17.00 0.4497500 NA 0.1364200 1.48270
## LENGTH 1.68 1.80 0.12 0.3853400 0.402830 -0.4041900 1.17490
## Hazard Ratio 1.68 1.80 0.12 1.4701000 NA 0.6675200 3.23770
## CHOL 4.40 5.90 1.50 0.1124800 1.626600 -3.0756000 3.30060
## Hazard Ratio 4.40 5.90 1.50 1.1191000 NA 0.0461620 27.12800
## LDL 2.37 3.83 1.46 -0.0317260 1.590600 -3.1492000 3.08580
## Hazard Ratio 2.37 3.83 1.46 0.9687700 NA 0.0428860 21.88400
## HDL 0.96 1.42 0.46 -0.2087600 0.505560 -1.1996000 0.78212
## Hazard Ratio 0.96 1.42 0.46 0.8115900 NA 0.3013000 2.18610
## SUMSCORE_5LEVELS 1.00 5.00 4.00 1.2765000 0.225590 0.8343900 1.71870
## Hazard Ratio 1.00 5.00 4.00 3.5842000 NA 2.3034000 5.57720
## HOMOC 10.50 16.00 5.50 0.0641290 0.045001 -0.0240710 0.15233
## Hazard Ratio 10.50 16.00 5.50 1.0662000 NA 0.9762200 1.16450
## CREAT 78.00 101.00 23.00 0.1523000 0.037558 0.0786910 0.22591
## Hazard Ratio 78.00 101.00 23.00 1.1645000 NA 1.0819000 1.25350
## IMT 0.75 1.07 0.32 0.1836600 0.058280 0.0694360 0.29789
## Hazard Ratio 0.75 1.07 0.32 1.2016000 NA 1.0719000 1.34700
## TRIG 1.13 2.23 1.10 -0.0404980 0.533860 -1.0869000 1.00590
## Hazard Ratio 1.13 2.23 1.10 0.9603100 NA 0.3372800 2.73420
## GLUT 5.30 6.50 1.20 0.0641980 0.035088 -0.0045735 0.13297
## Hazard Ratio 5.30 6.50 1.20 1.0663000 NA 0.9954400 1.14220
## packyrs 5.90 34.20 28.30 0.1662400 0.071570 0.0259670 0.30652
## Hazard Ratio 5.90 34.20 28.30 1.1809000 NA 1.0263000 1.35870
## SEX - 2:1 1.00 2.00 NA -0.1310400 0.162110 -0.4487700 0.18668
## Hazard Ratio 1.00 2.00 NA 0.8771800 NA 0.6384200 1.20520
## SMOKING - 1:2 2.00 1.00 NA -0.0013686 0.161460 -0.3178100 0.31508
## Hazard Ratio 2.00 1.00 NA 0.9986300 NA 0.7277400 1.37040
## SMOKING - 3:2 2.00 3.00 NA 0.0488110 0.201850 -0.3468100 0.44443
## Hazard Ratio 2.00 3.00 NA 1.0500000 NA 0.7069400 1.55960
## alcohol - 1:3 3.00 1.00 NA 0.1445200 0.120930 -0.0925020 0.38154
## Hazard Ratio 3.00 1.00 NA 1.1555000 NA 0.9116500 1.46450
## alcohol - 2:3 3.00 2.00 NA -0.0393420 0.147710 -0.3288400 0.25016
## Hazard Ratio 3.00 2.00 NA 0.9614200 NA 0.7197600 1.28420
## DIABETES - 1:0 1.00 2.00 NA 0.0680540 0.155510 -0.2367400 0.37285
## Hazard Ratio 1.00 2.00 NA 1.0704000 NA 0.7892000 1.45190
## albumin - 2:1 1.00 2.00 NA 0.2732000 0.117180 0.0435270 0.50287
## Hazard Ratio 1.00 2.00 NA 1.3142000 NA 1.0445000 1.65350
## albumin - 3:1 1.00 3.00 NA 0.4784600 0.209270 0.0683080 0.88862
## Hazard Ratio 1.00 3.00 NA 1.6136000 NA 1.0707000 2.43180
## STENOSIS - 1:0 1.00 2.00 NA 0.1494800 0.108760 -0.0636870 0.36266
## Hazard Ratio 1.00 2.00 NA 1.1612000 NA 0.9383000 1.43710vif(COXPH.FULL.COMPLETE.AREGIMPUTED_4)## AGE SEX=2 SMOKING=2 SMOKING=3
## 1.423801 1.834715 1.936069 1.535325
## alcohol=2 alcohol=3 BMI SYSTH
## 1.429097 1.569112 64.065892 3.937466
## SYSTBP DIASTH DIASTBP WEIGHT
## 3.435346 3.206930 2.673371 89.404506
## LENGTH CHOL LDL HDL
## 35.040767 611.492448 544.551054 56.706677
## DIABETES=1 SUMSCORE_5LEVELS HOMOC CREAT
## 2.251743 1.164305 1.432342 1.777291
## albumin=2 albumin=3 STENOSIS=1 IMT
## 1.178710 1.552418 1.212514 1.352500
## TRIG GLUT packyrs
## 149.510494 2.164995 1.379450COXPH.FULL.COMPLETE.AREGIMPUTED_4## Cox Proportional Hazards Model
##
## cph(formula = Surv(TEVENT, EVENT) ~ ifelse(AGE > 50, (AGE - 50)^2,
## 0) + SEX + SMOKING + alcohol + BMI + SYSTH + SYSTBP + DIASTH +
## DIASTBP + WEIGHT + LENGTH + CHOL + LDL + HDL + DIABETES +
## SUMSCORE_5LEVELS + HOMOC + log(CREAT) + albumin + STENOSIS +
## IMT + TRIG + GLUT + packyrs, data = SMART.AREGIMPUTED_4,
## x = T, y = T, surv = T)
##
## Model Tests Discrimination
## Indexes
## Obs 3873 LR chi2 296.57 R2 0.088
## Events 460 d.f. 27 R2(27,3873)0.067
## Center 9.3809 Pr(> chi2) 0.0000 R2(27,460)0.443
## Score chi2 363.32 Dxy 0.402
## Pr(> chi2) 0.0000
##
## Coef S.E. Wald Z Pr(>|Z|)
## AGE 0.0013 0.0002 5.66 <0.0001
## SEX=2 -0.1310 0.1621 -0.81 0.4189
## SMOKING=2 0.0014 0.1615 0.01 0.9932
## SMOKING=3 0.0502 0.2444 0.21 0.8373
## alcohol=2 -0.1839 0.1667 -1.10 0.2702
## alcohol=3 -0.1445 0.1209 -1.20 0.2321
## BMI 0.1085 0.1070 1.01 0.3107
## SYSTH 0.0015 0.0041 0.37 0.7122
## SYSTBP -0.0030 0.0042 -0.70 0.4866
## DIASTH 0.0086 0.0071 1.22 0.2221
## DIASTBP 0.0005 0.0074 0.07 0.9432
## WEIGHT -0.0470 0.0358 -1.31 0.1892
## LENGTH 3.2112 3.3569 0.96 0.3388
## CHOL 0.0750 1.0844 0.07 0.9449
## LDL -0.0217 1.0894 -0.02 0.9841
## HDL -0.4538 1.0990 -0.41 0.6797
## DIABETES=1 0.0681 0.1555 0.44 0.6617
## SUMSCORE_5LEVELS 0.3191 0.0564 5.66 <0.0001
## HOMOC 0.0117 0.0082 1.43 0.1541
## CREAT 0.5894 0.1453 4.06 <0.0001
## albumin=2 0.2732 0.1172 2.33 0.0197
## albumin=3 0.4785 0.2093 2.29 0.0222
## STENOSIS=1 0.1495 0.1088 1.37 0.1693
## IMT 0.5739 0.1821 3.15 0.0016
## TRIG -0.0368 0.4853 -0.08 0.9395
## GLUT 0.0535 0.0292 1.83 0.0673
## packyrs 0.0059 0.0025 2.32 0.0202##################################
# FULL
# After removing variables which are:
# High multicollinearity contributors
# Non-standard risk factors
# Minimal predictors of survival outcome based from initial exploration
# Minimal predictors of survival outcome based from domain knowledge and literature
##################################
COXPH.FULL.AREGIMPUTED_4 <-cph(Surv(TEVENT,EVENT) ~ ifelse(AGE>50, (AGE-50)^2,0) +
SEX +
SMOKING +
alcohol +
BMI +
SYSTH +
HDL+
DIABETES +
SUMSCORE_5LEVELS +
HOMOC +
log(CREAT) +
albumin +
STENOSIS +
IMT,
data = SMART.AREGIMPUTED_4,
x=T,
y=T,
surv=T)
anova(COXPH.FULL.AREGIMPUTED_4)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## AGE 31.66 1 <.0001
## SEX 0.08 1 0.7798
## SMOKING 1.53 2 0.4659
## alcohol 1.32 2 0.5159
## BMI 3.03 1 0.0816
## SYSTH 1.97 1 0.1606
## HDL 5.63 1 0.0177
## DIABETES 3.77 1 0.0521
## SUMSCORE_5LEVELS 33.70 1 <.0001
## HOMOC 3.03 1 0.0816
## CREAT 14.89 1 0.0001
## albumin 7.74 2 0.0208
## STENOSIS 2.04 1 0.1537
## IMT 8.53 1 0.0035
## TOTAL 315.74 17 <.0001summary(COXPH.FULL.AREGIMPUTED_4)## Effects Response : Surv(TEVENT, EVENT)
##
## Factor Low High Diff. Effect S.E. Lower 0.95 Upper 0.95
## AGE 52.00 68.00 16.00 0.388080 0.068969 0.2529000 0.523250
## Hazard Ratio 52.00 68.00 16.00 1.474100 NA 1.2878000 1.687500
## BMI 24.11 28.73 4.62 -0.114050 0.065492 -0.2424100 0.014314
## Hazard Ratio 24.11 28.73 4.62 0.892210 NA 0.7847300 1.014400
## SYSTH 127.00 157.00 30.00 0.092473 0.065911 -0.0367100 0.221660
## Hazard Ratio 127.00 157.00 30.00 1.096900 NA 0.9639600 1.248100
## HDL 0.96 1.42 0.46 -0.174110 0.073384 -0.3179400 -0.030275
## Hazard Ratio 0.96 1.42 0.46 0.840210 NA 0.7276500 0.970180
## SUMSCORE_5LEVELS 1.00 5.00 4.00 1.289000 0.222030 0.8538400 1.724200
## Hazard Ratio 1.00 5.00 4.00 3.629200 NA 2.3487000 5.607900
## HOMOC 10.50 16.00 5.50 0.076810 0.044099 -0.0096231 0.163240
## Hazard Ratio 10.50 16.00 5.50 1.079800 NA 0.9904200 1.177300
## CREAT 78.00 101.00 23.00 0.143120 0.037091 0.0704260 0.215820
## Hazard Ratio 78.00 101.00 23.00 1.153900 NA 1.0730000 1.240900
## IMT 0.75 1.07 0.32 0.167110 0.057217 0.0549680 0.279250
## Hazard Ratio 0.75 1.07 0.32 1.181900 NA 1.0565000 1.322100
## SEX - 2:1 1.00 2.00 NA -0.037842 0.135330 -0.3030800 0.227390
## Hazard Ratio 1.00 2.00 NA 0.962860 NA 0.7385400 1.255300
## SMOKING - 1:2 2.00 1.00 NA -0.167830 0.143840 -0.4497600 0.114090
## Hazard Ratio 2.00 1.00 NA 0.845500 NA 0.6377800 1.120900
## SMOKING - 3:2 2.00 3.00 NA 0.056140 0.200990 -0.3377900 0.450070
## Hazard Ratio 2.00 3.00 NA 1.057700 NA 0.7133400 1.568400
## alcohol - 1:3 3.00 1.00 NA 0.126330 0.120170 -0.1092000 0.361860
## Hazard Ratio 3.00 1.00 NA 1.134700 NA 0.8965500 1.436000
## alcohol - 2:3 3.00 2.00 NA -0.029610 0.146650 -0.3170400 0.257820
## Hazard Ratio 3.00 2.00 NA 0.970820 NA 0.7283000 1.294100
## DIABETES - 1:0 1.00 2.00 NA 0.213620 0.109970 -0.0019123 0.429140
## Hazard Ratio 1.00 2.00 NA 1.238100 NA 0.9980900 1.535900
## albumin - 2:1 1.00 2.00 NA 0.273640 0.116500 0.0452980 0.501980
## Hazard Ratio 1.00 2.00 NA 1.314700 NA 1.0463000 1.652000
## albumin - 3:1 1.00 3.00 NA 0.431190 0.207600 0.0242960 0.838080
## Hazard Ratio 1.00 3.00 NA 1.539100 NA 1.0246000 2.311900
## STENOSIS - 1:0 1.00 2.00 NA 0.153770 0.107790 -0.0574970 0.365040
## Hazard Ratio 1.00 2.00 NA 1.166200 NA 0.9441200 1.440600vif(COXPH.FULL.AREGIMPUTED_4)## AGE SEX=2 SMOKING=2 SMOKING=3
## 1.310056 1.278569 1.536609 1.410042
## alcohol=2 alcohol=3 BMI SYSTH
## 1.413500 1.549665 1.106940 1.173223
## HDL DIABETES=1 SUMSCORE_5LEVELS HOMOC
## 1.206997 1.125698 1.143414 1.378802
## CREAT albumin=2 albumin=3 STENOSIS=1
## 1.735913 1.165891 1.528349 1.190245
## IMT
## 1.315947COXPH.FULL.AREGIMPUTED_4## Cox Proportional Hazards Model
##
## cph(formula = Surv(TEVENT, EVENT) ~ ifelse(AGE > 50, (AGE - 50)^2,
## 0) + SEX + SMOKING + alcohol + BMI + SYSTH + HDL + DIABETES +
## SUMSCORE_5LEVELS + HOMOC + log(CREAT) + albumin + STENOSIS +
## IMT, data = SMART.AREGIMPUTED_4, x = T, y = T, surv = T)
##
## Model Tests Discrimination
## Indexes
## Obs 3873 LR chi2 280.66 R2 0.084
## Events 460 d.f. 17 R2(17,3873)0.066
## Center 3.3281 Pr(> chi2) 0.0000 R2(17,460)0.436
## Score chi2 349.00 Dxy 0.402
## Pr(> chi2) 0.0000
##
## Coef S.E. Wald Z Pr(>|Z|)
## AGE 0.0012 0.0002 5.63 <0.0001
## SEX=2 -0.0378 0.1353 -0.28 0.7798
## SMOKING=2 0.1678 0.1438 1.17 0.2433
## SMOKING=3 0.2240 0.2342 0.96 0.3389
## alcohol=2 -0.1559 0.1658 -0.94 0.3470
## alcohol=3 -0.1263 0.1202 -1.05 0.2932
## BMI -0.0247 0.0142 -1.74 0.0816
## SYSTH 0.0031 0.0022 1.40 0.1606
## HDL -0.3785 0.1595 -2.37 0.0177
## DIABETES=1 0.2136 0.1100 1.94 0.0521
## SUMSCORE_5LEVELS 0.3223 0.0555 5.81 <0.0001
## HOMOC 0.0140 0.0080 1.74 0.0816
## CREAT 0.5539 0.1435 3.86 0.0001
## albumin=2 0.2736 0.1165 2.35 0.0188
## albumin=3 0.4312 0.2076 2.08 0.0378
## STENOSIS=1 0.1538 0.1078 1.43 0.1537
## IMT 0.5222 0.1788 2.92 0.0035##################################
# Formulating the FULL
# Cox Proportional Hazards Model
# Using the combined complete and
# 5TH imputation results from AREG
##################################
SMART.AREGIMPUTED_5$EVENT <- as.numeric(SMART.AREGIMPUTED_5$EVENT)
SMART.AREGIMPUTED_5$SMOKING <- as.factor(SMART.AREGIMPUTED_5$SMOKING)
SMART.AREGIMPUTED_5$alcohol <- as.factor(SMART.AREGIMPUTED_5$alcohol)
SMART.AREGIMPUTED_5$albumin <- as.factor(SMART.AREGIMPUTED_5$albumin)
dd <- datadist(SMART.AREGIMPUTED_5)
options(datadist="dd")
##################################
# FULL COMPLETE
##################################
COXPH.FULL.COMPLETE.AREGIMPUTED_5 <-cph(Surv(TEVENT,EVENT) ~ ifelse(AGE>50, (AGE-50)^2,0) +
SEX +
SMOKING +
alcohol +
BMI +
SYSTH +
SYSTBP +
DIASTH +
DIASTBP +
WEIGHT +
LENGTH +
CHOL +
LDL +
HDL+
DIABETES +
SUMSCORE_5LEVELS +
HOMOC +
log(CREAT) +
albumin +
STENOSIS +
IMT +
TRIG +
GLUT +
packyrs,
data = SMART.AREGIMPUTED_5,
x=T,
y=T,
surv=T)
anova(COXPH.FULL.COMPLETE.AREGIMPUTED_5)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## AGE 35.82 1 <.0001
## SEX 0.69 1 0.4062
## SMOKING 0.08 2 0.9595
## alcohol 2.09 2 0.3509
## BMI 0.80 1 0.3712
## SYSTH 0.53 1 0.4685
## SYSTBP 1.28 1 0.2581
## DIASTH 0.09 1 0.7600
## DIASTBP 0.44 1 0.5092
## WEIGHT 1.39 1 0.2376
## LENGTH 0.76 1 0.3844
## CHOL 0.26 1 0.6099
## LDL 0.21 1 0.6498
## HDL 0.74 1 0.3886
## DIABETES 0.10 1 0.7462
## SUMSCORE_5LEVELS 33.23 1 <.0001
## HOMOC 0.02 1 0.8773
## CREAT 15.93 1 0.0001
## albumin 14.22 2 0.0008
## STENOSIS 1.98 1 0.1590
## IMT 8.67 1 0.0032
## TRIG 0.25 1 0.6152
## GLUT 2.79 1 0.0950
## packyrs 4.68 1 0.0305
## TOTAL 328.34 27 <.0001summary(COXPH.FULL.COMPLETE.AREGIMPUTED_5)## Effects Response : Surv(TEVENT, EVENT)
##
## Factor Low High Diff. Effect S.E. Lower 0.95 Upper 0.95
## AGE 52.00 68.00 16.00 0.4301400 0.071865 0.289280 0.570990
## Hazard Ratio 52.00 68.00 16.00 1.5375000 NA 1.335500 1.770000
## BMI 24.11 28.73 4.62 0.4403300 0.492380 -0.524720 1.405400
## Hazard Ratio 24.11 28.73 4.62 1.5532000 NA 0.591720 4.077100
## SYSTH 127.00 156.00 29.00 0.0844850 0.116530 -0.143920 0.312890
## Hazard Ratio 127.00 156.00 29.00 1.0882000 NA 0.865960 1.367400
## SYSTBP 126.00 152.00 26.00 -0.1252400 0.110750 -0.342300 0.091818
## Hazard Ratio 126.00 152.00 26.00 0.8822800 NA 0.710140 1.096200
## DIASTH 74.00 89.00 15.00 0.0319010 0.104430 -0.172780 0.236580
## Hazard Ratio 74.00 89.00 15.00 1.0324000 NA 0.841330 1.266900
## DIASTBP 73.00 86.00 13.00 0.0640560 0.097036 -0.126130 0.254240
## Hazard Ratio 73.00 86.00 13.00 1.0662000 NA 0.881500 1.289500
## WEIGHT 72.00 89.00 17.00 -0.7144200 0.604960 -1.900100 0.471290
## Hazard Ratio 72.00 89.00 17.00 0.4894800 NA 0.149550 1.602100
## LENGTH 1.68 1.80 0.12 0.3486800 0.400830 -0.436950 1.134300
## Hazard Ratio 1.68 1.80 0.12 1.4172000 NA 0.646010 3.109000
## CHOL 4.40 5.90 1.50 0.7892000 1.546700 -2.242200 3.820600
## Hazard Ratio 4.40 5.90 1.50 2.2016000 NA 0.106230 45.631000
## LDL 2.37 3.83 1.46 -0.6877900 1.515000 -3.657100 2.281500
## Hazard Ratio 2.37 3.83 1.46 0.5026900 NA 0.025808 9.791300
## HDL 0.96 1.42 0.46 -0.4164300 0.483040 -1.363200 0.530310
## Hazard Ratio 0.96 1.42 0.46 0.6594000 NA 0.255850 1.699500
## SUMSCORE_5LEVELS 1.00 5.00 4.00 1.3091000 0.227090 0.863980 1.754100
## Hazard Ratio 1.00 5.00 4.00 3.7027000 NA 2.372600 5.778500
## HOMOC 10.50 16.10 5.60 0.0071533 0.046316 -0.083623 0.097930
## Hazard Ratio 10.50 16.10 5.60 1.0072000 NA 0.919780 1.102900
## CREAT 78.00 101.00 23.00 0.1488100 0.037288 0.075728 0.221900
## Hazard Ratio 78.00 101.00 23.00 1.1605000 NA 1.078700 1.248400
## IMT 0.75 1.07 0.32 0.1701200 0.057789 0.056857 0.283390
## Hazard Ratio 0.75 1.07 0.32 1.1855000 NA 1.058500 1.327600
## TRIG 1.13 2.23 1.10 -0.2556900 0.508600 -1.252500 0.741160
## Hazard Ratio 1.13 2.23 1.10 0.7743900 NA 0.285780 2.098400
## GLUT 5.30 6.50 1.20 0.0588280 0.035239 -0.010239 0.127900
## Hazard Ratio 5.30 6.50 1.20 1.0606000 NA 0.989810 1.136400
## packyrs 5.90 34.20 28.30 0.1556900 0.071942 0.014681 0.296690
## Hazard Ratio 5.90 34.20 28.30 1.1685000 NA 1.014800 1.345400
## SEX - 2:1 1.00 2.00 NA -0.1345300 0.161970 -0.451990 0.182920
## Hazard Ratio 1.00 2.00 NA 0.8741200 NA 0.636360 1.200700
## SMOKING - 1:2 2.00 1.00 NA -0.0140640 0.161680 -0.330940 0.302820
## Hazard Ratio 2.00 1.00 NA 0.9860300 NA 0.718250 1.353700
## SMOKING - 3:2 2.00 3.00 NA 0.0520460 0.198480 -0.336970 0.441060
## Hazard Ratio 2.00 3.00 NA 1.0534000 NA 0.713930 1.554400
## alcohol - 1:3 3.00 1.00 NA 0.1590900 0.121030 -0.078122 0.396300
## Hazard Ratio 3.00 1.00 NA 1.1724000 NA 0.924850 1.486300
## alcohol - 2:3 3.00 2.00 NA -0.0402250 0.147920 -0.330130 0.249680
## Hazard Ratio 3.00 2.00 NA 0.9605700 NA 0.718830 1.283600
## DIABETES - 1:0 1.00 2.00 NA 0.0505060 0.156070 -0.255380 0.356390
## Hazard Ratio 1.00 2.00 NA 1.0518000 NA 0.774620 1.428200
## albumin - 2:1 1.00 2.00 NA 0.2777100 0.118500 0.045455 0.509960
## Hazard Ratio 1.00 2.00 NA 1.3201000 NA 1.046500 1.665200
## albumin - 3:1 1.00 3.00 NA 0.6964900 0.197790 0.308820 1.084200
## Hazard Ratio 1.00 3.00 NA 2.0067000 NA 1.361800 2.956900
## STENOSIS - 1:0 1.00 2.00 NA 0.1528100 0.108490 -0.059828 0.365450
## Hazard Ratio 1.00 2.00 NA 1.1651000 NA 0.941930 1.441200vif(COXPH.FULL.COMPLETE.AREGIMPUTED_5)## AGE SEX=2 SMOKING=2 SMOKING=3
## 1.418819 1.831725 1.955859 1.544054
## alcohol=2 alcohol=3 BMI SYSTH
## 1.435126 1.571437 63.692998 3.876737
## SYSTBP DIASTH DIASTBP WEIGHT
## 3.436950 3.081005 2.682241 88.457160
## LENGTH CHOL LDL HDL
## 34.762923 558.992648 495.027328 52.120441
## DIABETES=1 SUMSCORE_5LEVELS HOMOC CREAT
## 2.257665 1.183474 1.509397 1.793220
## albumin=2 albumin=3 STENOSIS=1 IMT
## 1.192460 1.610680 1.211036 1.337456
## TRIG GLUT packyrs
## 134.677350 2.172496 1.385593COXPH.FULL.COMPLETE.AREGIMPUTED_5## Cox Proportional Hazards Model
##
## cph(formula = Surv(TEVENT, EVENT) ~ ifelse(AGE > 50, (AGE - 50)^2,
## 0) + SEX + SMOKING + alcohol + BMI + SYSTH + SYSTBP + DIASTH +
## DIASTBP + WEIGHT + LENGTH + CHOL + LDL + HDL + DIABETES +
## SUMSCORE_5LEVELS + HOMOC + log(CREAT) + albumin + STENOSIS +
## IMT + TRIG + GLUT + packyrs, data = SMART.AREGIMPUTED_5,
## x = T, y = T, surv = T)
##
## Model Tests Discrimination
## Indexes
## Obs 3873 LR chi2 293.29 R2 0.087
## Events 460 d.f. 27 R2(27,3873)0.066
## Center 8.4236 Pr(> chi2) 0.0000 R2(27,460)0.439
## Score chi2 368.04 Dxy 0.396
## Pr(> chi2) 0.0000
##
## Coef S.E. Wald Z Pr(>|Z|)
## AGE 0.0013 0.0002 5.99 <0.0001
## SEX=2 -0.1345 0.1620 -0.83 0.4062
## SMOKING=2 0.0141 0.1617 0.09 0.9307
## SMOKING=3 0.0661 0.2412 0.27 0.7840
## alcohol=2 -0.1993 0.1671 -1.19 0.2329
## alcohol=3 -0.1591 0.1210 -1.31 0.1887
## BMI 0.0953 0.1066 0.89 0.3712
## SYSTH 0.0029 0.0040 0.72 0.4685
## SYSTBP -0.0048 0.0043 -1.13 0.2581
## DIASTH 0.0021 0.0070 0.31 0.7600
## DIASTBP 0.0049 0.0075 0.66 0.5092
## WEIGHT -0.0420 0.0356 -1.18 0.2376
## LENGTH 2.9056 3.3403 0.87 0.3844
## CHOL 0.5261 1.0311 0.51 0.6099
## LDL -0.4711 1.0376 -0.45 0.6498
## HDL -0.9053 1.0501 -0.86 0.3886
## DIABETES=1 0.0505 0.1561 0.32 0.7462
## SUMSCORE_5LEVELS 0.3273 0.0568 5.76 <0.0001
## HOMOC 0.0013 0.0083 0.15 0.8773
## CREAT 0.5759 0.1443 3.99 <0.0001
## albumin=2 0.2777 0.1185 2.34 0.0191
## albumin=3 0.6965 0.1978 3.52 0.0004
## STENOSIS=1 0.1528 0.1085 1.41 0.1590
## IMT 0.5316 0.1806 2.94 0.0032
## TRIG -0.2324 0.4624 -0.50 0.6152
## GLUT 0.0490 0.0294 1.67 0.0950
## packyrs 0.0055 0.0025 2.16 0.0305##################################
# FULL
# After removing variables which are:
# High multicollinearity contributors
# Non-standard risk factors
# Minimal predictors of survival outcome based from initial exploration
# Minimal predictors of survival outcome based from domain knowledge and literature
##################################
COXPH.FULL.AREGIMPUTED_5 <-cph(Surv(TEVENT,EVENT) ~ ifelse(AGE>50, (AGE-50)^2,0) +
SEX +
SMOKING +
alcohol +
BMI +
SYSTH +
HDL+
DIABETES +
SUMSCORE_5LEVELS +
HOMOC +
log(CREAT) +
albumin +
STENOSIS +
IMT,
data = SMART.AREGIMPUTED_5,
x=T,
y=T,
surv=T)
anova(COXPH.FULL.AREGIMPUTED_5)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## AGE 36.75 1 <.0001
## SEX 0.23 1 0.6330
## SMOKING 1.54 2 0.4621
## alcohol 1.65 2 0.4376
## BMI 2.85 1 0.0913
## SYSTH 0.73 1 0.3927
## HDL 5.79 1 0.0161
## DIABETES 2.87 1 0.0902
## SUMSCORE_5LEVELS 34.24 1 <.0001
## HOMOC 0.12 1 0.7297
## CREAT 14.31 1 0.0002
## albumin 14.00 2 0.0009
## STENOSIS 2.29 1 0.1301
## IMT 8.16 1 0.0043
## TOTAL 319.93 17 <.0001summary(COXPH.FULL.AREGIMPUTED_5)## Effects Response : Surv(TEVENT, EVENT)
##
## Factor Low High Diff. Effect S.E. Lower 0.95 Upper 0.95
## AGE 52.00 68.00 16.00 0.417560 0.068876 0.282560 0.552550
## Hazard Ratio 52.00 68.00 16.00 1.518300 NA 1.326500 1.737700
## BMI 24.11 28.73 4.62 -0.110470 0.065425 -0.238700 0.017763
## Hazard Ratio 24.11 28.73 4.62 0.895420 NA 0.787650 1.017900
## SYSTH 127.00 156.00 29.00 0.054260 0.063487 -0.070172 0.178690
## Hazard Ratio 127.00 156.00 29.00 1.055800 NA 0.932230 1.195700
## HDL 0.96 1.42 0.46 -0.176580 0.073406 -0.320450 -0.032708
## Hazard Ratio 0.96 1.42 0.46 0.838130 NA 0.725820 0.967820
## SUMSCORE_5LEVELS 1.00 5.00 4.00 1.309800 0.223860 0.871080 1.748600
## Hazard Ratio 1.00 5.00 4.00 3.705600 NA 2.389500 5.746600
## HOMOC 10.50 16.10 5.60 0.015627 0.045224 -0.073011 0.104260
## Hazard Ratio 10.50 16.10 5.60 1.015700 NA 0.929590 1.109900
## CREAT 78.00 101.00 23.00 0.137640 0.036383 0.066330 0.208950
## Hazard Ratio 78.00 101.00 23.00 1.147600 NA 1.068600 1.232400
## IMT 0.75 1.07 0.32 0.161310 0.056455 0.050656 0.271960
## Hazard Ratio 0.75 1.07 0.32 1.175000 NA 1.052000 1.312500
## SEX - 2:1 1.00 2.00 NA -0.064458 0.135000 -0.329050 0.200140
## Hazard Ratio 1.00 2.00 NA 0.937580 NA 0.719600 1.221600
## SMOKING - 1:2 2.00 1.00 NA -0.167940 0.144060 -0.450300 0.114420
## Hazard Ratio 2.00 1.00 NA 0.845410 NA 0.637440 1.121200
## SMOKING - 3:2 2.00 3.00 NA 0.058064 0.197470 -0.328970 0.445100
## Hazard Ratio 2.00 3.00 NA 1.059800 NA 0.719670 1.560600
## alcohol - 1:3 3.00 1.00 NA 0.139280 0.120460 -0.096822 0.375380
## Hazard Ratio 3.00 1.00 NA 1.149400 NA 0.907720 1.455500
## alcohol - 2:3 3.00 2.00 NA -0.039480 0.147280 -0.328150 0.249190
## Hazard Ratio 3.00 2.00 NA 0.961290 NA 0.720260 1.283000
## DIABETES - 1:0 1.00 2.00 NA 0.186040 0.109820 -0.029193 0.401270
## Hazard Ratio 1.00 2.00 NA 1.204500 NA 0.971230 1.493700
## albumin - 2:1 1.00 2.00 NA 0.280910 0.117820 0.049979 0.511840
## Hazard Ratio 1.00 2.00 NA 1.324300 NA 1.051200 1.668400
## albumin - 3:1 1.00 3.00 NA 0.673130 0.195120 0.290710 1.055500
## Hazard Ratio 1.00 3.00 NA 1.960400 NA 1.337400 2.873500
## STENOSIS - 1:0 1.00 2.00 NA 0.162680 0.107470 -0.047954 0.373320
## Hazard Ratio 1.00 2.00 NA 1.176700 NA 0.953180 1.452500vif(COXPH.FULL.AREGIMPUTED_5)## AGE SEX=2 SMOKING=2 SMOKING=3
## 1.309269 1.272356 1.552807 1.413467
## alcohol=2 alcohol=3 BMI SYSTH
## 1.422649 1.556864 1.108079 1.161651
## HDL DIABETES=1 SUMSCORE_5LEVELS HOMOC
## 1.212141 1.117513 1.165569 1.443350
## CREAT albumin=2 albumin=3 STENOSIS=1
## 1.723397 1.179223 1.567982 1.188038
## IMT
## 1.294708COXPH.FULL.AREGIMPUTED_5## Cox Proportional Hazards Model
##
## cph(formula = Surv(TEVENT, EVENT) ~ ifelse(AGE > 50, (AGE - 50)^2,
## 0) + SEX + SMOKING + alcohol + BMI + SYSTH + HDL + DIABETES +
## SUMSCORE_5LEVELS + HOMOC + log(CREAT) + albumin + STENOSIS +
## IMT, data = SMART.AREGIMPUTED_5, x = T, y = T, surv = T)
##
## Model Tests Discrimination
## Indexes
## Obs 3873 LR chi2 279.73 R2 0.083
## Events 460 d.f. 17 R2(17,3873)0.066
## Center 2.9113 Pr(> chi2) 0.0000 R2(17,460)0.435
## Score chi2 356.53 Dxy 0.394
## Pr(> chi2) 0.0000
##
## Coef S.E. Wald Z Pr(>|Z|)
## AGE 0.0013 0.0002 6.06 <0.0001
## SEX=2 -0.0645 0.1350 -0.48 0.6330
## SMOKING=2 0.1679 0.1441 1.17 0.2437
## SMOKING=3 0.2260 0.2307 0.98 0.3273
## alcohol=2 -0.1788 0.1664 -1.07 0.2826
## alcohol=3 -0.1393 0.1205 -1.16 0.2476
## BMI -0.0239 0.0142 -1.69 0.0913
## SYSTH 0.0019 0.0022 0.85 0.3927
## HDL -0.3839 0.1596 -2.41 0.0161
## DIABETES=1 0.1860 0.1098 1.69 0.0902
## SUMSCORE_5LEVELS 0.3275 0.0560 5.85 <0.0001
## HOMOC 0.0028 0.0081 0.35 0.7297
## CREAT 0.5326 0.1408 3.78 0.0002
## albumin=2 0.2809 0.1178 2.38 0.0171
## albumin=3 0.6731 0.1951 3.45 0.0006
## STENOSIS=1 0.1627 0.1075 1.51 0.1301
## IMT 0.5041 0.1764 2.86 0.0043##################################
# Consolidating all coefficients from the
# FULL Cox Proportional Hazards Model
# Using the combined complete and
# 1ST to 5TH imputation results from AREG
##################################
(COXPH.FULL.AREGIMPUTED_12345.Coefficients <- rbind(coef(COXPH.FULL.AREGIMPUTED_1),
coef(COXPH.FULL.AREGIMPUTED_2),
coef(COXPH.FULL.AREGIMPUTED_3),
coef(COXPH.FULL.AREGIMPUTED_4),
coef(COXPH.FULL.AREGIMPUTED_5)))## AGE SEX=2 SMOKING=2 SMOKING=3 alcohol=2 alcohol=3
## [1,] 0.001319438 -0.05323006 0.1836178 0.2504782 -0.1558516 -0.1263426
## [2,] 0.001290295 -0.05216943 0.1842736 0.2450232 -0.1599791 -0.1196699
## [3,] 0.001316533 -0.04721299 0.1932424 0.2983591 -0.1446361 -0.1145161
## [4,] 0.001212739 -0.03784236 0.1678314 0.2239712 -0.1559366 -0.1263267
## [5,] 0.001304874 -0.06445816 0.1679385 0.2260025 -0.1787601 -0.1392797
## BMI SYSTH HDL DIABETES=1 SUMSCORE_5LEVELS HOMOC
## [1,] -0.02475359 0.001068306 -0.3776243 0.2089031 0.3318611 0.001016311
## [2,] -0.02363049 0.002205609 -0.3845823 0.1856939 0.3332411 0.003646549
## [3,] -0.02409281 0.002894025 -0.3946006 0.1958399 0.3346853 0.004229653
## [4,] -0.02468578 0.003082448 -0.3784896 0.2136157 0.3222527 0.013965456
## [5,] -0.02391059 0.001871029 -0.3838719 0.1860407 0.3274619 0.002790467
## CREAT albumin=2 albumin=3 STENOSIS=1 IMT
## [1,] 0.5999677 0.2645359 0.5622142 0.1708450 0.5275760
## [2,] 0.5580850 0.2304765 0.6361029 0.1740932 0.5466388
## [3,] 0.5812481 0.1947722 0.5254523 0.1978645 0.4569895
## [4,] 0.5538597 0.2736406 0.4311872 0.1537693 0.5222199
## [5,] 0.5326395 0.2809080 0.6731279 0.1626805 0.5040841rownames(COXPH.FULL.AREGIMPUTED_12345.Coefficients) <- c("aregImpute_1",
"aregImpute_2",
"aregImpute_3",
"aregImpute_4",
"aregImpute_5")
barchart(COXPH.FULL.AREGIMPUTED_12345.Coefficients,
groups=rownames(COXPH.FULL.AREGIMPUTED_12345.Coefficients),
scales=list(x="free"),
auto.key = list(columns = 5),
layout = c(4,5),
xlab = "Estimated Coefficients",)
1.2.6 Model Selection
[A] Using the imputed data from iteration 3 (aregImputed_3), the full model initially consisted of 14 variables:
[A.1] AGE variable (numeric) coded using its squared value after 50 years [if (AGE>50) then (AGE-50)^2 else 0] called AGE_SQUAREDAFTER50 variable (numeric)
[A.2] SEX variable (factor)
[A.3] SMOKING variable (factor)
[A.4] ALCOHOL variable (factor)
[A.5] BMI variable (numeric)
[A.6] SYSTH variable (numeric)
[A.7] HDL variable (numeric)
[A.8] DIABETES variable (factor)
[A.9] CEREBRAL variable (numeric), CARDIAC variable (numeric), AAA variable (numeric) and PERIPH variable (numeric) coded using their linear combination [CEREBRAL + CARDIAC + (2*AAA) + PERIPH] called SUMSCORE_5LEVELS variable (numeric)
[A.10] HOMOC variable (numeric)
[A.11] CREAT variable (numeric) coded using its logarithm [log(CREAT)] called CREAT_LOG variable (numeric)
[A.12] ALBUMIN variable (factor)
[A.13] STENOSIS variable (factor)
[A.14] IMT variable (numeric)
[B] With backward elimination process based on the AIC criterion applied during variable selection, the reduced model eventually consisted of only 9 remaining variables:
[B.1] AGE variable (numeric) coded using its squared value after 50 years [if (AGE>50) then (AGE-50)^2 else 0] called AGE_SQUAREDAFTER50 variable (numeric)
[B.2] BMI variable (numeric)
[B.3] HDL variable (numeric)
[B.4] DIABETES variable (factor)
[B.5] CEREBRAL variable (numeric), CARDIAC variable (numeric), AAA variable (numeric) and PERIPH variable (numeric) coded using their linear combination [CEREBRAL + CARDIAC + (2*AAA) + PERIPH] called SUMSCORE_5LEVELS variable (numeric)
[B.6] CREAT variable (numeric) coded using its logarithm [log(CREAT)] called CREAT_LOG variable (numeric)
[B.7] ALBUMIN variable (factor)
[B.8] STENOSIS variable (factor)
[B.9] IMT variable (numeric)
[C] The reduced model was justified as the inclusion of the variables creating a full model did not show any significant improvement to model fit (p=0.654, Likelihood Ratio Test).
Code Chunk | Output
##################################
# Loading the 3RD imputation results from AREG
# for the subsequent model specification
##################################
##################################
# FULL MODEL
# with 14 variables
##################################
COXPH.FULL.AREGIMPUTED_3 <-cph(Surv(TEVENT,EVENT) ~ ifelse(AGE>50, (AGE-50)^2,0) +
SEX +
SMOKING +
alcohol +
BMI +
SYSTH +
HDL +
DIABETES +
SUMSCORE_5LEVELS +
HOMOC +
log(CREAT) +
albumin +
STENOSIS +
IMT,
data = SMART.AREGIMPUTED_3,
x=T,
y=T,
surv=T)
anova(COXPH.FULL.AREGIMPUTED_3)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## AGE 37.94 1 <.0001
## SEX 0.12 1 0.7269
## SMOKING 2.25 2 0.3250
## alcohol 1.11 2 0.5753
## BMI 2.88 1 0.0899
## SYSTH 1.69 1 0.1939
## HDL 6.08 1 0.0137
## DIABETES 3.15 1 0.0761
## SUMSCORE_5LEVELS 36.05 1 <.0001
## HOMOC 0.24 1 0.6207
## CREAT 15.67 1 0.0001
## albumin 7.32 2 0.0257
## STENOSIS 3.43 1 0.0642
## IMT 6.57 1 0.0103
## TOTAL 311.06 17 <.0001summary(COXPH.FULL.AREGIMPUTED_3)## Effects Response : Surv(TEVENT, EVENT)
##
## Factor Low High Diff. Effect S.E. Lower 0.95 Upper 0.95
## AGE 52.00 68.00 16.00 0.421290 0.068396 0.287240 0.555340
## Hazard Ratio 52.00 68.00 16.00 1.523900 NA 1.332700 1.742500
## BMI 24.11 28.73 4.62 -0.111310 0.065642 -0.239960 0.017347
## Hazard Ratio 24.11 28.73 4.62 0.894660 NA 0.786660 1.017500
## SYSTH 127.00 156.00 29.00 0.083927 0.064609 -0.042704 0.210560
## Hazard Ratio 127.00 156.00 29.00 1.087500 NA 0.958200 1.234400
## HDL 0.96 1.42 0.46 -0.181520 0.073610 -0.325790 -0.037244
## Hazard Ratio 0.96 1.42 0.46 0.834000 NA 0.721960 0.963440
## SUMSCORE_5LEVELS 1.00 5.00 4.00 1.338700 0.222960 0.901750 1.775700
## Hazard Ratio 1.00 5.00 4.00 3.814200 NA 2.463900 5.904600
## HOMOC 10.50 16.10 5.60 0.023686 0.047858 -0.070114 0.117490
## Hazard Ratio 10.50 16.10 5.60 1.024000 NA 0.932290 1.124700
## CREAT 78.00 101.00 23.00 0.150200 0.037942 0.075835 0.224570
## Hazard Ratio 78.00 101.00 23.00 1.162100 NA 1.078800 1.251800
## IMT 0.75 1.07 0.32 0.146240 0.057032 0.034457 0.258020
## Hazard Ratio 0.75 1.07 0.32 1.157500 NA 1.035100 1.294400
## SEX - 2:1 1.00 2.00 NA -0.047213 0.135210 -0.312210 0.217790
## Hazard Ratio 1.00 2.00 NA 0.953880 NA 0.731830 1.243300
## SMOKING - 1:2 2.00 1.00 NA -0.193240 0.144660 -0.476770 0.090286
## Hazard Ratio 2.00 1.00 NA 0.824280 NA 0.620780 1.094500
## SMOKING - 3:2 2.00 3.00 NA 0.105120 0.197840 -0.282640 0.492880
## Hazard Ratio 2.00 3.00 NA 1.110800 NA 0.753790 1.637000
## alcohol - 1:3 3.00 1.00 NA 0.114520 0.120600 -0.121850 0.350880
## Hazard Ratio 3.00 1.00 NA 1.121300 NA 0.885280 1.420300
## alcohol - 2:3 3.00 2.00 NA -0.030120 0.147370 -0.318970 0.258730
## Hazard Ratio 3.00 2.00 NA 0.970330 NA 0.726900 1.295300
## DIABETES - 1:0 1.00 2.00 NA 0.195840 0.110430 -0.020590 0.412270
## Hazard Ratio 1.00 2.00 NA 1.216300 NA 0.979620 1.510200
## albumin - 2:1 1.00 2.00 NA 0.194770 0.118990 -0.038447 0.427990
## Hazard Ratio 1.00 2.00 NA 1.215000 NA 0.962280 1.534200
## albumin - 3:1 1.00 3.00 NA 0.525450 0.207680 0.118400 0.932500
## Hazard Ratio 1.00 3.00 NA 1.691200 NA 1.125700 2.540900
## STENOSIS - 1:0 1.00 2.00 NA 0.197860 0.106910 -0.011678 0.407410
## Hazard Ratio 1.00 2.00 NA 1.218800 NA 0.988390 1.502900COXPH.FULL.AREGIMPUTED_3## Cox Proportional Hazards Model
##
## cph(formula = Surv(TEVENT, EVENT) ~ ifelse(AGE > 50, (AGE - 50)^2,
## 0) + SEX + SMOKING + alcohol + BMI + SYSTH + HDL + DIABETES +
## SUMSCORE_5LEVELS + HOMOC + log(CREAT) + albumin + STENOSIS +
## IMT, data = SMART.AREGIMPUTED_3, x = T, y = T, surv = T)
##
## Model Tests Discrimination
## Indexes
## Obs 3873 LR chi2 274.70 R2 0.082
## Events 460 d.f. 17 R2(17,3873)0.064
## Center 3.2859 Pr(> chi2) 0.0000 R2(17,460)0.429
## Score chi2 344.55 Dxy 0.391
## Pr(> chi2) 0.0000
##
## Coef S.E. Wald Z Pr(>|Z|)
## AGE 0.0013 0.0002 6.16 <0.0001
## SEX=2 -0.0472 0.1352 -0.35 0.7269
## SMOKING=2 0.1932 0.1447 1.34 0.1816
## SMOKING=3 0.2984 0.2320 1.29 0.1985
## alcohol=2 -0.1446 0.1659 -0.87 0.3833
## alcohol=3 -0.1145 0.1206 -0.95 0.3423
## BMI -0.0241 0.0142 -1.70 0.0899
## SYSTH 0.0029 0.0022 1.30 0.1939
## HDL -0.3946 0.1600 -2.47 0.0137
## DIABETES=1 0.1958 0.1104 1.77 0.0761
## SUMSCORE_5LEVELS 0.3347 0.0557 6.00 <0.0001
## HOMOC 0.0042 0.0085 0.49 0.6207
## CREAT 0.5812 0.1468 3.96 <0.0001
## albumin=2 0.1948 0.1190 1.64 0.1017
## albumin=3 0.5255 0.2077 2.53 0.0114
## STENOSIS=1 0.1979 0.1069 1.85 0.0642
## IMT 0.4570 0.1782 2.56 0.0103rcorr.cens(-as.numeric(COXPH.FULL.AREGIMPUTED_3$linear.pred),COXPH.FULL.AREGIMPUTED_3$y)[1]## C Index
## 0.6952528##################################
# REDUCED MODEL
# with 14 variables evaluated
# using backward stepwise selection
# resulting to 9 variables
##################################
BackwardElimination <- fastbw(COXPH.FULL.AREGIMPUTED_3,
rule="aic",
type="individual")
COXPH.BACKWARDELIMINATION.AREGIMPUTED_3 <- update(COXPH.FULL.AREGIMPUTED_3, ~COXPH.FULL.AREGIMPUTED_3$x[,BackwardElimination$parms.kept])
COXPH.BACKWARDELIMINATION.AREGIMPUTED_3## Cox Proportional Hazards Model
##
## cph(formula = Surv(TEVENT, EVENT) ~ COXPH.FULL.AREGIMPUTED_3$x[,
## BackwardElimination$parms.kept], data = SMART.AREGIMPUTED_3,
## x = T, y = T, surv = T)
##
## Model Tests Discrimination
## Indexes
## Obs 3873 LR chi2 269.65 R2 0.080
## Events 460 d.f. 10 R2(10,3873)0.065
## Center 2.9008 Pr(> chi2) 0.0000 R2(10,460)0.431
## Score chi2 340.60 Dxy 0.384
## Pr(> chi2) 0.0000
##
## Coef S.E. Wald Z Pr(>|Z|)
## AGE 0.0013 0.0002 6.47 <0.0001
## BMI -0.0249 0.0141 -1.76 0.0780
## HDL -0.4111 0.1528 -2.69 0.0071
## DIABETES=1 0.1896 0.1097 1.73 0.0840
## SUMSCORE_5LEVELS 0.3452 0.0540 6.39 <0.0001
## CREAT 0.6076 0.1334 4.56 <0.0001
## albumin=2 0.2321 0.1176 1.97 0.0485
## albumin=3 0.5644 0.2060 2.74 0.0061
## STENOSIS=1 0.2291 0.1051 2.18 0.0293
## IMT 0.5059 0.1749 2.89 0.0038COXPH.REDUCED.AREGIMPUTED_3 <-cph(Surv(TEVENT,EVENT) ~ ifelse(AGE>50, (AGE-50)^2,0) +
BMI +
HDL+
DIABETES +
SUMSCORE_5LEVELS +
log(CREAT) +
albumin +
STENOSIS +
IMT,
data = SMART.AREGIMPUTED_3,
x=T,
y=T,
surv=T)
anova(COXPH.REDUCED.AREGIMPUTED_3)## Wald Statistics Response: Surv(TEVENT, EVENT)
##
## Factor Chi-Square d.f. P
## AGE 41.87 1 <.0001
## BMI 3.11 1 0.0780
## HDL 7.24 1 0.0071
## DIABETES 2.99 1 0.0840
## SUMSCORE_5LEVELS 40.87 1 <.0001
## CREAT 20.75 1 <.0001
## albumin 9.09 2 0.0106
## STENOSIS 4.75 1 0.0293
## IMT 8.37 1 0.0038
## TOTAL 309.72 10 <.0001summary(COXPH.REDUCED.AREGIMPUTED_3)## Effects Response : Surv(TEVENT, EVENT)
##
## Factor Low High Diff. Effect S.E. Lower 0.95 Upper 0.95
## AGE 52.00 68.00 16.00 0.42636 0.065888 0.2972200 0.555500
## Hazard Ratio 52.00 68.00 16.00 1.53170 NA 1.3461000 1.742800
## BMI 24.11 28.73 4.62 -0.11510 0.065302 -0.2430900 0.012885
## Hazard Ratio 24.11 28.73 4.62 0.89127 NA 0.7842000 1.013000
## HDL 0.96 1.42 0.46 -0.18912 0.070306 -0.3269100 -0.051318
## Hazard Ratio 0.96 1.42 0.46 0.82769 NA 0.7211500 0.949980
## SUMSCORE_5LEVELS 1.00 5.00 4.00 1.38100 0.216010 0.9575800 1.804300
## Hazard Ratio 1.00 5.00 4.00 3.97870 NA 2.6054000 6.076000
## CREAT 78.00 101.00 23.00 0.15700 0.034464 0.0894550 0.224550
## Hazard Ratio 78.00 101.00 23.00 1.17000 NA 1.0936000 1.251800
## IMT 0.75 1.07 0.32 0.16190 0.055968 0.0522010 0.271590
## Hazard Ratio 0.75 1.07 0.32 1.17570 NA 1.0536000 1.312000
## DIABETES - 1:0 1.00 2.00 NA 0.18957 0.109700 -0.0254450 0.404580
## Hazard Ratio 1.00 2.00 NA 1.20870 NA 0.9748800 1.498700
## albumin - 2:1 1.00 2.00 NA 0.23207 0.117640 0.0014922 0.462640
## Hazard Ratio 1.00 2.00 NA 1.26120 NA 1.0015000 1.588300
## albumin - 3:1 1.00 3.00 NA 0.56442 0.206000 0.1606600 0.968180
## Hazard Ratio 1.00 3.00 NA 1.75840 NA 1.1743000 2.633100
## STENOSIS - 1:0 1.00 2.00 NA 0.22905 0.105070 0.0231120 0.434990
## Hazard Ratio 1.00 2.00 NA 1.25740 NA 1.0234000 1.545000COXPH.REDUCED.AREGIMPUTED_3## Cox Proportional Hazards Model
##
## cph(formula = Surv(TEVENT, EVENT) ~ ifelse(AGE > 50, (AGE - 50)^2,
## 0) + BMI + HDL + DIABETES + SUMSCORE_5LEVELS + log(CREAT) +
## albumin + STENOSIS + IMT, data = SMART.AREGIMPUTED_3, x = T,
## y = T, surv = T)
##
## Model Tests Discrimination
## Indexes
## Obs 3873 LR chi2 269.65 R2 0.080
## Events 460 d.f. 10 R2(10,3873)0.065
## Center 2.9008 Pr(> chi2) 0.0000 R2(10,460)0.431
## Score chi2 340.60 Dxy 0.384
## Pr(> chi2) 0.0000
##
## Coef S.E. Wald Z Pr(>|Z|)
## AGE 0.0013 0.0002 6.47 <0.0001
## BMI -0.0249 0.0141 -1.76 0.0780
## HDL -0.4111 0.1528 -2.69 0.0071
## DIABETES=1 0.1896 0.1097 1.73 0.0840
## SUMSCORE_5LEVELS 0.3452 0.0540 6.39 <0.0001
## CREAT 0.6076 0.1334 4.56 <0.0001
## albumin=2 0.2321 0.1176 1.97 0.0485
## albumin=3 0.5644 0.2060 2.74 0.0061
## STENOSIS=1 0.2291 0.1051 2.18 0.0293
## IMT 0.5059 0.1749 2.89 0.0038rcorr.cens(-as.numeric(COXPH.REDUCED.AREGIMPUTED_3$linear.pred),COXPH.REDUCED.AREGIMPUTED_3$y)[1]## C Index
## 0.6917632##################################
# Formulating the FULL and REDUCED models
##################################
SMART.AREGIMPUTED_3$AGE_SQUAREDAFTER50 <- ifelse(SMART.AREGIMPUTED_3$AGE>50, (SMART.AREGIMPUTED_3$AGE-50)^2,0)
SMART.AREGIMPUTED_3$CREAT_LOG <- log(SMART.AREGIMPUTED_3$CREAT)
COXPH.AREGIMPUTED_3.SurvivalResponse <- "Surv(TEVENT, EVENT)"
COXPH.AREGIMPUTED_3.SurvivalPredictorFull <- c("AGE_SQUAREDAFTER50",
"SEX",
"SMOKING",
"alcohol",
"BMI",
"SYSTH",
"HDL",
"DIABETES",
"SUMSCORE_5LEVELS",
"HOMOC",
"CREAT_LOG",
"albumin",
"STENOSIS",
"IMT")
COXPH.AREGIMPUTED_3.SurvivalPredictorReduced <- c("AGE_SQUAREDAFTER50",
"BMI",
"HDL",
"DIABETES",
"SUMSCORE_5LEVELS",
"CREAT_LOG",
"albumin",
"STENOSIS",
"IMT")
COXPH.AREGIMPUTED_3.CoxPHModelSummary <- SMART.AREGIMPUTED_3 %>%
finalfit(COXPH.AREGIMPUTED_3.SurvivalResponse,
COXPH.AREGIMPUTED_3.SurvivalPredictorFull,
COXPH.AREGIMPUTED_3.SurvivalPredictorReduced,
keep_models = TRUE,
add_dependent_label = FALSE) %>%
rename("Overall Survival" = label) %>%
rename(" " = levels) %>%
rename(" " = all)
kable(COXPH.AREGIMPUTED_3.CoxPHModelSummary)| Overall Survival | HR (univariable) | HR (multivariable full) | HR (multivariable) | |||
|---|---|---|---|---|---|---|
| 1 | AGE_SQUAREDAFTER50 | Mean (SD) | 189.0 (217.0) | 1.00 (1.00-1.00, p<0.001) | 1.00 (1.00-1.00, p<0.001) | 1.00 (1.00-1.00, p<0.001) |
| 15 | SEX | 1 | 2897 (74.8) | - | - | - |
| 16 | 2 | 976 (25.2) | 0.67 (0.53-0.85, p=0.001) | 0.95 (0.73-1.24, p=0.725) | - | |
| 17 | SMOKING | 1 | 695 (17.9) | - | - | - |
| 18 | 2 | 2731 (70.5) | 1.29 (0.99-1.68, p=0.060) | 1.21 (0.91-1.61, p=0.182) | - | |
| 19 | 3 | 447 (11.5) | 1.16 (0.74-1.80, p=0.516) | 1.35 (0.86-2.12, p=0.199) | - | |
| 5 | alcohol | 1 | 759 (19.6) | - | - | - |
| 6 | 2 | 410 (10.6) | 1.02 (0.74-1.39, p=0.914) | 0.87 (0.63-1.20, p=0.383) | - | |
| 7 | 3 | 2704 (69.8) | 0.78 (0.62-0.97, p=0.024) | 0.89 (0.70-1.13, p=0.342) | - | |
| 8 | BMI | Mean (SD) | 26.7 (3.8) | 0.98 (0.95-1.00, p=0.052) | 0.98 (0.95-1.00, p=0.090) | 0.98 (0.95-1.00, p=0.078) |
| 23 | SYSTH | Mean (SD) | 143.0 (22.2) | 1.01 (1.01-1.02, p<0.001) | 1.00 (1.00-1.01, p=0.194) | - |
| 12 | HDL | Mean (SD) | 1.2 (0.4) | 0.60 (0.45-0.80, p<0.001) | 0.67 (0.49-0.92, p=0.014) | 0.66 (0.49-0.89, p=0.007) |
| 10 | DIABETES | 0 | 3024 (78.1) | - | - | - |
| 11 | 1 | 849 (21.9) | 1.47 (1.20-1.80, p<0.001) | 1.22 (0.98-1.51, p=0.076) | 1.21 (0.97-1.50, p=0.084) | |
| 22 | SUMSCORE_5LEVELS | Mean (SD) | 1.3 (0.6) | 1.73 (1.57-1.90, p<0.001) | 1.40 (1.25-1.56, p<0.001) | 1.41 (1.27-1.57, p<0.001) |
| 13 | HOMOC | Mean (SD) | 14.1 (5.4) | 1.05 (1.04-1.06, p<0.001) | 1.00 (0.99-1.02, p=0.620) | - |
| 9 | CREAT_LOG | Mean (SD) | 4.5 (0.3) | 2.93 (2.44-3.53, p<0.001) | 1.79 (1.34-2.38, p<0.001) | 1.83 (1.41-2.38, p<0.001) |
| 2 | albumin | 1 | 3040 (78.5) | - | - | - |
| 3 | 2 | 696 (18.0) | 1.94 (1.56-2.41, p<0.001) | 1.22 (0.96-1.53, p=0.101) | 1.26 (1.00-1.59, p=0.048) | |
| 4 | 3 | 137 (3.5) | 3.75 (2.70-5.19, p<0.001) | 1.69 (1.12-2.54, p=0.012) | 1.76 (1.17-2.63, p=0.006) | |
| 20 | STENOSIS | 0 | 3136 (81.0) | - | - | - |
| 21 | 1 | 737 (19.0) | 1.75 (1.44-2.12, p<0.001) | 1.22 (0.99-1.50, p=0.064) | 1.26 (1.02-1.54, p=0.029) | |
| 14 | IMT | Mean (SD) | 0.9 (0.3) | 3.58 (2.68-4.76, p<0.001) | 1.58 (1.11-2.24, p=0.010) | 1.66 (1.18-2.34, p=0.004) |
##################################
# Conducting a likelihood ratio test
# to compare the FULL and REDUCED models
##################################
COXPH.FULLFINAL.AREGIMPUTED_3 <- coxph(Surv(TEVENT,EVENT) ~ AGE_SQUAREDAFTER50 +
SEX +
SMOKING +
alcohol +
BMI +
SYSTH +
HDL +
DIABETES +
SUMSCORE_5LEVELS +
HOMOC +
CREAT_LOG +
albumin +
STENOSIS +
IMT,
data = SMART.AREGIMPUTED_3)
COXPH.REDUCEDFINAL.AREGIMPUTED_3 <- coxph(Surv(TEVENT,EVENT) ~ AGE_SQUAREDAFTER50 +
BMI +
HDL+
DIABETES +
SUMSCORE_5LEVELS +
CREAT_LOG +
albumin +
STENOSIS +
IMT,
data = SMART.AREGIMPUTED_3)
anova(COXPH.REDUCEDFINAL.AREGIMPUTED_3,
COXPH.FULLFINAL.AREGIMPUTED_3,
test="LRT")## Analysis of Deviance Table
## Cox model: response is Surv(TEVENT, EVENT)
## Model 1: ~ AGE_SQUAREDAFTER50 + BMI + HDL + DIABETES + SUMSCORE_5LEVELS + CREAT_LOG + albumin + STENOSIS + IMT
## Model 2: ~ AGE_SQUAREDAFTER50 + SEX + SMOKING + alcohol + BMI + SYSTH + HDL + DIABETES + SUMSCORE_5LEVELS + HOMOC + CREAT_LOG + albumin + STENOSIS + IMT
## loglik Chisq Df Pr(>|Chi|)
## 1 -3370.0
## 2 -3367.4 5.0507 7 0.65381.2.7 Model Performance Estimation
[A] The reduced model containing 9 variables was selected as the final model. The p-values for the Likelihood Ratio Test, Wald Test, and Log-Rank Test were all significant, indicating that the model and the variables used were statistically sound for prediction. All three test statistics were in close agreement with the omnibus null hypothesis (that all of the betas are 0) sufficiently rejected. The concordance statistic which represents model discrimination performance was reasonably high at 0.692.
[B] The variables which were most predictive of the outcome (presence of cardiovascular events) as indicated by the most significant p-values were AGE_SQUAREDAFTER50 (numeric, p-value<0.001), SUMSCORE_5LEVELS (numeric, p-value<0.001) and CREAT_LOG (numeric, p-value<0.001). HDL (numeric, p-value=0.007), albumin (factor, p-values=0.048,0.006), STENOSIS (factor, p-value=0.029) and IMT (numeric, p-value=0.004) were sufficiently predictive variables. While, the BMI (numeric, p-value=0.078) and DIABETES (factor, p-value=0.084) variables were marginally predictive.
[C] 7/9 variables were associated with higher incidence of cardiovascular events. Their individual main effects holding the other variables constant were described as follows :
[C.1] A 10-year increase in age after 50 (AGE=60; AGE_SQUAREDAFTER50=10^2=100) increases the hazard by 14%.
[C.2] Having diabetes (DIABETES=1) increases the hazard by 21%.
[C.3] A 1-unit increase in the incidence of asymptomatic atherosclerosis (SUMSCORE_5LEVELS=1) increases the hazard by 41%.
[C.4] A 10-unit increase in creatinine (CREAT=10; CREAT_LOG=1) increases the hazard by 83%.
[C.5] Having micro-albumin (albumin=1(micro)) increases the hazard by 26%, while having macro-albumin (albumin=2(macro)) further increases the hazard by 76%.
[C.6] Having stenosis (STENOSIS=1) increases the hazard by 26%.
[C.7] A 1-unit increase in intima-media thickness (IMT=1) increases the hazard by 66%.
[D] 2/9 variables were associated with lower incidence of cardiovascular events. Their individual main effects holding the other variables constant were described as follows :
[D.1] A 5-unit increase in body mass index (BMI=5) reduces the hazard by 12%.
[D.2] A 1-unit increase in HDL (HDL=1) reduces the hazard by 66%.
[E] The proportionality assumption was evaluated using the Schoenfeld residuals against the transformed time which showed that:
[E.1] The Schoenfeld Test global p-value was insignificant indicating that the hazard rate determined from the model and the associated variables remained constant over time. The proportionality hazards assumption was met validating the model.
[E.2] Individually, the BMI, HDL, DIABETES, CREAT, albumin, STENOSIS and IMT variables showed insignificant Schoenfeld Test p-values indicating no time dependency. However, the AGE_SQUAREDAFTER50 and SUMSCORE_5LEVELS variables were potentially time-dependent given their marginally significant Schoenfeld Test p-values. These variables and their corresponding transformations were maintained with no adjustments in the model due to their relatively minimal effect on the overall results although these observation were noted.
Code Chunk | Output
##################################
# Summarizing the FINAL REDUCED model
##################################
summary(COXPH.REDUCEDFINAL.AREGIMPUTED_3) ## Call:
## coxph(formula = Surv(TEVENT, EVENT) ~ AGE_SQUAREDAFTER50 + BMI +
## HDL + DIABETES + SUMSCORE_5LEVELS + CREAT_LOG + albumin +
## STENOSIS + IMT, data = SMART.AREGIMPUTED_3)
##
## n= 3873, number of events= 460
##
## coef exp(coef) se(coef) z Pr(>|z|)
## AGE_SQUAREDAFTER50 0.0013327 1.0013336 0.0002059 6.473 9.62e-11 ***
## BMI -0.0249103 0.9753974 0.0141344 -1.762 0.07800 .
## HDL -0.4112635 0.6628123 0.1528392 -2.691 0.00713 **
## DIABETES1 0.1894940 1.2086379 0.1097039 1.727 0.08411 .
## SUMSCORE_5LEVELS 0.3452748 1.4123780 0.0540046 6.393 1.62e-10 ***
## CREAT_LOG 0.6064023 1.8338220 0.1334447 4.544 5.51e-06 ***
## albumin2 0.2321931 1.2613633 0.1176337 1.974 0.04840 *
## albumin3 0.5636867 1.7571386 0.2060667 2.735 0.00623 **
## STENOSIS1 0.2290771 1.2574389 0.1050720 2.180 0.02924 *
## IMT 0.5059860 1.6586202 0.1748953 2.893 0.00381 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## AGE_SQUAREDAFTER50 1.0013 0.9987 1.0009 1.0017
## BMI 0.9754 1.0252 0.9487 1.0028
## HDL 0.6628 1.5087 0.4912 0.8943
## DIABETES1 1.2086 0.8274 0.9748 1.4986
## SUMSCORE_5LEVELS 1.4124 0.7080 1.2705 1.5701
## CREAT_LOG 1.8338 0.5453 1.4118 2.3820
## albumin2 1.2614 0.7928 1.0016 1.5884
## albumin3 1.7571 0.5691 1.1733 2.6315
## STENOSIS1 1.2574 0.7953 1.0234 1.5450
## IMT 1.6586 0.6029 1.1773 2.3368
##
## Concordance= 0.692 (se = 0.014 )
## Likelihood ratio test= 269.6 on 10 df, p=<2e-16
## Wald test = 309.4 on 10 df, p=<2e-16
## Score (logrank) test = 340.6 on 10 df, p=<2e-16##################################
# Describing the main effects
##################################
tbl_regression(COXPH.REDUCEDFINAL.AREGIMPUTED_3,
exponentiate = TRUE) | Characteristic | HR1 | 95% CI1 | p-value |
|---|---|---|---|
| AGE_SQUAREDAFTER50 | 1.00 | 1.00, 1.00 | <0.001 |
| BMI | 0.98 | 0.95, 1.00 | 0.078 |
| HDL | 0.66 | 0.49, 0.89 | 0.007 |
| DIABETES | |||
| 0 | — | — | |
| 1 | 1.21 | 0.97, 1.50 | 0.084 |
| SUMSCORE_5LEVELS | 1.41 | 1.27, 1.57 | <0.001 |
| CREAT_LOG | 1.83 | 1.41, 2.38 | <0.001 |
| albumin | |||
| 1 | — | — | |
| 2 | 1.26 | 1.00, 1.59 | 0.048 |
| 3 | 1.76 | 1.17, 2.63 | 0.006 |
| STENOSIS | |||
| 0 | — | — | |
| 1 | 1.26 | 1.02, 1.54 | 0.029 |
| IMT | 1.66 | 1.18, 2.34 | 0.004 |
| 1 HR = Hazard Ratio, CI = Confidence Interval | |||
##################################
# Formulating the forest plot
##################################
(ggforest(COXPH.REDUCEDFINAL.AREGIMPUTED_3,
data=SMART.AREGIMPUTED_3,
main = "",
fontsize = 0.90))
##################################
# Plotting the Kaplan-Meier survival curves
##################################
COXPH.REDUCEDFINAL.AREGIMPUTED_3.KMEstimates <- survfit(COXPH.REDUCEDFINAL.AREGIMPUTED_3,
data = SMART.AREGIMPUTED_3)
COXPH.REDUCEDFINAL.AREGIMPUTED_3.KMPlot <- ggsurvplot(COXPH.REDUCEDFINAL.AREGIMPUTED_3.KMEstimates,
title = "Kaplan-Meier Survival Curve (Final Model)",
pval = FALSE,
conf.int = TRUE,
conf.int.style = "ribbon",
xlab = "Time (Days)",
ylab="Estimated Probability (Free of Cardiovascular Events)",
break.time.by = 365,
ggtheme = theme_bw(),
risk.table = "abs_pct",
risk.table.title="Number at Risk (Estimated Probability)",
risk.table.y.text.col = FALSE,
risk.table.y.text = TRUE,
fontsize = 3,
ncensor.plot = FALSE,
surv.median.line = "hv",
palette = c("#000000"))
ggpar(COXPH.REDUCEDFINAL.AREGIMPUTED_3.KMPlot,
font.title = c(14,"bold"),
font.x = c(12,"bold"),
font.y = c(12,"bold"),
font.legend=c(12),
font.xtickslab=c(9,"black"),
font.ytickslab=c(9,"black"))
##################################
# Testing for the proportional hazards assumption
##################################
(COXPH.REDUCEDFINAL.AREGIMPUTED_3.PHAssumptionCheck <- cox.zph(COXPH.REDUCEDFINAL.AREGIMPUTED_3))## chisq df p
## AGE_SQUAREDAFTER50 6.2279 1 0.013
## BMI 0.3371 1 0.561
## HDL 0.0483 1 0.826
## DIABETES 0.0069 1 0.934
## SUMSCORE_5LEVELS 4.0453 1 0.044
## CREAT_LOG 0.1978 1 0.657
## albumin 2.6737 2 0.263
## STENOSIS 1.4148 1 0.234
## IMT 0.8929 1 0.345
## GLOBAL 12.0725 10 0.280##################################
# Formulating the graphical verification
# of the proportional hazards assumption test results
# using the scaled Schoenfeld residuals against time
##################################
(COXPH.REDUCEDFINAL.AREGIMPUTED_3.PHAssumptionPlot <- ggcoxzph(COXPH.REDUCEDFINAL.AREGIMPUTED_3.PHAssumptionCheck,
point.col = "red",
point.size = 2,
point.shape = 19,
point.alpha = 0.50,
ggtheme = theme_survminer(),
font.main = c(12,"bold"),
font.x = c(12,"bold"),
font.y = c(12,"bold"),
font.xtickslab=c(9,"black"),
font.ytickslab=c(9,"black")))
1.2.8 Model Performance Validation
[A] The entire process of model development including variable selection was internally validated using a 200-cycle bootstrap to determine the optimism-adjusted model performance. Results showed that:
[A.1] Only 183 random seeds of the 200 cycles resulted to valid models. 17 of the random seeds did not generate final models potentially due to the unmet AIC criterion applied during model selection.
[A.2] Optimism in terms of model discrimination using the concordance statistic was estimated to be reasonably low at 0.035. In effect, the optimism-adjusted concordance statistic was computed to be 0.657 from the previously determined optimistic value of 0.692. Results indicate that the overfitting effects during model development were minimal.
Code Chunk | Output
##################################
# Implementing internal cross validation
##################################
##################################
# Determining the performance of the
# Model formulated from original data
# And evaluated on original data
##################################
ICV_Data <- SMART.AREGIMPUTED_3
ICV_Survival <- Surv(time=ICV_Data$TEVENT, event=ICV_Data$EVENT)
ICV_Original_CoxPH_Full <- cph(ICV_Survival ~ AGE_SQUAREDAFTER50 +
SEX +
SMOKING +
alcohol +
BMI +
SYSTH +
HDL +
DIABETES +
SUMSCORE_5LEVELS +
HOMOC +
CREAT_LOG +
albumin +
STENOSIS +
IMT,
data=ICV_Data,
x=T,
y=T)
ICV_Original_CoxPH_Backward <- fastbw(ICV_Original_CoxPH_Full,
rule="aic",
type="individual")
ICV_Original_CoxPH_Reduced <- update(ICV_Original_CoxPH_Full,
~ICV_Original_CoxPH_Full$x[,ICV_Original_CoxPH_Backward$parms.kept])
ICV_Original_CoxPH_Reduced_Coef <- as.data.frame(coef(ICV_Original_CoxPH_Reduced))
ICV_Original_CoxPH_Full_CoefAdjusted <- ICV_Original_CoxPH_Full$x[,(colnames(ICV_Original_CoxPH_Full$x) %in% rownames(ICV_Original_CoxPH_Reduced_Coef))]
ICV_OriginalOnOriginal_CoxPH_Reduced.LP <- ICV_Original_CoxPH_Full_CoefAdjusted %*% coef(ICV_Original_CoxPH_Reduced)
ICV_OriginalOnOriginal_CoxPH_Reduced.Concordance <- rcorr.cens(-as.numeric(ICV_OriginalOnOriginal_CoxPH_Reduced.LP),ICV_Original_CoxPH_Reduced$y)[1]
ICV_OriginalOnOriginal_CoxPH_Reduced.Concordance[[1]]## [1] 0.6917632##################################
# Conducting bootstrap validation
##################################
######################################
# Generating a random number list
######################################
set.seed(123456789)
RandomSeedList <- (sample.int(99999999,200))
length(RandomSeedList)## [1] 200ICV_BootstrapOnBootstrap_CoxPH_Reduced.Concordance.List <- c()
ICV_BootstrapOnOriginal_CoxPH_Reduced.Concordance.List <- c()
ICV_CoxPH_Reduced.Concordance.Optimism.List <- c()
ProcessedSeed.List <- c()
######################################
# Implementing the bootstrap cycles
######################################
for (r in 1:length(RandomSeedList)) {
##################################
# Generating the bootstrap data
##################################
(SelectedSeed <- as.integer(RandomSeedList[r]))
set.seed(SelectedSeed)
ICV_BootstrapRow <- sample(nrow(ICV_Data),
replace=T)
ICV_BootstrapData <- ICV_Data[ICV_BootstrapRow,]
ICV_BootstrapSurvival <- Surv(time=ICV_BootstrapData$TEVENT, event=ICV_BootstrapData$EVENT)
##################################
# Formulating the FULL
# Cox Proportional Hazards Model
# Using the bootstrap data
##################################
ICV_Bootstrap_CoxPH_Full <- cph(ICV_Survival ~ AGE_SQUAREDAFTER50 +
SEX +
SMOKING +
alcohol +
BMI +
SYSTH +
HDL +
DIABETES +
SUMSCORE_5LEVELS +
HOMOC +
CREAT_LOG +
albumin +
STENOSIS +
IMT,
data=ICV_BootstrapData,
x=T,
y=T)
##################################
# Conducting variable selection
# Backward elimination
##################################
ICV_Bootstrap_CoxPH_Backward <- fastbw(ICV_Bootstrap_CoxPH_Full,
rule="aic",
type="individual")
##################################
# Ignoring instances when no
# Reduced model is formulated
# Due to failure to meet
# The final model criterion
##################################
if(is.null(ICV_Bootstrap_CoxPH_Backward$factors.kept)!=TRUE) {
(ProcessedSeed <- as.integer(RandomSeedList[r]))
print(paste0("Implementing bootstrap cycle ",r))
##################################
# Formulating the REDUCED
# Cox Proportional Hazards Model
# Using the bootstrap data
##################################
ICV_Bootstrap_CoxPH_Reduced <- update(ICV_Bootstrap_CoxPH_Full,
~ICV_Bootstrap_CoxPH_Full$x[,ICV_Bootstrap_CoxPH_Backward$parms.kept, drop = FALSE])
ICV_Bootstrap_CoxPH_Reduced_Coef <- as.data.frame(coef(ICV_Bootstrap_CoxPH_Reduced))
ICV_Bootstrap_CoxPH_Reduced_Coef
ICV_Bootstrap_CoxPH_Full_CoefAdjusted <- ICV_Bootstrap_CoxPH_Full$x[,(colnames(ICV_Bootstrap_CoxPH_Full$x) %in% rownames(ICV_Bootstrap_CoxPH_Reduced_Coef)), drop = FALSE]
##################################
# Determining the performance of the
# Model formulated from bootstrap data
# And evaluated on bootstrap data
##################################
ICV_BootstrapOnBootstrap_CoxPH_Reduced.LP <- ICV_Bootstrap_CoxPH_Full_CoefAdjusted %*% coef(ICV_Bootstrap_CoxPH_Reduced)
ICV_BootstrapOnBootstrap_CoxPH_Reduced.Concordance <- rcorr.cens(-as.numeric(ICV_BootstrapOnBootstrap_CoxPH_Reduced.LP),ICV_Bootstrap_CoxPH_Reduced$y)[1]
ICV_BootstrapOnBootstrap_CoxPH_Reduced.Concordance
ICV_Original_CoxPH_Full_CoefAdjusted <- ICV_Original_CoxPH_Full$x[,(colnames(ICV_Original_CoxPH_Full$x) %in% rownames(ICV_Bootstrap_CoxPH_Reduced_Coef)), drop = FALSE]
##################################
# Determining the performance of the
# Model formulated from bootstrap data
# And evaluated on original data
##################################
ICV_BootstrapOnOriginal_CoxPH_Reduced.LP <- ICV_Original_CoxPH_Full_CoefAdjusted %*% coef(ICV_Bootstrap_CoxPH_Reduced)
ICV_BootstrapOnOriginal_CoxPH_Reduced.Concordance <- rcorr.cens(-as.numeric(ICV_BootstrapOnOriginal_CoxPH_Reduced.LP),ICV_Original_CoxPH_Reduced$y)[1]
ICV_BootstrapOnOriginal_CoxPH_Reduced.Concordance
##################################
# Computing for the individual
# Estimated performance optimism
##################################
ICV_CoxPH_Reduced.Concordance.Optimism <- ICV_BootstrapOnBootstrap_CoxPH_Reduced.Concordance - ICV_BootstrapOnOriginal_CoxPH_Reduced.Concordance
ICV_CoxPH_Reduced.Concordance.Optimism
ProcessedSeed.List <- append(ProcessedSeed.List,ProcessedSeed)
ICV_BootstrapOnBootstrap_CoxPH_Reduced.Concordance.List <- append(ICV_BootstrapOnBootstrap_CoxPH_Reduced.Concordance.List,ICV_BootstrapOnBootstrap_CoxPH_Reduced.Concordance[[1]])
ICV_BootstrapOnOriginal_CoxPH_Reduced.Concordance.List <- append(ICV_BootstrapOnOriginal_CoxPH_Reduced.Concordance.List,ICV_BootstrapOnOriginal_CoxPH_Reduced.Concordance[[1]])
ICV_CoxPH_Reduced.Concordance.Optimism.List <- append(ICV_CoxPH_Reduced.Concordance.Optimism.List,ICV_CoxPH_Reduced.Concordance.Optimism)
}
}## [1] "Implementing bootstrap cycle 1"
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## [1] "Implementing bootstrap cycle 200"##################################
# Consolidating all the individual
# Estimated performance optimism
##################################
ICV_CoxPH_Reduced.Concordance.EstimatedOptimismSummary <- cbind(seq(1:length(ProcessedSeed.List)),
ProcessedSeed.List,
ICV_BootstrapOnBootstrap_CoxPH_Reduced.Concordance.List,
ICV_BootstrapOnOriginal_CoxPH_Reduced.Concordance.List,
ICV_CoxPH_Reduced.Concordance.Optimism.List)
ICV_CoxPH_Reduced.Concordance.EstimatedOptimismSummary <- as.data.frame(ICV_CoxPH_Reduced.Concordance.EstimatedOptimismSummary)
colnames(ICV_CoxPH_Reduced.Concordance.EstimatedOptimismSummary) <- c("Item",
"Random Seed",
"Bootstrap",
"Test",
"Optimism")
print(ICV_CoxPH_Reduced.Concordance.EstimatedOptimismSummary,row.names=FALSE)## Item Random Seed Bootstrap Test Optimism
## 1 24357954 0.5543502 0.4566681 0.0976821298
## 2 65725996 0.5476381 0.5391635 0.0084746534
## 3 70053462 0.5398864 0.5608731 -0.0209866759
## 4 78017548 0.5162009 0.4729145 0.0432863839
## 5 84420140 0.5356534 0.5500449 -0.0143914874
## 6 606720 0.5438464 0.4830998 0.0607466176
## 7 10029333 0.5383122 0.4388762 0.0994360240
## 8 9876518 0.5246633 0.4485447 0.0761185569
## 9 82419514 0.5459457 0.4777053 0.0682403640
## 10 42862636 0.5586620 0.4933852 0.0652767149
## 11 54910456 0.5326734 0.6241630 -0.0914895863
## 12 63139597 0.5352076 0.4459614 0.0892461485
## 13 53332617 0.5595355 0.6232712 -0.0637357448
## 14 8034413 0.5375183 0.5113660 0.0261523609
## 15 52415042 0.5568198 0.5863339 -0.0295141053
## 16 14954495 0.5091375 0.6082396 -0.0991020789
## 17 41054996 0.5345242 0.6044238 -0.0698996254
## 18 70033269 0.5119724 0.5514553 -0.0394828673
## 19 57006029 0.5330833 0.5468488 -0.0137654541
## 20 15249657 0.5327894 0.6456055 -0.1128161218
## 21 15020852 0.5250868 0.3917604 0.1333264482
## 22 58737737 0.5351302 0.4565334 0.0785967572
## 23 47064181 0.5476764 0.4646823 0.0829940045
## 24 29510608 0.5223479 0.4874980 0.0348499476
## 25 2926223 0.5109874 0.3973687 0.1136186820
## 26 15597395 0.5238630 0.5483488 -0.0244858201
## 27 17565909 0.5185945 0.4932924 0.0253020292
## 28 53494443 0.5649787 0.5852961 -0.0203174207
## 29 60222957 0.5369637 0.6057860 -0.0688222657
## 30 70635560 0.5272916 0.6026313 -0.0753396549
## 31 48609906 0.5386576 0.4724031 0.0662544371
## 32 40534381 0.5448233 0.6009747 -0.0561514600
## 33 61196946 0.5227492 0.5196900 0.0030591920
## 34 68587780 0.5586833 0.4889976 0.0696857913
## 35 93490098 0.5155689 0.3973687 0.1182001905
## 36 82482027 0.5508948 0.5883103 -0.0374155014
## 37 81130178 0.5467641 0.5072917 0.0394724031
## 38 15641896 0.5287548 0.5904109 -0.0616560948
## 39 15033507 0.5453697 0.4837054 0.0616642842
## 40 95751689 0.5480139 0.4724695 0.0755443897
## 41 74283531 0.5213188 0.5312816 -0.0099628475
## 42 63712377 0.5579731 0.5223402 0.0356329443
## 43 31672772 0.5186395 0.5270855 -0.0084459905
## 44 88691650 0.5139201 0.4634307 0.0504894070
## 45 79451861 0.5650720 0.4812422 0.0838297772
## 46 90232912 0.5523498 0.4151870 0.1371627223
## 47 94043774 0.5180631 0.5349004 -0.0168373851
## 48 80510746 0.5347594 0.5500968 -0.0153373619
## 49 34102210 0.5871710 0.5835190 0.0036520128
## 50 17883462 0.5533584 0.4601823 0.0931761456
## 51 8772866 0.5452878 0.5443860 0.0009017428
## 52 87703613 0.5435862 0.3638459 0.1797402690
## 53 53348271 0.5564627 0.4044912 0.1519714136
## 54 24011095 0.5215326 0.3926762 0.1288564063
## 55 31341514 0.5379983 0.5029177 0.0350806154
## 56 80187434 0.5188556 0.5321097 -0.0132540722
## 57 43745901 0.5388941 0.5172778 0.0216163489
## 58 93922134 0.5156527 0.4729145 0.0427381497
## 59 66126492 0.5582502 0.4220120 0.1362382312
## 60 37431387 0.5105821 0.6026313 -0.0920491946
## 61 20990637 0.5549485 0.4915636 0.0633849659
## 62 81273149 0.5466236 0.3620047 0.1846188704
## 63 77598731 0.5386171 0.5100611 0.0285559467
## 64 10644229 0.5100029 0.3917604 0.1182425024
## 65 40926246 0.5427359 0.4835425 0.0591933633
## 66 80877223 0.5468970 0.5319482 0.0149488209
## 67 97912308 0.5436062 0.4014721 0.1421341367
## 68 31028144 0.5625228 0.4528942 0.1096286294
## 69 5257245 0.5424447 0.4108594 0.1315852929
## 70 59004516 0.5140184 0.5270855 -0.0130670811
## 71 34088822 0.5222488 0.5029177 0.0193310543
## 72 25666373 0.5553139 0.5673718 -0.0120579663
## 73 68623095 0.5616174 0.5434524 0.0181649762
## 74 63482681 0.5213092 0.5452823 -0.0239730733
## 75 76784074 0.5267115 0.3881025 0.1386090595
## 76 42512786 0.5118164 0.5196900 -0.0078736432
## 77 95549440 0.5655770 0.5394619 0.0261150536
## 78 13442618 0.5359978 0.4574561 0.0785417063
## 79 3819300 0.5238134 0.4803100 0.0435034027
## 80 74985875 0.5379478 0.5489198 -0.0109719623
## 81 94058848 0.5310678 0.5071976 0.0238702510
## 82 3110705 0.5623713 0.5370547 0.0253165882
## 83 34050107 0.5555959 0.5230932 0.0325027776
## 84 49851621 0.5284372 0.5672595 -0.0388222566
## 85 665609 0.5521291 0.6269742 -0.0748451068
## 86 79266495 0.5228111 0.4067401 0.1160709492
## 87 54231681 0.5446294 0.3953778 0.1492516263
## 88 33345182 0.5455184 0.5097709 0.0357475957
## 89 28525383 0.5509790 0.4883096 0.0626693043
## 90 48257725 0.5442941 0.5154579 0.0288362058
## 91 42446822 0.5564012 0.5429529 0.0134483427
## 92 45803378 0.5436713 0.4308251 0.1128461496
## 93 75002096 0.5202301 0.3973687 0.1228613181
## 94 43813903 0.5396526 0.5064173 0.0332352730
## 95 29858393 0.5431358 0.5049937 0.0381420823
## 96 75727172 0.5311697 0.5766541 -0.0454843251
## 97 81424081 0.5450912 0.5197719 0.0253193180
## 98 6960366 0.5302170 0.6243704 -0.0941534127
## 99 6160576 0.5704856 0.5235049 0.0469807085
## 100 19881212 0.5294031 0.4659226 0.0634805088
## 101 38081837 0.5410120 0.5681717 -0.0271596558
## 102 1300489 0.5146258 0.5514553 -0.0368295051
## 103 74339302 0.5436249 0.5724038 -0.0287788801
## 104 63614203 0.5558585 0.5149798 0.0408787033
## 105 9353482 0.5478802 0.5898317 -0.0419515134
## 106 70489628 0.5318149 0.4886864 0.0431285106
## 107 94299495 0.5407540 0.3793616 0.1613923964
## 108 78365082 0.5570113 0.4786430 0.0783683642
## 109 51232997 0.5332589 0.5455266 -0.0122677057
## 110 41328046 0.5176613 0.3973687 0.1202925796
## 111 90269939 0.5302311 0.5355729 -0.0053417569
## 112 76384369 0.5151686 0.4012478 0.1139207795
## 113 46582891 0.5263412 0.3756296 0.1507116125
## 114 20718053 0.5336356 0.6164226 -0.0827869949
## 115 36855289 0.5529581 0.4798063 0.0731517230
## 116 14162817 0.5592630 0.4606368 0.0986261844
## 117 83427810 0.5615706 0.5260432 0.0355273921
## 118 47754877 0.5437141 0.5357717 0.0079423431
## 119 96086577 0.5088295 0.5831400 -0.0743105216
## 120 23368041 0.5326061 0.3771182 0.1554878465
## 121 95652738 0.5375484 0.6082396 -0.0706912664
## 122 68085408 0.5349036 0.6156401 -0.0807364627
## 123 50435170 0.5410930 0.3969029 0.1441901285
## 124 72969291 0.5499562 0.5945811 -0.0446248941
## 125 39789576 0.5385506 0.5497778 -0.0112271982
## 126 70949671 0.5328445 0.5512574 -0.0184129327
## 127 28105689 0.5374746 0.3735121 0.1639624999
## 128 31067917 0.5451062 0.6248859 -0.0797796690
## 129 31401285 0.5551856 0.5191559 0.0360296747
## 130 36989444 0.5328276 0.3928864 0.1399412002
## 131 54475311 0.5655765 0.5235172 0.0420593403
## 132 75412473 0.5603522 0.4886381 0.0717140302
## 133 37666917 0.5403496 0.5066957 0.0336538418
## 134 92034563 0.5247866 0.6073238 -0.0825372185
## 135 64331799 0.5483060 0.5233357 0.0249703590
## 136 23895688 0.5393810 0.4336873 0.1056936277
## 137 72574901 0.5482064 0.5387577 0.0094487358
## 138 18762241 0.5596488 0.3924892 0.1671595466
## 139 76873985 0.5299231 0.5368263 -0.0069032005
## 140 22587402 0.5649705 0.4925085 0.0724619944
## 141 38632436 0.5136449 0.5514553 -0.0378104120
## 142 64784435 0.5732559 0.5167559 0.0564999641
## 143 40113223 0.5479252 0.5213320 0.0265932230
## 144 38821276 0.5143160 0.5029177 0.0113982655
## 145 29759834 0.5372913 0.4708544 0.0664368785
## 146 17904630 0.5506232 0.5496991 0.0009240361
## 147 42121783 0.5675506 0.4567932 0.1107574003
## 148 83221723 0.5283198 0.5995470 -0.0712272164
## 149 92199625 0.5230217 0.4364572 0.0865645783
## 150 11287975 0.5439220 0.5357189 0.0082030386
## 151 59525042 0.5346921 0.6067055 -0.0720133978
## 152 99933470 0.5212920 0.5069287 0.0143632795
## 153 449880 0.5343195 0.3917604 0.1425590751
## 154 843264 0.5432454 0.5305391 0.0127062930
## 155 45102456 0.5225750 0.4731356 0.0494393453
## 156 52544982 0.5290751 0.4924803 0.0365947426
## 157 24716042 0.5169548 0.6243704 -0.1074156743
## 158 11469175 0.5553580 0.5539526 0.0014053903
## 159 32654802 0.5533853 0.6116696 -0.0582843411
## 160 22701179 0.5313403 0.5945106 -0.0631702219
## 161 79657253 0.5346243 0.4433276 0.0912966807
## 162 55157417 0.5202242 0.5369032 -0.0166790569
## 163 80567238 0.5400093 0.5480367 -0.0080274217
## 164 35206940 0.5272666 0.5468515 -0.0195849253
## 165 56067189 0.5339541 0.5822565 -0.0483023850
## 166 61002397 0.5409392 0.5107176 0.0302215776
## 167 7344359 0.5282352 0.3491360 0.1790992217
## 168 36103481 0.5301925 0.3857844 0.1444080573
## 169 38501127 0.5236255 0.4531512 0.0704742476
## 170 9605557 0.5375807 0.3823767 0.1552039476
## 171 96305721 0.5351266 0.5369032 -0.0017766426
## 172 96556339 0.5504812 0.4951191 0.0553620939
## 173 55917499 0.5369041 0.4557687 0.0811354680
## 174 33175807 0.5340506 0.4327883 0.1012622579
## 175 20310397 0.5304154 0.5218889 0.0085265195
## 176 69353345 0.5121749 0.3961544 0.1160204480
## 177 61139070 0.5349114 0.4352515 0.0996598674
## 178 39016431 0.5330901 0.4406019 0.0924882369
## 179 22331385 0.5162823 0.3926762 0.1236060976
## 180 36657309 0.5439242 0.5944177 -0.0504935017
## 181 89633602 0.5124902 0.3973687 0.1151214350
## 182 91643999 0.5157113 0.4255803 0.0901310575
## 183 333980 0.5361666 0.4947092 0.0414574202##################################
# Computing for the mean of the individual
# Estimated performance optimism
##################################
(ICV_CoxPH_Reduced.Concordance.Optimism <- mean(ICV_CoxPH_Reduced.Concordance.Optimism.List))## [1] 0.03508444##################################
# Determining the optimism-adjusted
# Model performance
##################################
(ICV_CoxPH_Reduced.Concordance.OptimismAdjusted <- ICV_OriginalOnOriginal_CoxPH_Reduced.Concordance - ICV_CoxPH_Reduced.Concordance.Optimism) ## C Index
## 0.65667881.2.9 Model Presentation
[A] The reduced model was graphically represented by a nomogram which could generate the survival (probability of being free of a cardiovascular event) for an individual case given the following clinical variables :
[A.1] AGE variable (numeric) coded using its squared value after 50 years [if (AGE>50) then (AGE-50)^2 else 0]
[A.2] BMI variable (numeric)
[A.3] HDL variable (numeric)
[A.4] DIABETES variable (factor)
[A.5] CEREBRAL variable (numeric), CARDIAC variable (numeric), AAA variable (numeric) and PERIPH variable (numeric) coded using their linear combination [CEREBRAL + CARDIAC + (2*AAA) + PERIPH] called SUMSCORE_5LEVELS variable (numeric)
[A.6] CREAT variable (numeric) coded using its logarithm [log(CREAT)]
[A.7] ALBUMIN variable (factor)
[A.8] STENOSIS variable (factor)
[A.9] IMT variable (numeric)
Code Chunk | Output
COXPH.REDUCED.AREGIMPUTED_3 <-cph(Surv(TEVENT,EVENT) ~ ifelse(AGE>50, (AGE-50)^2,0) +
BMI +
HDL+
DIABETES +
SUMSCORE_5LEVELS +
log(CREAT) +
albumin +
STENOSIS +
IMT,
data = SMART.AREGIMPUTED_3,
surv=T)
dd <- datadist(SMART.AREGIMPUTED_3)
options(datadist="dd")
COXPH.REDUCED.AREGIMPUTED_3.PreNomogram <- Survival(COXPH.REDUCED.AREGIMPUTED_3)
COXPH.REDUCED.AREGIMPUTED_3.Nomogram <- nomogram(COXPH.REDUCED.AREGIMPUTED_3,
fun=list(function(x) COXPH.REDUCED.AREGIMPUTED_3.PreNomogram(365,x),
function(x) COXPH.REDUCED.AREGIMPUTED_3.PreNomogram(730,x),
function(x) COXPH.REDUCED.AREGIMPUTED_3.PreNomogram(1095,x),
function(x) COXPH.REDUCED.AREGIMPUTED_3.PreNomogram(1460,x),
function(x) COXPH.REDUCED.AREGIMPUTED_3.PreNomogram(1825,x),
function(x) COXPH.REDUCED.AREGIMPUTED_3.PreNomogram(2190,x),
function(x) COXPH.REDUCED.AREGIMPUTED_3.PreNomogram(2555,x),
function(x) COXPH.REDUCED.AREGIMPUTED_3.PreNomogram(2920,x),
function(x) COXPH.REDUCED.AREGIMPUTED_3.PreNomogram(3285,x)),
funlabel=c("1-Year Survival",
"2-Year Survival",
"3-Year Survival",
"4-Year Survival",
"5-Year Survival",
"6-Year Survival",
"7-Year Survival",
"8-Year Survival",
"9-Year Survival"),
AGE=c(15,seq(50,85,5)),
CREAT=c(60,80,100,150,200,400),
lp.at=c(0,1,2,2.4),
fun.at=c(0.93,0.90,0.85,0.80,0.70,0.60,0.50),
lp=FALSE,
maxscale=10)
plot(COXPH.REDUCED.AREGIMPUTED_3.Nomogram)
1.3 Model Validity Evaluation
1.3.1 Internal Overfitting
Internal overfitting was effectively managed by using a sufficiently large sample size in the study, considering literature and previous research results in the choice of candidate predictors and employing an objective selection of the final predictors.
1.3.2 External Generalizability
Although, external generalizability was not particularly assessed in the study, a large set of predictors representing important domains related to the subject matter was considered to ensure that the predictions made from the model are valid for plausibly related populations.
3. References
[Book] Clinical Prediction Models by Ewout Steyerberg
[Book] Survival Analysis: A Self-Learning Text by David Kleinbaum and Mitchel Klein
[Book] Applied Survival Analysis Using R by Dirk Moore
[Book] Regression Modeling Strategies by Frank Harrell
[Book] R for Health Data Science by Ewen Harrison and Riinu Pius
[Book] Supervised Machine Learning by Michael Foley
[Book] Data Science for Biological, Medical and Health Research by Thomas Love
[R Package] survival by Terry Therneau
[R Package] survminer by Alboukadel Kassambara
[R Package] mice by Gerko Vink and Stef van Buuren
[R Package] foreign by R Core Team
[R Package] rms by Frank Harrell
[R Package] Hmisc by Frank Harrell and Charles Dupont
[R Package] VIM by Matthias Templ
[R Package] gridExtra by Baptiste Auguie
[R Package] finalfit by Ewen Harrison
[R Package] knitr by Yihui Xie
[R Package] dplyr by Hadley Wickham
[R Package] gtsummary by Daniel Sjoberg
[R Package] tidyr by Hadley Wickham
[R Package] purrr by Lionel Henry
[R Package] moments by Lukasz Komsta and Frederick Novomestky
[R Package] lattice by Deepayan Sarkar
[Article] Survival Analysis by Lisa Sullivan
[Article] Survival
Analysis in R by Emily Zabor
[Article] Assessment of Discrimination in Survival Analysis by R-Studio Team
[Article] Cox Proportional-Hazards Regression by MedCalc Team
[Article] Cox Proportional-Hazards Model by R Studio Team
[Article] Exploring Time To Event / Survival Data by Thomas Love
[Article] Survival Analysis by Alboukadel Kassambara
[Article] Survival Analysis with R by Joseph Rickert
[Article] Cox Model Assumptions by Alboukadel Kassambara
[Article] Understanding Predictions in Survival Analysis by Scikit Team
[Publication] Standards for Reporting Diagnostic Accuracy Studies (STARD): Explanation and Elaboration by Patrick Bosuyt (British Medical Journal)
[Publication] Transparent Reporting of a Multivariable Prediction Model for Individual Prognosis Or Diagnosis (TRIPOD): Explanation and Elaboration by Karel Moons (Annals of Internal Medicine)
[Publication] A Tool to Assess Risk of Bias and Applicability of Prediction Model Studies (PROBAST): Explanation and Elaboration by Karel Moons (Annals of Internal Medicine)
[Publication] Guide to Presenting Clinical Prediction Models for Use in Clinical Settings by Laura J Bonnett, Kym Snell, Gary Collins and Richard Riley (British Medical Journal)
[Publication] Survival Analysis Part I: Basic Concepts and First Analyses by Taane Clark (British Journal of Cancer)
[Publication] Survival Analysis Part II: Multivariate Data Analysis – An Introduction to Concepts and Methods by Mike Bradburn (British Journal of Cancer)
[Publication] Survival Analysis Part III: Multivariate Data Analysis – Choosing a Model and Assessing its Adequacy and Fit by Mike Bradburn (British Journal of Cancer)
[Publication] Survival Analysis Part IV: Further Concepts and Methods in Survival Analysis by Taane Clark (British Journal of Cancer)
[Tutorial] Survival Analysis / Time-To-Event Analysis in R by Heidi Seibold (Datacamp)
[Article] Assessment of Discrimination in Survival Analysis by R-Studio Team
[Article] Cox Proportional-Hazards Regression by MedCalc Team
[Article] Cox Proportional-Hazards Model by R Studio Team
[Article] Exploring Time To Event / Survival Data by Thomas Love
[Article] Survival Analysis by Alboukadel Kassambara
[Article] Survival Analysis with R by Joseph Rickert
[Article] Cox Model Assumptions by Alboukadel Kassambara
[Article] Understanding Predictions in Survival Analysis by Scikit Team
[Publication] Standards for Reporting Diagnostic Accuracy Studies (STARD): Explanation and Elaboration by Patrick Bosuyt (British Medical Journal)
[Publication] Transparent Reporting of a Multivariable Prediction Model for Individual Prognosis Or Diagnosis (TRIPOD): Explanation and Elaboration by Karel Moons (Annals of Internal Medicine)
[Publication] A Tool to Assess Risk of Bias and Applicability of Prediction Model Studies (PROBAST): Explanation and Elaboration by Karel Moons (Annals of Internal Medicine)
[Publication] Guide to Presenting Clinical Prediction Models for Use in Clinical Settings by Laura J Bonnett, Kym Snell, Gary Collins and Richard Riley (British Medical Journal)
[Publication] Survival Analysis Part I: Basic Concepts and First Analyses by Taane Clark (British Journal of Cancer)
[Publication] Survival Analysis Part II: Multivariate Data Analysis – An Introduction to Concepts and Methods by Mike Bradburn (British Journal of Cancer)
[Publication] Survival Analysis Part III: Multivariate Data Analysis – Choosing a Model and Assessing its Adequacy and Fit by Mike Bradburn (British Journal of Cancer)
[Publication] Survival Analysis Part IV: Further Concepts and Methods in Survival Analysis by Taane Clark (British Journal of Cancer)
[Tutorial] Survival Analysis / Time-To-Event Analysis in R by Heidi Seibold (Datacamp)