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###########################################################################
# Title: Imputing interaction variables: performance of various approaches
# Author: Matthew J. Smith, Matteo Quartagno, Edmund Njeru Njagi
# Date: 9th August 2022
###########################################################################
# Set working directory
setwd("N:/ICON_all/Users/Matthew Smith/Research Fellow in Statistics/Methods/Imputing logistic regression interactions")
# Install necessary packages
#install.packages(c('mice','tidyr','mitools','smcfcs','gtools'))
library(mice)
library(tidyr)
library(mitools)
library(smcfcs)
library(gtools)
# Number of imputations
m <- 10
# Number of iterations
maxit <- 10
numit <- 10
# Number of simulations
number.sims <- 1000
n.sim <- seq(1,number.sims,1)
sims <- seq(1,length(n.sim),1)
{
# Define the function
sim.dt <- function(n=10000, seed=seed, ydiagmin=2005, ydiagmax=2010,
meanage=70, sdage=10, meancmb=2, sdcmb=0.5,
probtreat=0.3, probfem=0.5, probdep=1.2,
probstage=0.4, probcmb=0.3, probfrailty=0.2, probroute=0.2,
treatef=0.7, sexef=1.1, ageef=1.4,
dep2ef=1, dep3ef=1, dep4ef=1, dep5ef=1, stageef=1, cmbef=1,
frailef=1, routeef=1, depef=1, IntStageCmbef=1,
ccmbef=1, IntStageCcmbef=1
#, ind.var = 'treat + sex + agediag'
) {
# Set the seed
set.seed(seed)
# Simulate the variables
treat <- rbinom(n, 1, prob = probtreat) # Treatment: 0 = control, 1 = treated
sex <- rbinom(n, size = 1, prob = probfem) #Sex: 0 = male, 1 = female
agediag <- rnorm(n, meanage, sdage); agediag <- (agediag - mean(agediag))/10
dep <- rbeta(n, 1, probdep) # Deprivation: binomial distribution with 'b' as 1.2 by default
depcat <- ifelse(dep<0.2,1,
ifelse(dep<0.4,2,
ifelse(dep<0.6,3,
ifelse(dep<.8,4,
ifelse(dep>= .8, 5, 0)))));
dep2 <- ifelse(depcat==2,1,0)
dep3 <- ifelse(depcat==3,1,0)
dep4 <- ifelse(depcat==4,1,0)
dep5 <- ifelse(depcat==5,1,0)
stage <- rbinom(n, size = 1, prob = probstage) #Stage: 0 = (I-III), 1 = IV
cmb <- rbinom(n, size = 1, prob = probcmb) # Comorbidity: 0=no, 1=yes
frailty <- rbinom(n, size = 1, prob = probfrailty) # Frailty: 0 = not, 1 = frail
route <- rbinom(n, 1, prob = probroute) # Route: 0 = non-emergency, 1 = emergency
year <- runif(n, min = ydiagmin, max = ydiagmax) # Year of diagnosis
IntStageCmb <- stage*cmb
# Continuous form for comorbidity
ccmb <- rnorm(n, meancmb, sdcmb); ccmb <- (ccmb - mean(ccmb))
IntStageCcmb <- stage * ccmb
# Specify parameters for the outcome model
beta1 <- log(treatef) # Treatment
beta2 <- log(sexef) # Sex
beta3 <- log(ageef) # Age
beta4 <- log(dep2ef) # Deprivation 2
beta5 <- log(dep3ef) # Deprivation 3
beta6 <- log(dep4ef) # Deprivation 4
beta7 <- log(dep5ef) # Deprivation 5
beta8 <- log(stageef) # Stage
beta9 <- log(cmbef) # Comorbidity
beta10 <- log(frailef) # Frailty
beta11 <- log(routeef) # Route
beta12 <- log(depef) # Deprivation (continuous)
beta13 <- log(IntStageCmbef) # Interaction effect
beta14 <- log(ccmbef) # Effect of continuous form of comorbidity
beta15 <- log(IntStageCcmbef) # Interaction effect for continuous comorbidity
# Create the design matrix
coef.vec <- c(beta1,beta2,beta3,beta4,beta5,beta6,beta7,beta8,beta9,beta10,beta11,beta12,beta13,beta14,beta15)
design.mat <- cbind(treat,sex,agediag,dep2,dep3,dep4,dep5,stage,cmb,frailty,route,dep,IntStageCmb,ccmb,IntStageCcmb)
z <- -3 + (design.mat %*% coef.vec)
prdeath <- 1 / (1 + exp(-z)) # pass through an inv-logit function
death <- rbinom(n,1,prdeath) # Indicator of death within 30 days
# Put the variables into a data frame
df <- data.frame(death, prdeath, treat, sex, agediag, dep2, dep3, dep4, dep5, stage, cmb,
frailty, route, dep, IntStageCmb, ccmb, IntStageCcmb, year)
return(df)
}
# Create a data frame to hold the estimates
estimates <- data.frame(matrix(nrow = 1, ncol = 9))
colnames(estimates) <- c('Rep', 'Cmb', 'Stage', 'Int', 'CmbSE', 'StageSE', 'IntSE', 'DGM', 'Method')
estimates
}
# Run the simulations
{
########################################################################################################################
# Scenario 1: Base-case
# MAR, binary Z, 30% pZ, 20% missing X, OR = 1.3
########################################################################################################################
# Specify criteria for this scenario
beta.int <- 1.3 # Effect of interaction (i.e., OR = 1.3)
prob.cmb <- 0.3 # Prevalence of fully observed variable in interaction
z <- 20 # Proportion of missing data in stage variable
# Start the loop through the simulations...
for (i in n.sim) {
# Set the seed
seed <- i
# Generate the data
data <- sim.dt(n = 100000, seed = i, probcmb = prob.cmb,
treatef = 0.85, ageef = 1.3, sexef = 0.9, depef = 1.2,
cmbef = 0.9, stageef = 1.4, IntStageCmbef = beta.int)
print(paste0('Data for simulation ', i ,' generated'))
# Generate some missing data
n <- length(data$agediag)
p.stage <- c(z)
z.stage <- seq(-5.0, -0.0, 0.01)
# Outcome-dependent missing at random for Stage
stage.omar <- function(n, betas) {
data$p.miss <- (exp(betas))/(1+exp(betas)); summary(data$p.miss)
data$i.miss <- rbinom(1:n,1, prob=data$p.miss); prop.table(table(data$i.miss))
miss.prop <- (plyr::round_any(mean(data$i.miss), accuracy=0.01, f = round))*100; miss.prop
col_name <- paste0('stage.omar', '.', miss.prop, '.', i)
stage2 <- data.frame(ifelse(data$i.miss==1, NA, data$stage))
colnames(stage2) <- col_name
data <- cbind(data,stage2)
return(data)
}
count <- 0
start_time <- Sys.time()
count <- count + 1
for (j in z.stage) {
betas <- j + 1.0*(data$treat) + 1.0*(data$agediag) + 1.0*(data$sex) +
1.0*(data$dep) + 1.0*(data$cmb) + 1.0*(data$death)
data$p.miss <- (exp(betas))/(1+exp(betas)); summary(data$p.miss)
data$i.miss <- rbinom(1:n,1, prob=data$p.miss); prop.table(table(data$i.miss))
miss.prop <- (plyr::round_any(mean(data$i.miss), accuracy=0.01, f = round))*100; miss.prop
for (k in p.stage) {
if (miss.prop==(k) ) {
data <- stage.omar(n, betas)
}
}
data <- data[, !duplicated(colnames(data))]
}
print(paste0('Missing data for simulation ', i , ' generated'))
end_time <- Sys.time()
end_time - start_time
# Duplicate the data
data2 <- data
print(paste0('Data duplicated'))
# Redefine the variables as factors
data2$stage.var <- as.factor(data2[[paste0("stage.omar.20.", i)]]) # Stage variable
########################
# Complete case analysis
########################
# Check the results of the partially observed data
CCAmodel.1 <- glm( death ~ treat + agediag + sex + dep + cmb + stage.var + IntStageCmb,
data = data2, family = "binomial"); summary(CCAmodel.1); exp(CCAmodel.1$coefficients[-1])
CCAmodel.1a <- glm( death ~ treat + agediag + sex + dep + cmb + stage.var + cmb*stage.var,
data = data2, family = "binomial"); summary(CCAmodel.1a); exp(CCAmodel.1a$coefficients[-1])
print(paste0('Complete case analysis model done'))
####################
# Passive imputation
####################
# Specify the variables to be used in the imputation
data2 <- data2[,c('death','treat','agediag','sex','dep','cmb','stage.var')]
# Perform passive imputation
pass.imp <- mice(data2, meth = c('','','','','','','logreg'), m=m, maxit = maxit, seed = i) # Perform passive imputation
# For each imputed data set, create the interaction variable based on stage*comorbidity
pass.imp.data <- list()
for (j in 1:m) {
pass.imp.data[[j]] <- complete(pass.imp, j)
pass.imp.data[[j]]$stage.var <- as.numeric(pass.imp.data[[j]]$stage.var)
pass.imp.data[[j]]$stage.var <- pass.imp.data[[j]]$stage.var - 1
pass.imp.data[[j]]$IntStageCmb <- pass.imp.data[[j]]$cmb * as.numeric(pass.imp.data[[j]]$stage.var)
}
# For this simulation, obtain the coefficients for each of the imputed data sets
pass.imp.fit <- list()
for (j in 1:m) {
invisible(capture.output(pass.imp.fit.j <- glm(death ~ treat + agediag + sex + dep + cmb + stage.var + IntStageCmb,
data = pass.imp.data[[j]], family = "binomial")
))
pass.imp.fit[[j]] <- pass.imp.fit.j
print(paste0("Model ", j, " done"))
}
# Within this simulation, combine the estimates
pass.sim.coef <- MIextract(pass.imp.fit, fun = coef); pass.sim.coef
pass.sim.var <- MIextract(pass.imp.fit, fun = function(x) diag(vcov(x))); pass.sim.var
pass.sim.est <- MIcombine(pass.sim.coef, pass.sim.var); pass.sim.est
# Add the results to the estimates data set
estimates1 <- data.frame(Rep = i,
Cmb = pass.sim.est[["coefficients"]][["cmb"]],
Stage = pass.sim.est[["coefficients"]][["stage.var"]],
Int = pass.sim.est[["coefficients"]][["IntStageCmb"]],
CmbSE = pass.sim.est[["variance"]][6,6],
StageSE = pass.sim.est[["variance"]][7,7],
IntSE = pass.sim.est[["variance"]][8,8],
DGM = 1,
Method = 'Passive'
)
estimates <- rbind(estimates, estimates1)
# State the completion of the simulation
print(paste0('Passive imputation: ', 'simulation ', i, ' done'))
#######################
# Just another variable
#######################
# Obtain the data
data2 <- data
# Rename the variables of interest
data2$stage.var <- data2[[paste0("stage.omar.20.", i)]] # Stage variable
# Recode the interaction variable (because it must be missing when stage is missing)
data2$IntStageCmb <- data2$cmb * data2$stage.var
# Convert to factor variables
data2$stage.var <- as.factor(data2$stage.var)
data2$IntStageCmb <- as.factor(data2$IntStageCmb)
# Specify the variables to be used in the imputation
data2 <- data2[,c('death','treat','agediag','sex','dep','cmb','stage.var','IntStageCmb')]
# Perform passive imputation
jav.imp <- mice(data2, meth = c('','','','','','','logreg','logreg'), m=m, maxit = maxit, seed = i) # Perform passive imputation
# Extract the imputed data sets
jav.imp.data <- list()
for (j in 1:m) {
jav.imp.data[[j]] <- complete(jav.imp,j)
jav.imp.data[[j]]$stage.var <- as.numeric(jav.imp.data[[j]]$stage.var)
jav.imp.data[[j]]$IntStageCmb <- as.numeric(jav.imp.data[[j]]$IntStageCmb)
jav.imp.data[[j]]$stage.var <- jav.imp.data[[j]]$stage.var - 1
jav.imp.data[[j]]$IntStageCmb <- jav.imp.data[[j]]$IntStageCmb - 1
#print(head(jav.imp.data[[j]][is.na(data$stage.var), ], 10))
}
# Obtain coefficients for each of the data sets
jav.imp.fit <- list()
for (j in 1:m) {
invisible(capture.output(jav.imp.fit.j <- glm(death ~ treat + agediag + sex + dep + cmb + stage.var + IntStageCmb,
data = jav.imp.data[[j]], family = "binomial")
))
jav.imp.fit[[j]] <- jav.imp.fit.j
print(paste0("Model ", j, " done"))
}
# Within this simulation, combine the estimates
jav.sim.coef <- MIextract(jav.imp.fit, fun = coef); jav.sim.coef
jav.sim.var <- MIextract(jav.imp.fit, fun = function(x) diag(vcov(x))); jav.sim.var
jav.sim.est <- MIcombine(jav.sim.coef, jav.sim.var); jav.sim.est
# Add the results to the estimates data set
estimates1 <- data.frame(Rep = i,
Cmb = jav.sim.est[["coefficients"]][["cmb"]],
Stage = jav.sim.est[["coefficients"]][["stage.var"]],
Int = jav.sim.est[["coefficients"]][["IntStageCmb"]],
CmbSE = jav.sim.est[["variance"]][6,6],
StageSE = jav.sim.est[["variance"]][7,7],
IntSE = jav.sim.est[["variance"]][8,8],
DGM = 1,
Method = 'JAV'
)
estimates <- rbind(estimates, estimates1)
# State the completion of the simulation
print(paste0('JAV imputation: ', 'simulation ', i, ' done'))
########################
# Stratify-impute-append
########################
# Obtain the data
data2 <- data
# Redefine the variables as factors
data2$stage.var <- as.factor(data2[[paste0("stage.omar.20.", i)]]) # Stage variable
# Specify the variables to be used in the imputation
data2 <- data2[,c('death','treat','agediag','sex','dep','cmb','stage.var')]
# Stratify the data by levels of comorbidity
# For those without comorbidity
data2.cmb0 <- data2[data2$cmb == 0,]
data2.cmb0 <- subset(data2.cmb0, select = -(cmb))
# For those with comorbidity
data2.cmb1 <- data2[data2$cmb == 1,]
data2.cmb1 <- subset(data2.cmb1, select = -(cmb))
# Separately for each strata of comorbidity, impute the partially observed variables
# For those without comorbidity
# Impute
sia.imp.cmb0 <- mice(data2.cmb0, meth = c('','','','','','logreg'),
m=m, maxit = maxit, seed = i) # Perform passive imputation
# State the completion of the imputation for cmb0
print(paste0("Imputation for Cmb0 done"))
# For those with comorbidity
#Impute
sia.imp.cmb1 <- mice(data2.cmb1, meth = c('','','','','','logreg'),
m=m, maxit = maxit, seed = i) # Perform passive imputation
# State the completion of the imputation for cmb1
print(paste0("Imputation for Cmb1 done"))
# For each imputed data set, create the interaction variable based on stage*comorbidity
sia.imp.cmb0.data <- list()
sia.imp.cmb1.data <- list()
for (j in 1:m) {
# For those without comorbidity
sia.imp.cmb0.data[[j]] <- complete(sia.imp.cmb0, j)
sia.imp.cmb0.data[[j]]$cmb <- 0
sia.imp.cmb0.data[[j]]$stage.var <- as.numeric(sia.imp.cmb0.data[[j]]$stage.var)
sia.imp.cmb0.data[[j]]$stage.var <- sia.imp.cmb0.data[[j]]$stage.var - 1
sia.imp.cmb0.data[[j]]$IntStageCmb <- sia.imp.cmb0.data[[j]]$cmb * sia.imp.cmb0.data[[j]]$stage.var
# For those with comorbidity
sia.imp.cmb1.data[[j]] <- complete(sia.imp.cmb1, j)
sia.imp.cmb1.data[[j]]$cmb <- 1
sia.imp.cmb1.data[[j]]$stage.var <- as.numeric(sia.imp.cmb1.data[[j]]$stage.var)
sia.imp.cmb1.data[[j]]$stage.var <- sia.imp.cmb1.data[[j]]$stage.var - 1
sia.imp.cmb1.data[[j]]$IntStageCmb <- sia.imp.cmb1.data[[j]]$cmb * sia.imp.cmb1.data[[j]]$stage.var
}
# Append the imputed data sets for the two strata (giving K imputed data sets)
sia.sim.cmb.data.merge <- list()
for (j in 1:m) {
sia.sim.cmb.data.merge[[j]] <- rbind(sia.imp.cmb0.data[[j]], sia.imp.cmb1.data[[j]])
}
# Obtain coefficients for each of the data sets
sia.imp.fit <- list()
for (j in 1:m) {
invisible(capture.output(sia.imp.fit.j <- glm(death ~ treat + agediag + sex + dep + cmb + stage.var + IntStageCmb,
data = sia.sim.cmb.data.merge[[j]], family = "binomial") #; summary(sia.imp.fit.i)
))
sia.imp.fit[[j]] <- sia.imp.fit.j
print(paste0("Model ", j, " done"))
}
# Within each simulation, combine the estimates
print(paste0("Combining estimates"))
sia.sim.coef <- MIextract(sia.imp.fit, fun = coef); sia.sim.coef
sia.sim.var <- MIextract(sia.imp.fit, fun = function(x) diag(vcov(x))); sia.sim.var
sia.sim.est <- MIcombine(sia.sim.coef, sia.sim.var); sia.sim.est
# Add the results to the estimates data set
estimates1 <- data.frame(Rep = i,
Cmb = sia.sim.est[["coefficients"]][["cmb"]],
Stage = sia.sim.est[["coefficients"]][["stage.var"]],
Int = sia.sim.est[["coefficients"]][["IntStageCmb"]],
CmbSE = sia.sim.est[["variance"]][6,6],
StageSE = sia.sim.est[["variance"]][7,7],
IntSE = sia.sim.est[["variance"]][8,8],
DGM = 1,
Method = 'SIA'
)
estimates <- rbind(estimates, estimates1)
# State the completion of this simulation
print(paste0('SIA imputation: ', 'simulation ', i, ' done'))
####################################
# SMC-FCS
####################################
# Obtain the data
data2 <- data
# Redefine the variables as factors
data2$stage.var <- as.factor(data2[[paste0("stage.omar.20.", i)]]) # Stage variable
# Specify the variables to be used in the imputation
data.subset <- data2[,c('death','treat','agediag','sex','dep','cmb','stage.var')]
# Perform imputation on the variables ("SMC-FCS")
smcfcs.imp <- smcfcs(data.subset, smtype = 'logistic',
smformula = 'death ~ treat + agediag + sex + dep + cmb + stage.var + cmb*stage.var',
method = c('','','','','','','logreg'), m=m, numit=numit)
# Fit substantive model
smcfcslist <- imputationList(smcfcs.imp$impDatasets)
smcfcs.models <- with(smcfcslist, glm(death ~ treat + agediag + sex + dep +
cmb + stage.var + cmb*stage.var, family = 'binomial'))
smcfcs.sim.est <- MIcombine(smcfcs.models); smcfcs.sim.est
# Add the results to the estimates data set
estimates1 <- data.frame(Rep = i,
Cmb = smcfcs.sim.est[["coefficients"]][["cmb"]],
Stage = smcfcs.sim.est[["coefficients"]][["stage.var1"]],
Int = smcfcs.sim.est[["coefficients"]][["cmb:stage.var1"]],
CmbSE = smcfcs.sim.est[["variance"]][6,6],
StageSE = smcfcs.sim.est[["variance"]][7,7],
IntSE = smcfcs.sim.est[["variance"]][8,8],
DGM = 1,
Method = 'SMCFCS'
)
estimates <- rbind(estimates, estimates1)
# State the completion of this simulation
print(paste0('SMCFCS imputation: ', 'simulation ', i, ' done'))
}
########################################################################################################################
# Scenario 2: Low Odds Ratio
# MAR, binary Z, 30% pZ, 20% missing X, OR = 1.1
########################################################################################################################
# Specify criteria for this scenario
beta.int <- 1.1 # Effect of interaction (i.e., OR = 1.3)
prob.cmb <- 0.3 # Prevalence of fully observed variable in interaction
z <- 20 # Proportion of missing data in stage variable
# Start the loop through the simulations...
for (i in n.sim) {
# Set the seed
seed <- i
# Generate the data
data <- sim.dt(n = 100000, seed = i, probcmb = prob.cmb,
treatef = 0.85, ageef = 1.3, sexef = 0.9, depef = 1.2,
cmbef = 0.9, stageef = 1.4, IntStageCmbef = beta.int)
print(paste0('Data for simulation ', i ,' generated'))
# Generate some missing data
n <- length(data$agediag)
p.stage <- c(z)
z.stage <- seq(-5.0, -0.0, 0.01)
# Outcome-dependent missing at random for Stage
stage.omar <- function(n, betas) {
data$p.miss <- (exp(betas))/(1+exp(betas)); summary(data$p.miss)
data$i.miss <- rbinom(1:n,1, prob=data$p.miss); prop.table(table(data$i.miss))
miss.prop <- (plyr::round_any(mean(data$i.miss), accuracy=0.01, f = round))*100; miss.prop
col_name <- paste0('stage.omar', '.', miss.prop, '.', i)
stage2 <- data.frame(ifelse(data$i.miss==1, NA, data$stage))
colnames(stage2) <- col_name
data <- cbind(data,stage2)
return(data)
}
count <- 0
start_time <- Sys.time()
count <- count + 1
for (j in z.stage) {
betas <- j + 1.0*(data$treat) + 1.0*(data$agediag) + 1.0*(data$sex) +
1.0*(data$dep) + 1.0*(data$cmb) + 1.0*(data$death)
data$p.miss <- (exp(betas))/(1+exp(betas)); summary(data$p.miss)
data$i.miss <- rbinom(1:n,1, prob=data$p.miss); prop.table(table(data$i.miss))
miss.prop <- (plyr::round_any(mean(data$i.miss), accuracy=0.01, f = round))*100; miss.prop
for (k in p.stage) {
if (miss.prop==(k) ) {
data <- stage.omar(n, betas)
}
}
data <- data[, !duplicated(colnames(data))]
}
print(paste0('Missing data for simulation ', i , ' generated'))
end_time <- Sys.time()
end_time - start_time
# Duplicate the data
data2 <- data
print(paste0('Data duplicated'))
# Redefine the variables as factors
data2$stage.var <- as.factor(data2[[paste0("stage.omar.20.", i)]]) # Stage variable
########################
# Complete case analysis
########################
# Check the results of the partially observed data
CCAmodel.1 <- glm( death ~ treat + agediag + sex + dep + cmb + stage.var + IntStageCmb,
data = data2, family = "binomial"); summary(CCAmodel.1); exp(CCAmodel.1$coefficients[-1])
CCAmodel.1a <- glm( death ~ treat + agediag + sex + dep + cmb + stage.var + cmb*stage.var,
data = data2, family = "binomial"); summary(CCAmodel.1a); exp(CCAmodel.1a$coefficients[-1])
print(paste0('Complete case analysis model done'))
####################
# Passive imputation
####################
# Specify the variables to be used in the imputation
data2 <- data2[,c('death','treat','agediag','sex','dep','cmb','stage.var')]
# Perform passive imputation
pass.imp <- mice(data2, meth = c('','','','','','','logreg'), m=m, maxit = maxit, seed = i) # Perform passive imputation
# For each imputed data set, create the interaction variable based on stage*comorbidity
pass.imp.data <- list()
for (j in 1:m) {
pass.imp.data[[j]] <- complete(pass.imp, j)
pass.imp.data[[j]]$stage.var <- as.numeric(pass.imp.data[[j]]$stage.var)
pass.imp.data[[j]]$stage.var <- pass.imp.data[[j]]$stage.var - 1
pass.imp.data[[j]]$IntStageCmb <- pass.imp.data[[j]]$cmb * as.numeric(pass.imp.data[[j]]$stage.var)
}
# For this simulation, obtain the coefficients for each of the imputed data sets
pass.imp.fit <- list()
for (j in 1:m) {
invisible(capture.output(pass.imp.fit.j <- glm(death ~ treat + agediag + sex + dep + cmb + stage.var + IntStageCmb,
data = pass.imp.data[[j]], family = "binomial")
))
pass.imp.fit[[j]] <- pass.imp.fit.j
print(paste0("Model ", j, " done"))
}
# Within this simulation, combine the estimates
pass.sim.coef <- MIextract(pass.imp.fit, fun = coef); pass.sim.coef
pass.sim.var <- MIextract(pass.imp.fit, fun = function(x) diag(vcov(x))); pass.sim.var
pass.sim.est <- MIcombine(pass.sim.coef, pass.sim.var); pass.sim.est
# Add the results to the estimates data set
estimates1 <- data.frame(Rep = i,
Cmb = pass.sim.est[["coefficients"]][["cmb"]],
Stage = pass.sim.est[["coefficients"]][["stage.var"]],
Int = pass.sim.est[["coefficients"]][["IntStageCmb"]],
CmbSE = pass.sim.est[["variance"]][6,6],
StageSE = pass.sim.est[["variance"]][7,7],
IntSE = pass.sim.est[["variance"]][8,8],
DGM = 2,
Method = 'Passive'
)
estimates <- rbind(estimates, estimates1)
# State the completion of the simulation
print(paste0('Passive imputation: ', 'simulation ', i, ' done'))
#######################
# Just another variable
#######################
# Obtain the data
data2 <- data
# Rename the variables of interest
data2$stage.var <- data2[[paste0("stage.omar.20.", i)]] # Stage variable
# Recode the interaction variable (because it must be missing when stage is missing)
data2$IntStageCmb <- data2$cmb * data2$stage.var
# Convert to factor variables
data2$stage.var <- as.factor(data2$stage.var)
data2$IntStageCmb <- as.factor(data2$IntStageCmb)
# Specify the variables to be used in the imputation
data2 <- data2[,c('death','treat','agediag','sex','dep','cmb','stage.var','IntStageCmb')]
# Perform passive imputation
jav.imp <- mice(data2, meth = c('','','','','','','logreg','logreg'), m=m, maxit = maxit, seed = i) # Perform passive imputation
# Extract the imputed data sets
jav.imp.data <- list()
for (j in 1:m) {
jav.imp.data[[j]] <- complete(jav.imp,j)
jav.imp.data[[j]]$stage.var <- as.numeric(jav.imp.data[[j]]$stage.var)
jav.imp.data[[j]]$IntStageCmb <- as.numeric(jav.imp.data[[j]]$IntStageCmb)
jav.imp.data[[j]]$stage.var <- jav.imp.data[[j]]$stage.var - 1
jav.imp.data[[j]]$IntStageCmb <- jav.imp.data[[j]]$IntStageCmb - 1
#print(head(jav.imp.data[[j]][is.na(data$stage.var), ], 10))
}
# Obtain coefficients for each of the data sets
jav.imp.fit <- list()
for (j in 1:m) {
invisible(capture.output(jav.imp.fit.j <- glm(death ~ treat + agediag + sex + dep + cmb + stage.var + IntStageCmb,
data = jav.imp.data[[j]], family = "binomial")
))
jav.imp.fit[[j]] <- jav.imp.fit.j
print(paste0("Model ", j, " done"))
}
# Within this simulation, combine the estimates
jav.sim.coef <- MIextract(jav.imp.fit, fun = coef); jav.sim.coef
jav.sim.var <- MIextract(jav.imp.fit, fun = function(x) diag(vcov(x))); jav.sim.var
jav.sim.est <- MIcombine(jav.sim.coef, jav.sim.var); jav.sim.est
# Add the results to the estimates data set
estimates1 <- data.frame(Rep = i,
Cmb = jav.sim.est[["coefficients"]][["cmb"]],
Stage = jav.sim.est[["coefficients"]][["stage.var"]],
Int = jav.sim.est[["coefficients"]][["IntStageCmb"]],
CmbSE = jav.sim.est[["variance"]][6,6],
StageSE = jav.sim.est[["variance"]][7,7],
IntSE = jav.sim.est[["variance"]][8,8],
DGM = 2,
Method = 'JAV'
)
estimates <- rbind(estimates, estimates1)
# State the completion of the simulation
print(paste0('JAV imputation: ', 'simulation ', i, ' done'))
########################
# Stratify-impute-append
########################
# Obtain the data
data2 <- data
# Redefine the variables as factors
data2$stage.var <- as.factor(data2[[paste0("stage.omar.20.", i)]]) # Stage variable
# Specify the variables to be used in the imputation
data2 <- data2[,c('death','treat','agediag','sex','dep','cmb','stage.var')]
# Stratify the data by levels of comorbidity
# For those without comorbidity
data2.cmb0 <- data2[data2$cmb == 0,]
data2.cmb0 <- subset(data2.cmb0, select = -(cmb))
# For those with comorbidity
data2.cmb1 <- data2[data2$cmb == 1,]
data2.cmb1 <- subset(data2.cmb1, select = -(cmb))
# Separately for each strata of comorbidity, impute the partially observed variables
# For those without comorbidity
# Impute
sia.imp.cmb0 <- mice(data2.cmb0, meth = c('','','','','','logreg'),
m=m, maxit = maxit, seed = i) # Perform passive imputation
# State the completion of the imputation for cmb0
print(paste0("Imputation for Cmb0 done"))
# For those with comorbidity
#Impute
sia.imp.cmb1 <- mice(data2.cmb1, meth = c('','','','','','logreg'),
m=m, maxit = maxit, seed = i) # Perform passive imputation
# State the completion of the imputation for cmb1
print(paste0("Imputation for Cmb1 done"))
# For each imputed data set, create the interaction variable based on stage*comorbidity
sia.imp.cmb0.data <- list()
sia.imp.cmb1.data <- list()
for (j in 1:m) {
# For those without comorbidity
sia.imp.cmb0.data[[j]] <- complete(sia.imp.cmb0, j)
sia.imp.cmb0.data[[j]]$cmb <- 0
sia.imp.cmb0.data[[j]]$stage.var <- as.numeric(sia.imp.cmb0.data[[j]]$stage.var)
sia.imp.cmb0.data[[j]]$stage.var <- sia.imp.cmb0.data[[j]]$stage.var - 1
sia.imp.cmb0.data[[j]]$IntStageCmb <- sia.imp.cmb0.data[[j]]$cmb * sia.imp.cmb0.data[[j]]$stage.var
# For those with comorbidity
sia.imp.cmb1.data[[j]] <- complete(sia.imp.cmb1, j)
sia.imp.cmb1.data[[j]]$cmb <- 1
sia.imp.cmb1.data[[j]]$stage.var <- as.numeric(sia.imp.cmb1.data[[j]]$stage.var)
sia.imp.cmb1.data[[j]]$stage.var <- sia.imp.cmb1.data[[j]]$stage.var - 1
sia.imp.cmb1.data[[j]]$IntStageCmb <- sia.imp.cmb1.data[[j]]$cmb * sia.imp.cmb1.data[[j]]$stage.var
}
# Append the imputed data sets for the two strata (giving K imputed data sets)
sia.sim.cmb.data.merge <- list()
for (j in 1:m) {
sia.sim.cmb.data.merge[[j]] <- rbind(sia.imp.cmb0.data[[j]], sia.imp.cmb1.data[[j]])
}
# Obtain coefficients for each of the data sets
sia.imp.fit <- list()
for (j in 1:m) {
invisible(capture.output(sia.imp.fit.j <- glm(death ~ treat + agediag + sex + dep + cmb + stage.var + IntStageCmb,
data = sia.sim.cmb.data.merge[[j]], family = "binomial") #; summary(sia.imp.fit.i)
))
sia.imp.fit[[j]] <- sia.imp.fit.j
print(paste0("Model ", j, " done"))
}
# Within each simulation, combine the estimates
print(paste0("Combining estimates"))
sia.sim.coef <- MIextract(sia.imp.fit, fun = coef); sia.sim.coef
sia.sim.var <- MIextract(sia.imp.fit, fun = function(x) diag(vcov(x))); sia.sim.var
sia.sim.est <- MIcombine(sia.sim.coef, sia.sim.var); sia.sim.est
# Add the results to the estimates data set
estimates1 <- data.frame(Rep = i,
Cmb = sia.sim.est[["coefficients"]][["cmb"]],
Stage = sia.sim.est[["coefficients"]][["stage.var"]],
Int = sia.sim.est[["coefficients"]][["IntStageCmb"]],
CmbSE = sia.sim.est[["variance"]][6,6],
StageSE = sia.sim.est[["variance"]][7,7],
IntSE = sia.sim.est[["variance"]][8,8],
DGM = 2,
Method = 'SIA'
)
estimates <- rbind(estimates, estimates1)
# State the completion of this simulation
print(paste0('SIA imputation: ', 'simulation ', i, ' done'))
####################################
# SMC-FCS
####################################
# Obtain the data
data2 <- data
# Redefine the variables as factors
data2$stage.var <- as.factor(data2[[paste0("stage.omar.20.", i)]]) # Stage variable
# Specify the variables to be used in the imputation
data.subset <- data2[,c('death','treat','agediag','sex','dep','cmb','stage.var')]
# Perform imputation on the variables ("SMC-FCS")
smcfcs.imp <- smcfcs(data.subset, smtype = 'logistic',
smformula = 'death ~ treat + agediag + sex + dep + cmb + stage.var + cmb*stage.var',
method = c('','','','','','','logreg'), m=m, numit=numit)
# Fit substantive model
smcfcslist <- imputationList(smcfcs.imp$impDatasets)
smcfcs.models <- with(smcfcslist, glm(death ~ treat + agediag + sex + dep +
cmb + stage.var + cmb*stage.var, family = 'binomial'))
smcfcs.sim.est <- MIcombine(smcfcs.models); smcfcs.sim.est
# Add the results to the estimates data set
estimates1 <- data.frame(Rep = i,
Cmb = smcfcs.sim.est[["coefficients"]][["cmb"]],
Stage = smcfcs.sim.est[["coefficients"]][["stage.var1"]],
Int = smcfcs.sim.est[["coefficients"]][["cmb:stage.var1"]],
CmbSE = smcfcs.sim.est[["variance"]][6,6],
StageSE = smcfcs.sim.est[["variance"]][7,7],
IntSE = smcfcs.sim.est[["variance"]][8,8],
DGM = 2,
Method = 'SMCFCS'
)
estimates <- rbind(estimates, estimates1)
# State the completion of this simulation
print(paste0('SMCFCS imputation: ', 'simulation ', i, ' done'))
}
########################################################################################################################
# Scenario 3: High Odds Ratio
# MAR, binary Z, 30% pZ, 20% missing X, OR = 1.7
########################################################################################################################
# Specify criteria for this scenario
beta.int <- 1.7 # Effect of interaction (i.e., OR = 1.3)
prob.cmb <- 0.3 # Prevalence of fully observed variable in interaction
z <- 20 # Proportion of missing data in stage variable
# Start the loop through the simulations...
for (i in n.sim) {
# Set the seed
seed <- i
# Generate the data
data <- sim.dt(n = 100000, seed = i, probcmb = prob.cmb,
treatef = 0.85, ageef = 1.3, sexef = 0.9, depef = 1.2,
cmbef = 0.9, stageef = 1.4, IntStageCmbef = beta.int)
print(paste0('Data for simulation ', i ,' generated'))
# Generate some missing data
n <- length(data$agediag)
p.stage <- c(z)
z.stage <- seq(-5.0, -0.0, 0.01)
# Outcome-dependent missing at random for Stage
stage.omar <- function(n, betas) {
data$p.miss <- (exp(betas))/(1+exp(betas)); summary(data$p.miss)
data$i.miss <- rbinom(1:n,1, prob=data$p.miss); prop.table(table(data$i.miss))
miss.prop <- (plyr::round_any(mean(data$i.miss), accuracy=0.01, f = round))*100; miss.prop
col_name <- paste0('stage.omar', '.', miss.prop, '.', i)
stage2 <- data.frame(ifelse(data$i.miss==1, NA, data$stage))
colnames(stage2) <- col_name
data <- cbind(data,stage2)
return(data)
}
count <- 0
start_time <- Sys.time()
count <- count + 1
for (j in z.stage) {
betas <- j + 1.0*(data$treat) + 1.0*(data$agediag) + 1.0*(data$sex) +
1.0*(data$dep) + 1.0*(data$cmb) + 1.0*(data$death)
data$p.miss <- (exp(betas))/(1+exp(betas)); summary(data$p.miss)
data$i.miss <- rbinom(1:n,1, prob=data$p.miss); prop.table(table(data$i.miss))
miss.prop <- (plyr::round_any(mean(data$i.miss), accuracy=0.01, f = round))*100; miss.prop
for (k in p.stage) {
if (miss.prop==(k) ) {
data <- stage.omar(n, betas)
}
}
data <- data[, !duplicated(colnames(data))]
}
print(paste0('Missing data for simulation ', i , ' generated'))
end_time <- Sys.time()
end_time - start_time
# Duplicate the data
data2 <- data
print(paste0('Data duplicated'))
# Redefine the variables as factors
data2$stage.var <- as.factor(data2[[paste0("stage.omar.20.", i)]]) # Stage variable
########################
# Complete case analysis
########################
# Check the results of the partially observed data
CCAmodel.1 <- glm( death ~ treat + agediag + sex + dep + cmb + stage.var + IntStageCmb,
data = data2, family = "binomial"); summary(CCAmodel.1); exp(CCAmodel.1$coefficients[-1])
CCAmodel.1a <- glm( death ~ treat + agediag + sex + dep + cmb + stage.var + cmb*stage.var,
data = data2, family = "binomial"); summary(CCAmodel.1a); exp(CCAmodel.1a$coefficients[-1])
print(paste0('Complete case analysis model done'))
####################
# Passive imputation
####################
# Specify the variables to be used in the imputation
data2 <- data2[,c('death','treat','agediag','sex','dep','cmb','stage.var')]
# Perform passive imputation
pass.imp <- mice(data2, meth = c('','','','','','','logreg'), m=m, maxit = maxit, seed = i) # Perform passive imputation
# For each imputed data set, create the interaction variable based on stage*comorbidity
pass.imp.data <- list()
for (j in 1:m) {
pass.imp.data[[j]] <- complete(pass.imp, j)
pass.imp.data[[j]]$stage.var <- as.numeric(pass.imp.data[[j]]$stage.var)
pass.imp.data[[j]]$stage.var <- pass.imp.data[[j]]$stage.var - 1
pass.imp.data[[j]]$IntStageCmb <- pass.imp.data[[j]]$cmb * as.numeric(pass.imp.data[[j]]$stage.var)
}
# For this simulation, obtain the coefficients for each of the imputed data sets
pass.imp.fit <- list()
for (j in 1:m) {
invisible(capture.output(pass.imp.fit.j <- glm(death ~ treat + agediag + sex + dep + cmb + stage.var + IntStageCmb,
data = pass.imp.data[[j]], family = "binomial")
))
pass.imp.fit[[j]] <- pass.imp.fit.j
print(paste0("Model ", j, " done"))
}
# Within this simulation, combine the estimates
pass.sim.coef <- MIextract(pass.imp.fit, fun = coef); pass.sim.coef
pass.sim.var <- MIextract(pass.imp.fit, fun = function(x) diag(vcov(x))); pass.sim.var
pass.sim.est <- MIcombine(pass.sim.coef, pass.sim.var); pass.sim.est
# Add the results to the estimates data set
estimates1 <- data.frame(Rep = i,
Cmb = pass.sim.est[["coefficients"]][["cmb"]],
Stage = pass.sim.est[["coefficients"]][["stage.var"]],
Int = pass.sim.est[["coefficients"]][["IntStageCmb"]],
CmbSE = pass.sim.est[["variance"]][6,6],
StageSE = pass.sim.est[["variance"]][7,7],
IntSE = pass.sim.est[["variance"]][8,8],
DGM = 3,
Method = 'Passive'
)
estimates <- rbind(estimates, estimates1)
# State the completion of the simulation
print(paste0('Passive imputation: ', 'simulation ', i, ' done'))
#######################
# Just another variable
#######################
# Obtain the data
data2 <- data
# Rename the variables of interest
data2$stage.var <- data2[[paste0("stage.omar.20.", i)]] # Stage variable
# Recode the interaction variable (because it must be missing when stage is missing)
data2$IntStageCmb <- data2$cmb * data2$stage.var
# Convert to factor variables
data2$stage.var <- as.factor(data2$stage.var)
data2$IntStageCmb <- as.factor(data2$IntStageCmb)
# Specify the variables to be used in the imputation
data2 <- data2[,c('death','treat','agediag','sex','dep','cmb','stage.var','IntStageCmb')]
# Perform passive imputation
jav.imp <- mice(data2, meth = c('','','','','','','logreg','logreg'), m=m, maxit = maxit, seed = i) # Perform passive imputation
# Extract the imputed data sets
jav.imp.data <- list()
for (j in 1:m) {
jav.imp.data[[j]] <- complete(jav.imp,j)
jav.imp.data[[j]]$stage.var <- as.numeric(jav.imp.data[[j]]$stage.var)
jav.imp.data[[j]]$IntStageCmb <- as.numeric(jav.imp.data[[j]]$IntStageCmb)
jav.imp.data[[j]]$stage.var <- jav.imp.data[[j]]$stage.var - 1
jav.imp.data[[j]]$IntStageCmb <- jav.imp.data[[j]]$IntStageCmb - 1
#print(head(jav.imp.data[[j]][is.na(data$stage.var), ], 10))
}
# Obtain coefficients for each of the data sets
jav.imp.fit <- list()
for (j in 1:m) {
invisible(capture.output(jav.imp.fit.j <- glm(death ~ treat + agediag + sex + dep + cmb + stage.var + IntStageCmb,
data = jav.imp.data[[j]], family = "binomial")
))
jav.imp.fit[[j]] <- jav.imp.fit.j
print(paste0("Model ", j, " done"))
}
# Within this simulation, combine the estimates