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sncftm-simulations.R
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# ------ G-ESTIMATION OF STRUCTUARL NESTED CUMULATIVE FAILURE TIME MODELS ------
# --------------------------------- SIMULATIONS --------------------------------
#
# -------------------------------- BY: Joy Shi ---------------------------------
# -------------------------- LAST MODIFIED: 2021-06-21 -------------------------
#
# Functions for simulating time-to-event data and analyzing the data using
# structural nested cumulative failure time models.
#
# For all functions, arguments include:
# - n: number of participants
# - b: number of simulated data sets
# - hazard: baseline hazard of the outcome (when treatment=0, confounder=0)
# - seed: set seed value for simulations
# - analysis: options include
# "unadj" for unadjusted SNCFTM
# "adj" for confounding adjusted SNCFTM
# "iv" for instrumental variable SNCFTM
# "iv-cc" to simulate selecting a nested case-control sample in the
# full simulated cohort and running an instrumental variable
# SNCFTM in the case-control sample; marginal risks are
# calculated in the full simulated cohort
# "g-formula" for confounding adjustment using the g-formula
# (note: only marginal risks are calculated; psi is not
# calculated)
# - beta_ay: magnitude of the effect of A_k on Y_(k+1) at all time points
# ------------------------------------------------------------------------------
# ------------------ Loading and installing relevant packages ------------------
if (!require('parallel')) install.packages('parallel'); library('parallel')
if (!require('optimx')) install.packages('optimx'); library('optimx')
if (!require('gfoRmula')) install.packages('gfoRmula'); library('gfoRmula')
# --------------------------- Simulation parameters ----------------------------
b <- 1000
# -------------------------- Loading SNCFTM functions --------------------------
source('./SNCFTM Function/SNCFTM Confounding Function.R')
source('./SNCFTM Function/SNCFTM IV Function.R')
# --------------------- Function for simulations for DAG 1 ---------------------
# - Time-fixed instrument Z
# - Time-fixed baseline confounder U
# - Time-fixed exposure A
# - Time-fixed outcome Y
# ------------------------------------------------------------------------------
sncftm.sim1 <- function(n=25000, b, hazard, seed=76245, analysis, beta_ay=0){
# Creating list of seeds
set.seed(seed)
seed.list <- round(runif(b)*100000)
# Looping through b iterations
results <- do.call(rbind, lapply(1:b, function(i){
set.seed(seed.list[i])
# Generating data
id <- seq(1:n)
l <- rbinom(n, size=1, prob=0.25)
z <- rbinom(n, size=1, prob=0.5)
a <- rbinom(n, size=1, prob=(0.25*z+0.5*l))
logodds.y <- log(hazard/(1-hazard))+0.5*l+beta_ay*a
prob.y <- 1/(1+exp(-logodds.y))
y <- rbinom(n, size=1, p=prob.y)
time <- rep(1, n)
sim.data <- data.frame(id, time, l, z, a, y)
# Generating case-control sample
if (analysis=="iv-cc"){
# Select controls
id.list <- sample(sim.data[which(sim.data$y==0),"id"], size=sum(sim.data$y)*2, replace=T)
sim.controls <- data.frame(originalid=id.list, newid=1:length(id.list))
sim.controls <- merge(sim.controls, sim.data, by.x="originalid", by.y="id")
sim.controls$z.include <- 1
# Adding cases
sim.cases <- sim.data[which(sim.data$y==1),]
names(sim.cases)[1] <- "originalid"
sim.cases$newid <- (nrow(sim.controls)+1):(nrow(sim.controls)+nrow(sim.cases))
sim.cases$z.include <- 0
# Combining data
sim.ccdata <- rbind(sim.controls, sim.cases)
# Renaming ID variable of original simulated data
colnames(sim.data)[1] <- "newid"
}
# Analysis
if (analysis=="unadj"){
results.unadj <- sncftm.conf(data=sim.data, id="id", time="time", x="a",
x.modelvars=~1, x.linkfunction="logit", y="y", blipfunction=1, boot=F,
parallel=F)
results2 <- c(results.unadj$psi, results.unadj$psi.esteq, results.unadj$blip.results[,3], results.unadj$blip.results[,4])
names(results2) <- c("psi", "esteq", paste("y0.t", paste(1:max(sim.data$time)), sep=""), paste("yg.t", paste(1:max(sim.data$time)), sep=""))
} else if (analysis=="adj"){
results.adj <- sncftm.conf(data=sim.data, id="id", time="time", x="a",
x.modelvars=~l, x.linkfunction="logit", y="y", blipfunction=1, boot=F,
parallel=F)
results2 <- c(results.adj$psi, results.adj$psi.esteq, results.adj$blip.results[,3], results.adj$blip.results[,4])
names(results2) <- c("psi", "esteq", paste("y0.t", paste(1:max(sim.data$time)), sep=""),paste("yg.t", paste(1:max(sim.data$time)), sep=""))
} else if (analysis=="iv"){
results.iv <- sncftm.iv(data=sim.data, id="id", time="time", z="z", z.modelvars=~1,
z.family="binomial", x="a", y="y", blipfunction=1, boot=F, parallel=F)
results2 <- c(results.iv$psi, results.iv$psi.esteq, results.iv$blip.results[,3], results.iv$blip.results[,4])
names(results2) <- c("psi", "esteq", paste("y0.t", paste(1:max(sim.data$time)), sep=""), paste("yg.t", paste(1:max(sim.data$time)), sep=""))
} else if (analysis=="iv-cc"){
results.ivcc <- sncftm.iv(data=sim.ccdata, id="newid", time="time", z="z", z.modelvars=~1,
z.family="binomial", x="a", y="y", blipfunction=1, blip.data=sim.data, boot=F, parallel=F,
z.indicator="z.include")
results.pre <- c(results.ivcc$psi, results.ivcc$psi.esteq, results.ivcc$blip.results[,3], results.ivcc$blip.results[,4])
if (length(results.pre)<4){
results2 <- rep(NA,4)
results2[1:length(results.pre)] <- results.pre
} else{
results2 <- results.pre
}
names(results2) <- c("psi", "esteq", paste("y0.t", paste(1:max(sim.data$time)), sep=""), paste("yg.t", paste(1:max(sim.data$time)), sep=""))
} else if (analysis=="g-formula"){
y.model <- glm(y~a+l+a:l, data=sim.data)
sim.data0 <- sim.data
sim.data0$a <- 0
sim.data0$pred.y <- predict(y.model, newdata=sim.data0)
sim.data1 <- sim.data
sim.data1$a <- 1
sim.data1$pred.y <- predict(y.model, newdata=sim.data1)
results2 <- c(y0.t1=mean(sim.data0$pred.y), yg.t1=mean(sim.data1$pred.y))
}
return(results2)
}))
# Returning results
return(results)
}
# --------------------- Function for simulations for DAG 2 ---------------------
# - Time-fixed instrument Z
# - Time-fixed baseline confounder U
# - Time-fixed exposure A
# - Time-varying outcome Y (with two time points)
# ------------------------------------------------------------------------------
sncftm.sim2 <- function(n=25000, b, hazard, seed=84756, analysis, beta_ay=0){
# Creating list of seeds
set.seed(seed)
seed.list <- round(runif(b)*100000)
# Looping through b iterations
results <- do.call(rbind, lapply(1:b, function(i){
set.seed(seed.list[i])
# Generating data
id <- seq(1:n)
l <- rbinom(n, size=1, prob=0.25)
z <- rbinom(n, size=1, prob=0.5)
a <- rbinom(n, size=1, prob=(0.25*z+0.5*l))
logodds.y1 <- log(hazard/(1-hazard))+0.5*l+beta_ay*a
logodds.y2 <- log(hazard/(1-hazard))+0.5*l+beta_ay*a
prob.y1 <- 1/(1+exp(-logodds.y1))
prob.y2 <- 1/(1+exp(-logodds.y2))
y1 <- rbinom(n, size=1, p=prob.y1)
y2 <- rbinom(n, size=1, p=prob.y2)
y2 <- ifelse(y1==1, NA, y2)
sim.data <- rbind(data.frame(id, time=rep(1,n), l, z, a, y=y1),
data.frame(id, time=rep(2,n), l, z, a, y=y2))
sim.data <- sim.data[which(!is.na(sim.data$y)),]
sim.data <- sim.data[order(sim.data$id, sim.data$time),]
# Generating case-control sample
if (analysis=="iv-cc"){
# Selecting controls
id.list1 <- sample(id[which(y1==0)], size=sum(y1)*2, replace=T)
id.list2 <- sample(id[which(y1==0 & y2==0)], size=sum(y1==0 & y2==1)*2, replace=T)
sim.controls <- data.frame(originalid=c(id.list1, id.list2), newid=1:(length(id.list1)+length(id.list2)))
sim.controls <- merge(sim.controls, sim.data, by.x="originalid", by.y="id")
sim.controls$z.include <- 1
# Adding cases
sim.cases <- sim.data[which(sim.data$id %in% id[which(y1==1|y2==1)]),]
names(sim.cases)[1] <- "originalid"
sim.cases$newid <- (max(sim.controls$newid)+1):(max(sim.controls$newid)+nrow(sim.cases))
sim.cases$newid <- ave(sim.cases[['newid']], sim.cases[['originalid']], FUN=min)
sim.cases$z.include <- 0
# Combining data
sim.ccdata <- rbind(sim.controls, sim.cases)
# Renaming ID variable of original simulated data
colnames(sim.data)[1] <- "newid"
}
# Analysis
if (analysis=="unadj"){
results.unadj <- sncftm.conf(data=sim.data, id="id", time="time", x="a",
x.modelvars=~as.factor(time), x.linkfunction="logit", y="y", blipfunction=1, boot=F,
parallel=F)
results2 <- c(results.unadj$psi, results.unadj$psi.esteq, results.unadj$blip.results[,3], results.unadj$blip.results[,4])
names(results2) <- c("psi", "esteq", paste("y0.t", paste(1:max(sim.data$time)), sep=""),paste("yg.t", paste(1:max(sim.data$time)), sep=""))
} else if (analysis=="adj"){
results.adj <- sncftm.conf(data=sim.data, id="id", time="time", x="a",
x.modelvars=~l*as.factor(time), x.linkfunction="logit", y="y", blipfunction=1, boot=F,
parallel=F)
results2 <- c(results.adj$psi, results.adj$psi.esteq, results.adj$blip.results[,3], results.adj$blip.results[,4])
names(results2) <- c("psi", "esteq", paste("y0.t", paste(1:max(sim.data$time)), sep=""), paste("yg.t", paste(1:max(sim.data$time)), sep=""))
} else if (analysis=="iv"){
results.iv <- sncftm.iv(data=sim.data, id="id", time="time", z="z", z.modelvars=~1,
z.family="binomial", x="a", y="y", blipfunction=1, boot=F, parallel=F)
results2 <- c(results.iv$psi, results.iv$psi.esteq, results.iv$blip.results[,3], results.iv$blip.results[,4])
names(results2) <- c("psi", "esteq", paste("y0.t", paste(1:max(sim.data$time)), sep=""), paste("yg.t", paste(1:max(sim.data$time)), sep=""))
} else if (analysis=="iv-cc"){
results.ivcc <- sncftm.iv(data=sim.ccdata, id="newid", time="time", z="z", z.modelvars=~1,
z.family="binomial", x="a", y="y", blipfunction=1, blip.data=sim.data, boot=F, parallel=F,
z.indicator="z.include")
results.pre <- c(results.ivcc$psi, results.ivcc$psi.esteq, results.ivcc$blip.results[,3], results.ivcc$blip.results[,4])
if (length(results.pre)<6){
results2 <- rep(NA,6)
results2[1:length(results.pre)] <- results.pre
} else{
results2 <- results.pre
}
names(results2) <- c("psi", "esteq", paste("y0.t", paste(1:max(sim.data$time)), sep=""), paste("yg.t", paste(1:max(sim.data$time)), sep=""))
} else if (analysis=="g-formula"){
y.model <- glm(y~a*l*as.factor(time), data=sim.data)
# Creating expanded dataset
sim.expanded <- rbind(data.frame(id, time=rep(1,n), l, z, a),
data.frame(id, time=rep(2,n), l, z, a))
# Estimates for y0
sim.data0 <- sim.expanded
sim.data0$a <- 0
sim.data0$pred.y <- predict(y.model, newdata=sim.data0)
sim.data0$pred.survival <- ave(1-sim.data0$pred.y, sim.data0$id, FUN=cumprod)
sim.data0$cum.y <- 1-sim.data0$pred.survival
# Estimates for yg
sim.data1 <- sim.expanded
sim.data1$a <- 1
sim.data1$pred.y <- predict(y.model, newdata=sim.data1)
sim.data1$pred.survival <- ave(1-sim.data1$pred.y, sim.data1$id, FUN=cumprod)
sim.data1$cum.y <- 1-sim.data1$pred.survival
results2 <- c(aggregate(sim.data0$cum.y, list(sim.data0$time), FUN=mean)[,2],
aggregate(sim.data1$cum.y, list(sim.data1$time), FUN=mean)[,2])
names(results2) <- c(paste("y0.t", paste(1:max(sim.data$time)), sep=""), paste("yg.t", paste(1:max(sim.data$time)), sep=""))
}
return(results2)
}))
# Returning results
return(results)
}
# --------------------- Function for simulations for DAG 3 ---------------------
# - Time-fixed instrument Z
# - Time-varying confounder U (with two time points)
# - Time-varying exposure A
# - Time-varying outcome Y
# ------------------------------------------------------------------------------
sncftm.sim3 <- function(n=25000, b=1000, hazard, seed=84756, analysis, beta_ay=0){
# Creating list of seeds
set.seed(seed)
seed.list <- round(runif(b)*100000)
# Looping through b iterations
results <- do.call(rbind, lapply(1:b, function(i){
set.seed(seed.list[i])
# Generating data
id <- seq(1:n)
l1 <- rbinom(n, size=1, prob=0.25)
z <- rbinom(n, size=1, prob=0.5)
a1 <- rbinom(n, size=1, prob=(0.25*z+0.5*l1))
u <- rbinom(n, size=1, prob=0.25)
l2 <- rbinom(n, size=1, prob=(0.1+0.25*a1+0.25*l1+0.25*u))
a2 <- rbinom(n, size=1, prob=(0.25*z+0.5*l2))
logodds.y1 <- log(hazard/(1-hazard))+0.5*l1+beta_ay*a1
logodds.y2 <- log(hazard/(1-hazard))+0.5*u+beta_ay*a2
prob.y1 <- 1/(1+exp(-logodds.y1))
prob.y2 <- 1/(1+exp(-logodds.y2))
y1 <- rbinom(n, size=1, p=prob.y1)
y2 <- rbinom(n, size=1, p=prob.y2)
y2 <- ifelse(y1==1, NA, y2)
sim.data <- rbind(data.frame(id, time=rep(1,n), l=l1, z, a=a1, y=y1),
data.frame(id, time=rep(2,n), l=l2, z, a=a2, y=y2))
sim.data <- sim.data[which(!is.na(sim.data$y)),]
# Generating case-control sample
if (analysis=="iv-cc"){
# Selecting controls
id.list1 <- sample(id[which(y1==0)], size=sum(y1)*2, replace=T)
id.list2 <- sample(id[which(y1==0 & y2==0)], size=sum(y1==0 & y2==1)*2, replace=T)
sim.controls <- data.frame(originalid=c(id.list1, id.list2), newid=1:(length(id.list1)+length(id.list2)))
sim.controls <- merge(sim.controls, sim.data, by.x="originalid", by.y="id")
sim.controls$z.include <- 1
# Adding cases
sim.cases <- sim.data[which(sim.data$id %in% id[which(y1==1|y2==1)]),]
names(sim.cases)[1] <- "originalid"
sim.cases$newid <- (max(sim.controls$newid)+1):(max(sim.controls$newid)+nrow(sim.cases))
sim.cases$newid <- ave(sim.cases[['newid']], sim.cases[['originalid']], FUN=min)
sim.cases$z.include <- 0
# Combining data
sim.ccdata <- rbind(sim.controls, sim.cases)
# Renaming ID variable of original simulated data
colnames(sim.data)[1] <- "newid"
}
# Analysis
if (analysis=="unadj"){
results.unadj <- sncftm.conf(data=sim.data, id="id", time="time", x="a",
x.modelvars=~as.factor(time), x.linkfunction="logit", y="y", blipfunction=1, boot=F,
parallel=F)
results2 <- c(results.unadj$psi, results.unadj$psi.esteq, results.unadj$blip.results[,3], results.unadj$blip.results[,4])
names(results2) <- c("psi", "esteq", paste("y0.t", paste(1:max(sim.data$time)), sep=""),paste("yg.t", paste(1:max(sim.data$time)), sep=""))
} else if (analysis=="adj"){
results.adj <- sncftm.conf(data=sim.data, id="id", time="time", x="a",
x.modelvars=~l*as.factor(time), x.linkfunction="logit", y="y", blipfunction=1, boot=F,
parallel=F)
results2 <- c(results.adj$psi, results.adj$psi.esteq, results.adj$blip.results[,3], results.adj$blip.results[,4])
names(results2) <- c("psi", "esteq", paste("y0.t", paste(1:max(sim.data$time)), sep=""), paste("yg.t", paste(1:max(sim.data$time)), sep=""))
} else if (analysis=="iv"){
results.iv <- sncftm.iv(data=sim.data, id="id", time="time", z="z", z.modelvars=~1,
z.family="binomial", x="a", y="y", blipfunction=1, boot=F, parallel=F)
results2 <- c(results.iv$psi, results.iv$psi.esteq, results.iv$blip.results[,3], results.iv$blip.results[,4])
names(results2) <- c("psi", "esteq", paste("y0.t", paste(1:max(sim.data$time)), sep=""), paste("yg.t", paste(1:max(sim.data$time)), sep=""))
} else if (analysis=="iv-cc"){
results.ivcc <- sncftm.iv(data=sim.ccdata, id="newid", time="time", z="z", z.modelvars=~1,
z.family="binomial", x="a", y="y", blipfunction=1, blip.data=sim.data, boot=F, parallel=F,
z.indicator="z.include")
results.pre <- c(results.ivcc$psi, results.ivcc$psi.esteq, results.ivcc$blip.results[,3], results.ivcc$blip.results[,4])
if (length(results.pre)<6){
results2 <- rep(NA,6)
results2[1:length(results.pre)] <- results.pre
} else{
results2 <- results.pre
}
names(results2) <- c("psi", "esteq", paste("y0.t", paste(1:max(sim.data$time)), sep=""), paste("yg.t", paste(1:max(sim.data$time)), sep=""))
} else if (analysis=="g-formula"){
gformula.data <- sim.data
gformula.data$time <- gformula.data$time-1
interventions <- list(list(c(static, rep(0, 2))), list(c(static, rep(1, 2))))
results.gformula <- gformula(gformula.data, id="id", time_points=2, time_name="time",
covnames=c("l","a"), outcome_name="y", outcome_type="survival",
covtypes=c("binary", "binary"), histories=c(lagged, lagged),
histvars=list(c("a", "l"), c("l")),
covparams=list(covmodels=c(l~lag1_a + lag1_l, a~lag1_l)),
ymodel=y~a*l*time,
intvars=list('a', 'a'),
interventions=interventions,
int_descript <- c('Never treat', 'Always treat'),
seed=123,
model_fits=F)
interventions <- list(list(c(static, rep(0, 2))),
list(c(static, rep(1, 2))))
results2 <- as.numeric(c(results.gformula$result[2,4], results.gformula$result[5,4],
results.gformula$result[3,4], results.gformula$result[6,4]))
names(results2) <- c(paste("y0.t", paste(1:max(sim.data$time)), sep=""), paste("yg.t", paste(1:max(sim.data$time)), sep=""))
}
return(results2)
}))
# Returning results
return(results)
}
# ---------------------- Example execution of simulations ----------------------
sim.results1 <- sncftm.sim1(hazard=1/20, b=b, analysis="adj", beta_ay=0)
sim.results2 <- sncftm.sim2(hazard=1/20, b=b, analysis="iv", beta_ay=0.5)
sim.results3 <- sncftm.sim3(hazard=1/10, b=b, analysis="iv-cc", beta_ay=0)