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dat_sim_cox_scenario4a.R
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#------------------------------
#------------------------------
#simulates longitudinal data on treatment A and covariates L at 5 time points, and then generates event times according to a Cox model.
#U is an individual frailty.
#People who do not have the event are censored at time 5.
#
#SCENARIO 4a: severe violation of positivity assumption
#------------------------------
#------------------------------
#----
#number of visits (K+1)
n.visit=5
#----
#expit function
expit=function(x){exp(x)/(1+exp(x))}
#------------------
#parameter values
#------------------
#model for A|L
gamma.0=-1
gamma.L=0.5
#test scenario with strong impact of L on treatment, leading to potential positivity violation (eg only 1/62 patients with L0>2 had T.cens.0>1)
#gamma.0=-1
#gamma.L=1
#test scenario with higher treatment chances, leading to potential positivity violation at later time points
gamma.0=0.5
gamma.L=0.5
#model for hazard
alpha.0=-2
alpha.A=-0.5
alpha.L=0.5
alpha.U=0.5
#test scenario with no predictive value of the model (AUC and c-index around 0.5)
#alpha.A=0
#alpha.L=0
#alpha.U=0
#test scenario with high predictive value of the model (c-index around 0.7)
#alpha.A=-0.1
#alpha.L=1.5
#alpha.U=0.5
#------------------
#simulate data
#------------------
#----
#generate U, A, L
A=matrix(nrow=n,ncol=n.visit)
L=matrix(nrow=n,ncol=n.visit)
U=rnorm(n,0,0.1)
L[,1]=rnorm(n,U,1)
A[,1]=rbinom(n,1,expit(gamma.0+gamma.L*L[,1]))
for(k in 2:n.visit){
L[,k]=rnorm(n,0.8*L[,k-1]-A[,k-1]+0.1*(k-1)+U,1)
A[,k]=ifelse(A[,k-1]==1,1,rbinom(n,1,expit(gamma.0+gamma.L*L[,k])))
}
#----
#generate event times T.obs, and event indicators D.obs
T.obs=rep(NA,n)
for(k in 1:n.visit){
u.t=runif(n,0,1)
haz=exp(alpha.0+alpha.A*A[,k]+alpha.L*L[,k]+alpha.U*U)
new.t=-log(u.t)/haz
T.obs=ifelse(is.na(T.obs) & new.t<1,k-1+new.t,T.obs)
}
D.obs=ifelse(is.na(T.obs),0,1)
T.obs=ifelse(is.na(T.obs),5,T.obs)
#-----
#Create data frame
colnames(A)=paste0("A.",0:4)
colnames(L)=paste0("L.",0:4)
dat=data.frame(id=1:n,T.obs,D.obs,A,L)
#-----
#set A to 0 in time periods after event/censoring
dat$A.1=ifelse(dat$T.obs<1,0,dat$A.1)
dat$A.2=ifelse(dat$T.obs<2,0,dat$A.2)
dat$A.3=ifelse(dat$T.obs<3,0,dat$A.3)
dat$A.4=ifelse(dat$T.obs<4,0,dat$A.4)
#------------------
#some summaries: may be useful if you wish to change the parameter values used above, to consider other scenarios.
#------------------
#proportion always treated
always.treat=A[,1]+A[,2]+A[,3]+A[,4]+A[,5]
#proportion never treated
never.treat=(1-A[,1])+(1-A[,2])+(1-A[,3])+(1-A[,4])+(1-A[,5])
tabyl(always.treat)
tabyl(never.treat)
tabyl(dat$D.obs)
#------------------
#Reshape data into 'long' format (multiple rows per individual: 1 row for each visit)
#------------------
dat.long=reshape(data = dat,varying=c(paste0("A.",0:4),paste0("L.",0:4)),direction="long",idvar="id")
dat.long=dat.long[order(dat.long$id,dat.long$time),]
#generate start and stop times for each row
dat.long$time.stop=dat.long$time+1
dat.long=dat.long[dat.long$time<dat.long$T.obs,]
dat.long$time.stop=ifelse(dat.long$time.stop>dat.long$T.obs,dat.long$T.obs,dat.long$time.stop)
dat.long$event=ifelse(dat.long$time.stop==dat.long$T.obs & dat.long$D.obs==1,1,0)
#visit number
dat.long$visit=ave(rep(1,dim(dat.long)[1]),dat.long$id,FUN=cumsum)
#generate lagged A values
dat.long=dat.long %>%
group_by(id) %>%
mutate(Alag1 = lag(A,n=1),Alag2 = lag(A,n=2),Alag3 = lag(A,n=3),Alag4 = lag(A,n=4)) %>%
mutate(Alag1 = replace_na(Alag1,0),Alag2=replace_na(Alag2,0),Alag3=replace_na(Alag3,0),Alag4=replace_na(Alag4,0))
#generate lagged L values
dat.long=dat.long %>%
group_by(id) %>%
mutate(Llag1 = lag(L,n=1),Llag2 = lag(L,n=2),Llag3 = lag(L,n=3),Llag4 = lag(L,n=4)) %>%
mutate(Llag1=replace_na(Llag1,0),Llag2=replace_na(Llag2,0),Llag3=replace_na(Llag3,0),Llag4=replace_na(Llag4,0))
#baseline L
dat.long=dat.long %>%
group_by(id) %>%
mutate(L.baseline = first(L))