#' UNEQUALCENSIMPUTECOXINVERSION
#' @description The function UNEQUALCENSIMPUTECOXINVERSION will perform an imputation algorithm to handle unequal follow-up for recurrence and death. This function can be applied when we assume COX baseline hazards. This function performs imputation through inverting the survival function of the target distribution.
#' @param datWIDE defined as in MultiCure
#' @param beta A vector containing the most recent estimates of beta
#' @param alpha A vector containing the most recent estimates of alpha
#' @param ImputeDat This is a list with the following elements:
#' \itemize{
#' \item UnequalCens: A vector taking value 1 if the subject has unequal follow-up. Note: If subject is assumed cured in datWIDE, they are listed as UnequalCens = 0.
#' \item CovMissing: A matrix indicating which elements of Cov are missing. Not needed for this imputation.
#' \item CovImp: A list containing a single imputation of Cov
#' \item GImp: A vector with a recent single imputation of G
#' \item YRImp: A vector with a recent single imputation of Y_R
#' \item deltaRImp: A vector with a recent single imputation of delta_R
#' \item y: The integral of the target kernel over Yr0 to Yd
#' \item Basehaz13: A matrix containing the estimate of the baseline hazard function for the 1->3 transition specified intervals
#' \item Basehaz24: A matrix containing the estimate of the baseline hazard function for the 2->4 transition specified intervals
#' \item Basehaz14: A matrix containing the estimate of the baseline hazard function for the 1->4 transition specified intervals
#' \item Basehaz34: A matrix containing the estimate of the baseline hazard function for the 3->4 transition specified intervals
#' }
#' @param TransCov defined as in MultiCure
#'
#' @return a list containing
#' \itemize{
#' \item [[1]]: deltaRImp, A single imputation of delta_R
#' \item [[2]]: YRImp, A single imputation of Y_R
#'}
#' @export
UNEQUALCENSIMPUTECOXINVERSION = function(datWIDE, beta, alpha, ImputeDat, TransCov){
##################
### Initialize ###
##################
UnequalCens = ImputeDat[[1]]
CovImp = as.data.frame(ImputeDat[[3]])
GImp = ImputeDat[[4]]
YRImp = ImputeDat[[5]]
deltaRImp = ImputeDat[[6]]
y = ImputeDat[[7]]
Basehaz13 = ImputeDat[[8]]
Basehaz24 = ImputeDat[[9]]
Basehaz14 = ImputeDat[[10]]
Basehaz34 = ImputeDat[[11]]
Nobs = length(datWIDE[,1])
A1 = length(TransCov$Trans13)
A2 = length(TransCov$Trans24)
A3 = length(TransCov$Trans14)
A4 = length(TransCov$Trans34)
TRANS = c(rep(1,A1), rep(2,A2), rep(3,A3), rep(4,A4))
XB_beta13 = as.numeric(beta[TRANS==1] %*% t(cbind(CovImp[,TransCov$Trans13])))
XB_beta24 = as.numeric(beta[TRANS==2] %*% t(cbind(CovImp[,TransCov$Trans24])))
XB_beta14 = as.numeric(beta[TRANS==3] %*% t(cbind(CovImp[,TransCov$Trans14])))
XB_beta34 = as.numeric(beta[TRANS==4] %*% t(cbind(CovImp[,TransCov$Trans34])))
BasehazFun_13 = stepfun(x= Basehaz13[,2], y = c(Basehaz13[,3],0), right = F)
BasehazFun_24 = stepfun(x= Basehaz24[,2], y = c(Basehaz24[,3],0), right = F)
BasehazFun_14 = stepfun(x= Basehaz14[,2], y = c(Basehaz14[,3],0), right = F)
BasehazFun_34 = stepfun(x= Basehaz34[,2], y = c(Basehaz34[,3],0), right = F)
S1_D = exp(-as.numeric(sapply(datWIDE$Y_D,Baseline_Hazard, Basehaz13))*exp(XB_beta13))*
exp(-as.numeric(sapply(datWIDE$Y_D,Baseline_Hazard, Basehaz14))*exp(XB_beta14))
h14_D = BasehazFun_14(datWIDE$Y_D)*exp(XB_beta14)
TAU = max(datWIDE$Y_R[datWIDE$delta_R==1])
YRImp = ifelse(GImp==0,datWIDE$Y_D, ifelse(GImp==1 & UnequalCens == 0,datWIDE$Y_R,rep(NA,Nobs) ))
deltaRImp = ifelse(GImp==0,rep(0,Nobs), ifelse(GImp==1 & UnequalCens == 0,datWIDE$delta_R,rep(NA,Nobs) ))
######################
### Impute Delta R ###
######################
num = y
denom = (h14_D^datWIDE$delta_D)*S1_D
ratio = ifelse(num==0,num,num/(num + denom)) [GImp==1 & UnequalCens == 1]
deltaRImp[GImp==1 & UnequalCens == 1] = apply(matrix(ratio), 1,mSample)
YRImp[GImp==1 & UnequalCens == 1 & deltaRImp==0] = datWIDE$Y_D[GImp==1 & UnequalCens == 1 & deltaRImp==0]
INDICES = which(is.na(YRImp))
########################
### Define Functions ###
########################
if('T_R' %in% TransCov$Trans34){
fdCOX<-function(v, m){
XB_beta34MOD = as.numeric(beta[TRANS==4][TransCov$Trans34!= 'T_R'] %*% t(cbind(CovImp[[i]][m,TransCov$Trans34[TransCov$Trans34!='T_R']])))
XB_beta34MOD = XB_beta34MOD + as.numeric(beta[TRANS==4][TransCov$Trans34== 'T_R'] %*% t(cbind(v)))
Cumhazard13_temp = exp(XB_beta13[m])*as.numeric(Baseline_Hazard(v, Basehaz13 ))
Cumhazard14_temp = exp(XB_beta14[m])*as.numeric(Baseline_Hazard(v, Basehaz14 ))
Cumhazard34_temp = exp(XB_beta34MOD)*as.numeric(Baseline_Hazard(datWIDE$Y_D[m]-v, Basehaz34) )
Surv1_temp = exp(-Cumhazard13_temp-Cumhazard14_temp)
Surv3_temp = exp(-Cumhazard34_temp)
hazard13_temp = exp(XB_beta13[m])*BasehazFun_13(v)
hazard34_temp = ifelse(v == datWIDE$Y_D[m],0,exp(XB_beta34MOD)*BasehazFun_34(datWIDE$Y_D[m]-v))
return(hazard13_temp*Surv1_temp* Surv3_temp*((hazard34_temp)^datWIDE$delta_D[m]))
}
}else{
fdCOX<-function(v, m){
Cumhazard13_temp = exp(XB_beta13[m])*as.numeric(Baseline_Hazard(v, Basehaz13 ))
Cumhazard14_temp = exp(XB_beta14[m])*as.numeric(Baseline_Hazard(v, Basehaz14 ))
Cumhazard34_temp = exp(XB_beta34[m])*as.numeric(Baseline_Hazard(datWIDE$Y_D[m]-v, Basehaz34) )
Surv1_temp = exp(-Cumhazard13_temp-Cumhazard14_temp)
Surv3_temp = exp(-Cumhazard34_temp)
hazard13_temp = exp(XB_beta13[m])*BasehazFun_13(v)
hazard34_temp = ifelse(v == datWIDE$Y_D[m],0,exp(XB_beta34[m])*BasehazFun_34(datWIDE$Y_D[m]-v))
return(hazard13_temp*Surv1_temp* Surv3_temp*((hazard34_temp)^datWIDE$delta_D[m]))
}
}
DrawVAL = function(TIME, U, m){
g=cubature::adaptIntegrate(Vectorize(fdCOX), lowerLimit = TIME, upperLimit = datWIDE$Y_D[m],m, maxEval=10)
ZERO=(g$integral/y[m])-U
return(ZERO)
}
##################
### Impute T_R ### (By inverting the survival function of T_R)
##################
DrawVALWRAPPER = function(s){
m = INDICES[s]
U1 = runif(n=1, min = 0, max = 1)
draw = stats::uniroot(DrawVAL, interval = c(datWIDE$Y_R[m], datWIDE$Y_D[m]),U1, m, tol = 0.01, maxiter = 20)$root
if(draw >= datWIDE$Y_D[m] ){draw = datWIDE$Y_D[m] - (datWIDE$Y_D[m]/1000)}
if(draw <= datWIDE$Y_R[m] ){draw = datWIDE$Y_R[m] + (datWIDE$Y_R[m]/1000)}
#print(m)
return(draw)
}
DRAWS = sapply(as.numeric(c(1:length(INDICES))), DrawVALWRAPPER)
YRImp[INDICES] = DRAWS
return(list(deltaRImp, YRImp))
}
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.