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#' Calculate the Aalen-Johansen (1978) estimate in the Competing risk context. See Aalen, Odd O., and Søren Johansen. "An Empirical Transition Matrix for Non-Homogeneous Markov Chains Based on Censored Observations." Scandinavian Journal of Statistics 5, no. 3 (1978): 141-50. Accessed January 15, 2021. http://www.jstor.org/stable/4615704.
#'
#' @param times Event times.
#' @param causes Causes, with 0 coded as censored, 1 as cause of interest, other for competing.
#' @return a list with components
#' \itemize{
#' \item times Unique times
#' \item surv Aalen-Johansen estimator for cause 1.
#' }
#' @export
aalenjohansen<-function(times,causes){
utimes<-sort(unique(times))
fix<-kmall<-rep(NA,length(utimes))
for(jj in seq(length(utimes))){
kmall[jj]<-1-sum(causes[times==utimes[jj]]>0)/sum(times>=utimes[jj])
fix[jj]<-sum(causes[times==utimes[jj]]==1)/sum(times>=utimes[jj])
}
kmall<-c(1,cumprod(kmall))[-length(utimes)]
fhat<-c(0,cumsum(kmall*fix))
utimes<-c(0,utimes)
return(list(time=utimes,surv=1-fhat))
}
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