R/LINdf.R

In survivalREC: Nonparametric Estimation of the Distribution of Gap Times for Recurrent Events

#' Lin's estimator for the bivariate distribution function.
#' 
#' @description Provides estimates for the bivariate distribution function based
#' on the extension the Kaplan-Meier estimator of the distribution function for
#' the first event time and the Inverse Probability of Censoring Weights for the
#' second time.
#' @usage LINdf(object, x, y)
#' @param object An object of class multidf.
#' @param x The first time for obtaining estimates for the bivariate distribution
#' function.
#' @param y The second time for obtaining estimates for the bivariate 
#' distribution function. 
#' @return Vector with the Lin's estimates for the bivariate distribution 
#' function.
#' @references Lin, D. Y., Sun, W. and Ying, Z. (1999). Nonparametric estimation 
#' of the gap time distributions for serial events with censored data, 
#' Biometrika 86, 59-70.
#' 
#' @seealso \code{\link{IPCWdf}}, \code{\link{LDMdf}}, \code{\link{KMWdf}} and
#' \code{\link{WCHdf}}.
#' 
#' @examples
#' 
#' b3state<-multidf(gap1=bladder4state$y1, event1=bladder4state$d1, 
#'                  gap2=bladder4state$y2, status=bladder4state$d2, 
#'                  size=bladder4state$size)
#'              
#' LINdf(b3,x=13,y=20)
#' 
#' @author Gustavo Soutinho and Luis Meira-Machado

LINdf <-
function(object, x, y)
{
 obj <- object[[1]]
 ny <- length(y)
 est <- rep(0,ny)
 G <- KMW(obj$time1, obj$event1)
 p <- which(obj$time1 <= x)
 aux1 <- sum(G[p])
 aux <- rep(0,length(obj$time1))
 time2 <- obj$time - obj$time1
 for (i in 1:ny){
     for (j in 1:length(obj$time1)) { if (obj$time1[j] <= x & time2[j] > y[i])
             aux[j] <- 1/KM(obj$time, 1 - obj$status, t = obj$time1[j]+y[i])}
     aux <- aux/length(obj$time1)
     est[i] <- aux1 - sum(aux)
                } 
 return(est)                    
}