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# probanofix.R #
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#'
#' @title Probabitility of event when the follow-up is no fixed
#'
#' @description In the design with variable follow-up, each subject is followed until the end of the study (Tf = infinite), i.e. subjects who are
#' enrolled at the beginning of the enrolment phase are followed for a longer time than subjects who are enrolled later.
#' When there are no drop outs (i.e. = (0,0), the probability of failure in each arm can be directly estimated using the formulation
#' proposed by K Kim and A.A. Tsiatis (1990).
#'
#' @usage probanofix(surv,time,duraccrual,limit,gamma)
#'
#' @param surv Survival estimates
#' @param time Time estimate
#' @param duraccrual Accrual duration, expressed in t time units
#' @param limit Time limit to estimate the survival probability
#' @param gamma the probability of observing an event by time t
#'
#' @details The probanofix function estimates the probability of event when the follow-up is no fixed
#'
#' @return probanofix: event probability at time limit
#'
#' @references K. Kim, A.A. Tsiatis, Study duration for clinical trials with survival response and early stopping rule, Biometrics 46 (1990) 81-92
#'
#' @name probanofix
#' @export
#'
probanofix <- function(surv,time,duraccrual,limit,gamma)
{
lambda <- -log(surv)/time
# If time after the end of accrual
if (limit>duraccrual)
{
part1 <- exp(-(lambda+gamma)*limit)/(lambda+gamma)
part2 <- exp((lambda+gamma)*duraccrual)-1
probanofix <- 1-part1*part2/duraccrual
}
else
# If time before the end of accrual
{
part <- limit-1/(lambda+gamma)+exp(-(lambda+gamma)*limit)/(lambda+gamma)
probanofix <- part/limit
}
probanofix <- probanofix*lambda/(lambda+gamma)
return(probanofix)
}
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