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#' @title TTC_ic_wei function
#'
#' @description calculates the confidence interval of the time TTC.
#' Note that this function is for mixture cure model with Weibull distribution
#' considered for uncured patients.
#'
#'
#' @param z_ucured covariates matrix acting on survival function of uncured
#'
#'
#' @param z_pcured covariates matrix acting on cure proportion
#'
#'
#' @param object An object of class \code{curesurv}.
#'
#'
#' @param epsilon value fixed by user to estimate the TTC \eqn{\text{Pi}(t)\geq (1-\epsilon)}.
#' By default \eqn{\epsilon = 0.05}.
#'
#' @param level \code{1-alpha/2}-order quantile of a normal distribution
#'
#' @param TTC time to cure calculated by TTC_wei
#'
#' @param Dttc partial derivates of TTC by dTTCdtheta_wei
#'
#' @keywords internal
TTC_ic_wei <- function(object, z_pcured = z_pcured,
z_ucured = z_ucured, epsilon = 0.05, level,TTC=NULL,Dttc=NULL) {
if (!inherits(object, "curesurv"))
stop("Primary argument much be a curesurv object")
if(is.null(TTC)){
TTC <- TTC_wei(z_pcured = z_pcured,
z_ucured = z_ucured,
theta = object$coefficients,
epsilon = epsilon)
}
if(is.null(Dttc)){
Dttc<-dTTCdtheta_wei(z_ucured = z_ucured,
z_pcured = z_pcured,
theta = object$coefficients,
epsilon = epsilon, TTC)
}
if(object$pophaz.alpha) {
varTTC <- diag(Dttc %*%
object$varcov_star[1:(ncol(object$varcov_star)-1),1:(ncol(object$varcov_star)-1)] %*%
t(Dttc))
}else{
varTTC <- diag(Dttc %*%
object$varcov_star %*%
t(Dttc))
}
lower_bound <- TTC - stats::qnorm(level) * sqrt(varTTC)
upper_bound <- TTC + stats::qnorm(level) * sqrt(varTTC)
IC <- list(t = TTC,
TTC = TTC,
lower_bound = lower_bound,
upper_bound = upper_bound,
varTTC = varTTC)
return(IC)
}
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