R/pi_ic_adtneh2_loglog.R

In curesurv: Mixture and Non Mixture Parametric Cure Models to Estimate Cure Indicators

#' @title pi_ic_adtneh2_loglog function
#'
#' @description produces confidence interval of cure fraction pi using a
#'  time-to-null excess hazard model with linear effect on parameter tau
#'  The confidence intervals based on log-log method.
#'
#'
#' @param z_tau Covariates matrix acting on time-to-null parameter.
#'
#'
#' @param z_alpha Covariates matrix acting on parameter alpha of the density of
#'  time-to-null excess hazard model
#'
#'
#' @param x time at which the predictions are provided
#'
#'
#' @param object ouput from a model implemented in curesurv
#'
#'
#' @param level \code{(1-alpha/2)}-order quantile of a normal distribution
#'
#' @param cumLexc_topred a pre prediction, if NULL it is calculated
#'
#' @param Dpi partial derivative of pi by theta obtained by dpidtheta_adtneh2 function, if NULL it is calculated
#'
#' @keywords internal


pi_ic_adtneh2_loglog <-  function(z_tau = z_tau,
                                  z_alpha = z_alpha,
                                  x = x,
                                  object,
                                  level = level,
                                  cumLexc_topred=NULL,
                                  Dpi=NULL) {
  if(is.null(cumLexc_topred)){
    cumLexc_topred<-cumLexc_ad2_topred(z_tau,z_alpha,x,object$coefficient)
  }
  if(is.null(Dpi)){
    Dpi<-dpidtheta_adtneh2(z_tau,z_alpha,x,object,cumLexc_topred)
  }

  cumLexc <- cumLexc_topred$cumhaz
  pi <- cumLexc_topred$pi


  Dloglog <- sweep(Dpi, 1/(pi*log(pi)), MARGIN = 1, '*' )

  varloglogpi <- diag(Dloglog %*% object$varcov_star %*% t(Dloglog))


  lower_bound <-  exp(-exp(log(-log(pi)) + stats::qnorm(level) * sqrt(varloglogpi)))
  upper_bound <-  exp(-exp(log(-log(pi)) - stats::qnorm(level) * sqrt(varloglogpi)))

  IC <- list(pi = pi,
             lower_bound = lower_bound,
             upper_bound = upper_bound)

  return(IC)

}