R/sn_ic_adtneh2_loglog.R

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

#' @title sn_ic_adtneh2_loglog function
#'
#' @description calculates the net survival at time t. It also provides the
#' related confidence intervals using log-log method.
#'
#' @param object ouput from a model implemented in curesurv
#'
#' @param z_alpha Covariates matrix acting on parameter alpha of the density of
#'  time-to-null excess hazard model
#'
#' @param z_tau Covariates matrix acting on time-to-null parameter.
#'
#' @param x time at which the predictions are provided
#'
#' @param level (1-alpha/2)-order quantile of a normal distribution
#'
#' @param cumLexctopred a pre-prediction thing obtained from cumLexc_ad2_topred, calculated if not NULL
#'
#' @param Dsn partial derivatives of Sn obtained from dsndtheta_adtneh2 function, calculated if not NULL
#'
#' @author Juste Goungounga, Judith Breaud, Olayide Boussari, Laura Botta, Valerie Jooste
#'
#' @references Boussari O, Bordes L, Romain G, Colonna M, Bossard N, Remontet L,
#'  Jooste V. Modeling excess hazard with time-to-cure as a parameter.
#'   Biometrics. 2021 Dec;77(4):1289-1302. doi: 10.1111/biom.13361.
#'    Epub 2020 Sep 12. PMID: 32869288.
#' (\href{https://pubmed.ncbi.nlm.nih.gov/32869288/}{pubmed})
#'
#'
#'  Boussari O, Romain G, Remontet L, Bossard N, Mounier M, Bouvier AM,
#'  Binquet C, Colonna M, Jooste V. A new approach to estimate time-to-cure from
#'  cancer registries data. Cancer Epidemiol. 2018 Apr;53:72-80.
#'  doi: 10.1016/j.canep.2018.01.013. Epub 2018 Feb 4. PMID: 29414635.
#' (\href{https://pubmed.ncbi.nlm.nih.gov/29414635/}{pubmed})
#'
#' @keywords internal



sn_ic_adtneh2_loglog <-  function(z_tau,
                                  z_alpha,
                                  x,
                                  object,
                                  level = 0.975,
                                  cumLexctopred=NULL,
                                  Dsn=NULL){
  if (!inherits(object, "curesurv"))
    stop("Primary argument much be a curesurv object")
  if(is.null(cumLexctopred)){
    cumLexctopred=cumLexc_ad2_topred(z_tau = z_tau,z_alpha = z_alpha,x=x,theta=object$coefficient)
  }
  if(is.null(Dsn)){
    Dpi <- dpidtheta_adtneh2(z_tau = z_tau,
                             z_alpha = z_alpha,
                             x = x,
                             object,
                             cumLexctopred=cumLexctopred)
    Dsn<-dsndtheta_adtneh2(z_tau=z_tau,
                           z_alpha=z_alpha,
                           x=x,
                           object,
                           cumLexctopred=cumLexctopred,
                           Dpi=Dpi)  }

  sn <- cumLexctopred$netsurv

  Dloglog <- sweep(Dsn, 1/(sn*log(sn)), MARGIN = 1, '*' )

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


  lower_bound <-  exp(-exp(log(-log(sn)) + stats::qnorm(level) * sqrt(varloglogsn)))
  upper_bound <-  exp(-exp(log(-log(sn)) - stats::qnorm(level) * sqrt(varloglogsn)))

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

  return(IC)

}