R/LRT.r

In OneArm2stage: Phase II Single-Arm Two-Stage Designs with Time-to-Event Outcomes

##' Performs the one-sample log-rank test (OSLR) for the time-to-event data from
##' two-stage Phase II clinical trials assuming the failure time follows a
##' Weibull distribution. This can be used for designs with either unrestricted
##' or restricted follow-up .
##'
##' @title Conduct the Interim or Final Analysis Using the One-Sample Log-Rank
##' Test for Two-Stage TTE Trials
##' @param shape shape parameter for the Weibull distribution.
##' @param S0 the survival probability at a fixed time point x0 under the null
##' hypothesis.
##' @param x0 a fixed time point when the survival probability is S0 under null.
##' @param data the time-to-event data for either the interim or final analysis
##' from a two-stage survival trial, contains 2 variables:\cr
##'             \emph{time} the time period under observation before the time of
##'             interim analysis (for interim analysis) or during entire trial
##'             (for final analysis) for each patient.\cr
##'             \emph{status} the status indicator of patients (event = 1,
##'             censored  = 0).
##' @return  \emph{z} the OSLR test statistic for the interim or final analysis,
##'  depending on data used.\cr
##'          \emph{O} the observed number of events.\cr
##'          \emph{E} the expected number of events.
##'
##' @import utils
##' @export
##' @examples
##' dat<- read.csv(system.file("extdata", "kj1_final.csv", package = "OneArm2stage"))
##' LRT(shape=1, S0=0.62, x0=2, data=dat)
##'# O       E       Z
##'# 18.0000 16.3598 -0.4055

##'@references
##' Wu, J, Chen L, Wei J, Weiss H, Chauhan A. (2020). Two-stage phase II survival trial design. Pharmaceutical Statistics. 2020;19:214-229. https://doi.org/10.1002/pst.1983


LRT <- function(shape, S0, x0, data) {

 # if (dist == "WB") {
    scale0 = x0/(-log(S0))^(1/shape)
    s0 = function(u) 1 - pweibull(u, shape, scale0)

  H = function(u) -log(s0(u)) # Hazard function for null distribution s0

  Time = data$time
  Cens = data$status
  O = sum(Cens)
  E = sum(H(Time))
  Z = (E - O)/sqrt(E)  # OSLR test statistic
  ans = c(O = O, E = round(E, 4), Z = round(Z, 4))
  return(ans)
}