R/smartsize.R

In SMARTAR: Sequential Multiple Assignment Randomized Trial and Adaptive Randomization

#' sample size calculation
#'
#' Return a message that contains the estimated
#' strategy-specified means and their confidence interval,
#' as well as the asymptotic variance-covariance
#' matrix for these estimates.
#' @param sim A numeric matrix containing the values
#'  of treatment sequence-specific parameters to generate
#'   the SMART data, including the values of stage-specific
#'    treatments, intermediate outcome and final primary outcome.
#' @param family A character string to specify
#' the type of final primary outcome. The default is
#'  family=“gaussian”, which refers to the continuous
#'  primary outcome. If family=”binomial” then the
#'  primary outcome will be treated as binary variable.
#' @param delta The standardized effect size
#' for sample size calculation.
#' @param df The degrees of freedom for
#' the chisquare test.
#' @param alpha Type I error rate.
#' @param beta Type II error rate.
#' @param global If TRUE then power the SMART
#' based on a global test, otherwise power
#' the SMART based on a pairwise test.
#' The default is TRUE
#' @return Standardized effect size and
#' total sample size for SMART
##' \itemize{
##'    \item delta: standardized effect size
##'    \item n: total sample size
##'    }
#' @references Murphy, S. A. (2005). An experimental
#' design for the development of adaptive treatment
#' strategies. Statistics in Medicine. 24(10): 1455-1481.
#' @references Ogbagaber S. B., Karp, J., and
#' Wahed A.S. (2015). Design of sequentially randomization
#' trials for testing adaptive treatment strategies.
#' Statistics in Medicine. DOI: 10.1002/sim.6747.
#' @importFrom MASS ginv
#' @export

smartsize<-function(sim=NULL,delta=NULL,
                   df=NULL,alpha=0.05,beta=0.20,
                   global=TRUE,family=c("gaussian","binomial")[1]){
  Smat<-sim
  Al<-alpha
  Be<-beta
  FA<-family
  DF<-df
  DELTA<-delta
  if (global==TRUE){
    if (is.null(DELTA)) {
      Dmat<-atsscan(data=Smat)
      G<-nrow(Dmat)
      Vmat<-tvmat(sim=Smat,family=FA)
      Umat<-tumat(sim=Smat,family=FA)
      Cmat<-getcmat(control=1,nats=G)
      M<-Cmat%*%Vmat%*%t(Cmat)
      MAT<-ginv(M)
      Del<-t(Umat)%*%t(Cmat)%*%MAT%*%Cmat%*%Umat
      DF<-getdf(data=Smat)
      Lam<-getncp(alpha=Al,beta=Be,df=DF)
      if (Del<=0) {warning("Effect size cannot be
                           less than or equal to 0")}
             else {size<-Lam/Del}
      }
      else {
        Lam<-getncp(alpha=Al,beta=Be,df=DF)
        Del<-DELTA
        if (Del<=0) {warning("Effect size cannot
                             be less than or equal to 0")}
               else {size<-Lam/Del}
        }
  N<-ceiling(size)
  out<-as.data.frame(cbind(Lam,Del,DF,N))
  colnames(out)<-c("NCP","delta","df","N")
  message("The sample size is for total subjects
          registered in the trial. \n")
  }
  else if (global==FALSE) {
    Del<-DELTA
    if (Del<=0) {warning("Effect size cannot
                         be less than or equal to 0")}
           else {size<-(qnorm(1-Al/2)+qnorm(1-Be))^2*2*(1/Del)^2}
    N<-ceiling(size)
    out<-as.data.frame(cbind(Del,N))
    colnames(out)<-c("delta","N")
    message("The sample size is for subjects
            used in pairwise test. \n")
                           }
  return(out)
}