Nothing
R/nsurvival.R
In coprimary: Sample Size Calculation for Two Primary Time-to-Event Endpoints in Clinical Trials
Defines functions
nsurvival
Documented in
nsurvival
############################################
# nsurvival.R #
############################################
#'
#' @title Sample size calculation in clinical trials with one primary survival endpoint
#' @description
#' nsurvival() is used to determine the sample size for one time to event endpoint, such as Overall Survival (OS), Progression Free Survival
#' or the health related quality of life (HRQoL). If it is HRQoL, several HRQoL dimension can be considered.
#' @usage
#' nsurvival(design,Survhyp,alpha,duraccrual,durstudy,power,pe,look,fup,dropout,dqol)
#'
#'
#' @param design Superiority=c(1,sided)[with sided=1 if 1-sided and 2 if 2-sided]; Non inferiority=c(2); Equivalence=c(3)
#' @param Survhyp For Superiority=c(thyp,t,hype,Sc); for Non inferiority=c(thyp,t,hype,Sc,hypeA); for Equivalence=c(t,delta,Sc): parameters at time t
#' if thyp=1 then hype is survival rate in experimental arm under the null hypothesis and hypeA is the survival rate in the experimental arm under the alternative hypothesis;
#' if thyp=2 then hype is the hazard ratio under the null hypothesis and hypeA is the hazard ratio under the alternative hypothesis; Sc is survival rate in the control arm;
#' delta is the log hazard ratio equivalence margin. When endpoint is HRQoL, the survival rate is replaced by the rate of patients without HRQoL deterioration.
#' @param alpha Type I error, for Non inferiority, Equivalence and 1-sided superiority is a vector of length one.
#' For 2-sided superiority is a vector to length two c(alpha.low, alpha.up).
#' @param duraccrual Accrual duration, expressed in number of days, months or years
#' @param durstudy Study duration, expressed in number of days, months or years
#' @param power 1- Probability of a type II error. Default value=0.80.
#' @param pe Proportion (ratio) of patients assigned to the experimental arm (with 0<pe<1). Default value = 0.5.
#' @param look The number of interim analyses, c(1) for one final analysis; c(nb, bound, timing) for at least one interim analyses with bound=c(bound.eff,bound.fut):1-sided or bound=c(bound.lown,bound.up):2-sided.
#' nb the number of planned looks, bound.eff and bound.fut corresponds to the type of boundaries used for efficacy (i.e. reject H0) and futility (i.e. reject H1).
#' bound.fut=0: No futility monitoring, 1: Lan deMets O.Brien Fleming, 2: Lan deMets Pocock.
#' bound.low and bound.up the type of lower and upper boundaries used (1: Lan deMets O.Brien Fleming, 2: Lan deMets Pocock, 3: O.Brien Fleming, 4: Pocock). Default value = 1.
#' @param fup Follow-up information, No fixed:c(0) (follow-up until the end of study);
#' Fixed:c(1, durfollow) with durfollow is the duration of follow-up. Default value = 0.
#' @param dropout Drop out information, No drop out=c(0); Drop out=c(1,gammae,gammac) with gammae the hazard drop out rates in experimental arm
#' and control arm respectively. Default value = 0.
#' @param dqol number of targeted dimensions for the health related quality of life. Default value = 0.
#'
#' @details The nsurvival function computes the sample size for one time to event endpoint, such as OS, PFS or HRQoL.
#' HRQoL has become increasingly important in clinical trials over the past two decades.
#'
#' @return Event: number of events estimated
#' @return Total: number of patients
#' @return Ne: number for experimental arm for each endpoint
#' @return Nc: number for control arm for each endpoint
#' @return HR: Hazard ratio for each endpoint
#'
#' @examples
#' #############################################################
#' ############### Design superiority:one-sided ###############
#' #############################################################
#' ## 7-year survival rates Se=0.57 and Sc=0.53, alpha=0.05, accrual duration of 4 years,
#' ## study duration of 8 years and default values i.e power=0.80, pe=0.5, look=1, fup=0,
#' ## dropout=0, dqol=0
#'
#' ns1 <- nsurvival(design=c(1,1),Survhyp=c(1,7,0.57,0.53),alpha=0.05,duraccrual=4,durstudy=8)
#'
#' ############################################################
#' ############### Design superiority:two-sided ###############
#' ############################################################
#' ## 5-year rate without HRQoL deterioration Se=0.75 and Sc=0.65, alpha=c(0.04,0.01), accrual
#' ## duration of 2 years, study duration of 6 years, power=0.90, pe=0.55, follow-up 5 years,
#' ## 3 target variables for health related quality of life and default values i.e look=1, dropout=0
#'
#' ns2 <- nsurvival(design=c(1,2),Survhyp=c(1,5,0.75,0.65),alpha=c(0.04,0.01),duraccrual=2,
#' durstudy=6,power=0.90,pe=0.55,fup=c(1,5),dqol=3)
#'
#' ###########################################################
#' ############### Design non-inferiority ##################
#' ###########################################################
#' ## 5-year survival rates are equal under the alternative hypothesis, i.e Se=0.60 and Sc=SeA=0.70,
#' ## with alpha=0.05, accrual duration of 4 years, study duration of 8 years, two interim analysis
#' ## after the occurence 1/3 and 2/3 of the events and default values i.e power=0.80, pe=0.5, fup=0,
#' ## dropout=0, dqol=0
#'
#' ns3 <- nsurvival(design=c(2),Survhyp=c(1,5,0.60,0.70, 0.70),alpha=0.05,duraccrual=4,
#' durstudy=8,look=c(3,c(1,1),c(1/3,2/3)))
#'
#' ##########################################################
#' ############### Design superiority ##################
#' ##########################################################
#' ## 3-year rate without HRQoL deterioration Sc=0.80 and log hazard equivalence margin delta=0.1
#' ## with alpha=0.10, accrual duration of 3 years, study duration of 5 years, drop out hazard rate
#' ## of 0.05 per arm, 2 target variables for health related quality of life and default values i.e
#' ## power=0.80, pe=0.5, look=1, fup=0
#'
#' ns4 <- nsurvival(design=c(3),Survhyp=c(3,0.10,0.80),alpha=0.10,duraccrual=3,durstudy=5,
#' dropout=c(1,0.05,0.05),dqol=2)
#'
#' @name nsurvival
#' @export
#'
#' @import gsDesign graphics digest plyr proto
#' @importFrom stats pnorm
# nsurvival <- function(design,Survhyp,pe,alpha,power,duraccrual,durstudy,look,fup,dropout,dqol=NULL)
nsurvival <- function(design,Survhyp,alpha,duraccrual,durstudy,power=0.80,pe=0.5,look=1,fup=0,dropout=0,dqol=0)
{
beta=1-power
if (dqol!=0)
{
if (design[1]==1 & design[2]==2)
{
alfa<- c(round(alpha[1]/dqol,3),round(alpha[2]/dqol,3))
}
else
{
alfa<- round(alpha/dqol,3)
}
}
else
{
alfa=round(alpha,3)
}
# Survival decomposition
if (design[1]==3) {Survhyp <- c(2,Survhyp)}
time <- Survhyp[2]
Sc <- Survhyp[4]
if (Survhyp[1]==1)
{
Se <- Survhyp[3]
if (design[1]!=1)
{SeA <- Survhyp[5]}
}
if (Survhyp[1]==2)
{
time <- Survhyp[2]
if (design[1]==1 | design[1]==2) {Se <- exp(Survhyp[3]*log(Sc))}
if (design[1]==3) {Se <- exp(exp(-Survhyp[3])*log(Sc))}
if (design[1]==2)
{SeA <- exp(Survhyp[5]*log(Sc))}
}
if (design[1]==1)
{Survhyp.temp <- c(Survhyp[1],time,Se,Sc)}
if (design[1]==2)
{Survhyp.temp <- c(Survhyp[1],time,Se,Sc,SeA)}
if (design[1]==3)
{Survhyp.temp <- c(time,Se,Sc)}
if (dropout[1]==0)
{dropout <-rep(0,3)}
# Number of event / Hazard Ratio
if (design[1]==1)
{
if (design[2]==1)
{temp <- nbevent(c(Sc,Se),pe,alfa,beta,design)}
if (design[2]==2)
{temp <- nbevent(c(Sc,Se),pe,alfa[2],beta,c(1,1))}
nbevent <- temp$E
h <- temp$h
}
# Non inferiority: HR Alternative Hypothesis
if (design[1]==2)
{
temp.alt <- nbevent(c(Sc,Se,SeA),pe,alfa,beta,design)
h.alt <- temp.alt$h.alt
nbevent <- temp.alt$E
h <- temp.alt$h
}
# Equivalence: HR Alternative Hypothesis
if (design[1]==3)
{
temp <- nbevent(c(Sc,Se),pe,alfa,beta/2,c(1,1))
nbevent <- temp$E
h <- temp$h
}
if (look[1]!=1)
{
if (design[1]==2)
{design <- c(design,1)}
interim.bound <- matrix(0,nrow=look[1],ncol=5+design[2])
interim.bound[,1] <- c(look[-c(1,2,3)],1)
# Si non inferiority or Superiority One Sided
## Only H0
if (design[2]==1 & look[3]==0)
{
if (look[2]==1)
{sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa,beta=beta,sfu=sfLDOF,test.type=1)}
if (look[2]==2)
{sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa,beta=beta,sfu=sfLDPocock,test.type=1)}
if (look[2]==3)
{sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa,beta=beta,sfu="OF",test.type=1)}
if (look[2]==4)
{sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa,beta=beta,sfu="Pocock",test.type=1)}
nbevent <- nbevent*max(sequential$n.I)
interim.bound[,2] <- c(look[-c(1,2,3)],1)*nbevent
interim.bound[,3] <- pnorm(-sequential$upper$bound)*design[2]
interim.bound[,4] <- sequential$upper$bound
if (design[1]==2 & h<1)
{interim.bound[,4] <- -sequential$upper$bound}
dimnames(interim.bound) <- list(c(1:look[1]),c("Information","Events","pvalue reject H0","Boundary reject H0","Analysis Time Under H0","Analysis Time Under H1"))
}
if (design[2]==1 & look[3]!=0)
{
if (look[2]==1)
{
if (look[3]==1)
{sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa,beta=beta,sfu=sfLDOF,sfl=sfLDOF,test.type=4)}
if (look[3]==2)
{sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa,beta=beta,sfu=sfLDOF,sfl=sfLDPocock,test.type=4)}
}
if (look[2]==2)
{
if (look[3]==1)
{sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa,beta=beta,sfu=sfLDPocock,sfl=sfLDOF,test.type=4)}
if (look[3]==2)
{sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa,beta=beta,sfu=sfLDPocock,sfl=sfLDPocock,test.type=4)}
}
nbevent <- nbevent*max(sequential$n.I)
interim.bound[,2] <- c(look[-c(1,2,3)],1)*nbevent
interim.bound[,3] <- sequential$upper$bound
interim.bound[,4] <- sequential$lower$bound
if (design[1]==2 & h<1)
{
interim.bound[,3] <- -sequential$upper$bound
interim.bound[,4] <- -sequential$lower$bound
}
dimnames(interim.bound) <- list(c(1:look[1]),c("Information","Events","Boundary Reject H0","Boundary reject H1","Analysis Time Under H0","Analysis Time Under H1"))
}
if (design[2]==2)
{
# Inflation Parameter
if (look[3]==1)
{
if (look[2]==1)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],astar=alfa[1],beta=beta,sfu=sfLDOF,sfl=sfLDOF,test.type=5)
nbevent <- max(gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu=sfLDOF,test.type=1)$n.I)*nbevent
}
if (look[2]==2)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],astar=alfa[1],beta=beta,sfu=sfLDOF,sfl=sfLDPocock,test.type=5)
nbevent <- max(gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu=sfLDOF,test.type=1)$n.I)*nbevent
}
if (look[2]==3)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu=sfLDOF,sfl="OF",test.type=2)
nbevent <- max(sequential$n.I)*nbevent
}
if (look[2]==4)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu=sfLDOF,sfl="Pocock",test.type=2)
nbevent <- max(sequential$n.I)*nbevent
}
}
if (look[3]==2)
{
if (look[2]==1)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],astar=alfa[1],beta=beta,sfu=sfLDPocock,sfl=sfLDOF,test.type=5)
nbevent <- max(gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu=sfLDPocock,test.type=1)$n.I)*nbevent
}
if (look[2]==2)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],astar=alfa[1],beta=beta,sfu=sfLDPocock,sfl=sfLDPocock,test.type=5)
nbevent <- max(gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu=sfLDPocock,test.type=1)$n.I)*nbevent
}
if (look[2]==3)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu=sfLDPocock,sfl="OF",test.type=2)
nbevent <- max(sequential$n.I)*nbevent
}
if (look[2]==4)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu=sfLDPocock,sfl="Pocock",test.type=2)
nbevent <- max(sequential$n.I)*nbevent
}
}
if (look[3]==3)
{
if (look[2]==1)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu="OF",sfl=sfLDOF,test.type=2)
nbevent <- max(sequential$n.I)*nbevent
}
if (look[2]==2)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu="OF",sfl=sfLDPocock,test.type=2)
nbevent <- max(sequential$n.I)*nbevent
}
if (look[2]==3)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu="OF",sfl="OF",test.type=2)
nbevent <- max(sequential$n.I)*nbevent
}
if (look[2]==4)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu="OF",sfl="Pocock",test.type=2)
nbevent <- max(sequential$n.I)*nbevent
}
}
if (look[3]==4)
{
if (look[2]==1)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu="Pocock",sfl=sfLDOF,test.type=2)
nbevent <- max(sequential$n.I)*nbevent
}
if (look[2]==2)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu="Pocock",sfl=sfLDPocock,test.type=2)
nbevent <- max(sequential$n.I)*nbevent
}
if (look[2]==3)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu="Pocock",sfl="OF",test.type=2)
nbevent <- max(sequential$n.I)*nbevent
}
if (look[2]==4)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu="Pocock",sfl="Pocock",test.type=2)
nbevent <- max(sequential$n.I)*nbevent
}
}
interim.bound[,2] <- c(look[-c(1,2,3)],1)*nbevent
interim.bound[,4] <- sequential$lower$bound
interim.bound[,5] <- sequential$upper$bound
dimnames(interim.bound) <- list(c(1:look[1]),c("Information","Events","pvalue reject H0","Boundary reject H0-","Boundary reject H0+","Analysis Time Under H0","Analysis Time Under H1"))
if (alfa[1]==alfa[2])
{interim.bound[,3] <- pnorm(-sequential$upper$bound)*2}
}
}
# Number of patients included
## No Fixed Follow-up
if (fup[1]==0)
{
if (design[1]==1)
{
probae <- probanofix(Se,time,duraccrual,durstudy,dropout[2])
probac <- probanofix(Sc,time,duraccrual,durstudy,dropout[3])
}
if (design[1]==2)
{
probae <- probanofix(SeA,time,duraccrual,durstudy,dropout[2])
probac <- probanofix(Sc,time,duraccrual,durstudy,dropout[3])
}
if (design[1]==3)
{
probae <- probanofix(Se,time,duraccrual,durstudy,dropout[3])
probac <- probanofix(Sc,time,duraccrual,durstudy,dropout[3])
}
}
else
## Fixed Follow-Up
{
if (design[1]==1)
{
probae <- probafix(Se,time,duraccrual,fup[2],durstudy,dropout[2])
probac <- probafix(Sc,time,duraccrual,fup[2],durstudy,dropout[3])
}
if (design[1]==2)
{
probae <- probafix(SeA,time,duraccrual,fup[2],durstudy,dropout[2])
probac <- probafix(Sc,time,duraccrual,fup[2],durstudy,dropout[3])
}
if (design[1]==3)
{
probae <- probafix(Se,time,duraccrual,fup[2],durstudy,dropout[2])
probac <- probafix(Sc,time,duraccrual,fup[2],durstudy,dropout[3])
}
}
proba <- pe*probae+(1-pe)*probac
ntot <- nbevent/proba
ne.temp <- ceiling(ntot*pe)
nc.temp <- ceiling(ntot*(1-pe))
ntot <- ne.temp+nc.temp
if (fup[1]==0)
{delaigraph <- seq(0,durstudy,by=.01)}
else
{delaigraph <- seq(0,max(durstudy,duraccrual+fup[2]),by=.01)}
#############################################################################################################
#############################################################################################################
################### ############################
################### list of parameters returned ############################
################### ############################
#############################################################################################################
#############################################################################################################
if(fup[1]!=0)
{
if(dropout[1]!=0)
{
if (look[1]!=1)
{
if (design[1]==1)
{
if (design[2]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
Blower=alfa[1], Bupper=alfa[2],time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe),
subjectC=round(ntot*(1-pe)), interim=round(interim.bound,3))
}
if (design[2]==1)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe))
, interim=round(interim.bound,3))
}
}
else
{
if (design[1]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), SeA=round(SeA,3), HR=round(h,2), alt.HR=round(h.alt,3),events=round(nbevent),subjects=round(ntot),
subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)), interim=round(interim.bound,3))
}
if (design[1]==3)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,logHR=Survhyp[3],H01=round(exp(Survhyp[3])),H11=round(exp(Survhyp[3]),3), H02=round(exp(-Survhyp[3]),3), H12=round(exp(-Survhyp[3]),3),
events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)), interim=round(interim.bound,3))
}
}
}
else
{
if (design[1]==1)
{
if (design[2]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
Blower=alfa[1], Bupper=alfa[2],time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe),
subjectC=round(ntot*(1-pe)))
}
if (design[2]==1)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)))
}
}
else
{
if (design[1]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), SeA=round(SeA,3), HR=round(h,2), alt.HR=round(h.alt,3),events=round(nbevent),subjects=round(ntot),
subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)))
}
if (design[1]==3)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,logHR=Survhyp[3],H01=round(exp(Survhyp[3])),H11=round(exp(Survhyp[3]),3), H02=round(exp(-Survhyp[3]),3), H12=round(exp(-Survhyp[3]),3),
events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)))
}
}
}
}
else
{
if (look[1]!=1)
{
if (design[1]==1)
{
if (design[2]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
Blower=alfa[1], Bupper=alfa[2],time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe),
subjectC=round(ntot*(1-pe)), interim=round(interim.bound,3))
}
if (design[2]==1)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe))
, interim=round(interim.bound,3))
}
}
if (design[1]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), SeA=round(SeA,3), HR=round(h,2), alt.HR=round(h.alt,3),events=round(nbevent),subjects=round(ntot),
subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)), interim=round(interim.bound,3))
}
if (design[1]==3)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,logHR=Survhyp[3],H01=round(exp(Survhyp[3])),H11=round(exp(Survhyp[3]),3), H02=round(exp(-Survhyp[3]),3), H12=round(exp(-Survhyp[3]),3),
events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)), interim=round(interim.bound,3))
}
}
else
{
if (design[1]==1)
{
if (design[2]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
Blower=alfa[1], Bupper=alfa[2],time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe),
subjectC=round(ntot*(1-pe)))
}
if (design[2]==1)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)))
}
}
else
{
if (design[1]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), SeA=round(SeA,3), HR=round(h,2), alt.HR=round(h.alt,3),events=round(nbevent),subjects=round(ntot),
subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)))
}
if (design[1]==3)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,logHR=Survhyp[3],H01=round(exp(Survhyp[3])),H11=round(exp(Survhyp[3]),3), H02=round(exp(-Survhyp[3]),3), H12=round(exp(-Survhyp[3]),3),
events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)))
}
}
}
}
}
else
{
if(dropout[1]!=0)
{
if (look[1]!=1)
{
if (design[1]==1)
{
if (design[2]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
Blower=alfa[1], Bupper=alfa[2],time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe),
subjectC=round(ntot*(1-pe)), interim=round(interim.bound,3))
}
if (design[2]==1)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe))
, interim=round(interim.bound,3))
}
}
else
{
if (design[1]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), SeA=round(SeA,3), HR=round(h,2), alt.HR=round(h.alt,3),events=round(nbevent),subjects=round(ntot),
subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)), interim=round(interim.bound,3))
}
if (design[1]==3)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,logHR=Survhyp[3],H01=round(exp(Survhyp[3])),H11=round(exp(Survhyp[3]),3), H02=round(exp(-Survhyp[3]),3), H12=round(exp(-Survhyp[3]),3),
events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)), interim=round(interim.bound,3))
}
}
}
else
{
if (design[1]==1)
{
if (design[2]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
Blower=alfa[1], Bupper=alfa[2],time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe),
subjectC=round(ntot*(1-pe)))
}
if (design[2]==1)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)))
}
}
else
{
if (design[1]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), SeA=round(SeA,3), HR=round(h,2), alt.HR=round(h.alt,3),events=round(nbevent),subjects=round(ntot),
subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)))
}
if (design[1]==3)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,logHR=Survhyp[3],H01=round(exp(Survhyp[3])),H11=round(exp(Survhyp[3]),3), H02=round(exp(-Survhyp[3]),3), H12=round(exp(-Survhyp[3]),3),
events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)))
}
}
}
}
else
{
if (look[1]!=1)
{
if (design[1]==1)
{
if (design[2]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
Blower=alfa[1], Bupper=alfa[2],time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe),
subjectC=round(ntot*(1-pe)), interim=round(interim.bound,3))
}
if (design[2]==1)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe))
, interim=round(interim.bound,3))
}
}
else
{
if (design[1]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), SeA=round(SeA,3), HR=round(h,2), alt.HR=round(h.alt,3),events=round(nbevent),subjects=round(ntot),
subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)), interim=round(interim.bound,3))
}
if (design[1]==3)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,logHR=Survhyp[3],H01=round(exp(Survhyp[3])),H11=round(exp(Survhyp[3]),3), H02=round(exp(-Survhyp[3]),3), H12=round(exp(-Survhyp[3]),3),
events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)), interim=round(interim.bound,3))
}
}
}
else
{
if (design[1]==1)
{
if (design[2]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
Blower=alfa[1], Bupper=alfa[2],time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe),
subjectC=round(ntot*(1-pe)))
}
if (design[2]==1)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)))
}
}
else
{
if (design[1]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), SeA=round(SeA,3), HR=round(h,2), alt.HR=round(h.alt,3),events=round(nbevent),subjects=round(ntot),
subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)))
}
if (design[1]==3)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,logHR=Survhyp[3],H01=round(exp(Survhyp[3])),H11=round(exp(Survhyp[3]),3), H02=round(exp(-Survhyp[3]),3), H12=round(exp(-Survhyp[3]),3),
events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)))
}
}
}
}
}
return(l9)
}
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R Package Documentation
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Defines functions nsurvival
Documented in nsurvival
############################################
# nsurvival.R #
############################################
#'
#' @title Sample size calculation in clinical trials with one primary survival endpoint
#' @description
#' nsurvival() is used to determine the sample size for one time to event endpoint, such as Overall Survival (OS), Progression Free Survival
#' or the health related quality of life (HRQoL). If it is HRQoL, several HRQoL dimension can be considered.
#' @usage
#' nsurvival(design,Survhyp,alpha,duraccrual,durstudy,power,pe,look,fup,dropout,dqol)
#'
#'
#' @param design Superiority=c(1,sided)[with sided=1 if 1-sided and 2 if 2-sided]; Non inferiority=c(2); Equivalence=c(3)
#' @param Survhyp For Superiority=c(thyp,t,hype,Sc); for Non inferiority=c(thyp,t,hype,Sc,hypeA); for Equivalence=c(t,delta,Sc): parameters at time t
#' if thyp=1 then hype is survival rate in experimental arm under the null hypothesis and hypeA is the survival rate in the experimental arm under the alternative hypothesis;
#' if thyp=2 then hype is the hazard ratio under the null hypothesis and hypeA is the hazard ratio under the alternative hypothesis; Sc is survival rate in the control arm;
#' delta is the log hazard ratio equivalence margin. When endpoint is HRQoL, the survival rate is replaced by the rate of patients without HRQoL deterioration.
#' @param alpha Type I error, for Non inferiority, Equivalence and 1-sided superiority is a vector of length one.
#' For 2-sided superiority is a vector to length two c(alpha.low, alpha.up).
#' @param duraccrual Accrual duration, expressed in number of days, months or years
#' @param durstudy Study duration, expressed in number of days, months or years
#' @param power 1- Probability of a type II error. Default value=0.80.
#' @param pe Proportion (ratio) of patients assigned to the experimental arm (with 0<pe<1). Default value = 0.5.
#' @param look The number of interim analyses, c(1) for one final analysis; c(nb, bound, timing) for at least one interim analyses with bound=c(bound.eff,bound.fut):1-sided or bound=c(bound.lown,bound.up):2-sided.
#' nb the number of planned looks, bound.eff and bound.fut corresponds to the type of boundaries used for efficacy (i.e. reject H0) and futility (i.e. reject H1).
#' bound.fut=0: No futility monitoring, 1: Lan deMets O.Brien Fleming, 2: Lan deMets Pocock.
#' bound.low and bound.up the type of lower and upper boundaries used (1: Lan deMets O.Brien Fleming, 2: Lan deMets Pocock, 3: O.Brien Fleming, 4: Pocock). Default value = 1.
#' @param fup Follow-up information, No fixed:c(0) (follow-up until the end of study);
#' Fixed:c(1, durfollow) with durfollow is the duration of follow-up. Default value = 0.
#' @param dropout Drop out information, No drop out=c(0); Drop out=c(1,gammae,gammac) with gammae the hazard drop out rates in experimental arm
#' and control arm respectively. Default value = 0.
#' @param dqol number of targeted dimensions for the health related quality of life. Default value = 0.
#'
#' @details The nsurvival function computes the sample size for one time to event endpoint, such as OS, PFS or HRQoL.
#' HRQoL has become increasingly important in clinical trials over the past two decades.
#'
#' @return Event: number of events estimated
#' @return Total: number of patients
#' @return Ne: number for experimental arm for each endpoint
#' @return Nc: number for control arm for each endpoint
#' @return HR: Hazard ratio for each endpoint
#'
#' @examples
#' #############################################################
#' ############### Design superiority:one-sided ###############
#' #############################################################
#' ## 7-year survival rates Se=0.57 and Sc=0.53, alpha=0.05, accrual duration of 4 years,
#' ## study duration of 8 years and default values i.e power=0.80, pe=0.5, look=1, fup=0,
#' ## dropout=0, dqol=0
#'
#' ns1 <- nsurvival(design=c(1,1),Survhyp=c(1,7,0.57,0.53),alpha=0.05,duraccrual=4,durstudy=8)
#'
#' ############################################################
#' ############### Design superiority:two-sided ###############
#' ############################################################
#' ## 5-year rate without HRQoL deterioration Se=0.75 and Sc=0.65, alpha=c(0.04,0.01), accrual
#' ## duration of 2 years, study duration of 6 years, power=0.90, pe=0.55, follow-up 5 years,
#' ## 3 target variables for health related quality of life and default values i.e look=1, dropout=0
#'
#' ns2 <- nsurvival(design=c(1,2),Survhyp=c(1,5,0.75,0.65),alpha=c(0.04,0.01),duraccrual=2,
#' durstudy=6,power=0.90,pe=0.55,fup=c(1,5),dqol=3)
#'
#' ###########################################################
#' ############### Design non-inferiority ##################
#' ###########################################################
#' ## 5-year survival rates are equal under the alternative hypothesis, i.e Se=0.60 and Sc=SeA=0.70,
#' ## with alpha=0.05, accrual duration of 4 years, study duration of 8 years, two interim analysis
#' ## after the occurence 1/3 and 2/3 of the events and default values i.e power=0.80, pe=0.5, fup=0,
#' ## dropout=0, dqol=0
#'
#' ns3 <- nsurvival(design=c(2),Survhyp=c(1,5,0.60,0.70, 0.70),alpha=0.05,duraccrual=4,
#' durstudy=8,look=c(3,c(1,1),c(1/3,2/3)))
#'
#' ##########################################################
#' ############### Design superiority ##################
#' ##########################################################
#' ## 3-year rate without HRQoL deterioration Sc=0.80 and log hazard equivalence margin delta=0.1
#' ## with alpha=0.10, accrual duration of 3 years, study duration of 5 years, drop out hazard rate
#' ## of 0.05 per arm, 2 target variables for health related quality of life and default values i.e
#' ## power=0.80, pe=0.5, look=1, fup=0
#'
#' ns4 <- nsurvival(design=c(3),Survhyp=c(3,0.10,0.80),alpha=0.10,duraccrual=3,durstudy=5,
#' dropout=c(1,0.05,0.05),dqol=2)
#'
#' @name nsurvival
#' @export
#'
#' @import gsDesign graphics digest plyr proto
#' @importFrom stats pnorm
# nsurvival <- function(design,Survhyp,pe,alpha,power,duraccrual,durstudy,look,fup,dropout,dqol=NULL)
nsurvival <- function(design,Survhyp,alpha,duraccrual,durstudy,power=0.80,pe=0.5,look=1,fup=0,dropout=0,dqol=0)
{
beta=1-power
if (dqol!=0)
{
if (design[1]==1 & design[2]==2)
{
alfa<- c(round(alpha[1]/dqol,3),round(alpha[2]/dqol,3))
}
else
{
alfa<- round(alpha/dqol,3)
}
}
else
{
alfa=round(alpha,3)
}
# Survival decomposition
if (design[1]==3) {Survhyp <- c(2,Survhyp)}
time <- Survhyp[2]
Sc <- Survhyp[4]
if (Survhyp[1]==1)
{
Se <- Survhyp[3]
if (design[1]!=1)
{SeA <- Survhyp[5]}
}
if (Survhyp[1]==2)
{
time <- Survhyp[2]
if (design[1]==1 | design[1]==2) {Se <- exp(Survhyp[3]*log(Sc))}
if (design[1]==3) {Se <- exp(exp(-Survhyp[3])*log(Sc))}
if (design[1]==2)
{SeA <- exp(Survhyp[5]*log(Sc))}
}
if (design[1]==1)
{Survhyp.temp <- c(Survhyp[1],time,Se,Sc)}
if (design[1]==2)
{Survhyp.temp <- c(Survhyp[1],time,Se,Sc,SeA)}
if (design[1]==3)
{Survhyp.temp <- c(time,Se,Sc)}
if (dropout[1]==0)
{dropout <-rep(0,3)}
# Number of event / Hazard Ratio
if (design[1]==1)
{
if (design[2]==1)
{temp <- nbevent(c(Sc,Se),pe,alfa,beta,design)}
if (design[2]==2)
{temp <- nbevent(c(Sc,Se),pe,alfa[2],beta,c(1,1))}
nbevent <- temp$E
h <- temp$h
}
# Non inferiority: HR Alternative Hypothesis
if (design[1]==2)
{
temp.alt <- nbevent(c(Sc,Se,SeA),pe,alfa,beta,design)
h.alt <- temp.alt$h.alt
nbevent <- temp.alt$E
h <- temp.alt$h
}
# Equivalence: HR Alternative Hypothesis
if (design[1]==3)
{
temp <- nbevent(c(Sc,Se),pe,alfa,beta/2,c(1,1))
nbevent <- temp$E
h <- temp$h
}
if (look[1]!=1)
{
if (design[1]==2)
{design <- c(design,1)}
interim.bound <- matrix(0,nrow=look[1],ncol=5+design[2])
interim.bound[,1] <- c(look[-c(1,2,3)],1)
# Si non inferiority or Superiority One Sided
## Only H0
if (design[2]==1 & look[3]==0)
{
if (look[2]==1)
{sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa,beta=beta,sfu=sfLDOF,test.type=1)}
if (look[2]==2)
{sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa,beta=beta,sfu=sfLDPocock,test.type=1)}
if (look[2]==3)
{sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa,beta=beta,sfu="OF",test.type=1)}
if (look[2]==4)
{sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa,beta=beta,sfu="Pocock",test.type=1)}
nbevent <- nbevent*max(sequential$n.I)
interim.bound[,2] <- c(look[-c(1,2,3)],1)*nbevent
interim.bound[,3] <- pnorm(-sequential$upper$bound)*design[2]
interim.bound[,4] <- sequential$upper$bound
if (design[1]==2 & h<1)
{interim.bound[,4] <- -sequential$upper$bound}
dimnames(interim.bound) <- list(c(1:look[1]),c("Information","Events","pvalue reject H0","Boundary reject H0","Analysis Time Under H0","Analysis Time Under H1"))
}
if (design[2]==1 & look[3]!=0)
{
if (look[2]==1)
{
if (look[3]==1)
{sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa,beta=beta,sfu=sfLDOF,sfl=sfLDOF,test.type=4)}
if (look[3]==2)
{sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa,beta=beta,sfu=sfLDOF,sfl=sfLDPocock,test.type=4)}
}
if (look[2]==2)
{
if (look[3]==1)
{sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa,beta=beta,sfu=sfLDPocock,sfl=sfLDOF,test.type=4)}
if (look[3]==2)
{sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa,beta=beta,sfu=sfLDPocock,sfl=sfLDPocock,test.type=4)}
}
nbevent <- nbevent*max(sequential$n.I)
interim.bound[,2] <- c(look[-c(1,2,3)],1)*nbevent
interim.bound[,3] <- sequential$upper$bound
interim.bound[,4] <- sequential$lower$bound
if (design[1]==2 & h<1)
{
interim.bound[,3] <- -sequential$upper$bound
interim.bound[,4] <- -sequential$lower$bound
}
dimnames(interim.bound) <- list(c(1:look[1]),c("Information","Events","Boundary Reject H0","Boundary reject H1","Analysis Time Under H0","Analysis Time Under H1"))
}
if (design[2]==2)
{
# Inflation Parameter
if (look[3]==1)
{
if (look[2]==1)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],astar=alfa[1],beta=beta,sfu=sfLDOF,sfl=sfLDOF,test.type=5)
nbevent <- max(gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu=sfLDOF,test.type=1)$n.I)*nbevent
}
if (look[2]==2)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],astar=alfa[1],beta=beta,sfu=sfLDOF,sfl=sfLDPocock,test.type=5)
nbevent <- max(gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu=sfLDOF,test.type=1)$n.I)*nbevent
}
if (look[2]==3)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu=sfLDOF,sfl="OF",test.type=2)
nbevent <- max(sequential$n.I)*nbevent
}
if (look[2]==4)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu=sfLDOF,sfl="Pocock",test.type=2)
nbevent <- max(sequential$n.I)*nbevent
}
}
if (look[3]==2)
{
if (look[2]==1)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],astar=alfa[1],beta=beta,sfu=sfLDPocock,sfl=sfLDOF,test.type=5)
nbevent <- max(gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu=sfLDPocock,test.type=1)$n.I)*nbevent
}
if (look[2]==2)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],astar=alfa[1],beta=beta,sfu=sfLDPocock,sfl=sfLDPocock,test.type=5)
nbevent <- max(gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu=sfLDPocock,test.type=1)$n.I)*nbevent
}
if (look[2]==3)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu=sfLDPocock,sfl="OF",test.type=2)
nbevent <- max(sequential$n.I)*nbevent
}
if (look[2]==4)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu=sfLDPocock,sfl="Pocock",test.type=2)
nbevent <- max(sequential$n.I)*nbevent
}
}
if (look[3]==3)
{
if (look[2]==1)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu="OF",sfl=sfLDOF,test.type=2)
nbevent <- max(sequential$n.I)*nbevent
}
if (look[2]==2)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu="OF",sfl=sfLDPocock,test.type=2)
nbevent <- max(sequential$n.I)*nbevent
}
if (look[2]==3)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu="OF",sfl="OF",test.type=2)
nbevent <- max(sequential$n.I)*nbevent
}
if (look[2]==4)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu="OF",sfl="Pocock",test.type=2)
nbevent <- max(sequential$n.I)*nbevent
}
}
if (look[3]==4)
{
if (look[2]==1)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu="Pocock",sfl=sfLDOF,test.type=2)
nbevent <- max(sequential$n.I)*nbevent
}
if (look[2]==2)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu="Pocock",sfl=sfLDPocock,test.type=2)
nbevent <- max(sequential$n.I)*nbevent
}
if (look[2]==3)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu="Pocock",sfl="OF",test.type=2)
nbevent <- max(sequential$n.I)*nbevent
}
if (look[2]==4)
{
sequential <- gsDesign(k=look[1],timing=look[-c(1,2,3)],alpha=alfa[2],beta=beta,sfu="Pocock",sfl="Pocock",test.type=2)
nbevent <- max(sequential$n.I)*nbevent
}
}
interim.bound[,2] <- c(look[-c(1,2,3)],1)*nbevent
interim.bound[,4] <- sequential$lower$bound
interim.bound[,5] <- sequential$upper$bound
dimnames(interim.bound) <- list(c(1:look[1]),c("Information","Events","pvalue reject H0","Boundary reject H0-","Boundary reject H0+","Analysis Time Under H0","Analysis Time Under H1"))
if (alfa[1]==alfa[2])
{interim.bound[,3] <- pnorm(-sequential$upper$bound)*2}
}
}
# Number of patients included
## No Fixed Follow-up
if (fup[1]==0)
{
if (design[1]==1)
{
probae <- probanofix(Se,time,duraccrual,durstudy,dropout[2])
probac <- probanofix(Sc,time,duraccrual,durstudy,dropout[3])
}
if (design[1]==2)
{
probae <- probanofix(SeA,time,duraccrual,durstudy,dropout[2])
probac <- probanofix(Sc,time,duraccrual,durstudy,dropout[3])
}
if (design[1]==3)
{
probae <- probanofix(Se,time,duraccrual,durstudy,dropout[3])
probac <- probanofix(Sc,time,duraccrual,durstudy,dropout[3])
}
}
else
## Fixed Follow-Up
{
if (design[1]==1)
{
probae <- probafix(Se,time,duraccrual,fup[2],durstudy,dropout[2])
probac <- probafix(Sc,time,duraccrual,fup[2],durstudy,dropout[3])
}
if (design[1]==2)
{
probae <- probafix(SeA,time,duraccrual,fup[2],durstudy,dropout[2])
probac <- probafix(Sc,time,duraccrual,fup[2],durstudy,dropout[3])
}
if (design[1]==3)
{
probae <- probafix(Se,time,duraccrual,fup[2],durstudy,dropout[2])
probac <- probafix(Sc,time,duraccrual,fup[2],durstudy,dropout[3])
}
}
proba <- pe*probae+(1-pe)*probac
ntot <- nbevent/proba
ne.temp <- ceiling(ntot*pe)
nc.temp <- ceiling(ntot*(1-pe))
ntot <- ne.temp+nc.temp
if (fup[1]==0)
{delaigraph <- seq(0,durstudy,by=.01)}
else
{delaigraph <- seq(0,max(durstudy,duraccrual+fup[2]),by=.01)}
#############################################################################################################
#############################################################################################################
################### ############################
################### list of parameters returned ############################
################### ############################
#############################################################################################################
#############################################################################################################
if(fup[1]!=0)
{
if(dropout[1]!=0)
{
if (look[1]!=1)
{
if (design[1]==1)
{
if (design[2]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
Blower=alfa[1], Bupper=alfa[2],time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe),
subjectC=round(ntot*(1-pe)), interim=round(interim.bound,3))
}
if (design[2]==1)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe))
, interim=round(interim.bound,3))
}
}
else
{
if (design[1]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), SeA=round(SeA,3), HR=round(h,2), alt.HR=round(h.alt,3),events=round(nbevent),subjects=round(ntot),
subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)), interim=round(interim.bound,3))
}
if (design[1]==3)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,logHR=Survhyp[3],H01=round(exp(Survhyp[3])),H11=round(exp(Survhyp[3]),3), H02=round(exp(-Survhyp[3]),3), H12=round(exp(-Survhyp[3]),3),
events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)), interim=round(interim.bound,3))
}
}
}
else
{
if (design[1]==1)
{
if (design[2]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
Blower=alfa[1], Bupper=alfa[2],time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe),
subjectC=round(ntot*(1-pe)))
}
if (design[2]==1)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)))
}
}
else
{
if (design[1]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), SeA=round(SeA,3), HR=round(h,2), alt.HR=round(h.alt,3),events=round(nbevent),subjects=round(ntot),
subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)))
}
if (design[1]==3)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,logHR=Survhyp[3],H01=round(exp(Survhyp[3])),H11=round(exp(Survhyp[3]),3), H02=round(exp(-Survhyp[3]),3), H12=round(exp(-Survhyp[3]),3),
events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)))
}
}
}
}
else
{
if (look[1]!=1)
{
if (design[1]==1)
{
if (design[2]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
Blower=alfa[1], Bupper=alfa[2],time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe),
subjectC=round(ntot*(1-pe)), interim=round(interim.bound,3))
}
if (design[2]==1)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe))
, interim=round(interim.bound,3))
}
}
if (design[1]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), SeA=round(SeA,3), HR=round(h,2), alt.HR=round(h.alt,3),events=round(nbevent),subjects=round(ntot),
subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)), interim=round(interim.bound,3))
}
if (design[1]==3)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,logHR=Survhyp[3],H01=round(exp(Survhyp[3])),H11=round(exp(Survhyp[3]),3), H02=round(exp(-Survhyp[3]),3), H12=round(exp(-Survhyp[3]),3),
events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)), interim=round(interim.bound,3))
}
}
else
{
if (design[1]==1)
{
if (design[2]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
Blower=alfa[1], Bupper=alfa[2],time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe),
subjectC=round(ntot*(1-pe)))
}
if (design[2]==1)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)))
}
}
else
{
if (design[1]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), SeA=round(SeA,3), HR=round(h,2), alt.HR=round(h.alt,3),events=round(nbevent),subjects=round(ntot),
subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)))
}
if (design[1]==3)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup[2],durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,logHR=Survhyp[3],H01=round(exp(Survhyp[3])),H11=round(exp(Survhyp[3]),3), H02=round(exp(-Survhyp[3]),3), H12=round(exp(-Survhyp[3]),3),
events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)))
}
}
}
}
}
else
{
if(dropout[1]!=0)
{
if (look[1]!=1)
{
if (design[1]==1)
{
if (design[2]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
Blower=alfa[1], Bupper=alfa[2],time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe),
subjectC=round(ntot*(1-pe)), interim=round(interim.bound,3))
}
if (design[2]==1)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe))
, interim=round(interim.bound,3))
}
}
else
{
if (design[1]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), SeA=round(SeA,3), HR=round(h,2), alt.HR=round(h.alt,3),events=round(nbevent),subjects=round(ntot),
subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)), interim=round(interim.bound,3))
}
if (design[1]==3)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,logHR=Survhyp[3],H01=round(exp(Survhyp[3])),H11=round(exp(Survhyp[3]),3), H02=round(exp(-Survhyp[3]),3), H12=round(exp(-Survhyp[3]),3),
events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)), interim=round(interim.bound,3))
}
}
}
else
{
if (design[1]==1)
{
if (design[2]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
Blower=alfa[1], Bupper=alfa[2],time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe),
subjectC=round(ntot*(1-pe)))
}
if (design[2]==1)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)))
}
}
else
{
if (design[1]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), SeA=round(SeA,3), HR=round(h,2), alt.HR=round(h.alt,3),events=round(nbevent),subjects=round(ntot),
subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)))
}
if (design[1]==3)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,logHR=Survhyp[3],H01=round(exp(Survhyp[3])),H11=round(exp(Survhyp[3]),3), H02=round(exp(-Survhyp[3]),3), H12=round(exp(-Survhyp[3]),3),
events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)))
}
}
}
}
else
{
if (look[1]!=1)
{
if (design[1]==1)
{
if (design[2]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
Blower=alfa[1], Bupper=alfa[2],time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe),
subjectC=round(ntot*(1-pe)), interim=round(interim.bound,3))
}
if (design[2]==1)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe))
, interim=round(interim.bound,3))
}
}
else
{
if (design[1]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), SeA=round(SeA,3), HR=round(h,2), alt.HR=round(h.alt,3),events=round(nbevent),subjects=round(ntot),
subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)), interim=round(interim.bound,3))
}
if (design[1]==3)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,logHR=Survhyp[3],H01=round(exp(Survhyp[3])),H11=round(exp(Survhyp[3]),3), H02=round(exp(-Survhyp[3]),3), H12=round(exp(-Survhyp[3]),3),
events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)), interim=round(interim.bound,3))
}
}
}
else
{
if (design[1]==1)
{
if (design[2]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
Blower=alfa[1], Bupper=alfa[2],time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe),
subjectC=round(ntot*(1-pe)))
}
if (design[2]==1)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), HR=round(h,3),events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)))
}
}
else
{
if (design[1]==2)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,Se=round(Se,3), SeA=round(SeA,3), HR=round(h,2), alt.HR=round(h.alt,3),events=round(nbevent),subjects=round(ntot),
subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)))
}
if (design[1]==3)
{
l9 <- list(alpha=alfa,power=1-beta, accrual=duraccrual,followup=fup,durstuty=durstudy,ExpArm=pe,dropout=c(dropout[2],dropout[3]),look=look[1],
time=time, Sc=Sc,logHR=Survhyp[3],H01=round(exp(Survhyp[3])),H11=round(exp(Survhyp[3]),3), H02=round(exp(-Survhyp[3]),3), H12=round(exp(-Survhyp[3]),3),
events=round(nbevent),subjects=round(ntot), subjectE=round(ntot*pe), subjectC=round(ntot*(1-pe)))
}
}
}
}
}
return(l9)
}
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