cpstop {PWEALL}

The stopping probability based on the stopping boundary

Description

This will calculate the stopping probability given the stopping boundary. All the calculation is based on the proportional hazards assumption and the Cox model.

Usage

cpstop(Dplan=300,pi1=0.5,Beta1=log(0.8),Beta0=log(1),
        prop=seq(0.1,0.9,by=0.1),HRbound=rep(0.85,length(prop)))

Arguments

Dplan

Planned number of events at study end

pi1

Allocation probability for the treatment group

Beta1

designed log hazard ratio, i.e. under alternative hypothesis

Beta0

null log hazard ratio, i.e. under null hypothesis

prop

proportion of Dplan observed

HRbound

the stopping boundary

Details

This will calculate the stopping probability given the stopping boundary. All the calculation is based on the proportional hazards assumption and the Cox model.

Value

pstop0

Stopping probability under null hypothesis

pstop1

Stopping probability under alternative hypothesis

Note

This will calculate the stopping probability given the stopping boundary

Author(s)

Xiaodong Luo

References

Halperin, Lan, Ware, Johnson and DeMets (1982). Controlled Clinical Trials.

See Also

cp,cpboundary

Examples

###Calculate the stopping boundary at 10-90 percent of the target 300 events 
###when the condition power are c(0.2,0.3,0.4) with 2:1 allocation ratio 
###between the treatment group and the control group, we pick the boundary 
###based on 20 percent conditional power according to design, i.e. under alternative
targetD<-800 ###target number of events at study end
#############Allocation prob for the treatment group#############
pi1<-2/3
propevent<-seq(0.1,0.9,by=0.1) ###proportion of events at interim
HRbound<-cpboundary(Dplan=targetD,pi1=pi1,prop=propevent)$CPDbound[,1]  ###picking a boundary
pa<-cpstop(pi1=pi1,HRbound=HRbound)    ###stopping probabilities under null and alternative  
pa

###Calculate the stopping probability under non-constant hazard ratio
n1<-length(propevent)

####time point at which hazard rates and hazard ratios change
tchange<-c(0,6,12,24)                       
###annual event rates=0.09(1st yr), 0.07(2nd yr) and 0.05(2+yr) for control
ratet<-c(0.09/12,0.09/12,0.07/12,0.05/12)   
###annual censoring rate=0%(1st yr) and 1.5%(after) for control and treatment
ratec0<-c(0/12,0/12,0.015/12,0.015/12)      
ratec1<-ratec0                              
###annual treatment discontinuation rate=4% (1st yr) and 3% (after)
rate31<-c(0.04/12,0.04/12,0.03/12,0.03/12)  
rate30<-rep(0,length(tchange))              

############Recruitment curve##################
oa<-c(100,200,300,300,400,400,400,400,400,400,400,400,300,200)
ntotal<-sum(oa)
ntotal

taur<-length(oa)
ut<-seq(1,taur,by=1)
u<-oa/ntotal


#############Type-1 error rate#############
alpha<-0.05

####null hypothesis
eta0<-log(1)

####constant HR
etac<-log(0.8)

####non-constant HR
eta<-c(log(1),log(0.75),log(0.75),log(0.75)) ###6-m delayed 


####target number of events where calculations are performed##############
sevent<-propevent*targetD
nse<-length(sevent)
xtimeline<-xbeta<-xvar<-pxstop<-matrix(0,ncol=2,nrow=nse)
xtimeline[,1]<-xbeta[,1]<-xvar[,1]<-pxstop[,1]<-sevent
i<-1
tbegin<-proc.time()
for (i in 1:nse){
###find timeline
xtimeline[i,2]<-pwecxpwufindt(target=sevent[i],ntotal=ntotal,
                taur=taur,u=u,ut=ut,pi1=0.5,
                rate11=exp(eta)*ratet,rate21=exp(eta)*ratet,rate31=rate31,ratec1=ratec1,
                rate10=ratet,rate20=ratet,rate30=rate30,ratec0=ratec0,
                tchange=tchange,eps=0.001,init=taur,epsilon=0.000001,maxiter=100)$tau1

#Overall hazard ratio and varaince
xbeta[i,2]<-ovbeta(tfix=xtimeline[i,2],taur=taur,u=u,ut=ut,pi1=pi1,
                rate11=exp(eta)*ratet,rate21=exp(eta)*ratet,rate31=rate31,ratec1=ratec1,
                rate10=ratet,rate20=ratet,rate30=rate30,ratec0=ratec0,
                tchange=tchange,eps=0.001,veps=0.001,epsbeta=1.0e-10)$b1
xvar[i,2]<-overallvar(tfix=xtimeline[i,2],taur=taur,u=u,ut=ut,pi1=pi1,
                rate11=exp(eta)*ratet,rate21=exp(eta)*ratet,rate31=rate31,ratec1=ratec1,
                rate10=ratet,rate20=ratet,rate30=rate30,ratec0=ratec0,
                tchange=tchange,eps=0.001,veps=0.001,beta=xbeta[i,2])$vbeta
}
##stopping prob
pxstop[,2]<-1-pnorm(sqrt(ntotal)*(log(HRbound)-xbeta[,2])/sqrt(xvar[,2]))
tend<-proc.time()

xout<-cbind(xtimeline[,1],xtimeline[,2],xbeta[,2],xvar[,2]/ntotal,
            1/pi1/(1-pi1)/xtimeline[,1],pxstop[,2],pa$pstop0,pa$pstop1)
xnames<-c("# of events", "Time", "Estbeta", "TrueV", "ApproxV", "NCHR", "Null", "CHR")
colnames(xout)<-xnames
options(digits=2)
xout