R/SAN FUNCTION TWO DIRECTION.R
In AshZhong/Goahead:
Defines functions
Fix_SS_SAN_Normal_Prob
SAN_Bayesian_Vary_Var
SAN_Normal_Cutoff
SAN_findIGcutoff
library(shiny)
SAN_findIGcutoff<-function(n=30,
prior.mean=1/3,prior.k=1,
prior.a=1,prior.b=1,
ssq=1,
rate=0.8,CT=0.25,
seed.num=369,
stop.criterion=10^-3,direction='Greater'){
####prior####
###mu1~N(prior.mean1,prior.k1*1/var)
#### 1/var~gamma(prior.a1,rate=prior.b1)
####
cutoff<-NA
set.seed(seed.num)
S=1
upper=abs(CT)+1
lower=-abs(CT)-1
########control.group####
ssq=ssq*n
while(S==1){
temp=(upper+lower)/2
mupost_temp=(prior.k*prior.mean+n*temp)/(prior.k+n)
kpost_temp=prior.k+n
apost_temp=prior.a+n/2
bpost_temp=prior.b+1/2*ssq+prior.k*n*(temp-prior.mean)^2/(2*(prior.k+n))
mupost_upper=(prior.k*prior.mean+n*upper)/(prior.k+n)
kpost_upper=prior.k+n
apost_upper=prior.a+n/2
bpost_upper=prior.b+1/2*ssq+prior.k*n*(upper-prior.mean)^2/(2*(prior.k+n))
mupost_lower=(prior.k*prior.mean+n*lower)/(prior.k+n)
kpost_lower=prior.k+n
apost_lower=prior.a+n/2
bpost_lower=prior.b+1/2*ssq+prior.k*n*(lower-prior.mean)^2/(2*(prior.k+n))
if(direction=='Greater'){
probupper=1-pt((CT-mupost_upper)/sqrt(bpost_upper/(apost_upper*kpost_upper)),df=2*apost_upper)
problower=1-pt((CT-mupost_lower)/sqrt(bpost_lower/(apost_lower*kpost_lower)),df=2*apost_lower)
probtemp=1-pt((CT-mupost_temp)/sqrt(bpost_temp/(apost_temp*kpost_temp)),df=2*apost_temp)
if(problower>=rate){
if(abs(problower-rate)<=stop.criterion){
S=0
cutoff=lower
}
upper=lower
lower=-2*abs(lower)
}else if(probupper<=rate){
if(abs(probupper-rate)<=stop.criterion){
S=0
cutoff=upper
}
upper=2*abs(upper)
lower=upper
}else{
if(abs(probtemp-rate)<=stop.criterion){
S=0
cutoff=temp
}
if(probtemp<rate){lower=temp}
if(probtemp>rate){upper=temp}
}
}
if(direction=='Less'){
probupper=pt((CT-mupost_upper)/sqrt(bpost_upper/(apost_upper*kpost_upper)),df=2*apost_upper)
problower=pt((CT-mupost_lower)/sqrt(bpost_lower/(apost_lower*kpost_lower)),df=2*apost_lower)
probtemp=pt((CT-mupost_temp)/sqrt(bpost_temp/(apost_temp*kpost_temp)),df=2*apost_temp)
if(problower<=rate){
if(abs(problower-rate)<=stop.criterion){
S=0
cutoff=lower
}
upper=lower
lower=-2*abs(lower)
}else if(probupper>=rate){
if(abs(probupper-rate)<=stop.criterion){
S=0
cutoff=upper
}
upper=2*abs(upper)
lower=upper
}else{
if(abs(probtemp-rate)<=stop.criterion){
S=0
cutoff=temp
}
if(probtemp>rate){lower=temp}
if(probtemp<rate){upper=temp}
}
}
}
return(cutoff)
}
SAN_Normal_Cutoff<-function(n=30,
prior.mean=1/3,prior.sd=1,
prior.k=1,prior.a=1,prior.b=1,
sd=1,ssq=1,
CT1.go=0.25,
false.go.CT1=TRUE,FGR.CT1=0.25,
CT1.nogo=0.25,
false.nogo.CT1=TRUE,FNGR.CT1=0.25,
CT2.go=0.3,
false.go.CT2=TRUE, FGR.CT2=0.5,
CT2.nogo=0.3,
false.nogo.CT2=TRUE, FNGR.CT2=0.5,
method='Bayesian',direction='Greater',
fix.var=TRUE,noninfo=TRUE,
seed.num=369,
stop.criterion=10^-3,
logic.go='and',logic.nogo='or'){
flag=rep(0,4)
overlap.flag=0
est1.go=NA
est2.go=NA
est1.nogo=NA
est2.nogo=NA
flag=rep(0,4)
overlap.flag=0
sd.n=sd/sqrt(n)
if(is.na(CT1.go)){
false.go.CT1=FALSE
}
if(is.na(CT1.nogo)){
false.nogo.CT1=FALSE
}
if(is.na(CT2.go)){
false.go.CT2=FALSE
}
if(is.na(CT2.nogo)){
false.nogo.CT2=FALSE
}
if(direction=='Greater'){
if(method=='Bayesian'&(fix.var==TRUE)){
sd.post=sqrt(1/((1/prior.sd)^2+(1/sd.n)^2))
if(false.go.CT1==TRUE){
temp=qnorm(1-FGR.CT1,mean=CT1.go,sd=sd.post)
est1.go=(temp-(sd.n^2/(prior.sd^2+sd.n^2))*prior.mean)/(prior.sd^2/(prior.sd^2+sd.n^2))
}
if(false.go.CT2==TRUE){
temp=qnorm(1-FGR.CT2,mean=CT2.go,sd=sd.post)
est2.go=(temp-(sd.n^2/(prior.sd^2+sd.n^2))*prior.mean)/(prior.sd^2/(prior.sd^2+sd.n^2))
}
if(false.nogo.CT1==TRUE){
temp=qnorm(FNGR.CT1,mean=CT1.nogo,sd=sd.post)
est1.nogo=(temp-(sd.n^2/(prior.sd^2+sd.n^2))*prior.mean)/(prior.sd^2/(prior.sd^2+sd.n^2))
}
if(false.nogo.CT2==TRUE){
temp=qnorm(FNGR.CT2,mean=CT2.nogo,sd=sd.post)
est2.nogo=(temp-(sd.n^2/(prior.sd^2+sd.n^2))*prior.mean)/(prior.sd^2/(prior.sd^2+sd.n^2))
}
}
if(method=='Bayesian'&(fix.var==FALSE)){
if(noninfo==TRUE){
prior.k=0
prior.a=-1/2
prior.b=0
prior.mean=0
}
if(false.go.CT1==TRUE){
est1.go<-SAN_findIGcutoff(n=n,
prior.mean=prior.mean,prior.k=prior.k ,
prior.a=prior.a,prior.b=prior.b,
ssq=ssq,
rate=1-FGR.CT1,CT=CT1.go,
seed.num=seed.num,
stop.criterion=stop.criterion,direction='Greater')
}
if(false.go.CT2==TRUE){
est2.go<-SAN_findIGcutoff(n=n,
prior.mean=prior.mean,prior.k=prior.k ,
prior.a=prior.a,prior.b=prior.b,
ssq=ssq,
rate=1-FGR.CT2,CT=CT2.go,
seed.num=seed.num,
stop.criterion=stop.criterion,direction='Greater')
}
if(false.nogo.CT1==TRUE){
est1.nogo<-SAN_findIGcutoff(n=n,
prior.mean=prior.mean,prior.k=prior.k ,
prior.a=prior.a,prior.b=prior.b,
ssq=ssq,
rate=1-FNGR.CT1,CT=CT1.nogo,
seed.num=seed.num,
stop.criterion=stop.criterion,direction='Less')
}
if(false.nogo.CT2==TRUE){
est2.nogo<-SAN_findIGcutoff(n=n,
prior.mean=prior.mean,prior.k=prior.k ,
prior.a=prior.a,prior.b=prior.b,
ssq=ssq,
rate=1-FNGR.CT2,CT=CT2.nogo,
seed.num=seed.num,
stop.criterion=stop.criterion,direction='Less')
}
}
if(method=='Frequentist'){
if(false.go.CT1==TRUE){
est1.go=qnorm(1-FGR.CT1,mean=CT1.go,sd=sd.n)
}
if(false.go.CT2==TRUE){
est2.go=qnorm(1-FGR.CT2,mean=CT2.go,sd=sd.n)
}
if(false.nogo.CT1==TRUE){
est1.nogo=qnorm(FNGR.CT1,mean=CT1.nogo,sd=sd.n)
}
if(false.nogo.CT2==TRUE){
est2.nogo=qnorm(FNGR.CT2,mean=CT2.nogo,sd=sd.n)
}
}
if(any(is.na(c(est1.go,est2.go)))){logic.go='and'}
if(any(is.na(c(est1.nogo,est2.nogo)))){logic.nogo='and'}
if(logic.go=='and'){
go_cutoff=max(est1.go,est2.go,na.rm=TRUE)
}
if(logic.go=='or'){
go_cutoff=min(est1.go,est2.go,na.rm=TRUE)
}
if(logic.nogo=='and')
{
nogo_cutoff=min(est1.nogo,est2.nogo,na.rm=TRUE)
}
if(logic.nogo=='or')
{
nogo_cutoff=max(est1.nogo,est2.nogo,na.rm=TRUE)
}
if(go_cutoff>=nogo_cutoff){return(list(cutoff=c(go_cutoff,nogo_cutoff),flag=flag,overlap=overlap.flag))}
else{
overlap.flag=1
return(list(cutoff=c(go_cutoff,nogo_cutoff),flag=flag,overlap=overlap.flag))}
if(all(flag==0)==FALSE){return(list(cutoff=c(NA,NA),flag=flag,overlap=overlap.flag))}
}
if(direction=='Less'){
if(method=='Bayesian'&(fix.var==TRUE)){
sd.post=sqrt(1/((1/prior.sd)^2+(1/sd.n)^2))
if(false.go.CT1==TRUE){
temp=qnorm(FGR.CT1,mean=CT1.go,sd=sd.post)
est1.go=(temp-(sd.n^2/(prior.sd^2+sd.n^2))*prior.mean)/(prior.sd^2/(prior.sd^2+sd.n^2))
}
if(false.go.CT2==TRUE){
temp=qnorm(FGR.CT2,mean=CT2.go,sd=sd.post)
est2.go=(temp-(sd.n^2/(prior.sd^2+sd.n^2))*prior.mean)/(prior.sd^2/(prior.sd^2+sd.n^2))
}
if(false.nogo.CT1==TRUE){
temp=qnorm(1-FNGR.CT1,mean=CT1.nogo,sd=sd.post)
est1.nogo=(temp-(sd.n^2/(prior.sd^2+sd.n^2))*prior.mean)/(prior.sd^2/(prior.sd^2+sd.n^2))
}
if(false.nogo.CT2==TRUE){
temp=qnorm(1-FNGR.CT2,mean=CT2.nogo,sd=sd.post)
est2.nogo=(temp-(sd.n^2/(prior.sd^2+sd.n^2))*prior.mean)/(prior.sd^2/(prior.sd^2+sd.n^2))
}
}
if(method=='Bayesian'&(fix.var==FALSE)){
if(noninfo==TRUE){
prior.k=0
prior.a=-1/2
prior.b=0
prior.mean=0
}
if(false.go.CT1==TRUE){
est1.go<-SAN_findIGcutoff(n=n,
prior.mean=prior.mean,prior.k=prior.k ,
prior.a=prior.a,prior.b=prior.b,
ssq=ssq,
rate=1-FGR.CT1,CT=CT1.go,
seed.num=seed.num,
stop.criterion=stop.criterion,direction='Less')
}
if(false.go.CT2==TRUE){
est2.go<-SAN_findIGcutoff(n=n,
prior.mean=prior.mean,prior.k=prior.k ,
prior.a=prior.a,prior.b=prior.b,
ssq=ssq,
rate=1-FGR.CT2,CT=CT2.go,
seed.num=seed.num,
stop.criterion=stop.criterion,direction='Less')
}
if(false.nogo.CT1==TRUE){
est1.nogo<-SAN_findIGcutoff(n=n,
prior.mean=prior.mean,prior.k=prior.k ,
prior.a=prior.a,prior.b=prior.b,
ssq=ssq,
rate=1-FNGR.CT1,CT=CT1.nogo,
seed.num=seed.num,
stop.criterion=stop.criterion,direction='Greater')
}
if(false.nogo.CT2==TRUE){
est2.nogo<-SAN_findIGcutoff(n=n,
prior.mean=prior.mean,prior.k=prior.k ,
prior.a=prior.a,prior.b=prior.b,
ssq=ssq,
rate=1-FNGR.CT2,CT=CT2.nogo,
seed.num=seed.num,
stop.criterion=stop.criterion,direction='Greater')
}
}
if(method=='Frequentist'){
if(false.go.CT1==TRUE){
est1.go=qnorm(FGR.CT1,mean=CT1.go,sd=sd.n)
}
if(false.go.CT2==TRUE){
est2.go=qnorm(FGR.CT2,mean=CT2.go,sd=sd.n)
}
if(false.nogo.CT1==TRUE){
est1.nogo=qnorm(1-FNGR.CT1,mean=CT1.nogo,sd=sd.n)
}
if(false.nogo.CT2==TRUE){
est2.nogo=qnorm(1-FNGR.CT2,mean=CT2.nogo,sd=sd.n)
}
}
if(any(is.na(c(est1.go,est2.go)))){logic.go='and'}
if(any(is.na(c(est1.nogo,est2.nogo)))){logic.nogo='and'}
if(logic.go=='and'){
go_cutoff=min(est1.go,est2.go,na.rm=TRUE)
}
if(logic.go=='or'){
go_cutoff=max(est1.go,est2.go,na.rm=TRUE)
}
if(logic.nogo=='and')
{
nogo_cutoff=max(est1.nogo,est2.nogo,na.rm=TRUE)
}
if(logic.nogo=='or')
{
nogo_cutoff=min(est1.nogo,est2.nogo,na.rm=TRUE)
}
if(go_cutoff<=nogo_cutoff){return(list(cutoff=c(go_cutoff,nogo_cutoff),flag=flag,overlap=overlap.flag))}
else{
overlap.flag=1
return(list(cutoff=c(go_cutoff,nogo_cutoff),flag=flag,overlap=overlap.flag))}
if(all(flag==0)==FALSE){return(list(cutoff=c(NA,NA),flag=flag,overlap=overlap.flag))}
}
}
SAN_Bayesian_Vary_Var<-function(n=c(10,100),
prior.mean=1/3,
prior.k=1,prior.a=1,prior.b=1,
mean=c(0.3,0.5), sd=1,
CT1.go=0.25,
false.go.CT1=TRUE,FGR.CT1=0.25,
CT1.nogo=0.25,
false.nogo.CT1=TRUE,FNGR.CT1=0.25,
CT2.go=0.3,
false.go.CT2=TRUE, FGR.CT2=0.5,
CT2.nogo=0.3,
false.nogo.CT2=TRUE, FNGR.CT2=0.5,
overlap.option='GO',direction='Greater',
noninfo=TRUE,
seed.num=369, n_repeat=1000,
logic.go='and',logic.nogo='or'){
set.seed(seed.num)
go_prob<-matrix(NA,ncol=length(n),nrow=length(mean))
nogo_prob<-matrix(NA,ncol=length(n),nrow=length(mean))
inconclusive_prob<-matrix(NA,ncol=length(n),nrow=length(mean))
overlap.flag=rep(0,length(n))
for (ii in 1:length(mean)){
for (ii2 in 1:length(n)){
x=matrix(rnorm(n_repeat*n[ii2],mean[ii],sd),nrow=n_repeat)
mean_x=apply(x,1,mean)
ssq_x=apply(x,1,function(x){sum(x^2)})
if(is.na(CT1.go)) false.go.CT1=FALSE
if(is.na(CT1.nogo)) false.nogo.CT1=FALSE
if(is.na(CT2.go)) false.go.CT2=FALSE
if(is.na(CT2.nogo)) false.nogo.CT2=FALSE
if(false.go.CT1==TRUE) pp_go_1 = rep(0,n_repeat)
if(false.nogo.CT1==TRUE) pp_nogo_1 = rep(0,n_repeat)
if(false.go.CT2==TRUE) pp_go_2 = rep(0,n_repeat)
if(false.nogo.CT2==TRUE) pp_nogo_2 = rep(0,n_repeat)
for (i in 1:n_repeat){
if(noninfo==TRUE){
prior.mean=0
prior.k=0
prior.a=-1/2
prior.b=0
}
mupost=(prior.k*prior.mean+n[ii2]*mean_x[i])/(prior.k+n[ii2])
kpost=prior.k+n[ii2]
apost=prior.a+n[ii2]/2
bpost=prior.b+1/2*ssq_x[i]+prior.k*n[ii2]*(mean_x[i]-prior.mean)^2/(2*(prior.k+n[ii2]))
if(direction=='Greater'){ # closed form. pmvt returns upper area
if(false.go.CT1==TRUE) pp_go_1[i] = 1-pt((CT1.go-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
if(false.nogo.CT1==TRUE) pp_nogo_1[i] = 1-pt((CT1.nogo-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
if(false.go.CT2==TRUE) pp_go_2[i] = 1-pt((CT2.go-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
if(false.nogo.CT2==TRUE) pp_nogo_2[i] = 1-pt((CT2.nogo-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
}
if(direction=='Less'){
if(false.go.CT1==TRUE) pp_go_1[i] = pt((CT1.go-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
if(false.nogo.CT1==TRUE) pp_nogo_1[i] = pt((CT1.nogo-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
if(false.go.CT2==TRUE) pp_go_2[i] = pt((CT2.go-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
if(false.nogo.CT2==TRUE) pp_nogo_2[i] = pt((CT2.nogo-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
}
}
if(false.go.CT1==TRUE & false.go.CT2==TRUE){
if(logic.go=='and')
go_prob[ii,ii2] = mean(pp_go_1>=1-FGR.CT1 & pp_go_2>=1-FGR.CT2)
if(logic.go=='or')
go_prob[ii,ii2] = mean(pp_go_1>=1-FGR.CT1 | pp_go_2>=1-FGR.CT2)
} else if(false.go.CT1==TRUE){
go_prob[ii,ii2] = mean(pp_go_1>=1-FGR.CT1)
} else if(false.go.CT2==TRUE){
go_prob[ii,ii2] = mean(pp_go_2>=1-FGR.CT2)
}
if(false.nogo.CT1==TRUE & false.nogo.CT2==TRUE){
if(logic.nogo=='and')
nogo_prob[ii,ii2] = mean(pp_nogo_1<FNGR.CT1 & pp_nogo_2<FNGR.CT2)
if(logic.nogo=='or')
nogo_prob[ii,ii2] = mean(pp_nogo_1<FNGR.CT1 | pp_nogo_2<FNGR.CT2)
} else if(false.nogo.CT1==TRUE){
nogo_prob[ii,ii2] = mean(pp_nogo_1<FNGR.CT1)
} else if(false.nogo.CT2==TRUE){
nogo_prob[ii,ii2] = mean(pp_nogo_2<FNGR.CT2)
}
if (go_prob[ii,ii2]+nogo_prob[ii,ii2]>1){
overlap.flag[ii2] = 1
if (overlap.option=='GO'){
nogo_prob[ii,ii2] = 1-go_prob[ii,ii2]
} else if (overlap.option=='NOGO'){
go_prob[ii,ii2] = 1-nogo_prob[ii,ii2]
}
}
inconclusive_prob[ii,ii2]=1-go_prob[ii,ii2]-nogo_prob[ii,ii2]
}
}
return(list(go_prob,nogo_prob,inconclusive_prob,overlap.flag))
}
#### this has plot number 3
Fix_SS_SAN_Normal_Prob<-function(n=100,
prior.mean=1/3,prior.sd=1,
prior.k=1,prior.a=1,prior.b=1,
sd=1,ssq=1,
mean=c(0.0,0.9),
CT1.go=0.25,
false.go.CT1=TRUE,FGR.CT1=0.25,
CT1.nogo=0.25,
false.nogo.CT1=TRUE,FNGR.CT1=0.25,
CT2.go=0.3,
false.go.CT2=TRUE, FGR.CT2=0.5,
CT2.nogo=0.3,
false.nogo.CT2=TRUE, FNGR.CT2=0.5,
overlap.option='GO',plot.figure=TRUE,
method='Bayesian',direction='Greater',
fix.var=TRUE,noninfo=TRUE,
seed.num=369,
stop.criterion=10^-3,
logic.go='and',logic.nogo='or'){
meanseq=round(seq(min(mean),max(mean),length=10),3)
go_prob<-rep(NA,length(mean))
nogo_prob<-rep(NA,length(mean))
inconclusive_prob<-rep(NA,length(mean))
go_prob_plot<-rep(NA,length(meanseq))
nogo_prob_plot<-rep(NA,length(meanseq))
inconclusive_prob_plot<-rep(NA,length(meanseq))
index=1
unsatisfied.flag=0
overlap.flag=0
sd.n=sd/sqrt(n)
temp=SAN_Normal_Cutoff(n=n,
prior.mean=prior.mean,prior.sd = prior.sd,
prior.k = prior.k,prior.a=prior.a,prior.b=prior.b,
sd=sd,ssq=ssq,
CT1.go=CT1.go,
false.go.CT1 = false.go.CT1, FGR.CT1=FGR.CT1,
CT1.nogo=CT1.nogo,
false.nogo.CT1 = false.nogo.CT1, FNGR.CT1 = FNGR.CT1,
CT2.go=CT2.go,
false.go.CT2 = false.go.CT2, FGR.CT2=FGR.CT2,
CT2.nogo=CT2.nogo,
false.nogo.CT2 = false.nogo.CT2, FNGR.CT2 = FNGR.CT2,
method=method,direction=direction,
fix.var=fix.var,noninfo=noninfo,
seed.num=seed.num,
stop.criterion=stop.criterion,
logic.go=logic.go,logic.nogo = logic.nogo)
###SAN####
true_go_cutoff<-ifelse(temp$overlap==0,temp$cutoff[1],(overlap.option=='GO')*temp$cutoff[1]+(overlap.option=='NOGO')*(temp$cutoff[2]))
true_nogo_cutoff<-ifelse(temp$overlap==0,temp$cutoff[2],(overlap.option=='GO')*temp$cutoff[1]+(overlap.option=='NOGO')*(temp$cutoff[2]))
overlap.flag = temp$overlap
if(method=='Frequentist' | (method=='Bayesian' & fix.var==TRUE) ){
if(direction=='Greater'){
if(all(temp$flag==0)&temp$overlap==0){
go_prob=1-pnorm(temp$cutoff[1],mean=mean,sd=sd.n)
nogo_prob=pnorm(temp$cutoff[2],mean=mean,sd=sd.n)
inconclusive_prob=1-go_prob-nogo_prob
go_prob_plot=1-pnorm(temp$cutoff[1],mean=meanseq,sd=sd.n)
nogo_prob_plot=pnorm(temp$cutoff[2],mean=meanseq,sd=sd.n)
inconclusive_prob_plot=1-go_prob_plot-nogo_prob_plot
}
if(all(temp$flag==0)&temp$overlap==1&overlap.option=="GO"){
go_prob=1-pnorm(temp$cutoff[1],mean=mean,sd=sd.n)
nogo_prob=pnorm(temp$cutoff[1],mean=mean,sd=sd.n)
inconclusive_prob=1-go_prob-nogo_prob
go_prob_plot=1-pnorm(temp$cutoff[1],mean=meanseq,sd=sd.n)
nogo_prob_plot=pnorm(temp$cutoff[1],mean=meanseq,sd=sd.n)
inconclusive_prob_plot=1-go_prob_plot-nogo_prob_plot
}
if(all(temp$flag==0)&temp$overlap==1&overlap.option=="NOGO"){
go_prob=1-pnorm(temp$cutoff[2],mean=mean,sd=sd.n)
nogo_prob=pnorm(temp$cutoff[2],mean=mean,sd=sd.n)
inconclusive_prob=1-go_prob-nogo_prob
go_prob_plot=1-pnorm(temp$cutoff[2],mean=meanseq,sd=sd.n)
nogo_prob_plot=pnorm(temp$cutoff[2],mean=meanseq,sd=sd.n)
inconclusive_prob_plot=1-go_prob_plot-nogo_prob_plot
}
if(all(temp$flag==0)==FALSE){
unsatisfied.flag=1
nogo_prob=rep(NA,length(mean))
go_prob=rep(NA,length(mean))
inconclusive_prob=rep(NA,length(mean))
}
}
if(direction=='Less'){
if(all(temp$flag==0)&temp$overlap==0){
go_prob=pnorm(temp$cutoff[1],mean=mean,sd=sd.n)
nogo_prob=1-pnorm(temp$cutoff[2],mean=mean,sd=sd.n)
inconclusive_prob=1-go_prob-nogo_prob
go_prob_plot=pnorm(temp$cutoff[1],mean=meanseq,sd=sd.n)
nogo_prob_plot=1-pnorm(temp$cutoff[2],mean=meanseq,sd=sd.n)
inconclusive_prob_plot=1-go_prob_plot-nogo_prob_plot
}
if(all(temp$flag==0)&temp$overlap==1&overlap.option=="GO"){
go_prob=pnorm(temp$cutoff[1],mean=mean,sd=sd.n)
nogo_prob=1-pnorm(temp$cutoff[1],mean=mean,sd=sd.n)
inconclusive_prob=1-go_prob-nogo_prob
go_prob_plot=pnorm(temp$cutoff[1],mean=meanseq,sd=sd.n)
nogo_prob_plot=1-pnorm(temp$cutoff[1],mean=meanseq,sd=sd.n)
inconclusive_prob_plot=1-go_prob_plot-nogo_prob_plot
}
if(all(temp$flag==0)&temp$overlap==1&overlap.option=="NOGO"){
go_prob_plot=pnorm(temp$cutoff[2],mean=meanseq,sd=sd.n)
nogo_prob_plot=1-pnorm(temp$cutoff[2],mean=meanseq,sd=sd.n)
inconclusive_prob_plot=1-go_prob-nogo_prob_plot
go_prob=pnorm(temp$cutoff[2],mean=mean,sd=sd.n)
nogo_prob=1-pnorm(temp$cutoff[2],mean=mean,sd=sd.n)
inconclusive_prob=1-go_prob-nogo_prob
}
if(all(temp$flag==0)==FALSE){
unsatisfied.flag=1
nogo_prob=rep(NA,length(mean))
go_prob=rep(NA,length(mean))
inconclusive_prob=rep(NA,length(mean))
}
}
}
if(method=='Bayesian' & fix.var==FALSE ){
n_repeat=1000
temp2 = SAN_Bayesian_Vary_Var(n=n,
prior.mean=prior.mean,
prior.k=prior.k,prior.a=prior.a,prior.b=prior.b,
sd=sd,mean=mean,
CT1.go=CT1.go,false.go.CT1=false.go.CT1,
FGR.CT1=FGR.CT1,
CT1.nogo=CT1.nogo,
false.nogo.CT1=false.nogo.CT1,FNGR.CT1=FNGR.CT1,
CT2.go=CT2.go,false.go.CT2=false.go.CT2, FGR.CT2=FGR.CT2,
CT2.nogo=CT2.nogo,false.nogo.CT2=false.nogo.CT2,FNGR.CT2=FNGR.CT2,
overlap.option=overlap.option,direction=direction,
noninfo=noninfo,
seed.num=seed.num,n_repeat=n_repeat,
logic.go=logic.go,logic.nogo=logic.nogo)
go_prob = as.numeric(temp2[[1]])
nogo_prob = as.numeric(temp2[[2]])
inconclusive_prob = as.numeric(temp2[[3]])
# plot
temp3 = SAN_Bayesian_Vary_Var(n=n,
prior.mean=prior.mean,
prior.k=prior.k,prior.a=prior.a,prior.b=prior.b,
sd=sd,mean=meanseq,
CT1.go=CT1.go,false.go.CT1=false.go.CT1,
FGR.CT1=FGR.CT1,
CT1.nogo=CT1.nogo,
false.nogo.CT1=false.nogo.CT1,FNGR.CT1=FNGR.CT1,
CT2.go=CT2.go,false.go.CT2=false.go.CT2, FGR.CT2=FGR.CT2,
CT2.nogo=CT2.nogo,false.nogo.CT2=false.nogo.CT2,FNGR.CT2=FNGR.CT2,
overlap.option=overlap.option,direction=direction,
noninfo=noninfo,
seed.num=seed.num,n_repeat=n_repeat,
logic.go=logic.go,logic.nogo=logic.nogo)
go_prob_plot = as.numeric(temp3[[1]])
nogo_prob_plot = as.numeric(temp3[[2]])
inconclusive_prob_plot = as.numeric(temp3[[3]])
}
########################################################################
if(plot.figure==TRUE){
delta=meanseq
p_nogo=nogo_prob_plot*100
p_grey=inconclusive_prob_plot*100
p_go=go_prob_plot*100
if(true_go_cutoff!=true_nogo_cutoff){
par(mfrow=c(1,1),pty="m",bty="l",cex=1.4)
plot(delta,p_go,xlab=expression(paste("True ",mean,sep="")),
ylab="Prob of GO/ NOGO/ Inconclusive (%)",xlim=range(delta),
ylim=c(0,100),type="n",axes=F)
axis(1, at=meanseq, labels=meanseq)
axis(2, at=seq(0,100,10),labels=T)
#text(rep(-0.6,6),seq(0,100,20),seq(0,100,20),adj=1,xpd=T)
box()
#abline(h=seq(0,100,10),lty=3,col=rgb(0.8,0.8,0.8),lwd=1)
points(delta,p_nogo,type="b",pch=16,col=rgb(0.9,0,0),lwd=3,lty=1)
points(delta,p_grey,type="b",pch=4,col=rgb(0.9,0.6,0),lwd=3,lty=6)
points(delta,p_go,type="b",pch=2,col=rgb(0,0.7,0),lwd=3,lty=2)
text(min(mean),140,bquote(n==~.(n)),xpd=T,adj=0,cex=0.8,col=rgb(0, 0,0))
if(overlap.flag==0&unsatisfied.flag==0){
if(direction=='Greater'){
text(min(mean),130,bquote(GO~symbol("\336")~Observed~average~effect~symbol("\263")~.(round(temp$cutoff[1],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0, 0.7,0))
text(min(mean),120,bquote(NOGO~symbol("\336")~Observed~average~effect~symbol("\243")~.(round(temp$cutoff[2],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0.9, 0,0))
text(min(mean),110,bquote(Inconclusive~symbol("\336")~anything~between~GO~and~NOGO),xpd=T,adj=0,cex=0.8,col=rgb(0.9,0.6,0))
}
if(direction=='Less'){
text(min(mean),130,bquote(GO~symbol("\336")~Observed~average~effect~symbol("\243")~.(round(temp$cutoff[1],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0, 0.7,0))
text(min(mean),120,bquote(NOGO~symbol("\336")~Observed~average~effect~symbol("\263")~.(round(temp$cutoff[2],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0.9, 0,0))
text(min(mean),110,bquote(Inconclusive~symbol("\336")~anything~between~GO~and~NOGO),xpd=T,adj=0,cex=0.8,col=rgb(0.9,0.6,0))
}
}
if(overlap.flag==1&unsatisfied.flag==0&overlap.option=='GO'){
if(direction=="Greater"){
text(min(mean),130,bquote(GO~symbol("\336")~Observed~average~effect~symbol("\263")~.(round(temp$cutoff[1],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0, 0.7,0))
text(min(mean),120,bquote(NOGO~symbol("\336")~Observed~average~effect~symbol("\243")~.(round(temp$cutoff[1],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0.9, 0,0))
#text(min(mean),115,paste0('Warning: GO and NOGO zones are overlaped at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
#text(min(mean),110,paste0('The zones are classfied by cutoff of ', overlap.option),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
}
if(direction=="Less"){
text(min(mean),130,bquote(GO~symbol("\336")~Observed~average~effect~symbol("\243")~.(round(temp$cutoff[1],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0, 0.7,0))
text(min(mean),120,bquote(NOGO~symbol("\336")~Observed~average~effect~symbol("\263")~.(round(temp$cutoff[1],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0.9, 0,0))
#text(min(mean),115,paste0('Warning: GO and NOGO zones are overlaped at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
#text(min(mean),110,paste0('The zones are classfied by cutoff of ', overlap.option),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
}
}
if(overlap.flag==1&unsatisfied.flag==0&overlap.option=='NOGO'){
if(direction=="Greater"){
text(min(mean),130,bquote(GO~symbol("\336")~Observed~average~effect~symbol("\263")~.(round(temp$cutoff[2],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0, 0.7,0))
text(min(mean),120,bquote(NOGO~symbol("\336")~Observed~average~effect~symbol("\243")~.(round(temp$cutoff[2],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0.9, 0,0))
#text(min(mean),115,paste0('Warning: GO and NOGO zones are overlaped at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
#text(min(mean),110,paste0('The zones are classfied by cutoff of ', overlap.option),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
}
if(direction=="Less"){
text(min(mean),130,bquote(GO~symbol("\336")~Observed~average~effect~symbol("\243")~.(round(temp$cutoff[2],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0, 0.7,0))
text(min(mean),120,bquote(NOGO~symbol("\336")~Observed~average~effect~symbol("\263")~.(round(temp$cutoff[2],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0.9, 0,0))
#text(min(mean),115,paste0('Warning: GO and NOGO zones are overlaped at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
#text(min(mean),110,paste0('The zones are classfied by cutoff of ', overlap.option),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
}
}
if(unsatisfied.flag==1){
text(min(mean),130,paste0('Warning: We could not find classification of zones to satisfy your both GO and NOGO criterions at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0,0))
text(min(mean),120,paste0('Please check and modify your desicion rule or the range of sample size!'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0,0))
}
}
}
###################################################################
if(plot.figure==TRUE){
delta=meanseq
p_nogo=nogo_prob_plot*100
p_grey=inconclusive_prob_plot*100
p_go=go_prob_plot*100
if(true_go_cutoff==true_nogo_cutoff){
par(mfrow=c(1,1),pty="m",bty="l",cex=1.4)
plot(delta,p_go,xlab=expression(paste("True ",mean,sep="")),
ylab="Prob of GO/ NOGO/ Inconclusive (%)",xlim=range(delta),
ylim=c(0,100),type="n",axes=F)
axis(1, at=meanseq, labels=meanseq)
axis(2, at=seq(0,100,10),labels=T)
#text(rep(-0.6,6),seq(0,100,20),seq(0,100,20),adj=1,xpd=T)
box()
points(delta,p_nogo,type="b",pch=16,col=rgb(0.9,0,0),lwd=3,lty=1)
#points(delta,p_grey,type="b",pch=4,col=rgb(0.9,0.6,0),lwd=3,lty=6)
points(delta,p_go,type="b",pch=2,col=rgb(0,0.7,0),lwd=3,lty=2)
text(min(mean),140,bquote(n==~.(n)),xpd=T,adj=0,cex=0.8,col=rgb(0, 0,0))
if(overlap.flag==0&unsatisfied.flag==0){
if(direction=='Greater'){
text(min(mean),130,bquote(GO~symbol("\336")~Observed~average~effect~symbol("\263")~.(round(temp$cutoff[1],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0, 0.7,0))
text(min(mean),120,bquote(NOGO~symbol("\336")~Observed~average~effect~symbol("\243")~.(round(temp$cutoff[2],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0.9, 0,0))
#text(min(mean),110,bquote(Inconclusive~symbol("\336")~anything~between~GO~and~NOGO),xpd=T,adj=0,cex=0.8,col=rgb(0.9,0.6,0))
}
if(direction=='Less'){
text(min(mean),130,bquote(GO~symbol("\336")~Observed~average~effect~symbol("\243")~.(round(temp$cutoff[1],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0, 0.7,0))
text(min(mean),120,bquote(NOGO~symbol("\336")~Observed~average~effect~symbol("\263")~.(round(temp$cutoff[2],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0.9, 0,0))
#text(min(mean),110,bquote(Inconclusive~symbol("\336")~anything~between~GO~and~NOGO),xpd=T,adj=0,cex=0.8,col=rgb(0.9,0.6,0))
}
}
if(overlap.flag==1&unsatisfied.flag==0&overlap.option=='GO'){
if(direction=="Greater"){
text(min(mean),130,bquote(GO~symbol("\336")~Observed~average~effect~symbol("\263")~.(round(temp$cutoff[1],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0, 0.7,0))
text(min(mean),120,bquote(NOGO~symbol("\336")~Observed~average~effect~symbol("\243")~.(round(temp$cutoff[1],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0.9, 0,0))
#text(min(mean),115,paste0('Warning: GO and NOGO zones are overlaped at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
#text(min(mean),110,paste0('The zones are classfied by cutoff of ', overlap.option),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
}
if(direction=="Less"){
text(min(mean),130,bquote(GO~symbol("\336")~Observed~average~effect~symbol("\243")~.(round(temp$cutoff[1],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0, 0.7,0))
text(min(mean),120,bquote(NOGO~symbol("\336")~Observed~average~effect~symbol("\263")~.(round(temp$cutoff[1],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0.9, 0,0))
#text(min(mean),115,paste0('Warning: GO and NOGO zones are overlaped at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
#text(min(mean),110,paste0('The zones are classfied by cutoff of ', overlap.option),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
}
}
if(overlap.flag==1&unsatisfied.flag==0&overlap.option=='NOGO'){
if(direction=="Greater"){
text(min(mean),130,bquote(GO~symbol("\336")~Observed~average~effect~symbol("\263")~.(round(temp$cutoff[2],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0, 0.7,0))
text(min(mean),120,bquote(NOGO~symbol("\336")~Observed~average~effect~symbol("\243")~.(round(temp$cutoff[2],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0.9, 0,0))
#text(min(mean),115,paste0('Warning: GO and NOGO zones are overlaped at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
#text(min(mean),110,paste0('The zones are classfied by cutoff of ', overlap.option),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
}
if(direction=="Less"){
text(min(mean),130,bquote(GO~symbol("\336")~Observed~average~effect~symbol("\243")~.(round(temp$cutoff[2],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0, 0.7,0))
text(min(mean),120,bquote(NOGO~symbol("\336")~Observed~average~effect~symbol("\263")~.(round(temp$cutoff[2],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0.9, 0,0))
#text(min(mean),115,paste0('Warning: GO and NOGO zones are overlaped at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
#text(min(mean),110,paste0('The zones are classfied by cutoff of ', overlap.option),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
}
}
if(unsatisfied.flag==1){
text(min(mean),130,paste0('Warning: We could not find classification of zones to satisfy your both GO and NOGO criterions at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0,0))
text(min(mean),120,paste0('Please check and modify your desicion rule or the range of sample size!'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0,0))
}
}
}
###################################################################
return(list(go_prob=go_prob,nogo_prob=nogo_prob,
inconclusive_prob=inconclusive_prob,
overlap.flag=overlap.flag,overlap.option=overlap.option,
unsatisfied.flag=unsatisfied.flag,cutoff=temp$cutoff,true_cutoff=c(true_go_cutoff,true_nogo_cutoff))
)
}
Vary_SS_SAN_Normal_Prob<-function(nmin=250,nmax=300,prior.mean=1/3,prior.sd=1,
prior.k=1,prior.a=1,prior.b=1,
mean=0.3,
sd=1,ssq=1,
CT1.go=0.25,
false.go.CT1=TRUE,FGR.CT1=0.25,
CT1.nogo=0.25,
false.nogo.CT1=TRUE,FNGR.CT1=0.25,
CT2.go=0.3,
false.go.CT2=TRUE, FGR.CT2=0.5,
CT2.nogo=0.3,
false.nogo.CT2=TRUE, FNGR.CT2=0.5,
overlap.option='GO',plot.cutoff=TRUE,plot.prob=TRUE,
method="Bayesian",direction="Greater",fix.var=TRUE,noninfo=TRUE,
seed.num=369,
stop.criterion=10^-3,
logic.go='and',logic.nogo='or'){
nseq=unique(round(c(seq(nmin,(nmax+nmin)/2,length=6)[-6],seq((nmax+nmin)/2,nmax,length=6))))
go_prob<-matrix(NA,ncol=length(nseq),nrow=length(mean))
nogo_prob<-matrix(NA,ncol=length(nseq),nrow=length(mean))
inconclusive_prob<-matrix(NA,ncol=length(nseq),nrow=length(mean))
go_cutoff<-rep(NA,length(nseq))
nogo_cutoff<-rep(NA,length(nseq))
index=1
n_unsatisfied=NA
n_overlap=NA
ncore <- detectCores()
cl<-makeCluster(ncore)
registerDoParallel(cl)
results<-foreach(i = nseq,.export=c('SAN_Normal_Cutoff','SAN_findIGcutoff'),.packages=c('mvtnorm'),.combine=rbind) %dopar% {
temp=SAN_Normal_Cutoff(n=i,
prior.mean=prior.mean,prior.sd=prior.sd,
prior.k = prior.k,prior.a=prior.a,prior.b=prior.b,
sd=sd,ssq=ssq,
CT1.go=CT1.go,
false.go.CT1 = false.go.CT1, FGR.CT1=FGR.CT1,
CT1.nogo=CT1.nogo,
false.nogo.CT1 = false.nogo.CT1, FNGR.CT1 = FNGR.CT1,
CT2.go=CT2.go,
false.go.CT2 = false.go.CT2, FGR.CT2=FGR.CT2,
CT2.nogo=CT2.nogo,
false.nogo.CT2 = false.nogo.CT2, FNGR.CT2 = FNGR.CT2,
method=method,direction=direction,
fix.var = fix.var,noninfo=noninfo,
seed.num = seed.num,stop.criterion=stop.criterion,
logic.go=logic.go,logic.nogo=logic.nogo)
c(temp$overlap,temp$cutoff)
}
stopCluster(cl)
go_cutoff<-results[,2]
nogo_cutoff<-results[,3]
overlap<-results[,1]
for(mean.index in 1:length(mean)){
true_go_cutoff<-go_cutoff
true_nogo_cutoff<-nogo_cutoff
true_go_cutoff[overlap==1]<-(overlap.option=='GO')*go_cutoff[overlap==1]+(overlap.option=='NOGO')*nogo_cutoff[overlap==1]
true_nogo_cutoff[overlap==1]<-(overlap.option=='GO')*go_cutoff[overlap==1]+(overlap.option=='NOGO')*nogo_cutoff[overlap==1]
}
if(method=='Frequentist' | (method=='Bayesian' & fix.var==TRUE) ){
for(mean.index in 1:length(mean)){
mean_temp=mean[mean.index]
sd.i=sqrt(sd^2/nseq)
if(direction=='Greater'){
go_prob[mean.index,]=1-pnorm(true_go_cutoff,mean=mean_temp,sd=sd.i)
nogo_prob[mean.index,]=pnorm(true_nogo_cutoff,mean=mean_temp,sd=sd.i)
}
if(direction=='Less'){
go_prob[mean.index,]=pnorm(true_go_cutoff,mean=mean_temp,sd=sd.i)
nogo_prob[mean.index,]=1-pnorm(true_nogo_cutoff,mean=mean_temp,sd=sd.i)
}
inconclusive_prob[mean.index,]=1-go_prob[mean.index,]-nogo_prob[mean.index,]
}
}
if(method=='Bayesian' & fix.var==FALSE ){
n_repeat=1000
temp2 = SAN_Bayesian_Vary_Var(n=nseq,
prior.mean=prior.mean,
prior.k=prior.k,prior.a=prior.a,prior.b=prior.b,
mean=mean, sd=sd,
CT1.go=CT1.go,
false.go.CT1=false.go.CT1,FGR.CT1=FGR.CT1,
CT1.nogo=CT1.nogo,
false.nogo.CT1=false.nogo.CT1,FNGR.CT1=FNGR.CT1,
CT2.go=CT2.go,
false.go.CT2=false.go.CT2, FGR.CT2=FGR.CT2,
CT2.nogo=CT2.nogo,
false.nogo.CT2=false.nogo.CT2, FNGR.CT2=FNGR.CT2,
overlap.option=overlap.option,direction=direction,
noninfo=noninfo,
seed.num=seed.num, n_repeat=n_repeat,
logic.go=logic.go,logic.nogo=logic.nogo)
go_prob = temp2[[1]]
nogo_prob = temp2[[2]]
inconclusive_prob = temp2[[3]]
}
n_overlap=n_overlap[-1]
n_unsatisfied=n_unsatisfied[-1]
####plot figure
if(plot.prob==TRUE){
for(j in 1:length(mean)){
p_go=go_prob[j,]*100
p_nogo=nogo_prob[j,]*100
class(p_nogo)
dim(p_nogo)
p_grey=100-p_go-p_nogo
par(mfrow=c(1,1),pty="m",bty="l",cex=1.4)
cum_p_nogo=p_nogo
cum_p_grey=p_nogo+p_grey
cum_p_go=p_nogo+p_grey+p_go
delta=nseq
plot(delta,cum_p_go,xlab="Sample size",
ylab="Prob of GO/ NOGO/ Inconclusive (%)",xlim=c(nmin,nmax),
ylim=c(0,100),type="n",axes=F,pch=NA)
axis(1, at=nseq,labels=nseq)
axis(2, at=seq(0,100,10),labels=T)
#text(rep(-0.6,6),seq(0,100,20),seq(0,100,20),adj=1,xpd=T)
box()
#abline(h=seq(0,100,10),lty=3,col=rgb(0.8,0.8,0.8),lwd=1)
polygon(c(delta,rev(delta)),c(cum_p_nogo,rev(rep(0,length(delta)))),col=rgb(0.9,0,0),border=NA)
polygon(c(delta,rev(delta)),c(cum_p_grey,rev(cum_p_nogo)),col=rgb(0.9,0.6,0),border=NA)
polygon(c(delta,rev(delta)),c(cum_p_go,rev(cum_p_grey)),col=rgb(0,0.7,0),border=NA)
text((nmin+nmax)/2,120,paste0("True mean=",round(mean[j],3),", sd=",round(sd,3)),xpd=T,adj=0.5,cex=0.8)
if(length(n_overlap)!=0){
text(nmin,115,paste0('Warning: GO and NOGO cut-offs are overlaped at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
#text(nmin,110,paste(n_overlap),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
#print(n_overlap)
text(nmin,110,paste0('The zones are classfied by cutoff of ', overlap.option),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
}
if(length(n_unsatisfied)!=0){
text(nmin,115,paste0('Warning: We could not find cutoffs to satisfy your both GO and NOGO criterions.'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0,0))
text(nmin,110,paste0('Please check and modify your desicion rule!'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0,0))
}
}
}
if(plot.cutoff==TRUE){
par(mfrow=c(1,1),pty="m",bty="l",cex=1.4)
ylim_max=max(c(go_cutoff,nogo_cutoff,round(CT1.go,3),round(CT2.go,3),round(CT1.nogo,3),round(CT2.nogo,3)),na.rm=TRUE)+0.1
ylim_min=min(c(go_cutoff,nogo_cutoff,round(CT1.go,3),round(CT2.go,3),round(CT1.nogo,3),round(CT2.nogo,3)),na.rm=TRUE)-0.1
plot(NA,NA,xlab='Sample size',ylab="Observed mean",xlim=c(max(0,range(nseq)[1]-10),range(nseq)[2]+10),ylim=c(ylim_min,ylim_max),type="n",axes=F,col=rgb(1,0,0),lty=1,lwd=2)
axis(1, at=nseq,labels=nseq)
axis(2, at=round(c(seq(ylim_min,ylim_max,round((ylim_max-ylim_min)/10,digits=2)),CT1.go,CT2.go,CT1.nogo,CT2.nogo),digits=2),labels=T)
#text(rep(-0.6,6),seq(0,100,20),seq(0,300,20),adj=1,xpd=T)
box()
lines(nseq,nogo_cutoff,col=rgb(0.9,0,0),lwd=2)
lines(nseq,go_cutoff,col=rgb(0,0.7,0),lwd=2)
legend('bottomright',legend=c("Cut off of GO","Cut off of NOGO"),
col=c(rgb(0,0.7,0),rgb(0.9,0,0)),
lwd=c(2,2),
lty=c(1,1),cex=0.5)
if(length(n_overlap)!=0){
text(nmin,ylim_max+abs(ylim_max-ylim_min)/10,paste0('Warning: GO and NOGO zones are overlaped at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
#text(nmin,110,paste(n_overlap),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
#print(n_overlap)
text(nmin,ylim_max+abs(ylim_max-ylim_min)/20,paste0('The zones are classfied by cutoff of ', overlap.option),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
}
if(length(n_unsatisfied)!=0){
text(nmin,ylim_max+abs(ylim_max-ylim_min)/10,paste0('Warning: We could not find classification of zones to satisfy your both GO and NOGO criterions at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0,0))
text(nmin,ylim_max+abs(ylim_max-ylim_min)/20,paste0('Please check and modify your desicion rule or the range of sample size!'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0,0))
}
}
return(list(n_unsatisfied,n_overlap))
}
Interim_SAN<-function(interim_n=c(50,100,150),num_interim=3,
CT1.go=c(0.25,0.25,0.25),
false.go.CT1=c(TRUE,TRUE,TRUE),FGR.CT1=c(0.25,0.25,0.25),
CT1.nogo=c(0.25,0.25,0.25),
false.nogo.CT1=c(TRUE,TRUE,TRUE),FNGR.CT1=c(0.25,0.25,0.25),
CT2.go=c(0.25,0.25,0.25),
false.go.CT2=c(TRUE,TRUE,TRUE),FGR.CT2=c(0.25,0.25,0.25),
CT2.nogo=c(0.25,0.25,0.25),
false.nogo.CT2=c(TRUE,TRUE,TRUE),FNGR.CT2=c(0.25,0.25,0.25),
overlap.option=c('GO','GO','GO'),
method='Bayesian',direction="Greater",
task=c('Futility','Superiority','Futility and superiority'),
seed.num=369,nsim_IA=10000,stop.criterion=10^-3,
prior.mean = 1,prior.sd=1,
prior.k=1,prior.a=1,
prior.b=1,sd=1,ssq=1,
mean=c(0.25),fix.var=TRUE,noninfo=TRUE,
logic.go=c('and','or','and'),logic.nogo=c('or','and','and')){
interim_n=sort(interim_n)
###SAN####
temptable=c()
for(meanindex in 1:length(mean)){
set.seed(seed.num)
diff_interim_n<-diff(interim_n)
generate_n<-c(interim_n[1],diff_interim_n)
mean_x=matrix(NA,nrow=nsim_IA,ncol=num_interim)
if(method=='Bayesian' & fix.var==FALSE){
ssq_x=mean_x
}
x=c()
for(k in 1:num_interim){
x=cbind(x,matrix(rnorm(nsim_IA*generate_n[k],mean[meanindex],sd),nrow=nsim_IA))
mean_x[,k]=apply(x,1,mean)
if(method=='Bayesian' & fix.var==FALSE){
ssq_x[,k]=apply(x,1,function(x){sum(x^2)})
}
}
#####
go_matrix<-matrix(NA,nrow=nsim_IA,ncol=num_interim)
nogo_matrix<-matrix(NA,nrow=nsim_IA,ncol=num_interim)
inconclusive_matrix<-matrix(NA,nrow=nsim_IA,ncol=num_interim)
table<-matrix(NA,ncol=num_interim+1,nrow=6)
IA_go_matrix<-matrix(NA,nrow=nsim_IA,ncol=num_interim) ###whether continue to next stage
if(method=='Frequentist' | (method=='Bayesian' & fix.var==TRUE) ){
go_cutoff<-rep(NA,num_interim)
nogo_cutoff<-rep(NA,num_interim)
true_go_cutoff<-rep(NA,num_interim)
true_nogo_cutoff<-rep(NA,num_interim)
overlap<-rep(NA,num_interim)
for(j in 1:num_interim ){
temp<-SAN_Normal_Cutoff(n=interim_n[j],
prior.mean = prior.mean,prior.sd = prior.sd,
prior.k=prior.k,prior.a=prior.a,
prior.b=prior.b,sd=sd,ssq=NA, #ssq is unused
CT1.go=CT1.go[j],
false.go.CT1=false.go.CT1[j],FGR.CT1=FGR.CT1[j],
CT1.nogo=CT1.nogo[j],
false.nogo.CT1=false.nogo.CT1[j],FNGR.CT1=FNGR.CT1[j],
CT2.go=CT2.go[j],
false.go.CT2=false.go.CT2[j], FGR.CT2=FGR.CT2[j],
CT2.nogo=CT2.nogo[j],
false.nogo.CT2=false.nogo.CT2[j], FNGR.CT2=FNGR.CT2[j],
method=method,direction=direction[j],
fix.var=fix.var,noninfo=noninfo,
seed.num = seed.num,stop.criterion = stop.criterion,
logic.go=logic.go[j],logic.nogo=logic.nogo[j])
go_cutoff[j]<-temp$cutoff[1]
nogo_cutoff[j]<-temp$cutoff[2]
overlap[j]<-temp$overlap
###SAN####
true_go_cutoff[j]<-ifelse(overlap[j]==0,go_cutoff[j],(overlap.option[j]=='GO')*go_cutoff[j]+(overlap.option[j]=='NOGO')*(nogo_cutoff[j]))
true_nogo_cutoff[j]<-ifelse(overlap[j]==0,nogo_cutoff[j],(overlap.option[j]=='GO')*(go_cutoff[j])+(overlap.option[j]=='NOGO')*(nogo_cutoff[j]))
####
}
for(j in 1:num_interim ){
if(direction[j]=='Greater'){
go_matrix[,j]<-mean_x[,j]>=true_go_cutoff[j]
nogo_matrix[,j]<-mean_x[,j]<true_nogo_cutoff[j]
inconclusive_matrix[,j]<-rep(1,nsim_IA)-go_matrix[,j]-nogo_matrix[,j]
}
if(direction[j]=='Less'){
go_matrix[,j]<-mean_x[,j]<=true_go_cutoff[j]
nogo_matrix[,j]<-mean_x[,j]>true_nogo_cutoff[j]
inconclusive_matrix[,j]<-rep(1,nsim_IA)-go_matrix[,j]-nogo_matrix[,j]
}
}
}
if(method=='Bayesian' & fix.var==FALSE){
for(j in 1:num_interim ){
if(is.na(CT1.go[j])) false.go.CT1[j]=FALSE
if(is.na(CT1.nogo[j])) false.nogo.CT1[j]=FALSE
if(is.na(CT2.go[j])) false.go.CT2[j]=FALSE
if(is.na(CT2.nogo[j])) false.nogo.CT2[j]=FALSE
if(false.go.CT1[j]==TRUE) pp_go_1 = rep(0,nsim_IA)
if(false.nogo.CT1[j]==TRUE) pp_nogo_1 = rep(0,nsim_IA)
if(false.go.CT2[j]==TRUE) pp_go_2 = rep(0,nsim_IA)
if(false.nogo.CT2[j]==TRUE) pp_nogo_2 = rep(0,nsim_IA)
for (i in 1:nsim_IA){
if(noninfo==TRUE){
prior.mean=0
prior.k=0
prior.a=-1/2
prior.b=0
}
mupost=(prior.k*prior.mean+interim_n[j]*mean_x[i,j])/(prior.k+interim_n[j])
kpost=prior.k+interim_n[j]
apost=prior.a+interim_n[j]/2
bpost=prior.b+1/2*ssq_x[i,j]+prior.k*interim_n[j]*(mean_x[i,j]-prior.mean)^2/(2*(prior.k+interim_n[j]))
if(direction[j]=='Greater'){ # closed form. pmvt returns upper area
if(false.go.CT1[j]==TRUE) pp_go_1[i] = 1-pt((CT1.go[j]-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
if(false.nogo.CT1[j]==TRUE) pp_nogo_1[i] = 1-pt((CT1.nogo[j]-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
if(false.go.CT2[j]==TRUE) pp_go_2[i] = 1-pt((CT2.go[j]-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
if(false.nogo.CT2[j]==TRUE) pp_nogo_2[i] = 1-pt((CT2.nogo[j]-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
}
if(direction[j]=='Less'){
if(false.go.CT1[j]==TRUE) pp_go_1[i] = pt((CT1.go[j]-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
if(false.nogo.CT1[j]==TRUE) pp_nogo_1[i] = pt((CT1.nogo[j]-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
if(false.go.CT2[j]==TRUE) pp_go_2[i] = pt((CT2.go[j]-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
if(false.nogo.CT2[j]==TRUE) pp_nogo_2[i] = pt((CT2.nogo[j]-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
}
}
if(false.go.CT1[j]==TRUE & false.go.CT2[j]==TRUE){
if(logic.go[j]=='and')
go_matrix[,j] = pp_go_1>=1-FGR.CT1[j] & pp_go_2>=1-FGR.CT2[j]
if(logic.go[j]=='or')
go_matrix[,j] = pp_go_1>=1-FGR.CT1[j] | pp_go_2>=1-FGR.CT2[j]
} else if(false.go.CT1[j]==TRUE){
go_matrix[,j] = pp_go_1>=1-FGR.CT1[j]
} else if(false.go.CT2[j]==TRUE){
go_matrix[,j] = pp_go_2>=1-FGR.CT2[j]
}
if(false.nogo.CT1[j]==TRUE & false.nogo.CT2[j]==TRUE){
if(logic.nogo[j]=='and')
nogo_matrix[,j] = pp_nogo_1<FNGR.CT1[j] & pp_nogo_2<FNGR.CT2[j]
if(logic.nogo[j]=='or')
nogo_matrix[,j] = pp_nogo_1<FNGR.CT1[j] | pp_nogo_2<FNGR.CT2[j]
} else if(false.nogo.CT1[j]==TRUE){
nogo_matrix[,j] = pp_nogo_1<FNGR.CT1[j]
} else if(false.nogo.CT2[j]==TRUE){
nogo_matrix[,j] = pp_nogo_2<FNGR.CT2[j]
}
if (overlap.option[j]=='GO'){
nogo_matrix[nogo_matrix[,j]==go_matrix[,j] & nogo_matrix[,j]==1,j] = 0
} else if (overlap.option[j]=='NOGO'){
go_matrix[go_matrix[,j]==nogo_matrix[,j] & go_matrix[,j]==1,j] = 0
}
inconclusive_matrix[,j] = rep(1,nsim_IA)-go_matrix[,j]-nogo_matrix[,j]
}
}
for(ii in 1:(num_interim)){
if(task[ii]=='Futility'){
IA_go_matrix[,ii]=inconclusive_matrix[,ii]+go_matrix[,ii]
}
if(task[ii]=='Superiority'){
IA_go_matrix[,ii]=inconclusive_matrix[,ii]+nogo_matrix[,ii]
}
if(task[ii]=='Futility and superiority'){
IA_go_matrix[,ii]=inconclusive_matrix[,ii]
}
}
cum_IA_go_matrix<-t(apply(IA_go_matrix,1,cumprod))
for(j in 1:(num_interim)){
table[1,j]=interim_n[j]
table[2,j]=mean[meanindex]
table[3,j]=task[j]
if(j==1){
if(task[j]=='Superiority'|task[j]=='Futility and superiority'){
table[4,j]=round(sum(go_matrix[,j]==1)/nsim_IA,3)}else{table[4,j]=0}
if(task[j]=='Futility'|task[j]=='Futility and superiority'){
table[6,j]=round(sum(nogo_matrix[,j]==1)/nsim_IA,3)
}else{table[6,j]=0}
}else{
if(task[j]=='Superiority'|task[j]=='Futility and superiority'){
table[4,j]=round(sum(go_matrix[,j]==1&cum_IA_go_matrix[,j-1]==1)/nsim_IA,3)}else{table[4,j]=0}
if(task[j]=='Futility'|task[j]=='Futility and superiority'){
table[6,j]=round(sum(nogo_matrix[,j]==1&cum_IA_go_matrix[,j-1]==1)/nsim_IA,3)
}else{table[6,j]=0}
}
table[5,j]=round(sum(cum_IA_go_matrix[,j]==1)/nsim_IA,3)
# if(task[j]=='Futility'){
# table[7,j]=ifelse(direction[j]=='Greater',HTML(paste0('-/<',round(true_nogo_cutoff[j],3))),HTML(paste0('-/>',round(true_nogo_cutoff[j],3))))
# }
# if(task[j]=='Superiority'){
# table[7,j]=ifelse(direction[j]=='Greater',HTML(paste0('>=',round(true_go_cutoff[j],3),'/-')),HTML(paste0('<=',round(true_go_cutoff[j],3),'/-')))
# }
# if(task[j]=='Futility and superiority'){
# table[7,j]=ifelse(direction[j]=='Greater',HTML(paste0('>=',round(true_go_cutoff[j],3),' /','<',round(true_nogo_cutoff[j],3))),HTML(paste0('<=',round(true_go_cutoff[j],3),' / ','>',round(true_nogo_cutoff[j],3))))
# }
# table[10,j]=ifelse(direction[j]=='Greater',HTML(paste0('>=',round(go_cutoff[j],3))),HTML(paste0('<=',round(go_cutoff[j],3))))
# table[9,j]=ifelse(direction[j]=='Greater',HTML(paste0('<',round(nogo_cutoff[j],3))),HTML(paste0('>',round(nogo_cutoff[j],3))))
# table[8,j]<-ifelse(overlap[j]==1,paste0('GO/NOGO zones overlapped, classified by criterion of ',overlap.option[j]),'None')
}
expectss<-round(sum(as.numeric(table[1,1:num_interim])*(c(as.numeric(table[4,1:num_interim-1])+as.numeric(table[6,1:num_interim-1]),as.numeric(table[5,num_interim-1])))),3)
table[1,num_interim+1]=HTML(paste0(expectss,' (expected)'))
table[2,num_interim+1]=mean[meanindex]
table[3,num_interim+1]=''
table[4,num_interim+1]=round(sum(as.numeric(table[4,1:num_interim])),3)
table[5,num_interim+1]=round(as.numeric(table[5,num_interim]),3)
table[6,num_interim+1]=round(sum(as.numeric(table[6,1:num_interim])),3)
# table[7,num_interim+1]=''
# table[8,num_interim+1]=''
# table[9,num_interim+1]=''
# table[10,num_interim+1]=''
table<-as.table(table)
tablecolname<-c(paste0('Interim analysis ',1:(num_interim-1)),'Final analysis',"Summary")
tablerowname<-c('Sample size','True mean','Task','Success','To next interim/final or inconclusive',
'Stop')
table<-cbind(tablerowname,rep(meanindex,6),table)
colnames(table)<-c(" ",'Setting',tablecolname)
temptable=rbind(temptable,table)
}
return(temptable)
}
#Interim_SAN(interim_n = c(66,131,197),CT1.go=c(1,0.6,1),CT1.nogo=c(1,0.6,1),FGR.CT1=c(1-0.707,0.653,0.0238),FNGR.CT1=c(0.707,1-0.653,1-0.0238),CT2.go=c(NA,NA,NA),CT2.nogo=c(NA,NA,NA),method='Frequentist',direction=c(rep('Less',1),'Greater','Less'),task=c('Futility','Superiority','Superiority'),mean=c(1.1,2))
# Fix_SS_SAN_Normal_Prob(n=50,
# prior.mean=1,prior.sd=1000,
# prior.k=1,prior.a=1,prior.b=1,
# sd=1,ssq=1,
# mean=c(2,5),
# CT1.go=4.8,
# false.go.CT1=TRUE,FGR.CT1=0.8,
# CT1.nogo=4.8,
# false.nogo.CT1=TRUE,FNGR.CT1=0.8,
# CT2.go=0.3,
# false.go.CT2=FALSE, FGR.CT2=0.5,
# CT2.nogo=0.3,
# false.nogo.CT2=FALSE, FNGR.CT2=0.5,
# overlap.option='GO',plot.figure=TRUE,
# method='Frequentist',direction='Greater',
# fix.var=TRUE,noninfo=TRUE,
# seed.num=369,nsim=10000,
# stop.criterion=10^-3,
# logic.go='and',logic.nogo='or')
#
AshZhong/Goahead documentation built on May 5, 2022, 12:30 a.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Defines functions Fix_SS_SAN_Normal_Prob SAN_Bayesian_Vary_Var SAN_Normal_Cutoff SAN_findIGcutoff
library(shiny)
SAN_findIGcutoff<-function(n=30,
prior.mean=1/3,prior.k=1,
prior.a=1,prior.b=1,
ssq=1,
rate=0.8,CT=0.25,
seed.num=369,
stop.criterion=10^-3,direction='Greater'){
####prior####
###mu1~N(prior.mean1,prior.k1*1/var)
#### 1/var~gamma(prior.a1,rate=prior.b1)
####
cutoff<-NA
set.seed(seed.num)
S=1
upper=abs(CT)+1
lower=-abs(CT)-1
########control.group####
ssq=ssq*n
while(S==1){
temp=(upper+lower)/2
mupost_temp=(prior.k*prior.mean+n*temp)/(prior.k+n)
kpost_temp=prior.k+n
apost_temp=prior.a+n/2
bpost_temp=prior.b+1/2*ssq+prior.k*n*(temp-prior.mean)^2/(2*(prior.k+n))
mupost_upper=(prior.k*prior.mean+n*upper)/(prior.k+n)
kpost_upper=prior.k+n
apost_upper=prior.a+n/2
bpost_upper=prior.b+1/2*ssq+prior.k*n*(upper-prior.mean)^2/(2*(prior.k+n))
mupost_lower=(prior.k*prior.mean+n*lower)/(prior.k+n)
kpost_lower=prior.k+n
apost_lower=prior.a+n/2
bpost_lower=prior.b+1/2*ssq+prior.k*n*(lower-prior.mean)^2/(2*(prior.k+n))
if(direction=='Greater'){
probupper=1-pt((CT-mupost_upper)/sqrt(bpost_upper/(apost_upper*kpost_upper)),df=2*apost_upper)
problower=1-pt((CT-mupost_lower)/sqrt(bpost_lower/(apost_lower*kpost_lower)),df=2*apost_lower)
probtemp=1-pt((CT-mupost_temp)/sqrt(bpost_temp/(apost_temp*kpost_temp)),df=2*apost_temp)
if(problower>=rate){
if(abs(problower-rate)<=stop.criterion){
S=0
cutoff=lower
}
upper=lower
lower=-2*abs(lower)
}else if(probupper<=rate){
if(abs(probupper-rate)<=stop.criterion){
S=0
cutoff=upper
}
upper=2*abs(upper)
lower=upper
}else{
if(abs(probtemp-rate)<=stop.criterion){
S=0
cutoff=temp
}
if(probtemp<rate){lower=temp}
if(probtemp>rate){upper=temp}
}
}
if(direction=='Less'){
probupper=pt((CT-mupost_upper)/sqrt(bpost_upper/(apost_upper*kpost_upper)),df=2*apost_upper)
problower=pt((CT-mupost_lower)/sqrt(bpost_lower/(apost_lower*kpost_lower)),df=2*apost_lower)
probtemp=pt((CT-mupost_temp)/sqrt(bpost_temp/(apost_temp*kpost_temp)),df=2*apost_temp)
if(problower<=rate){
if(abs(problower-rate)<=stop.criterion){
S=0
cutoff=lower
}
upper=lower
lower=-2*abs(lower)
}else if(probupper>=rate){
if(abs(probupper-rate)<=stop.criterion){
S=0
cutoff=upper
}
upper=2*abs(upper)
lower=upper
}else{
if(abs(probtemp-rate)<=stop.criterion){
S=0
cutoff=temp
}
if(probtemp>rate){lower=temp}
if(probtemp<rate){upper=temp}
}
}
}
return(cutoff)
}
SAN_Normal_Cutoff<-function(n=30,
prior.mean=1/3,prior.sd=1,
prior.k=1,prior.a=1,prior.b=1,
sd=1,ssq=1,
CT1.go=0.25,
false.go.CT1=TRUE,FGR.CT1=0.25,
CT1.nogo=0.25,
false.nogo.CT1=TRUE,FNGR.CT1=0.25,
CT2.go=0.3,
false.go.CT2=TRUE, FGR.CT2=0.5,
CT2.nogo=0.3,
false.nogo.CT2=TRUE, FNGR.CT2=0.5,
method='Bayesian',direction='Greater',
fix.var=TRUE,noninfo=TRUE,
seed.num=369,
stop.criterion=10^-3,
logic.go='and',logic.nogo='or'){
flag=rep(0,4)
overlap.flag=0
est1.go=NA
est2.go=NA
est1.nogo=NA
est2.nogo=NA
flag=rep(0,4)
overlap.flag=0
sd.n=sd/sqrt(n)
if(is.na(CT1.go)){
false.go.CT1=FALSE
}
if(is.na(CT1.nogo)){
false.nogo.CT1=FALSE
}
if(is.na(CT2.go)){
false.go.CT2=FALSE
}
if(is.na(CT2.nogo)){
false.nogo.CT2=FALSE
}
if(direction=='Greater'){
if(method=='Bayesian'&(fix.var==TRUE)){
sd.post=sqrt(1/((1/prior.sd)^2+(1/sd.n)^2))
if(false.go.CT1==TRUE){
temp=qnorm(1-FGR.CT1,mean=CT1.go,sd=sd.post)
est1.go=(temp-(sd.n^2/(prior.sd^2+sd.n^2))*prior.mean)/(prior.sd^2/(prior.sd^2+sd.n^2))
}
if(false.go.CT2==TRUE){
temp=qnorm(1-FGR.CT2,mean=CT2.go,sd=sd.post)
est2.go=(temp-(sd.n^2/(prior.sd^2+sd.n^2))*prior.mean)/(prior.sd^2/(prior.sd^2+sd.n^2))
}
if(false.nogo.CT1==TRUE){
temp=qnorm(FNGR.CT1,mean=CT1.nogo,sd=sd.post)
est1.nogo=(temp-(sd.n^2/(prior.sd^2+sd.n^2))*prior.mean)/(prior.sd^2/(prior.sd^2+sd.n^2))
}
if(false.nogo.CT2==TRUE){
temp=qnorm(FNGR.CT2,mean=CT2.nogo,sd=sd.post)
est2.nogo=(temp-(sd.n^2/(prior.sd^2+sd.n^2))*prior.mean)/(prior.sd^2/(prior.sd^2+sd.n^2))
}
}
if(method=='Bayesian'&(fix.var==FALSE)){
if(noninfo==TRUE){
prior.k=0
prior.a=-1/2
prior.b=0
prior.mean=0
}
if(false.go.CT1==TRUE){
est1.go<-SAN_findIGcutoff(n=n,
prior.mean=prior.mean,prior.k=prior.k ,
prior.a=prior.a,prior.b=prior.b,
ssq=ssq,
rate=1-FGR.CT1,CT=CT1.go,
seed.num=seed.num,
stop.criterion=stop.criterion,direction='Greater')
}
if(false.go.CT2==TRUE){
est2.go<-SAN_findIGcutoff(n=n,
prior.mean=prior.mean,prior.k=prior.k ,
prior.a=prior.a,prior.b=prior.b,
ssq=ssq,
rate=1-FGR.CT2,CT=CT2.go,
seed.num=seed.num,
stop.criterion=stop.criterion,direction='Greater')
}
if(false.nogo.CT1==TRUE){
est1.nogo<-SAN_findIGcutoff(n=n,
prior.mean=prior.mean,prior.k=prior.k ,
prior.a=prior.a,prior.b=prior.b,
ssq=ssq,
rate=1-FNGR.CT1,CT=CT1.nogo,
seed.num=seed.num,
stop.criterion=stop.criterion,direction='Less')
}
if(false.nogo.CT2==TRUE){
est2.nogo<-SAN_findIGcutoff(n=n,
prior.mean=prior.mean,prior.k=prior.k ,
prior.a=prior.a,prior.b=prior.b,
ssq=ssq,
rate=1-FNGR.CT2,CT=CT2.nogo,
seed.num=seed.num,
stop.criterion=stop.criterion,direction='Less')
}
}
if(method=='Frequentist'){
if(false.go.CT1==TRUE){
est1.go=qnorm(1-FGR.CT1,mean=CT1.go,sd=sd.n)
}
if(false.go.CT2==TRUE){
est2.go=qnorm(1-FGR.CT2,mean=CT2.go,sd=sd.n)
}
if(false.nogo.CT1==TRUE){
est1.nogo=qnorm(FNGR.CT1,mean=CT1.nogo,sd=sd.n)
}
if(false.nogo.CT2==TRUE){
est2.nogo=qnorm(FNGR.CT2,mean=CT2.nogo,sd=sd.n)
}
}
if(any(is.na(c(est1.go,est2.go)))){logic.go='and'}
if(any(is.na(c(est1.nogo,est2.nogo)))){logic.nogo='and'}
if(logic.go=='and'){
go_cutoff=max(est1.go,est2.go,na.rm=TRUE)
}
if(logic.go=='or'){
go_cutoff=min(est1.go,est2.go,na.rm=TRUE)
}
if(logic.nogo=='and')
{
nogo_cutoff=min(est1.nogo,est2.nogo,na.rm=TRUE)
}
if(logic.nogo=='or')
{
nogo_cutoff=max(est1.nogo,est2.nogo,na.rm=TRUE)
}
if(go_cutoff>=nogo_cutoff){return(list(cutoff=c(go_cutoff,nogo_cutoff),flag=flag,overlap=overlap.flag))}
else{
overlap.flag=1
return(list(cutoff=c(go_cutoff,nogo_cutoff),flag=flag,overlap=overlap.flag))}
if(all(flag==0)==FALSE){return(list(cutoff=c(NA,NA),flag=flag,overlap=overlap.flag))}
}
if(direction=='Less'){
if(method=='Bayesian'&(fix.var==TRUE)){
sd.post=sqrt(1/((1/prior.sd)^2+(1/sd.n)^2))
if(false.go.CT1==TRUE){
temp=qnorm(FGR.CT1,mean=CT1.go,sd=sd.post)
est1.go=(temp-(sd.n^2/(prior.sd^2+sd.n^2))*prior.mean)/(prior.sd^2/(prior.sd^2+sd.n^2))
}
if(false.go.CT2==TRUE){
temp=qnorm(FGR.CT2,mean=CT2.go,sd=sd.post)
est2.go=(temp-(sd.n^2/(prior.sd^2+sd.n^2))*prior.mean)/(prior.sd^2/(prior.sd^2+sd.n^2))
}
if(false.nogo.CT1==TRUE){
temp=qnorm(1-FNGR.CT1,mean=CT1.nogo,sd=sd.post)
est1.nogo=(temp-(sd.n^2/(prior.sd^2+sd.n^2))*prior.mean)/(prior.sd^2/(prior.sd^2+sd.n^2))
}
if(false.nogo.CT2==TRUE){
temp=qnorm(1-FNGR.CT2,mean=CT2.nogo,sd=sd.post)
est2.nogo=(temp-(sd.n^2/(prior.sd^2+sd.n^2))*prior.mean)/(prior.sd^2/(prior.sd^2+sd.n^2))
}
}
if(method=='Bayesian'&(fix.var==FALSE)){
if(noninfo==TRUE){
prior.k=0
prior.a=-1/2
prior.b=0
prior.mean=0
}
if(false.go.CT1==TRUE){
est1.go<-SAN_findIGcutoff(n=n,
prior.mean=prior.mean,prior.k=prior.k ,
prior.a=prior.a,prior.b=prior.b,
ssq=ssq,
rate=1-FGR.CT1,CT=CT1.go,
seed.num=seed.num,
stop.criterion=stop.criterion,direction='Less')
}
if(false.go.CT2==TRUE){
est2.go<-SAN_findIGcutoff(n=n,
prior.mean=prior.mean,prior.k=prior.k ,
prior.a=prior.a,prior.b=prior.b,
ssq=ssq,
rate=1-FGR.CT2,CT=CT2.go,
seed.num=seed.num,
stop.criterion=stop.criterion,direction='Less')
}
if(false.nogo.CT1==TRUE){
est1.nogo<-SAN_findIGcutoff(n=n,
prior.mean=prior.mean,prior.k=prior.k ,
prior.a=prior.a,prior.b=prior.b,
ssq=ssq,
rate=1-FNGR.CT1,CT=CT1.nogo,
seed.num=seed.num,
stop.criterion=stop.criterion,direction='Greater')
}
if(false.nogo.CT2==TRUE){
est2.nogo<-SAN_findIGcutoff(n=n,
prior.mean=prior.mean,prior.k=prior.k ,
prior.a=prior.a,prior.b=prior.b,
ssq=ssq,
rate=1-FNGR.CT2,CT=CT2.nogo,
seed.num=seed.num,
stop.criterion=stop.criterion,direction='Greater')
}
}
if(method=='Frequentist'){
if(false.go.CT1==TRUE){
est1.go=qnorm(FGR.CT1,mean=CT1.go,sd=sd.n)
}
if(false.go.CT2==TRUE){
est2.go=qnorm(FGR.CT2,mean=CT2.go,sd=sd.n)
}
if(false.nogo.CT1==TRUE){
est1.nogo=qnorm(1-FNGR.CT1,mean=CT1.nogo,sd=sd.n)
}
if(false.nogo.CT2==TRUE){
est2.nogo=qnorm(1-FNGR.CT2,mean=CT2.nogo,sd=sd.n)
}
}
if(any(is.na(c(est1.go,est2.go)))){logic.go='and'}
if(any(is.na(c(est1.nogo,est2.nogo)))){logic.nogo='and'}
if(logic.go=='and'){
go_cutoff=min(est1.go,est2.go,na.rm=TRUE)
}
if(logic.go=='or'){
go_cutoff=max(est1.go,est2.go,na.rm=TRUE)
}
if(logic.nogo=='and')
{
nogo_cutoff=max(est1.nogo,est2.nogo,na.rm=TRUE)
}
if(logic.nogo=='or')
{
nogo_cutoff=min(est1.nogo,est2.nogo,na.rm=TRUE)
}
if(go_cutoff<=nogo_cutoff){return(list(cutoff=c(go_cutoff,nogo_cutoff),flag=flag,overlap=overlap.flag))}
else{
overlap.flag=1
return(list(cutoff=c(go_cutoff,nogo_cutoff),flag=flag,overlap=overlap.flag))}
if(all(flag==0)==FALSE){return(list(cutoff=c(NA,NA),flag=flag,overlap=overlap.flag))}
}
}
SAN_Bayesian_Vary_Var<-function(n=c(10,100),
prior.mean=1/3,
prior.k=1,prior.a=1,prior.b=1,
mean=c(0.3,0.5), sd=1,
CT1.go=0.25,
false.go.CT1=TRUE,FGR.CT1=0.25,
CT1.nogo=0.25,
false.nogo.CT1=TRUE,FNGR.CT1=0.25,
CT2.go=0.3,
false.go.CT2=TRUE, FGR.CT2=0.5,
CT2.nogo=0.3,
false.nogo.CT2=TRUE, FNGR.CT2=0.5,
overlap.option='GO',direction='Greater',
noninfo=TRUE,
seed.num=369, n_repeat=1000,
logic.go='and',logic.nogo='or'){
set.seed(seed.num)
go_prob<-matrix(NA,ncol=length(n),nrow=length(mean))
nogo_prob<-matrix(NA,ncol=length(n),nrow=length(mean))
inconclusive_prob<-matrix(NA,ncol=length(n),nrow=length(mean))
overlap.flag=rep(0,length(n))
for (ii in 1:length(mean)){
for (ii2 in 1:length(n)){
x=matrix(rnorm(n_repeat*n[ii2],mean[ii],sd),nrow=n_repeat)
mean_x=apply(x,1,mean)
ssq_x=apply(x,1,function(x){sum(x^2)})
if(is.na(CT1.go)) false.go.CT1=FALSE
if(is.na(CT1.nogo)) false.nogo.CT1=FALSE
if(is.na(CT2.go)) false.go.CT2=FALSE
if(is.na(CT2.nogo)) false.nogo.CT2=FALSE
if(false.go.CT1==TRUE) pp_go_1 = rep(0,n_repeat)
if(false.nogo.CT1==TRUE) pp_nogo_1 = rep(0,n_repeat)
if(false.go.CT2==TRUE) pp_go_2 = rep(0,n_repeat)
if(false.nogo.CT2==TRUE) pp_nogo_2 = rep(0,n_repeat)
for (i in 1:n_repeat){
if(noninfo==TRUE){
prior.mean=0
prior.k=0
prior.a=-1/2
prior.b=0
}
mupost=(prior.k*prior.mean+n[ii2]*mean_x[i])/(prior.k+n[ii2])
kpost=prior.k+n[ii2]
apost=prior.a+n[ii2]/2
bpost=prior.b+1/2*ssq_x[i]+prior.k*n[ii2]*(mean_x[i]-prior.mean)^2/(2*(prior.k+n[ii2]))
if(direction=='Greater'){ # closed form. pmvt returns upper area
if(false.go.CT1==TRUE) pp_go_1[i] = 1-pt((CT1.go-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
if(false.nogo.CT1==TRUE) pp_nogo_1[i] = 1-pt((CT1.nogo-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
if(false.go.CT2==TRUE) pp_go_2[i] = 1-pt((CT2.go-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
if(false.nogo.CT2==TRUE) pp_nogo_2[i] = 1-pt((CT2.nogo-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
}
if(direction=='Less'){
if(false.go.CT1==TRUE) pp_go_1[i] = pt((CT1.go-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
if(false.nogo.CT1==TRUE) pp_nogo_1[i] = pt((CT1.nogo-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
if(false.go.CT2==TRUE) pp_go_2[i] = pt((CT2.go-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
if(false.nogo.CT2==TRUE) pp_nogo_2[i] = pt((CT2.nogo-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
}
}
if(false.go.CT1==TRUE & false.go.CT2==TRUE){
if(logic.go=='and')
go_prob[ii,ii2] = mean(pp_go_1>=1-FGR.CT1 & pp_go_2>=1-FGR.CT2)
if(logic.go=='or')
go_prob[ii,ii2] = mean(pp_go_1>=1-FGR.CT1 | pp_go_2>=1-FGR.CT2)
} else if(false.go.CT1==TRUE){
go_prob[ii,ii2] = mean(pp_go_1>=1-FGR.CT1)
} else if(false.go.CT2==TRUE){
go_prob[ii,ii2] = mean(pp_go_2>=1-FGR.CT2)
}
if(false.nogo.CT1==TRUE & false.nogo.CT2==TRUE){
if(logic.nogo=='and')
nogo_prob[ii,ii2] = mean(pp_nogo_1<FNGR.CT1 & pp_nogo_2<FNGR.CT2)
if(logic.nogo=='or')
nogo_prob[ii,ii2] = mean(pp_nogo_1<FNGR.CT1 | pp_nogo_2<FNGR.CT2)
} else if(false.nogo.CT1==TRUE){
nogo_prob[ii,ii2] = mean(pp_nogo_1<FNGR.CT1)
} else if(false.nogo.CT2==TRUE){
nogo_prob[ii,ii2] = mean(pp_nogo_2<FNGR.CT2)
}
if (go_prob[ii,ii2]+nogo_prob[ii,ii2]>1){
overlap.flag[ii2] = 1
if (overlap.option=='GO'){
nogo_prob[ii,ii2] = 1-go_prob[ii,ii2]
} else if (overlap.option=='NOGO'){
go_prob[ii,ii2] = 1-nogo_prob[ii,ii2]
}
}
inconclusive_prob[ii,ii2]=1-go_prob[ii,ii2]-nogo_prob[ii,ii2]
}
}
return(list(go_prob,nogo_prob,inconclusive_prob,overlap.flag))
}
#### this has plot number 3
Fix_SS_SAN_Normal_Prob<-function(n=100,
prior.mean=1/3,prior.sd=1,
prior.k=1,prior.a=1,prior.b=1,
sd=1,ssq=1,
mean=c(0.0,0.9),
CT1.go=0.25,
false.go.CT1=TRUE,FGR.CT1=0.25,
CT1.nogo=0.25,
false.nogo.CT1=TRUE,FNGR.CT1=0.25,
CT2.go=0.3,
false.go.CT2=TRUE, FGR.CT2=0.5,
CT2.nogo=0.3,
false.nogo.CT2=TRUE, FNGR.CT2=0.5,
overlap.option='GO',plot.figure=TRUE,
method='Bayesian',direction='Greater',
fix.var=TRUE,noninfo=TRUE,
seed.num=369,
stop.criterion=10^-3,
logic.go='and',logic.nogo='or'){
meanseq=round(seq(min(mean),max(mean),length=10),3)
go_prob<-rep(NA,length(mean))
nogo_prob<-rep(NA,length(mean))
inconclusive_prob<-rep(NA,length(mean))
go_prob_plot<-rep(NA,length(meanseq))
nogo_prob_plot<-rep(NA,length(meanseq))
inconclusive_prob_plot<-rep(NA,length(meanseq))
index=1
unsatisfied.flag=0
overlap.flag=0
sd.n=sd/sqrt(n)
temp=SAN_Normal_Cutoff(n=n,
prior.mean=prior.mean,prior.sd = prior.sd,
prior.k = prior.k,prior.a=prior.a,prior.b=prior.b,
sd=sd,ssq=ssq,
CT1.go=CT1.go,
false.go.CT1 = false.go.CT1, FGR.CT1=FGR.CT1,
CT1.nogo=CT1.nogo,
false.nogo.CT1 = false.nogo.CT1, FNGR.CT1 = FNGR.CT1,
CT2.go=CT2.go,
false.go.CT2 = false.go.CT2, FGR.CT2=FGR.CT2,
CT2.nogo=CT2.nogo,
false.nogo.CT2 = false.nogo.CT2, FNGR.CT2 = FNGR.CT2,
method=method,direction=direction,
fix.var=fix.var,noninfo=noninfo,
seed.num=seed.num,
stop.criterion=stop.criterion,
logic.go=logic.go,logic.nogo = logic.nogo)
###SAN####
true_go_cutoff<-ifelse(temp$overlap==0,temp$cutoff[1],(overlap.option=='GO')*temp$cutoff[1]+(overlap.option=='NOGO')*(temp$cutoff[2]))
true_nogo_cutoff<-ifelse(temp$overlap==0,temp$cutoff[2],(overlap.option=='GO')*temp$cutoff[1]+(overlap.option=='NOGO')*(temp$cutoff[2]))
overlap.flag = temp$overlap
if(method=='Frequentist' | (method=='Bayesian' & fix.var==TRUE) ){
if(direction=='Greater'){
if(all(temp$flag==0)&temp$overlap==0){
go_prob=1-pnorm(temp$cutoff[1],mean=mean,sd=sd.n)
nogo_prob=pnorm(temp$cutoff[2],mean=mean,sd=sd.n)
inconclusive_prob=1-go_prob-nogo_prob
go_prob_plot=1-pnorm(temp$cutoff[1],mean=meanseq,sd=sd.n)
nogo_prob_plot=pnorm(temp$cutoff[2],mean=meanseq,sd=sd.n)
inconclusive_prob_plot=1-go_prob_plot-nogo_prob_plot
}
if(all(temp$flag==0)&temp$overlap==1&overlap.option=="GO"){
go_prob=1-pnorm(temp$cutoff[1],mean=mean,sd=sd.n)
nogo_prob=pnorm(temp$cutoff[1],mean=mean,sd=sd.n)
inconclusive_prob=1-go_prob-nogo_prob
go_prob_plot=1-pnorm(temp$cutoff[1],mean=meanseq,sd=sd.n)
nogo_prob_plot=pnorm(temp$cutoff[1],mean=meanseq,sd=sd.n)
inconclusive_prob_plot=1-go_prob_plot-nogo_prob_plot
}
if(all(temp$flag==0)&temp$overlap==1&overlap.option=="NOGO"){
go_prob=1-pnorm(temp$cutoff[2],mean=mean,sd=sd.n)
nogo_prob=pnorm(temp$cutoff[2],mean=mean,sd=sd.n)
inconclusive_prob=1-go_prob-nogo_prob
go_prob_plot=1-pnorm(temp$cutoff[2],mean=meanseq,sd=sd.n)
nogo_prob_plot=pnorm(temp$cutoff[2],mean=meanseq,sd=sd.n)
inconclusive_prob_plot=1-go_prob_plot-nogo_prob_plot
}
if(all(temp$flag==0)==FALSE){
unsatisfied.flag=1
nogo_prob=rep(NA,length(mean))
go_prob=rep(NA,length(mean))
inconclusive_prob=rep(NA,length(mean))
}
}
if(direction=='Less'){
if(all(temp$flag==0)&temp$overlap==0){
go_prob=pnorm(temp$cutoff[1],mean=mean,sd=sd.n)
nogo_prob=1-pnorm(temp$cutoff[2],mean=mean,sd=sd.n)
inconclusive_prob=1-go_prob-nogo_prob
go_prob_plot=pnorm(temp$cutoff[1],mean=meanseq,sd=sd.n)
nogo_prob_plot=1-pnorm(temp$cutoff[2],mean=meanseq,sd=sd.n)
inconclusive_prob_plot=1-go_prob_plot-nogo_prob_plot
}
if(all(temp$flag==0)&temp$overlap==1&overlap.option=="GO"){
go_prob=pnorm(temp$cutoff[1],mean=mean,sd=sd.n)
nogo_prob=1-pnorm(temp$cutoff[1],mean=mean,sd=sd.n)
inconclusive_prob=1-go_prob-nogo_prob
go_prob_plot=pnorm(temp$cutoff[1],mean=meanseq,sd=sd.n)
nogo_prob_plot=1-pnorm(temp$cutoff[1],mean=meanseq,sd=sd.n)
inconclusive_prob_plot=1-go_prob_plot-nogo_prob_plot
}
if(all(temp$flag==0)&temp$overlap==1&overlap.option=="NOGO"){
go_prob_plot=pnorm(temp$cutoff[2],mean=meanseq,sd=sd.n)
nogo_prob_plot=1-pnorm(temp$cutoff[2],mean=meanseq,sd=sd.n)
inconclusive_prob_plot=1-go_prob-nogo_prob_plot
go_prob=pnorm(temp$cutoff[2],mean=mean,sd=sd.n)
nogo_prob=1-pnorm(temp$cutoff[2],mean=mean,sd=sd.n)
inconclusive_prob=1-go_prob-nogo_prob
}
if(all(temp$flag==0)==FALSE){
unsatisfied.flag=1
nogo_prob=rep(NA,length(mean))
go_prob=rep(NA,length(mean))
inconclusive_prob=rep(NA,length(mean))
}
}
}
if(method=='Bayesian' & fix.var==FALSE ){
n_repeat=1000
temp2 = SAN_Bayesian_Vary_Var(n=n,
prior.mean=prior.mean,
prior.k=prior.k,prior.a=prior.a,prior.b=prior.b,
sd=sd,mean=mean,
CT1.go=CT1.go,false.go.CT1=false.go.CT1,
FGR.CT1=FGR.CT1,
CT1.nogo=CT1.nogo,
false.nogo.CT1=false.nogo.CT1,FNGR.CT1=FNGR.CT1,
CT2.go=CT2.go,false.go.CT2=false.go.CT2, FGR.CT2=FGR.CT2,
CT2.nogo=CT2.nogo,false.nogo.CT2=false.nogo.CT2,FNGR.CT2=FNGR.CT2,
overlap.option=overlap.option,direction=direction,
noninfo=noninfo,
seed.num=seed.num,n_repeat=n_repeat,
logic.go=logic.go,logic.nogo=logic.nogo)
go_prob = as.numeric(temp2[[1]])
nogo_prob = as.numeric(temp2[[2]])
inconclusive_prob = as.numeric(temp2[[3]])
# plot
temp3 = SAN_Bayesian_Vary_Var(n=n,
prior.mean=prior.mean,
prior.k=prior.k,prior.a=prior.a,prior.b=prior.b,
sd=sd,mean=meanseq,
CT1.go=CT1.go,false.go.CT1=false.go.CT1,
FGR.CT1=FGR.CT1,
CT1.nogo=CT1.nogo,
false.nogo.CT1=false.nogo.CT1,FNGR.CT1=FNGR.CT1,
CT2.go=CT2.go,false.go.CT2=false.go.CT2, FGR.CT2=FGR.CT2,
CT2.nogo=CT2.nogo,false.nogo.CT2=false.nogo.CT2,FNGR.CT2=FNGR.CT2,
overlap.option=overlap.option,direction=direction,
noninfo=noninfo,
seed.num=seed.num,n_repeat=n_repeat,
logic.go=logic.go,logic.nogo=logic.nogo)
go_prob_plot = as.numeric(temp3[[1]])
nogo_prob_plot = as.numeric(temp3[[2]])
inconclusive_prob_plot = as.numeric(temp3[[3]])
}
########################################################################
if(plot.figure==TRUE){
delta=meanseq
p_nogo=nogo_prob_plot*100
p_grey=inconclusive_prob_plot*100
p_go=go_prob_plot*100
if(true_go_cutoff!=true_nogo_cutoff){
par(mfrow=c(1,1),pty="m",bty="l",cex=1.4)
plot(delta,p_go,xlab=expression(paste("True ",mean,sep="")),
ylab="Prob of GO/ NOGO/ Inconclusive (%)",xlim=range(delta),
ylim=c(0,100),type="n",axes=F)
axis(1, at=meanseq, labels=meanseq)
axis(2, at=seq(0,100,10),labels=T)
#text(rep(-0.6,6),seq(0,100,20),seq(0,100,20),adj=1,xpd=T)
box()
#abline(h=seq(0,100,10),lty=3,col=rgb(0.8,0.8,0.8),lwd=1)
points(delta,p_nogo,type="b",pch=16,col=rgb(0.9,0,0),lwd=3,lty=1)
points(delta,p_grey,type="b",pch=4,col=rgb(0.9,0.6,0),lwd=3,lty=6)
points(delta,p_go,type="b",pch=2,col=rgb(0,0.7,0),lwd=3,lty=2)
text(min(mean),140,bquote(n==~.(n)),xpd=T,adj=0,cex=0.8,col=rgb(0, 0,0))
if(overlap.flag==0&unsatisfied.flag==0){
if(direction=='Greater'){
text(min(mean),130,bquote(GO~symbol("\336")~Observed~average~effect~symbol("\263")~.(round(temp$cutoff[1],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0, 0.7,0))
text(min(mean),120,bquote(NOGO~symbol("\336")~Observed~average~effect~symbol("\243")~.(round(temp$cutoff[2],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0.9, 0,0))
text(min(mean),110,bquote(Inconclusive~symbol("\336")~anything~between~GO~and~NOGO),xpd=T,adj=0,cex=0.8,col=rgb(0.9,0.6,0))
}
if(direction=='Less'){
text(min(mean),130,bquote(GO~symbol("\336")~Observed~average~effect~symbol("\243")~.(round(temp$cutoff[1],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0, 0.7,0))
text(min(mean),120,bquote(NOGO~symbol("\336")~Observed~average~effect~symbol("\263")~.(round(temp$cutoff[2],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0.9, 0,0))
text(min(mean),110,bquote(Inconclusive~symbol("\336")~anything~between~GO~and~NOGO),xpd=T,adj=0,cex=0.8,col=rgb(0.9,0.6,0))
}
}
if(overlap.flag==1&unsatisfied.flag==0&overlap.option=='GO'){
if(direction=="Greater"){
text(min(mean),130,bquote(GO~symbol("\336")~Observed~average~effect~symbol("\263")~.(round(temp$cutoff[1],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0, 0.7,0))
text(min(mean),120,bquote(NOGO~symbol("\336")~Observed~average~effect~symbol("\243")~.(round(temp$cutoff[1],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0.9, 0,0))
#text(min(mean),115,paste0('Warning: GO and NOGO zones are overlaped at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
#text(min(mean),110,paste0('The zones are classfied by cutoff of ', overlap.option),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
}
if(direction=="Less"){
text(min(mean),130,bquote(GO~symbol("\336")~Observed~average~effect~symbol("\243")~.(round(temp$cutoff[1],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0, 0.7,0))
text(min(mean),120,bquote(NOGO~symbol("\336")~Observed~average~effect~symbol("\263")~.(round(temp$cutoff[1],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0.9, 0,0))
#text(min(mean),115,paste0('Warning: GO and NOGO zones are overlaped at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
#text(min(mean),110,paste0('The zones are classfied by cutoff of ', overlap.option),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
}
}
if(overlap.flag==1&unsatisfied.flag==0&overlap.option=='NOGO'){
if(direction=="Greater"){
text(min(mean),130,bquote(GO~symbol("\336")~Observed~average~effect~symbol("\263")~.(round(temp$cutoff[2],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0, 0.7,0))
text(min(mean),120,bquote(NOGO~symbol("\336")~Observed~average~effect~symbol("\243")~.(round(temp$cutoff[2],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0.9, 0,0))
#text(min(mean),115,paste0('Warning: GO and NOGO zones are overlaped at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
#text(min(mean),110,paste0('The zones are classfied by cutoff of ', overlap.option),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
}
if(direction=="Less"){
text(min(mean),130,bquote(GO~symbol("\336")~Observed~average~effect~symbol("\243")~.(round(temp$cutoff[2],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0, 0.7,0))
text(min(mean),120,bquote(NOGO~symbol("\336")~Observed~average~effect~symbol("\263")~.(round(temp$cutoff[2],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0.9, 0,0))
#text(min(mean),115,paste0('Warning: GO and NOGO zones are overlaped at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
#text(min(mean),110,paste0('The zones are classfied by cutoff of ', overlap.option),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
}
}
if(unsatisfied.flag==1){
text(min(mean),130,paste0('Warning: We could not find classification of zones to satisfy your both GO and NOGO criterions at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0,0))
text(min(mean),120,paste0('Please check and modify your desicion rule or the range of sample size!'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0,0))
}
}
}
###################################################################
if(plot.figure==TRUE){
delta=meanseq
p_nogo=nogo_prob_plot*100
p_grey=inconclusive_prob_plot*100
p_go=go_prob_plot*100
if(true_go_cutoff==true_nogo_cutoff){
par(mfrow=c(1,1),pty="m",bty="l",cex=1.4)
plot(delta,p_go,xlab=expression(paste("True ",mean,sep="")),
ylab="Prob of GO/ NOGO/ Inconclusive (%)",xlim=range(delta),
ylim=c(0,100),type="n",axes=F)
axis(1, at=meanseq, labels=meanseq)
axis(2, at=seq(0,100,10),labels=T)
#text(rep(-0.6,6),seq(0,100,20),seq(0,100,20),adj=1,xpd=T)
box()
points(delta,p_nogo,type="b",pch=16,col=rgb(0.9,0,0),lwd=3,lty=1)
#points(delta,p_grey,type="b",pch=4,col=rgb(0.9,0.6,0),lwd=3,lty=6)
points(delta,p_go,type="b",pch=2,col=rgb(0,0.7,0),lwd=3,lty=2)
text(min(mean),140,bquote(n==~.(n)),xpd=T,adj=0,cex=0.8,col=rgb(0, 0,0))
if(overlap.flag==0&unsatisfied.flag==0){
if(direction=='Greater'){
text(min(mean),130,bquote(GO~symbol("\336")~Observed~average~effect~symbol("\263")~.(round(temp$cutoff[1],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0, 0.7,0))
text(min(mean),120,bquote(NOGO~symbol("\336")~Observed~average~effect~symbol("\243")~.(round(temp$cutoff[2],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0.9, 0,0))
#text(min(mean),110,bquote(Inconclusive~symbol("\336")~anything~between~GO~and~NOGO),xpd=T,adj=0,cex=0.8,col=rgb(0.9,0.6,0))
}
if(direction=='Less'){
text(min(mean),130,bquote(GO~symbol("\336")~Observed~average~effect~symbol("\243")~.(round(temp$cutoff[1],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0, 0.7,0))
text(min(mean),120,bquote(NOGO~symbol("\336")~Observed~average~effect~symbol("\263")~.(round(temp$cutoff[2],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0.9, 0,0))
#text(min(mean),110,bquote(Inconclusive~symbol("\336")~anything~between~GO~and~NOGO),xpd=T,adj=0,cex=0.8,col=rgb(0.9,0.6,0))
}
}
if(overlap.flag==1&unsatisfied.flag==0&overlap.option=='GO'){
if(direction=="Greater"){
text(min(mean),130,bquote(GO~symbol("\336")~Observed~average~effect~symbol("\263")~.(round(temp$cutoff[1],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0, 0.7,0))
text(min(mean),120,bquote(NOGO~symbol("\336")~Observed~average~effect~symbol("\243")~.(round(temp$cutoff[1],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0.9, 0,0))
#text(min(mean),115,paste0('Warning: GO and NOGO zones are overlaped at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
#text(min(mean),110,paste0('The zones are classfied by cutoff of ', overlap.option),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
}
if(direction=="Less"){
text(min(mean),130,bquote(GO~symbol("\336")~Observed~average~effect~symbol("\243")~.(round(temp$cutoff[1],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0, 0.7,0))
text(min(mean),120,bquote(NOGO~symbol("\336")~Observed~average~effect~symbol("\263")~.(round(temp$cutoff[1],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0.9, 0,0))
#text(min(mean),115,paste0('Warning: GO and NOGO zones are overlaped at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
#text(min(mean),110,paste0('The zones are classfied by cutoff of ', overlap.option),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
}
}
if(overlap.flag==1&unsatisfied.flag==0&overlap.option=='NOGO'){
if(direction=="Greater"){
text(min(mean),130,bquote(GO~symbol("\336")~Observed~average~effect~symbol("\263")~.(round(temp$cutoff[2],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0, 0.7,0))
text(min(mean),120,bquote(NOGO~symbol("\336")~Observed~average~effect~symbol("\243")~.(round(temp$cutoff[2],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0.9, 0,0))
#text(min(mean),115,paste0('Warning: GO and NOGO zones are overlaped at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
#text(min(mean),110,paste0('The zones are classfied by cutoff of ', overlap.option),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
}
if(direction=="Less"){
text(min(mean),130,bquote(GO~symbol("\336")~Observed~average~effect~symbol("\243")~.(round(temp$cutoff[2],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0, 0.7,0))
text(min(mean),120,bquote(NOGO~symbol("\336")~Observed~average~effect~symbol("\263")~.(round(temp$cutoff[2],digits=3))),xpd=T,adj=0,cex=0.8,col=rgb(0.9, 0,0))
#text(min(mean),115,paste0('Warning: GO and NOGO zones are overlaped at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
#text(min(mean),110,paste0('The zones are classfied by cutoff of ', overlap.option),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
}
}
if(unsatisfied.flag==1){
text(min(mean),130,paste0('Warning: We could not find classification of zones to satisfy your both GO and NOGO criterions at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0,0))
text(min(mean),120,paste0('Please check and modify your desicion rule or the range of sample size!'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0,0))
}
}
}
###################################################################
return(list(go_prob=go_prob,nogo_prob=nogo_prob,
inconclusive_prob=inconclusive_prob,
overlap.flag=overlap.flag,overlap.option=overlap.option,
unsatisfied.flag=unsatisfied.flag,cutoff=temp$cutoff,true_cutoff=c(true_go_cutoff,true_nogo_cutoff))
)
}
Vary_SS_SAN_Normal_Prob<-function(nmin=250,nmax=300,prior.mean=1/3,prior.sd=1,
prior.k=1,prior.a=1,prior.b=1,
mean=0.3,
sd=1,ssq=1,
CT1.go=0.25,
false.go.CT1=TRUE,FGR.CT1=0.25,
CT1.nogo=0.25,
false.nogo.CT1=TRUE,FNGR.CT1=0.25,
CT2.go=0.3,
false.go.CT2=TRUE, FGR.CT2=0.5,
CT2.nogo=0.3,
false.nogo.CT2=TRUE, FNGR.CT2=0.5,
overlap.option='GO',plot.cutoff=TRUE,plot.prob=TRUE,
method="Bayesian",direction="Greater",fix.var=TRUE,noninfo=TRUE,
seed.num=369,
stop.criterion=10^-3,
logic.go='and',logic.nogo='or'){
nseq=unique(round(c(seq(nmin,(nmax+nmin)/2,length=6)[-6],seq((nmax+nmin)/2,nmax,length=6))))
go_prob<-matrix(NA,ncol=length(nseq),nrow=length(mean))
nogo_prob<-matrix(NA,ncol=length(nseq),nrow=length(mean))
inconclusive_prob<-matrix(NA,ncol=length(nseq),nrow=length(mean))
go_cutoff<-rep(NA,length(nseq))
nogo_cutoff<-rep(NA,length(nseq))
index=1
n_unsatisfied=NA
n_overlap=NA
ncore <- detectCores()
cl<-makeCluster(ncore)
registerDoParallel(cl)
results<-foreach(i = nseq,.export=c('SAN_Normal_Cutoff','SAN_findIGcutoff'),.packages=c('mvtnorm'),.combine=rbind) %dopar% {
temp=SAN_Normal_Cutoff(n=i,
prior.mean=prior.mean,prior.sd=prior.sd,
prior.k = prior.k,prior.a=prior.a,prior.b=prior.b,
sd=sd,ssq=ssq,
CT1.go=CT1.go,
false.go.CT1 = false.go.CT1, FGR.CT1=FGR.CT1,
CT1.nogo=CT1.nogo,
false.nogo.CT1 = false.nogo.CT1, FNGR.CT1 = FNGR.CT1,
CT2.go=CT2.go,
false.go.CT2 = false.go.CT2, FGR.CT2=FGR.CT2,
CT2.nogo=CT2.nogo,
false.nogo.CT2 = false.nogo.CT2, FNGR.CT2 = FNGR.CT2,
method=method,direction=direction,
fix.var = fix.var,noninfo=noninfo,
seed.num = seed.num,stop.criterion=stop.criterion,
logic.go=logic.go,logic.nogo=logic.nogo)
c(temp$overlap,temp$cutoff)
}
stopCluster(cl)
go_cutoff<-results[,2]
nogo_cutoff<-results[,3]
overlap<-results[,1]
for(mean.index in 1:length(mean)){
true_go_cutoff<-go_cutoff
true_nogo_cutoff<-nogo_cutoff
true_go_cutoff[overlap==1]<-(overlap.option=='GO')*go_cutoff[overlap==1]+(overlap.option=='NOGO')*nogo_cutoff[overlap==1]
true_nogo_cutoff[overlap==1]<-(overlap.option=='GO')*go_cutoff[overlap==1]+(overlap.option=='NOGO')*nogo_cutoff[overlap==1]
}
if(method=='Frequentist' | (method=='Bayesian' & fix.var==TRUE) ){
for(mean.index in 1:length(mean)){
mean_temp=mean[mean.index]
sd.i=sqrt(sd^2/nseq)
if(direction=='Greater'){
go_prob[mean.index,]=1-pnorm(true_go_cutoff,mean=mean_temp,sd=sd.i)
nogo_prob[mean.index,]=pnorm(true_nogo_cutoff,mean=mean_temp,sd=sd.i)
}
if(direction=='Less'){
go_prob[mean.index,]=pnorm(true_go_cutoff,mean=mean_temp,sd=sd.i)
nogo_prob[mean.index,]=1-pnorm(true_nogo_cutoff,mean=mean_temp,sd=sd.i)
}
inconclusive_prob[mean.index,]=1-go_prob[mean.index,]-nogo_prob[mean.index,]
}
}
if(method=='Bayesian' & fix.var==FALSE ){
n_repeat=1000
temp2 = SAN_Bayesian_Vary_Var(n=nseq,
prior.mean=prior.mean,
prior.k=prior.k,prior.a=prior.a,prior.b=prior.b,
mean=mean, sd=sd,
CT1.go=CT1.go,
false.go.CT1=false.go.CT1,FGR.CT1=FGR.CT1,
CT1.nogo=CT1.nogo,
false.nogo.CT1=false.nogo.CT1,FNGR.CT1=FNGR.CT1,
CT2.go=CT2.go,
false.go.CT2=false.go.CT2, FGR.CT2=FGR.CT2,
CT2.nogo=CT2.nogo,
false.nogo.CT2=false.nogo.CT2, FNGR.CT2=FNGR.CT2,
overlap.option=overlap.option,direction=direction,
noninfo=noninfo,
seed.num=seed.num, n_repeat=n_repeat,
logic.go=logic.go,logic.nogo=logic.nogo)
go_prob = temp2[[1]]
nogo_prob = temp2[[2]]
inconclusive_prob = temp2[[3]]
}
n_overlap=n_overlap[-1]
n_unsatisfied=n_unsatisfied[-1]
####plot figure
if(plot.prob==TRUE){
for(j in 1:length(mean)){
p_go=go_prob[j,]*100
p_nogo=nogo_prob[j,]*100
class(p_nogo)
dim(p_nogo)
p_grey=100-p_go-p_nogo
par(mfrow=c(1,1),pty="m",bty="l",cex=1.4)
cum_p_nogo=p_nogo
cum_p_grey=p_nogo+p_grey
cum_p_go=p_nogo+p_grey+p_go
delta=nseq
plot(delta,cum_p_go,xlab="Sample size",
ylab="Prob of GO/ NOGO/ Inconclusive (%)",xlim=c(nmin,nmax),
ylim=c(0,100),type="n",axes=F,pch=NA)
axis(1, at=nseq,labels=nseq)
axis(2, at=seq(0,100,10),labels=T)
#text(rep(-0.6,6),seq(0,100,20),seq(0,100,20),adj=1,xpd=T)
box()
#abline(h=seq(0,100,10),lty=3,col=rgb(0.8,0.8,0.8),lwd=1)
polygon(c(delta,rev(delta)),c(cum_p_nogo,rev(rep(0,length(delta)))),col=rgb(0.9,0,0),border=NA)
polygon(c(delta,rev(delta)),c(cum_p_grey,rev(cum_p_nogo)),col=rgb(0.9,0.6,0),border=NA)
polygon(c(delta,rev(delta)),c(cum_p_go,rev(cum_p_grey)),col=rgb(0,0.7,0),border=NA)
text((nmin+nmax)/2,120,paste0("True mean=",round(mean[j],3),", sd=",round(sd,3)),xpd=T,adj=0.5,cex=0.8)
if(length(n_overlap)!=0){
text(nmin,115,paste0('Warning: GO and NOGO cut-offs are overlaped at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
#text(nmin,110,paste(n_overlap),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
#print(n_overlap)
text(nmin,110,paste0('The zones are classfied by cutoff of ', overlap.option),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
}
if(length(n_unsatisfied)!=0){
text(nmin,115,paste0('Warning: We could not find cutoffs to satisfy your both GO and NOGO criterions.'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0,0))
text(nmin,110,paste0('Please check and modify your desicion rule!'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0,0))
}
}
}
if(plot.cutoff==TRUE){
par(mfrow=c(1,1),pty="m",bty="l",cex=1.4)
ylim_max=max(c(go_cutoff,nogo_cutoff,round(CT1.go,3),round(CT2.go,3),round(CT1.nogo,3),round(CT2.nogo,3)),na.rm=TRUE)+0.1
ylim_min=min(c(go_cutoff,nogo_cutoff,round(CT1.go,3),round(CT2.go,3),round(CT1.nogo,3),round(CT2.nogo,3)),na.rm=TRUE)-0.1
plot(NA,NA,xlab='Sample size',ylab="Observed mean",xlim=c(max(0,range(nseq)[1]-10),range(nseq)[2]+10),ylim=c(ylim_min,ylim_max),type="n",axes=F,col=rgb(1,0,0),lty=1,lwd=2)
axis(1, at=nseq,labels=nseq)
axis(2, at=round(c(seq(ylim_min,ylim_max,round((ylim_max-ylim_min)/10,digits=2)),CT1.go,CT2.go,CT1.nogo,CT2.nogo),digits=2),labels=T)
#text(rep(-0.6,6),seq(0,100,20),seq(0,300,20),adj=1,xpd=T)
box()
lines(nseq,nogo_cutoff,col=rgb(0.9,0,0),lwd=2)
lines(nseq,go_cutoff,col=rgb(0,0.7,0),lwd=2)
legend('bottomright',legend=c("Cut off of GO","Cut off of NOGO"),
col=c(rgb(0,0.7,0),rgb(0.9,0,0)),
lwd=c(2,2),
lty=c(1,1),cex=0.5)
if(length(n_overlap)!=0){
text(nmin,ylim_max+abs(ylim_max-ylim_min)/10,paste0('Warning: GO and NOGO zones are overlaped at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
#text(nmin,110,paste(n_overlap),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
#print(n_overlap)
text(nmin,ylim_max+abs(ylim_max-ylim_min)/20,paste0('The zones are classfied by cutoff of ', overlap.option),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0.6,0))
}
if(length(n_unsatisfied)!=0){
text(nmin,ylim_max+abs(ylim_max-ylim_min)/10,paste0('Warning: We could not find classification of zones to satisfy your both GO and NOGO criterions at some sample sizes'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0,0))
text(nmin,ylim_max+abs(ylim_max-ylim_min)/20,paste0('Please check and modify your desicion rule or the range of sample size!'),xpd=T,adj=0,cex=0.5,col=rgb(0.9,0,0))
}
}
return(list(n_unsatisfied,n_overlap))
}
Interim_SAN<-function(interim_n=c(50,100,150),num_interim=3,
CT1.go=c(0.25,0.25,0.25),
false.go.CT1=c(TRUE,TRUE,TRUE),FGR.CT1=c(0.25,0.25,0.25),
CT1.nogo=c(0.25,0.25,0.25),
false.nogo.CT1=c(TRUE,TRUE,TRUE),FNGR.CT1=c(0.25,0.25,0.25),
CT2.go=c(0.25,0.25,0.25),
false.go.CT2=c(TRUE,TRUE,TRUE),FGR.CT2=c(0.25,0.25,0.25),
CT2.nogo=c(0.25,0.25,0.25),
false.nogo.CT2=c(TRUE,TRUE,TRUE),FNGR.CT2=c(0.25,0.25,0.25),
overlap.option=c('GO','GO','GO'),
method='Bayesian',direction="Greater",
task=c('Futility','Superiority','Futility and superiority'),
seed.num=369,nsim_IA=10000,stop.criterion=10^-3,
prior.mean = 1,prior.sd=1,
prior.k=1,prior.a=1,
prior.b=1,sd=1,ssq=1,
mean=c(0.25),fix.var=TRUE,noninfo=TRUE,
logic.go=c('and','or','and'),logic.nogo=c('or','and','and')){
interim_n=sort(interim_n)
###SAN####
temptable=c()
for(meanindex in 1:length(mean)){
set.seed(seed.num)
diff_interim_n<-diff(interim_n)
generate_n<-c(interim_n[1],diff_interim_n)
mean_x=matrix(NA,nrow=nsim_IA,ncol=num_interim)
if(method=='Bayesian' & fix.var==FALSE){
ssq_x=mean_x
}
x=c()
for(k in 1:num_interim){
x=cbind(x,matrix(rnorm(nsim_IA*generate_n[k],mean[meanindex],sd),nrow=nsim_IA))
mean_x[,k]=apply(x,1,mean)
if(method=='Bayesian' & fix.var==FALSE){
ssq_x[,k]=apply(x,1,function(x){sum(x^2)})
}
}
#####
go_matrix<-matrix(NA,nrow=nsim_IA,ncol=num_interim)
nogo_matrix<-matrix(NA,nrow=nsim_IA,ncol=num_interim)
inconclusive_matrix<-matrix(NA,nrow=nsim_IA,ncol=num_interim)
table<-matrix(NA,ncol=num_interim+1,nrow=6)
IA_go_matrix<-matrix(NA,nrow=nsim_IA,ncol=num_interim) ###whether continue to next stage
if(method=='Frequentist' | (method=='Bayesian' & fix.var==TRUE) ){
go_cutoff<-rep(NA,num_interim)
nogo_cutoff<-rep(NA,num_interim)
true_go_cutoff<-rep(NA,num_interim)
true_nogo_cutoff<-rep(NA,num_interim)
overlap<-rep(NA,num_interim)
for(j in 1:num_interim ){
temp<-SAN_Normal_Cutoff(n=interim_n[j],
prior.mean = prior.mean,prior.sd = prior.sd,
prior.k=prior.k,prior.a=prior.a,
prior.b=prior.b,sd=sd,ssq=NA, #ssq is unused
CT1.go=CT1.go[j],
false.go.CT1=false.go.CT1[j],FGR.CT1=FGR.CT1[j],
CT1.nogo=CT1.nogo[j],
false.nogo.CT1=false.nogo.CT1[j],FNGR.CT1=FNGR.CT1[j],
CT2.go=CT2.go[j],
false.go.CT2=false.go.CT2[j], FGR.CT2=FGR.CT2[j],
CT2.nogo=CT2.nogo[j],
false.nogo.CT2=false.nogo.CT2[j], FNGR.CT2=FNGR.CT2[j],
method=method,direction=direction[j],
fix.var=fix.var,noninfo=noninfo,
seed.num = seed.num,stop.criterion = stop.criterion,
logic.go=logic.go[j],logic.nogo=logic.nogo[j])
go_cutoff[j]<-temp$cutoff[1]
nogo_cutoff[j]<-temp$cutoff[2]
overlap[j]<-temp$overlap
###SAN####
true_go_cutoff[j]<-ifelse(overlap[j]==0,go_cutoff[j],(overlap.option[j]=='GO')*go_cutoff[j]+(overlap.option[j]=='NOGO')*(nogo_cutoff[j]))
true_nogo_cutoff[j]<-ifelse(overlap[j]==0,nogo_cutoff[j],(overlap.option[j]=='GO')*(go_cutoff[j])+(overlap.option[j]=='NOGO')*(nogo_cutoff[j]))
####
}
for(j in 1:num_interim ){
if(direction[j]=='Greater'){
go_matrix[,j]<-mean_x[,j]>=true_go_cutoff[j]
nogo_matrix[,j]<-mean_x[,j]<true_nogo_cutoff[j]
inconclusive_matrix[,j]<-rep(1,nsim_IA)-go_matrix[,j]-nogo_matrix[,j]
}
if(direction[j]=='Less'){
go_matrix[,j]<-mean_x[,j]<=true_go_cutoff[j]
nogo_matrix[,j]<-mean_x[,j]>true_nogo_cutoff[j]
inconclusive_matrix[,j]<-rep(1,nsim_IA)-go_matrix[,j]-nogo_matrix[,j]
}
}
}
if(method=='Bayesian' & fix.var==FALSE){
for(j in 1:num_interim ){
if(is.na(CT1.go[j])) false.go.CT1[j]=FALSE
if(is.na(CT1.nogo[j])) false.nogo.CT1[j]=FALSE
if(is.na(CT2.go[j])) false.go.CT2[j]=FALSE
if(is.na(CT2.nogo[j])) false.nogo.CT2[j]=FALSE
if(false.go.CT1[j]==TRUE) pp_go_1 = rep(0,nsim_IA)
if(false.nogo.CT1[j]==TRUE) pp_nogo_1 = rep(0,nsim_IA)
if(false.go.CT2[j]==TRUE) pp_go_2 = rep(0,nsim_IA)
if(false.nogo.CT2[j]==TRUE) pp_nogo_2 = rep(0,nsim_IA)
for (i in 1:nsim_IA){
if(noninfo==TRUE){
prior.mean=0
prior.k=0
prior.a=-1/2
prior.b=0
}
mupost=(prior.k*prior.mean+interim_n[j]*mean_x[i,j])/(prior.k+interim_n[j])
kpost=prior.k+interim_n[j]
apost=prior.a+interim_n[j]/2
bpost=prior.b+1/2*ssq_x[i,j]+prior.k*interim_n[j]*(mean_x[i,j]-prior.mean)^2/(2*(prior.k+interim_n[j]))
if(direction[j]=='Greater'){ # closed form. pmvt returns upper area
if(false.go.CT1[j]==TRUE) pp_go_1[i] = 1-pt((CT1.go[j]-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
if(false.nogo.CT1[j]==TRUE) pp_nogo_1[i] = 1-pt((CT1.nogo[j]-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
if(false.go.CT2[j]==TRUE) pp_go_2[i] = 1-pt((CT2.go[j]-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
if(false.nogo.CT2[j]==TRUE) pp_nogo_2[i] = 1-pt((CT2.nogo[j]-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
}
if(direction[j]=='Less'){
if(false.go.CT1[j]==TRUE) pp_go_1[i] = pt((CT1.go[j]-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
if(false.nogo.CT1[j]==TRUE) pp_nogo_1[i] = pt((CT1.nogo[j]-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
if(false.go.CT2[j]==TRUE) pp_go_2[i] = pt((CT2.go[j]-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
if(false.nogo.CT2[j]==TRUE) pp_nogo_2[i] = pt((CT2.nogo[j]-mupost)/sqrt(bpost/(apost*kpost)),df=2*apost)
}
}
if(false.go.CT1[j]==TRUE & false.go.CT2[j]==TRUE){
if(logic.go[j]=='and')
go_matrix[,j] = pp_go_1>=1-FGR.CT1[j] & pp_go_2>=1-FGR.CT2[j]
if(logic.go[j]=='or')
go_matrix[,j] = pp_go_1>=1-FGR.CT1[j] | pp_go_2>=1-FGR.CT2[j]
} else if(false.go.CT1[j]==TRUE){
go_matrix[,j] = pp_go_1>=1-FGR.CT1[j]
} else if(false.go.CT2[j]==TRUE){
go_matrix[,j] = pp_go_2>=1-FGR.CT2[j]
}
if(false.nogo.CT1[j]==TRUE & false.nogo.CT2[j]==TRUE){
if(logic.nogo[j]=='and')
nogo_matrix[,j] = pp_nogo_1<FNGR.CT1[j] & pp_nogo_2<FNGR.CT2[j]
if(logic.nogo[j]=='or')
nogo_matrix[,j] = pp_nogo_1<FNGR.CT1[j] | pp_nogo_2<FNGR.CT2[j]
} else if(false.nogo.CT1[j]==TRUE){
nogo_matrix[,j] = pp_nogo_1<FNGR.CT1[j]
} else if(false.nogo.CT2[j]==TRUE){
nogo_matrix[,j] = pp_nogo_2<FNGR.CT2[j]
}
if (overlap.option[j]=='GO'){
nogo_matrix[nogo_matrix[,j]==go_matrix[,j] & nogo_matrix[,j]==1,j] = 0
} else if (overlap.option[j]=='NOGO'){
go_matrix[go_matrix[,j]==nogo_matrix[,j] & go_matrix[,j]==1,j] = 0
}
inconclusive_matrix[,j] = rep(1,nsim_IA)-go_matrix[,j]-nogo_matrix[,j]
}
}
for(ii in 1:(num_interim)){
if(task[ii]=='Futility'){
IA_go_matrix[,ii]=inconclusive_matrix[,ii]+go_matrix[,ii]
}
if(task[ii]=='Superiority'){
IA_go_matrix[,ii]=inconclusive_matrix[,ii]+nogo_matrix[,ii]
}
if(task[ii]=='Futility and superiority'){
IA_go_matrix[,ii]=inconclusive_matrix[,ii]
}
}
cum_IA_go_matrix<-t(apply(IA_go_matrix,1,cumprod))
for(j in 1:(num_interim)){
table[1,j]=interim_n[j]
table[2,j]=mean[meanindex]
table[3,j]=task[j]
if(j==1){
if(task[j]=='Superiority'|task[j]=='Futility and superiority'){
table[4,j]=round(sum(go_matrix[,j]==1)/nsim_IA,3)}else{table[4,j]=0}
if(task[j]=='Futility'|task[j]=='Futility and superiority'){
table[6,j]=round(sum(nogo_matrix[,j]==1)/nsim_IA,3)
}else{table[6,j]=0}
}else{
if(task[j]=='Superiority'|task[j]=='Futility and superiority'){
table[4,j]=round(sum(go_matrix[,j]==1&cum_IA_go_matrix[,j-1]==1)/nsim_IA,3)}else{table[4,j]=0}
if(task[j]=='Futility'|task[j]=='Futility and superiority'){
table[6,j]=round(sum(nogo_matrix[,j]==1&cum_IA_go_matrix[,j-1]==1)/nsim_IA,3)
}else{table[6,j]=0}
}
table[5,j]=round(sum(cum_IA_go_matrix[,j]==1)/nsim_IA,3)
# if(task[j]=='Futility'){
# table[7,j]=ifelse(direction[j]=='Greater',HTML(paste0('-/<',round(true_nogo_cutoff[j],3))),HTML(paste0('-/>',round(true_nogo_cutoff[j],3))))
# }
# if(task[j]=='Superiority'){
# table[7,j]=ifelse(direction[j]=='Greater',HTML(paste0('>=',round(true_go_cutoff[j],3),'/-')),HTML(paste0('<=',round(true_go_cutoff[j],3),'/-')))
# }
# if(task[j]=='Futility and superiority'){
# table[7,j]=ifelse(direction[j]=='Greater',HTML(paste0('>=',round(true_go_cutoff[j],3),' /','<',round(true_nogo_cutoff[j],3))),HTML(paste0('<=',round(true_go_cutoff[j],3),' / ','>',round(true_nogo_cutoff[j],3))))
# }
# table[10,j]=ifelse(direction[j]=='Greater',HTML(paste0('>=',round(go_cutoff[j],3))),HTML(paste0('<=',round(go_cutoff[j],3))))
# table[9,j]=ifelse(direction[j]=='Greater',HTML(paste0('<',round(nogo_cutoff[j],3))),HTML(paste0('>',round(nogo_cutoff[j],3))))
# table[8,j]<-ifelse(overlap[j]==1,paste0('GO/NOGO zones overlapped, classified by criterion of ',overlap.option[j]),'None')
}
expectss<-round(sum(as.numeric(table[1,1:num_interim])*(c(as.numeric(table[4,1:num_interim-1])+as.numeric(table[6,1:num_interim-1]),as.numeric(table[5,num_interim-1])))),3)
table[1,num_interim+1]=HTML(paste0(expectss,' (expected)'))
table[2,num_interim+1]=mean[meanindex]
table[3,num_interim+1]=''
table[4,num_interim+1]=round(sum(as.numeric(table[4,1:num_interim])),3)
table[5,num_interim+1]=round(as.numeric(table[5,num_interim]),3)
table[6,num_interim+1]=round(sum(as.numeric(table[6,1:num_interim])),3)
# table[7,num_interim+1]=''
# table[8,num_interim+1]=''
# table[9,num_interim+1]=''
# table[10,num_interim+1]=''
table<-as.table(table)
tablecolname<-c(paste0('Interim analysis ',1:(num_interim-1)),'Final analysis',"Summary")
tablerowname<-c('Sample size','True mean','Task','Success','To next interim/final or inconclusive',
'Stop')
table<-cbind(tablerowname,rep(meanindex,6),table)
colnames(table)<-c(" ",'Setting',tablecolname)
temptable=rbind(temptable,table)
}
return(temptable)
}
#Interim_SAN(interim_n = c(66,131,197),CT1.go=c(1,0.6,1),CT1.nogo=c(1,0.6,1),FGR.CT1=c(1-0.707,0.653,0.0238),FNGR.CT1=c(0.707,1-0.653,1-0.0238),CT2.go=c(NA,NA,NA),CT2.nogo=c(NA,NA,NA),method='Frequentist',direction=c(rep('Less',1),'Greater','Less'),task=c('Futility','Superiority','Superiority'),mean=c(1.1,2))
# Fix_SS_SAN_Normal_Prob(n=50,
# prior.mean=1,prior.sd=1000,
# prior.k=1,prior.a=1,prior.b=1,
# sd=1,ssq=1,
# mean=c(2,5),
# CT1.go=4.8,
# false.go.CT1=TRUE,FGR.CT1=0.8,
# CT1.nogo=4.8,
# false.nogo.CT1=TRUE,FNGR.CT1=0.8,
# CT2.go=0.3,
# false.go.CT2=FALSE, FGR.CT2=0.5,
# CT2.nogo=0.3,
# false.nogo.CT2=FALSE, FNGR.CT2=0.5,
# overlap.option='GO',plot.figure=TRUE,
# method='Frequentist',direction='Greater',
# fix.var=TRUE,noninfo=TRUE,
# seed.num=369,nsim=10000,
# stop.criterion=10^-3,
# logic.go='and',logic.nogo='or')
#
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.