Nothing
R/IM.R
In HCTDesign: Group Sequential Design for Historical Control Trial with Survival Outcome
Defines functions
IM
Documented in
IM
#' @title Monitoring the trial at interim looks for a trial with efficacy and futility boundaries
#' @description Calculates one-sided boundary values at the observed number of events.
#' @details The number of events have to be entered sequentially. See example.
#' @param d2 vector of number of events at which you want to monitor the trial.
#' @param dmax maximum number of events in the experimental group calculated from design function.
#' @param alpha type I error.
#' @param beta type II error.
#' @param last.look logical which indicates whether the current look is the last look or not. Default is FALSE.
#' @param d1 total number of events in the historical control group.
#' @param opt type of spending function: "OBF", "Gamma", "Rho" or "Pocock". Default is "OBF".
#' @param param Parameter for Gamma family or Rho family. Default value is 4.
#' @param etam value of the drift parameter obtained from design function.
#' @author Tushar Patni, Yimei Li, Jianrong Wu, and Arzu Onar-Thomas.
#' @return A list containing efficacy and futility boundary values along with the p-values and transformed information time for the current look. Post-hoc power is also calculated in case of early stopping of the trial.
#' @examples
#' #Interim look for the trial when the number of events is 13(first look).
#' gg<-IM(c(13),dmax=57,alpha=0.05,beta=0.1,etam=3.0726,d1=65,opt="OBF",last.look=FALSE)
#' #Interim look for the trial when the number of events is 35(second look).
#' gg<-IM(c(13,35),dmax=57,alpha=0.05,beta=0.1,etam=3.0726,d1=65,opt="OBF",last.look=FALSE)
#' @import stats
#' @references
#' \insertRef{doi:10.1002/pst.1756}{HCTDesign}
#' @references
#' \insertRef{doi:10.1080/10543406.2019.1684305}{HCTDesign}
#' @importFrom diversitree set.defaults
#' @export
IM<-function(d2,dmax,last.look,d1,etam,alpha,beta,opt,param){
ti=d2/dmax
if (last.look==FALSE) {
k<-length(ti)
if (k==1){
R<-dmax/d1
ts<-(1+R)*ti/(1+R*ti)
if (opt=="OBF"){
alpha1<-2-2*pnorm(qnorm(1-alpha/2)/sqrt(ts))
beta1<-2-2*pnorm(qnorm(1-beta/2)/sqrt(ts))
}
if (opt=="Gamma") {
gamma=-(param)
alpha1=alpha*(1-exp(gamma*(ts)))/(1-exp(gamma))
beta1=beta*(1-exp(gamma*(ts)))/(1-exp(gamma))
}
if(opt=="Rho"){
rho=param
alpha1=alpha*(ts)^rho
beta1=beta*(ts)^rho
}
if(opt=="Pocock"){
alpha1=alpha*log(1+(exp(1)-1)*ts)
beta1=beta*log(1+(exp(1)-1)*ts)
}
ub<-qnorm(1-alpha1)
lb<-qnorm(beta1,mean = etam*sqrt(ts))
p1<-NULL
p2<-NULL
p1[1]<-pnorm(ub[length(ti)],lower.tail = F)
p2[1]<-pnorm(lb[length(ti)],lower.tail = F)
k1<-NULL
k2<-NULL
k1[1]<-pnorm(ub[1],lower.tail = F)
k2[1]<-pnorm(lb[1],mean = etam*sqrt(ts[1]))
posthoc<-NA
}
else {
R<-dmax/d1
alpha1=beta1=NULL
alpha1[1]=beta1[1]=0
ts=NULL
fx1<-function(x,ub,covm,tprob){#fx1 for solving lower bound# 310
kn=length(ub)
lb=rep(-Inf,kn)
pmv=mvtnorm::pmvnorm(lower=c(lb,x),upper=c(ub,Inf),sigma=covm)[1]
tprob-pmv}
fx2<-function(x,lb,etam,ts,covm,tprob){#fx2 for solving upper bound# 315
kn=length(lb)
ub=rep(Inf,kn)
lmean=etam*sqrt(ts[1:(kn+1)])
pmv=mvtnorm::pmvnorm(lower=c(lb,-Inf),upper=c(ub,x),mean=lmean,sigma=covm)[1]
tprob-pmv}
covmatrix=matrix(rep(0,(length(ti)+1)*(length(ti)+1)),ncol=length(ti)+1,byrow=T)
for (i in 1:length(ti)) {
ts[i]=(1+R)*ti[i]/(1+R*ti[i])
if(opt=="OBF") {
alpha1[i+1]=2-2*pnorm(qnorm(1-alpha/2)/sqrt(ts[i]))
beta1[i+1]=2-2*pnorm(qnorm(1-beta/2)/sqrt(ts[i]))
}
if (opt=="Gamma"){
gamma=-(param)
alpha1[i+1]=alpha*(1-exp(gamma*(ts[i])))/(1-exp(gamma))
beta1[i+1]=beta*(1-exp(gamma*(ts[i])))/(1-exp(gamma))
}
if(opt=="Rho"){
rho=param
alpha1[i+1]=alpha*(ts[i])^rho
beta1[i+1]=beta*(ts[i])^rho}
if(opt=="Pocock"){
alpha1[i+1]=alpha*log(1+(exp(1)-1)*ts[i])
beta1[i+1]=beta*log(1+(exp(1)-1)*ts[i])}
}
tij=c(0, ts)
for (i in 1:(length(ti)+1)) {
for (j in 1:(length(ti)+1)) {
covmatrix[i,j]=min(tij[i],tij[j])/sqrt(tij[i]*tij[j])}}
ub=lb=rep(0,length(ti))
ub[1]=qnorm(1-alpha1[2])
ubi=NULL
for (i in c(2:length(ti))){
ubi=c(ubi,ub[i-1])
ub[i]=uniroot(fx1,lower=-10,upper=10,ub=ubi,
covm=covmatrix[2:(i+1),2:(i+1)],tprob=alpha1[i+1]-alpha1[i])$root}
lb[1]=qnorm(beta1[2])+etam*sqrt(ts[1])
lbi=NULL
for (i in 2:length(ti)) {
lbi=c(lbi,lb[i-1])
lb[i]=uniroot(fx2,lower=-10,upper=10,lb=lbi,etam=etam,ts=ts,
covm=covmatrix[2:(i+1),2:(i+1)],tprob=beta1[i+1]-beta1[i])$root}
p1<-NULL
p2<-NULL
p1<-pnorm(ub[length(ti)],lower.tail = F)
p2<-pnorm(lb[length(ti)],lower.tail = F)
k1<-NULL
k2<-NULL
k1[1]<-pnorm(ub[1],lower.tail = F)
k2[1]<-pnorm(lb[1],mean = etam*sqrt(ts[1]))
for (i in 2:length(lb)){
k1[i]<-mvtnorm::pmvnorm(lower=c(lb[1:(i-1)],ub[i]),upper=c(ub[1:(i-1)],Inf),sigma=covmatrix[2:(i+1),2:(i+1)])[1]
k2[i]<-mvtnorm::pmvnorm(lower=c(lb[1:(i-1)],-Inf),upper=c(ub[1:(i-1)],lb[i]),sigma=covmatrix[2:(i+1),2:(i+1)],mean = etam*sqrt(ts[1:i]))[1]
}
posthoc<-NA
}
}
else{
R<-dmax/d1
alpha1=beta1=NULL
alpha1[1]=beta1[1]=0
ts=NULL
covmatrix=matrix(rep(0,(length(ti)+1)*(length(ti)+1)),ncol=length(ti)+1,byrow=T)
fx1<-function(x,ub,covm,tprob){#fx1 for solving lower bound# 310
kn=length(ub)
lb=rep(-Inf,kn)
pmv=mvtnorm::pmvnorm(lower=c(lb,x),upper=c(ub,Inf),sigma=covm)[1]
tprob-pmv}
fx2<-function(x,lb,etam,ts,covm,tprob){#fx2 for solving upper bound# 315
kn=length(lb)
ub=rep(Inf,kn)
lmean=etam*sqrt(ts[1:(kn+1)])
pmv=mvtnorm::pmvnorm(lower=c(lb,-Inf),upper=c(ub,x),mean=lmean,sigma=covm)[1]
tprob-pmv}
for (i in 1:length(ti)) {
ts[i]=(1+R)*ti[i]/(1+R*ti[i])
if(opt=="OBF") {
alpha1[i+1]=2-2*pnorm(qnorm(1-alpha/2)/sqrt(ts[i]))
beta1[i+1]=2-2*pnorm(qnorm(1-beta/2)/sqrt(ts[i]))
}
if (opt=="Gamma") {
gamma=-(param)
alpha1[i+1]=alpha*(1-exp(gamma*(ts[i])))/(1-exp(gamma))
beta1[i+1]=beta*(1-exp(gamma*(ts[i])))/(1-exp(gamma))
}
if(opt=="Rho"){
rho=param
alpha1[i+1]=alpha*(ts[i])^rho
beta1[i+1]=beta*(ts[i])^rho}
if(opt=="Pocock"){
alpha1[i+1]=alpha*log(1+(exp(1)-1)*ts[i])
beta1[i+1]=beta*log(1+(exp(1)-1)*ts[i])}
}
alpha1[length(ti)+1]<-alpha
##
if(length(ti)==1){
ub<-qnorm(1-alpha1[2])
lb<-ub
p1<-NULL
p2<-NULL
p1[1]<-pnorm(ub,lower.tail = F)
p2[1]<-pnorm(lb,lower.tail = F)
k1<-NULL
k2<-NULL
k1[1]<-pnorm(ub,lower.tail = F)
k2[1]<-pnorm(lb,mean = etam*sqrt(ts[1]))
posthoc<-1-k2}
else{
tij=c(0, ts)
for (i in 1:(length(ti)+1)) {
for (j in 1:(length(ti)+1)) {
covmatrix[i,j]=min(tij[i],tij[j])/sqrt(tij[i]*tij[j])}}
ub=lb=rep(0,length(ti))
ub[1]=qnorm(1-alpha1[2])
ubi=NULL
for (i in c(2:length(ti))){
ubi=c(ubi,ub[i-1])
ub[i]=uniroot(fx1,lower=-10,upper=10,ub=ubi,
covm=covmatrix[2:(i+1),2:(i+1)],tprob=alpha1[i+1]-alpha1[i])$root}
lb[1]=qnorm(beta1[2])+etam*sqrt(ts[1])
lbi=NULL
for (i in 2:length(ti)) {
lbi=c(lbi,lb[i-1])
lb[i]=uniroot(fx2,lower=-10,upper=10,lb=lbi,etam=etam,ts=ts,
covm=covmatrix[2:(i+1),2:(i+1)],tprob=beta1[i+1]-beta1[i])$root}
lb[length(ti)]<-ub[length(ti)]
p1<-NULL
p2<-NULL
p1[1]<-pnorm(ub[length(ti)],lower.tail = F)
p2[1]<-pnorm(lb[length(ti)],lower.tail = F)
k1<-NULL
k2<-NULL
k1[1]<-pnorm(ub[1],lower.tail = F)
k2[1]<-pnorm(lb[1],mean = etam*sqrt(ts[1]))
for (i in 2:length(lb)){
k1[i]<-mvtnorm::pmvnorm(lower=c(lb[1:(i-1)],ub[i]),upper=c(ub[1:(i-1)],Inf),sigma=covmatrix[2:(i+1),2:(i+1)])[1]
k2[i]<-mvtnorm::pmvnorm(lower=c(lb[1:(i-1)],-Inf),upper=c(ub[1:(i-1)],lb[i]),sigma=covmatrix[2:(i+1),2:(i+1)],mean = etam*sqrt(ts[1:i]))[1]
}
#browser()
if(ts[length(ts)]!=1){
posthoc<-NULL
posthoc[1]<-pnorm(lb[1],mean = etam*sqrt(ts[1]))
for( k in 2:length(lb)){
posthoc[k]<-mvtnorm::pmvnorm(lower = c(lb[k-1],-Inf),upper = c(ub[k-1],lb[k]),mean = etam*sqrt(ts[(k-1):k]),sigma = covmatrix[k:(k+1),k:(k+1)])
}
posthoc<-1-sum(posthoc)}
else{posthoc<-NA}}
}
ans=list(Efficacy=data.frame("Efficacy boundary in z-score scale"=ub[length(ti)],"Efficacy boundary in p-value scale"=p1,check.names = F),Futility=data.frame("Futility boundary in z-score scale"=lb[length(ti)],"Futility boundary in p-value scale"=p2,check.names = F),"Information time"=ts[length(ti)],post_hoc_power=posthoc)
return(ans)
}
IM<-set.defaults(IM,opt="OBF",last.look=FALSE,param=4)
###########################################################
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HCTDesign documentation built on Aug. 29, 2025, 5:23 p.m.
R Package Documentation
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Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Defines functions IM
Documented in IM
#' @title Monitoring the trial at interim looks for a trial with efficacy and futility boundaries
#' @description Calculates one-sided boundary values at the observed number of events.
#' @details The number of events have to be entered sequentially. See example.
#' @param d2 vector of number of events at which you want to monitor the trial.
#' @param dmax maximum number of events in the experimental group calculated from design function.
#' @param alpha type I error.
#' @param beta type II error.
#' @param last.look logical which indicates whether the current look is the last look or not. Default is FALSE.
#' @param d1 total number of events in the historical control group.
#' @param opt type of spending function: "OBF", "Gamma", "Rho" or "Pocock". Default is "OBF".
#' @param param Parameter for Gamma family or Rho family. Default value is 4.
#' @param etam value of the drift parameter obtained from design function.
#' @author Tushar Patni, Yimei Li, Jianrong Wu, and Arzu Onar-Thomas.
#' @return A list containing efficacy and futility boundary values along with the p-values and transformed information time for the current look. Post-hoc power is also calculated in case of early stopping of the trial.
#' @examples
#' #Interim look for the trial when the number of events is 13(first look).
#' gg<-IM(c(13),dmax=57,alpha=0.05,beta=0.1,etam=3.0726,d1=65,opt="OBF",last.look=FALSE)
#' #Interim look for the trial when the number of events is 35(second look).
#' gg<-IM(c(13,35),dmax=57,alpha=0.05,beta=0.1,etam=3.0726,d1=65,opt="OBF",last.look=FALSE)
#' @import stats
#' @references
#' \insertRef{doi:10.1002/pst.1756}{HCTDesign}
#' @references
#' \insertRef{doi:10.1080/10543406.2019.1684305}{HCTDesign}
#' @importFrom diversitree set.defaults
#' @export
IM<-function(d2,dmax,last.look,d1,etam,alpha,beta,opt,param){
ti=d2/dmax
if (last.look==FALSE) {
k<-length(ti)
if (k==1){
R<-dmax/d1
ts<-(1+R)*ti/(1+R*ti)
if (opt=="OBF"){
alpha1<-2-2*pnorm(qnorm(1-alpha/2)/sqrt(ts))
beta1<-2-2*pnorm(qnorm(1-beta/2)/sqrt(ts))
}
if (opt=="Gamma") {
gamma=-(param)
alpha1=alpha*(1-exp(gamma*(ts)))/(1-exp(gamma))
beta1=beta*(1-exp(gamma*(ts)))/(1-exp(gamma))
}
if(opt=="Rho"){
rho=param
alpha1=alpha*(ts)^rho
beta1=beta*(ts)^rho
}
if(opt=="Pocock"){
alpha1=alpha*log(1+(exp(1)-1)*ts)
beta1=beta*log(1+(exp(1)-1)*ts)
}
ub<-qnorm(1-alpha1)
lb<-qnorm(beta1,mean = etam*sqrt(ts))
p1<-NULL
p2<-NULL
p1[1]<-pnorm(ub[length(ti)],lower.tail = F)
p2[1]<-pnorm(lb[length(ti)],lower.tail = F)
k1<-NULL
k2<-NULL
k1[1]<-pnorm(ub[1],lower.tail = F)
k2[1]<-pnorm(lb[1],mean = etam*sqrt(ts[1]))
posthoc<-NA
}
else {
R<-dmax/d1
alpha1=beta1=NULL
alpha1[1]=beta1[1]=0
ts=NULL
fx1<-function(x,ub,covm,tprob){#fx1 for solving lower bound# 310
kn=length(ub)
lb=rep(-Inf,kn)
pmv=mvtnorm::pmvnorm(lower=c(lb,x),upper=c(ub,Inf),sigma=covm)[1]
tprob-pmv}
fx2<-function(x,lb,etam,ts,covm,tprob){#fx2 for solving upper bound# 315
kn=length(lb)
ub=rep(Inf,kn)
lmean=etam*sqrt(ts[1:(kn+1)])
pmv=mvtnorm::pmvnorm(lower=c(lb,-Inf),upper=c(ub,x),mean=lmean,sigma=covm)[1]
tprob-pmv}
covmatrix=matrix(rep(0,(length(ti)+1)*(length(ti)+1)),ncol=length(ti)+1,byrow=T)
for (i in 1:length(ti)) {
ts[i]=(1+R)*ti[i]/(1+R*ti[i])
if(opt=="OBF") {
alpha1[i+1]=2-2*pnorm(qnorm(1-alpha/2)/sqrt(ts[i]))
beta1[i+1]=2-2*pnorm(qnorm(1-beta/2)/sqrt(ts[i]))
}
if (opt=="Gamma"){
gamma=-(param)
alpha1[i+1]=alpha*(1-exp(gamma*(ts[i])))/(1-exp(gamma))
beta1[i+1]=beta*(1-exp(gamma*(ts[i])))/(1-exp(gamma))
}
if(opt=="Rho"){
rho=param
alpha1[i+1]=alpha*(ts[i])^rho
beta1[i+1]=beta*(ts[i])^rho}
if(opt=="Pocock"){
alpha1[i+1]=alpha*log(1+(exp(1)-1)*ts[i])
beta1[i+1]=beta*log(1+(exp(1)-1)*ts[i])}
}
tij=c(0, ts)
for (i in 1:(length(ti)+1)) {
for (j in 1:(length(ti)+1)) {
covmatrix[i,j]=min(tij[i],tij[j])/sqrt(tij[i]*tij[j])}}
ub=lb=rep(0,length(ti))
ub[1]=qnorm(1-alpha1[2])
ubi=NULL
for (i in c(2:length(ti))){
ubi=c(ubi,ub[i-1])
ub[i]=uniroot(fx1,lower=-10,upper=10,ub=ubi,
covm=covmatrix[2:(i+1),2:(i+1)],tprob=alpha1[i+1]-alpha1[i])$root}
lb[1]=qnorm(beta1[2])+etam*sqrt(ts[1])
lbi=NULL
for (i in 2:length(ti)) {
lbi=c(lbi,lb[i-1])
lb[i]=uniroot(fx2,lower=-10,upper=10,lb=lbi,etam=etam,ts=ts,
covm=covmatrix[2:(i+1),2:(i+1)],tprob=beta1[i+1]-beta1[i])$root}
p1<-NULL
p2<-NULL
p1<-pnorm(ub[length(ti)],lower.tail = F)
p2<-pnorm(lb[length(ti)],lower.tail = F)
k1<-NULL
k2<-NULL
k1[1]<-pnorm(ub[1],lower.tail = F)
k2[1]<-pnorm(lb[1],mean = etam*sqrt(ts[1]))
for (i in 2:length(lb)){
k1[i]<-mvtnorm::pmvnorm(lower=c(lb[1:(i-1)],ub[i]),upper=c(ub[1:(i-1)],Inf),sigma=covmatrix[2:(i+1),2:(i+1)])[1]
k2[i]<-mvtnorm::pmvnorm(lower=c(lb[1:(i-1)],-Inf),upper=c(ub[1:(i-1)],lb[i]),sigma=covmatrix[2:(i+1),2:(i+1)],mean = etam*sqrt(ts[1:i]))[1]
}
posthoc<-NA
}
}
else{
R<-dmax/d1
alpha1=beta1=NULL
alpha1[1]=beta1[1]=0
ts=NULL
covmatrix=matrix(rep(0,(length(ti)+1)*(length(ti)+1)),ncol=length(ti)+1,byrow=T)
fx1<-function(x,ub,covm,tprob){#fx1 for solving lower bound# 310
kn=length(ub)
lb=rep(-Inf,kn)
pmv=mvtnorm::pmvnorm(lower=c(lb,x),upper=c(ub,Inf),sigma=covm)[1]
tprob-pmv}
fx2<-function(x,lb,etam,ts,covm,tprob){#fx2 for solving upper bound# 315
kn=length(lb)
ub=rep(Inf,kn)
lmean=etam*sqrt(ts[1:(kn+1)])
pmv=mvtnorm::pmvnorm(lower=c(lb,-Inf),upper=c(ub,x),mean=lmean,sigma=covm)[1]
tprob-pmv}
for (i in 1:length(ti)) {
ts[i]=(1+R)*ti[i]/(1+R*ti[i])
if(opt=="OBF") {
alpha1[i+1]=2-2*pnorm(qnorm(1-alpha/2)/sqrt(ts[i]))
beta1[i+1]=2-2*pnorm(qnorm(1-beta/2)/sqrt(ts[i]))
}
if (opt=="Gamma") {
gamma=-(param)
alpha1[i+1]=alpha*(1-exp(gamma*(ts[i])))/(1-exp(gamma))
beta1[i+1]=beta*(1-exp(gamma*(ts[i])))/(1-exp(gamma))
}
if(opt=="Rho"){
rho=param
alpha1[i+1]=alpha*(ts[i])^rho
beta1[i+1]=beta*(ts[i])^rho}
if(opt=="Pocock"){
alpha1[i+1]=alpha*log(1+(exp(1)-1)*ts[i])
beta1[i+1]=beta*log(1+(exp(1)-1)*ts[i])}
}
alpha1[length(ti)+1]<-alpha
##
if(length(ti)==1){
ub<-qnorm(1-alpha1[2])
lb<-ub
p1<-NULL
p2<-NULL
p1[1]<-pnorm(ub,lower.tail = F)
p2[1]<-pnorm(lb,lower.tail = F)
k1<-NULL
k2<-NULL
k1[1]<-pnorm(ub,lower.tail = F)
k2[1]<-pnorm(lb,mean = etam*sqrt(ts[1]))
posthoc<-1-k2}
else{
tij=c(0, ts)
for (i in 1:(length(ti)+1)) {
for (j in 1:(length(ti)+1)) {
covmatrix[i,j]=min(tij[i],tij[j])/sqrt(tij[i]*tij[j])}}
ub=lb=rep(0,length(ti))
ub[1]=qnorm(1-alpha1[2])
ubi=NULL
for (i in c(2:length(ti))){
ubi=c(ubi,ub[i-1])
ub[i]=uniroot(fx1,lower=-10,upper=10,ub=ubi,
covm=covmatrix[2:(i+1),2:(i+1)],tprob=alpha1[i+1]-alpha1[i])$root}
lb[1]=qnorm(beta1[2])+etam*sqrt(ts[1])
lbi=NULL
for (i in 2:length(ti)) {
lbi=c(lbi,lb[i-1])
lb[i]=uniroot(fx2,lower=-10,upper=10,lb=lbi,etam=etam,ts=ts,
covm=covmatrix[2:(i+1),2:(i+1)],tprob=beta1[i+1]-beta1[i])$root}
lb[length(ti)]<-ub[length(ti)]
p1<-NULL
p2<-NULL
p1[1]<-pnorm(ub[length(ti)],lower.tail = F)
p2[1]<-pnorm(lb[length(ti)],lower.tail = F)
k1<-NULL
k2<-NULL
k1[1]<-pnorm(ub[1],lower.tail = F)
k2[1]<-pnorm(lb[1],mean = etam*sqrt(ts[1]))
for (i in 2:length(lb)){
k1[i]<-mvtnorm::pmvnorm(lower=c(lb[1:(i-1)],ub[i]),upper=c(ub[1:(i-1)],Inf),sigma=covmatrix[2:(i+1),2:(i+1)])[1]
k2[i]<-mvtnorm::pmvnorm(lower=c(lb[1:(i-1)],-Inf),upper=c(ub[1:(i-1)],lb[i]),sigma=covmatrix[2:(i+1),2:(i+1)],mean = etam*sqrt(ts[1:i]))[1]
}
#browser()
if(ts[length(ts)]!=1){
posthoc<-NULL
posthoc[1]<-pnorm(lb[1],mean = etam*sqrt(ts[1]))
for( k in 2:length(lb)){
posthoc[k]<-mvtnorm::pmvnorm(lower = c(lb[k-1],-Inf),upper = c(ub[k-1],lb[k]),mean = etam*sqrt(ts[(k-1):k]),sigma = covmatrix[k:(k+1),k:(k+1)])
}
posthoc<-1-sum(posthoc)}
else{posthoc<-NA}}
}
ans=list(Efficacy=data.frame("Efficacy boundary in z-score scale"=ub[length(ti)],"Efficacy boundary in p-value scale"=p1,check.names = F),Futility=data.frame("Futility boundary in z-score scale"=lb[length(ti)],"Futility boundary in p-value scale"=p2,check.names = F),"Information time"=ts[length(ti)],post_hoc_power=posthoc)
return(ans)
}
IM<-set.defaults(IM,opt="OBF",last.look=FALSE,param=4)
###########################################################
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We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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