Nothing
R/gsSurv.R
In gsDesign: Group Sequential Design
Defines functions
eEvents1
eEvents
periods
print.eEvents
LFPWE
print.nSurv
KTZ
KT
nSurv
gsnSurv
tEventsIA
nEventsIA
gsSurv
print.gsSurv
xtable.gsSurv
Documented in
eEvents
gsSurv
nEventsIA
nSurv
print.eEvents
print.gsSurv
print.nSurv
tEventsIA
xtable.gsSurv
###################################################
### code chunk number 2: eEvents1
###################################################
eEvents1<-function(lambda=1, eta=0, gamma=1, R=1, S=NULL,
T=2, Tfinal=NULL, minfup=0, simple=TRUE)
{
if (is.null(Tfinal))
{ Tfinal <- T
minfupia <- minfup
}
else minfupia <- max(0, minfup-(Tfinal - T))
nlambda <- length(lambda)
if (length(eta)==1 & nlambda > 1)
eta <- array(eta,nlambda)
T1 <- cumsum(S)
T1 <- c(T1[T1<T],T)
T2 <- T - cumsum(R)
T2[T2 < minfupia] <- minfupia
i <- 1:length(gamma)
gamma[i>length(unique(T2))] <- 0
T2 <- unique(c(T,T2[T2 > 0]))
T3 <- sort(unique(c(T1,T2)))
if (sum(R) >= T) T2 <- c(T2,0)
nperiod <- length(T3)
s <- T3-c(0,T3[1:(nperiod-1)])
lam <- array(lambda[nlambda],nperiod)
et <- array(eta[nlambda],nperiod)
gam <- array(0,nperiod)
for(i in length(T1):1)
{ indx <- T3<=T1[i]
lam[indx]<-lambda[i]
et[indx]<-eta[i]
}
for(i in min(length(gamma)+1,length(T2)):2)
gam[T3>T2[i]]<-gamma[i-1]
q <- exp(-(lam+et)*s)
Q <- cumprod(q)
indx<-1:(nperiod-1)
Qm1 <- c(1,Q[indx])
p <- lam/(lam+et)*Qm1*(1-q)
p[is.nan(p)] <- 0
P <- cumsum(p)
B <- gam/(lam+et)*lam*(s-(1-q)/(lam+et))
B[is.nan(B)]<-0
A <- c(0,P[indx])*gam*s+Qm1*B
if (!simple)
return(list(lambda=lambda, eta=eta, gamma=gamma, R=R, S=S,
T=T, Tfinal=Tfinal, minfup=minfup, d=sum(A),
n=sum(gam*s), q=q,Q=Q,p=p,P=P,B=B,A=A,T1=T1,
T2=T2,T3=T3,lam=lam,et=et,gam=gam))
else
return(list(lambda=lambda, eta=eta, gamma=gamma, R=R, S=S,
T=T, Tfinal=Tfinal, minfup=minfup, d=sum(A),
n=sum(gam*s)))
}
###################################################
### code chunk number 4: eEvents
###################################################
eEvents<-function(lambda=1, eta=0, gamma=1, R=1, S=NULL, T=2,
Tfinal=NULL, minfup=0, digits=4)
{ if (is.null(Tfinal))
{ if (minfup >= T)
stop("Minimum follow-up greater than study duration.")
Tfinal <- T
minfupia <- minfup
}
else minfupia <- max(0, minfup-(Tfinal - T))
if (!is.matrix(lambda))
lambda <- matrix(lambda, nrow=length(lambda))
if (!is.matrix(eta))
eta <- matrix(eta,nrow=nrow(lambda),ncol=ncol(lambda))
if (!is.matrix(gamma))
gamma<-matrix(gamma,nrow=length(R),ncol=ncol(lambda))
n <- array(0,ncol(lambda))
d <- n
for(i in 1:ncol(lambda))
{ a <- eEvents1(lambda=lambda[,i],eta=eta[,i],
gamma=gamma[,i],R=R,S=S,T=T,
Tfinal=Tfinal, minfup=minfup)
n[i]<-a$n
d[i]<-a$d
}
T1 <- cumsum(S)
T1 <- unique(c(0,T1[T1<T],T))
nper <- length(T1)-1
names1 <- round(T1[1:nper],digits)
namesper <- paste("-",round(T1[2:(nper+1)],digits),sep="")
namesper <- paste(names1,namesper,sep="")
if (nper < dim(lambda)[1])
lambda <- matrix(lambda[1:nper,],nrow=nper)
if (nper < dim(eta)[1])
eta <- matrix(eta[1:nper,],nrow=nper)
rownames(lambda) <- namesper
rownames(eta) <- namesper
colnames(lambda) <- paste("Stratum",1:ncol(lambda))
colnames(eta) <- paste("Stratum",1:ncol(eta))
T2 <- cumsum(R)
T2[T - T2 < minfupia] <- T - minfupia
T2 <- unique(c(0,T2))
nper <- length(T2)-1
names1 <- round(c(T2[1:nper]),digits)
namesper <- paste("-",round(T2[2:(nper+1)],digits),sep="")
namesper <- paste(names1,namesper,sep="")
if (nper < length(gamma))
gamma <- matrix(gamma[1:nper,],nrow=nper)
rownames(gamma) <- namesper
colnames(gamma) <- paste("Stratum",1:ncol(gamma))
x <- list(lambda=lambda, eta=eta, gamma=gamma, R=R,
S=S, T=T, Tfinal=Tfinal,
minfup=minfup, d=d, n=n, digits=digits)
class(x) <- "eEvents"
return(x)
}
###################################################
### code chunk number 5: periods
###################################################
periods <- function(S, T, minfup, digits)
{ periods <- cumsum(S)
if (length(periods)==0) periods <- max(0, T - minfup)
else
{ maxT <- max(0,min(T - minfup, max(periods)))
periods <- periods[periods <= maxT]
if (max(periods) < T - minfup)
periods <- c(periods, T - minfup)
}
nper <- length(periods)
names1 <- c(0, round(periods[1:(nper-1)],digits))
names <- paste("-",periods,sep="")
names <- paste(names1,names,sep="")
return(list(periods,names))
}
###################################################
### code chunk number 6: print.eEvents
###################################################
print.eEvents <- function(x,digits=4,...){
if (class(x) != "eEvents")
stop("print.eEvents: primary argument must have class eEvents")
cat("Study duration: Tfinal=",
round(x$Tfinal,digits), "\n", sep="")
cat("Analysis time: T=",
round(x$T,digits), "\n", sep="")
cat("Accrual duration: ",
round(min(x$T - max(0, x$minfup-(x$Tfinal - x$T)),
sum(x$R)),digits), "\n", sep="")
cat("Min. end-of-study follow-up: minfup=",
round(x$minfup,digits), "\n", sep="")
cat("Expected events (total): ",
round(sum(x$d),digits), "\n",sep="")
if (length(x$d)>1)
{ cat("Expected events by stratum: d=",
round(x$d[1],digits))
for(i in 2:length(x$d))
cat(paste("",round(x$d[i],digits)))
cat("\n")
}
cat("Expected sample size (total): ",
round(sum(x$n),digits), "\n", sep="")
if (length(x$n)>1)
{ cat("Sample size by stratum: n=",
round(x$n[1],digits))
for(i in 2:length(x$n))
cat(paste("",round(x$n[i],digits)))
cat("\n")
}
nstrata <- dim(x$lambda)[2]
cat("Number of strata: ",
nstrata, "\n", sep="")
cat("Accrual rates:\n")
print(round(x$gamma,digits))
cat("Event rates:\n")
print(round(x$lambda,digits))
cat("Censoring rates:\n")
print(round(x$eta,digits))
return(x)
}
###################################################
### code chunk number 12: nameperiod
###################################################
"nameperiod" <- function(R, digits=2)
{ if (length(R)==1) return(paste("0-",round(R,digits),sep=""))
R0 <- c(0,R[1:(length(R)-1)])
return(paste(round(R0,digits),"-",round(R,digits),sep=""))
}
###################################################
### code chunk number 14: LFPWE
###################################################
LFPWE <- function(alpha=.025, sided=1, beta=.1,
lambdaC=log(2) / 6, hr=.5, hr0=1, etaC=0, etaE=0,
gamma=1, ratio=1, R=18, S=NULL, T=24, minfup=NULL)
{ # set up parameters
zalpha <- -qnorm(alpha/sided)
zbeta <- -qnorm(beta)
if (is.null(minfup)) minfup <- max(0,T-sum(R))
if (length(R)==1) {R <- T-minfup
}else if (sum(R) != T-minfup)
{ cR<-cumsum(R)
nR<-length(R)
if (cR[length(cR)] < T - minfup) {cR[length(cR)]<-T-minfup
}else
{ cR[cR>T-minfup]<-T-minfup
cR <- unique(cR)
}
if (length(cR)>1) {R <- cR-c(0,cR[1:(length(cR)-1)])
}else R <- cR
if (nR != length(R))
{ if (is.vector(gamma)) {gamma <- gamma[1:length(R)]
}else gamma<-gamma[1:length(R),]
}
}
ngamma <- length(R)
if (is.null(S)) {nlambda <- 1
}else nlambda <- length(S) + 1
Qe <- ratio / (1 + ratio)
Qc <- 1 - Qe
# compute H0 failure rates as average of control, experimental
if (length(ratio)==1){
lambdaC0 <- (1 + hr * ratio) / (1 + hr0 * ratio) * lambdaC
gammaC <- gamma*Qc
gammaE <- gamma*Qe
}else{
lambdaC0 <- lambdaC %*% diag((1 + hr * ratio) / (1 + hr0 * ratio))
gammaC <- gamma%*%diag(Qc)
gammaE <- gamma%*%diag(Qe)
}
# do computations
eDC0 <- sum(eEvents(lambda=lambdaC0, eta=etaC, gamma=gammaC,
R=R, S=S, T=T, minfup=minfup)$d)
eDE0 <- sum(eEvents(lambda=lambdaC0 * hr0, eta=etaE, gamma=gammaE,
R=R, S=S, T=T, minfup=minfup)$d)
eDC <- eEvents(lambda=lambdaC, eta=etaC, gamma=gammaC,
R=R, S=S, T=T, minfup=minfup)
eDE <- eEvents(lambda=lambdaC * hr, eta=etaE, gamma=gammaE,
R=R, S=S, T=T, minfup=minfup)
n <- ((zalpha * sqrt(1 / eDC0 + 1 / eDE0) +
zbeta * sqrt(1 / sum(eDC$d) + 1 / sum(eDE$d))
) / log(hr / hr0))^2
mx <- sum(eDC$n + eDE$n)
rval <- list(alpha=alpha, sided=sided, beta=beta, power=1-beta,
lambdaC=lambdaC, etaC=etaC, etaE=etaE, gamma=n * gamma,
ratio=ratio, R=R, S=S, T=T, minfup=minfup,
hr=hr, hr0=hr0, n=n * mx, d=n * sum(eDC$d + eDE$d),
eDC=eDC$d*n, eDE=eDE$d*n, eDC0=eDC0*n, eDE0=eDE0*n,
eNC=eDC$n*n, eNE=eDE$n*n, variable="Accrual rate")
class(rval) <- "nSurv"
return(rval)
}
print.nSurv<-function(x,digits=4,...){
if (class(x) != "nSurv")
stop("Primary argument must have class nSurv")
x$digits<-digits
x$sided <- 1
cat("Fixed design, two-arm trial with time-to-event\n")
cat("outcome (Lachin and Foulkes, 1986).\n")
cat("Solving for: ",x$variable,"\n")
cat("Hazard ratio H1/H0=",
round(x$hr,digits),
"/", round(x$hr0,digits),"\n",sep="")
cat("Study duration: T=",
round(x$T,digits), "\n", sep="")
cat("Accrual duration: ",
round(x$T-x$minfup,digits),"\n",sep="")
cat("Min. end-of-study follow-up: minfup=",
round(x$minfup,digits), "\n", sep="")
cat("Expected events (total, H1): ",
round(x$d,digits), "\n",sep="")
cat("Expected sample size (total): ",
round(x$n,digits), "\n", sep="")
enrollper <- periods(x$S, x$T, x$minfup, x$digits)
cat("Accrual rates:\n")
print(round(x$gamma,digits))
cat("Control event rates (H1):\n")
print(round(x$lambda,digits))
if (max(abs(x$etaC-x$etaE))==0)
{ cat("Censoring rates:\n")
print(round(x$etaC,digits))
}
else
{ cat("Control censoring rates:\n")
print(round(x$etaC,digits))
cat("Experimental censoring rates:\n")
print(round(x$etaE,digits))
}
cat("Power: 100*(1-beta)=",
round((1-x$beta)*100,digits), "%\n",sep="")
cat("Type I error (", x$sided,
"-sided): 100*alpha=",
100*x$alpha, "%\n", sep="")
if (min(x$ratio==1)==1)
cat("Equal randomization: ratio=1\n")
else cat("Randomization (Exp/Control): ratio=",
x$ratio, "\n")
}
###################################################
### code chunk number 19: KTZ
###################################################
KTZ <- function(x=NULL, minfup=NULL, n1Target=NULL,
lambdaC=log(2) / 6, etaC=0, etaE=0,
gamma=1, ratio=1, R=18, S=NULL, beta=.1,
alpha=.025, sided=1, hr0=1, hr=.5, simple=TRUE)
{ zalpha<- -qnorm(alpha/sided)
Qc <- 1/(1+ratio)
Qe <- 1 - Qc
# set minimum follow-up to x if that is missing and x is given
if (!is.null(x) && is.null(minfup))
{ minfup <- x
if (sum(R)==Inf)
stop("If minimum follow-up is sought, enrollment duration must be finite")
T <- sum(R)+minfup
variable <- "Follow-up duration"
}
else if (!is.null(x)&&!is.null(minfup))
{ # otherwise, if x is given, set it to accrual duration
T <- x+minfup
R[length(R)]<-Inf
variable <- "Accrual duration"
}
else
{ # otherwise, set follow-up time to accrual plus follow-up
T <- sum(R) + minfup
variable <- "Power"
}
# compute H0 failure rates as average of control, experimental
if (length(ratio)==1){
lambdaC0 <- (1 + hr * ratio) / (1 + hr0 * ratio) * lambdaC
gammaC <- gamma*Qc
gammaE <- gamma*Qe
}else{
lambdaC0 <- lambdaC %*% diag((1 + hr * ratio) / (1 + hr0 * ratio))
gammaC <- gamma%*%diag(Qc)
gammaE <- gamma%*%diag(Qe)
}
# do computations
eDC <- eEvents(lambda=lambdaC, eta=etaC, gamma=gammaC,
R=R, S=S, T=T, minfup=minfup)
eDE <- eEvents(lambda=lambdaC * hr, eta=etaE, gamma=gammaE,
R=R, S=S, T=T, minfup=minfup)
# if this is all that is needed, return difference
# from targeted number of events
if (simple && !is.null(n1Target))
return(sum(eDC$d+eDE$d)-n1Target)
eDC0 <- eEvents(lambda=lambdaC0, eta=etaC, gamma=gammaC,
R=R, S=S, T=T, minfup=minfup)
eDE0 <- eEvents(lambda=lambdaC0 * hr0, eta=etaE, gamma=gammaE,
R=R, S=S, T=T, minfup=minfup)
# compute Z-value related to power from power equation
zb <- (log(hr0 / hr) -
zalpha * sqrt(1 / sum(eDC0$d) + 1 / sum(eDE0$d)))/
sqrt(1 / sum(eDC$d) + 1 / sum(eDE$d))
# if that is all that is needed, return difference from
# targeted value
if (simple)
{ if (!is.null(beta)) return(zb + qnorm(beta))
else return(pnorm(-zb))
}
# compute power
power <- pnorm(zb)
beta <- 1-power
# set accrual period durations
if (sum(R) != T-minfup)
{ if (length(R)==1) R <- T-minfup
else
{ nR <- length(R)
cR <- cumsum(R)
cR[cR>T-minfup] <- T - minfup
cR <- unique(cR)
cR[length(R)] <- T - minfup
if (length(cR)==1) R <- cR
else R <- cR - c(0,cR[1:(length(cR)-1)])
if (length(R) != nR)
{ gamma <- matrix(gamma[1:length(R),], nrow=length(R))
gdim <- dim(gamma)
}
}
}
rval <- list(alpha=alpha, sided=sided, beta=beta, power=power,
lambdaC=lambdaC, etaC=etaC, etaE=etaE,
gamma=gamma, ratio=ratio, R=R, S=S, T=T,
minfup=minfup, hr=hr, hr0=hr0, n=sum(eDC$n + eDE$n),
d=sum(eDC$d + eDE$d), tol=NULL, eDC=eDC$d, eDE=eDE$d,
eDC0=eDC0$d, eDE0=eDE0$d, eNC=eDC$n, eNE=eDE$n,
variable=variable)
class(rval)<-"nSurv"
return(rval)
}
###################################################
### code chunk number 21: KT
###################################################
KT <- function(alpha=.025, sided=1, beta=.1,
lambdaC=log(2) / 6, hr=.5, hr0=1, etaC=0, etaE=0,
gamma=1, ratio=1, R=18, S=NULL, minfup=NULL,
n1Target=NULL, tol = .Machine$double.eps^0.25)
{ # set up parameters
ngamma <- length(R)
if (is.null(S)) {nlambda <- 1
}else nlambda <- length(S) + 1
Qe <- ratio / (1 + ratio)
Qc <- 1 - Qe
if (!is.matrix(lambdaC)) lambdaC <- matrix(lambdaC)
ldim <- dim(lambdaC)
nstrata <- ldim[2]
nlambda <- ldim[1]
etaC <- matrix(etaC,nrow=nlambda,ncol=nstrata)
etaE <- matrix(etaE,nrow=nlambda,ncol=nstrata)
if (!is.matrix(gamma)) gamma <- matrix(gamma)
gdim <- dim(gamma)
eCdim <- dim(etaC)
eEdim <- dim(etaE)
# search for trial duration needed to achieve desired power
if (is.null(minfup))
{ if (sum(R)==Inf){
stop("Enrollment duration must be specified as finite")}
left <- KTZ(.01, lambdaC=lambdaC, n1Target=n1Target,
etaC=etaC, etaE=etaE, gamma=gamma, ratio=ratio,
R=R, S=S, beta=beta, alpha=alpha, sided=sided,
hr0=hr0, hr=hr)
right <- KTZ(1000, lambdaC=lambdaC, n1Target=n1Target,
etaC=etaC, etaE=etaE, gamma=gamma, ratio=ratio,
R=R, S=S, beta=beta, alpha=alpha, sided=sided,
hr0=hr0, hr=hr)
if (left>0) stop("Enrollment duration over-powers trial")
if (right<0) stop("Enrollment duration insufficient to power trial")
y <- uniroot(f=KTZ,interval=c(.01,10000), lambdaC=lambdaC,
etaC=etaC, etaE=etaE, gamma=gamma, ratio=ratio,
R=R, S=S, beta=beta, alpha=alpha, sided=sided,
hr0=hr0, hr=hr, tol=tol, n1Target=n1Target)
minfup <- y$root
xx<-KTZ(x=y$root,lambdaC=lambdaC,
etaC=etaC, etaE=etaE, gamma=gamma, ratio=ratio,
R=R, S=S, minfup=NULL, beta=beta, alpha=alpha,
sided=sided, hr0=hr0, hr=hr, simple=F)
xx$tol <- tol
return(xx)
}else
{ y <- uniroot(f=KTZ, interval=minfup+c(.01,10000), lambdaC=lambdaC,
n1Target=n1Target,
etaC=etaC, etaE=etaE, gamma=gamma, ratio=ratio,
R=R, S=S, minfup=minfup, beta=beta,
alpha=alpha, sided=sided, hr0=hr0, hr=hr, tol=tol)
xx <- KTZ(x=y$root,lambdaC=lambdaC,
etaC=etaC, etaE=etaE, gamma=gamma, ratio=ratio,
R=R, S=S, minfup=minfup, beta=beta, alpha=alpha,
sided=sided, hr0=hr0, hr=hr, simple=F)
xx$tol<-tol
return(xx)
}
}
###################################################
### code chunk number 25: nSurv
###################################################
nSurv <- function(lambdaC=log(2)/6, hr=.6, hr0=1, eta = 0, etaE=NULL,
gamma=1, R=12, S=NULL, T=NULL, minfup = NULL, ratio = 1,
alpha = 0.025, beta = 0.10, sided = 1, tol = .Machine$double.eps^0.25)
{ if (is.null(etaE)) etaE<-eta
# set up rates as matrices with row and column names
# default is 1 stratum if lambdaC not input as matrix
if (is.vector(lambdaC)) lambdaC <- matrix(lambdaC)
ldim <- dim(lambdaC)
nstrata <- ldim[2]
nlambda <- ldim[1]
rownames(lambdaC) <- paste("Period", 1:nlambda)
colnames(lambdaC) <- paste("Stratum", 1:nstrata)
etaC <- matrix(eta,nrow=nlambda,ncol=nstrata)
etaE <- matrix(etaE,nrow=nlambda,ncol=nstrata)
if (!is.matrix(gamma)) gamma <- matrix(gamma)
gdim <- dim(gamma)
eCdim <- dim(etaC)
eEdim <- dim(etaE)
if (is.null(minfup) || is.null(T))
xx<-KT(lambdaC=lambdaC, hr=hr, hr0=hr0, etaC=etaC, etaE=etaE,
gamma=gamma, R=R, S=S, minfup = minfup, ratio = ratio,
alpha=alpha, sided=sided, beta = beta, tol = tol)
else if (is.null(beta))
xx<-KTZ(lambdaC=lambdaC, hr=hr, hr0=hr0, etaC=etaC, etaE=etaE,
gamma=gamma, R=R, S=S, minfup = minfup, ratio = ratio,
alpha=alpha, sided=sided, beta = beta, simple=F)
else
xx<-LFPWE(lambdaC=lambdaC, hr=hr, hr0=hr0, etaC=etaC, etaE=etaE,
gamma=gamma, R=R, S=S, T=T, minfup = minfup, ratio = ratio,
alpha=alpha, sided=sided, beta = beta)
nameR<-nameperiod(cumsum(xx$R))
stratnames <- paste("Stratum",1:ncol(xx$lambdaC))
if (is.null(xx$S)) nameS<-"0-Inf"
else nameS <- nameperiod(cumsum(c(xx$S,Inf)))
rownames(xx$lambdaC)<-nameS
colnames(xx$lambdaC)<-stratnames
rownames(xx$etaC)<-nameS
colnames(xx$etaC)<-stratnames
rownames(xx$etaE)<-nameS
colnames(xx$etaE)<-stratnames
rownames(xx$gamma)<-nameR
colnames(xx$gamma)<-stratnames
return(xx)
}
###################################################
### code chunk number 33: gsnSurv
###################################################
gsnSurv <- function(x,nEvents)
{ if (x$variable=="Accrual rate")
{ Ifct <- nEvents/x$d
rval <- list(lambdaC=x$lambdaC, etaC=x$etaC, etaE=x$etaE,
gamma=x$gamma*Ifct, ratio=x$ratio, R=x$R, S=x$S, T=x$T,
minfup=x$minfup, hr=x$hr, hr0=x$hr0, n=x$n*Ifct, d=nEvents,
eDC=x$eDC*Ifct,eDE=x$eDE*Ifct,eDC0=x$eDC0*Ifct,
eDE0=x$eDE0*Ifct,eNC=x$eNC*Ifct,eNE=x$eNE*Ifct,
variable=x$variable)
}
else if (x$variable=="Accrual duration")
{ y<-KT(n1Target=nEvents,minfup=x$minfup,lambdaC=x$lambdaC,etaC=x$etaC,
etaE=x$etaE,R=x$R,S=x$S,hr=x$hr,hr0=x$hr0,gamma=x$gamma,
ratio=x$ratio,tol=x$tol)
rval <- list(lambdaC=x$lambdaC, etaC=x$etaC, etaE=x$etaE,
gamma=x$gamma, ratio=x$ratio, R=y$R, S=x$S, T=y$T,
minfup=y$minfup, hr=x$hr, hr0=x$hr0, n=y$n, d=nEvents,
eDC=y$eDC,eDE=y$eDE,eDC0=y$eDC0,
eDE0=y$eDE0,eNC=y$eNC,eNE=y$eNE,tol=x$tol,
variable=x$variable)
}
else
{ y<-KT(n1Target=nEvents,minfup=NULL,lambdaC=x$lambdaC,etaC=x$etaC,
etaE=x$etaE,R=x$R,S=x$S,hr=x$hr,hr0=x$hr0,gamma=x$gamma,
ratio=x$ratio,tol=x$tol)
rval <- list(lambdaC=x$lambdaC, etaC=x$etaC, etaE=x$etaE,
gamma=x$gamma, ratio=x$ratio, R=x$R, S=x$S, T=y$T,
minfup=y$minfup, hr=x$hr, hr0=x$hr0, n=y$n, d=nEvents,
eDC=y$eDC,eDE=y$eDE,eDC0=y$eDC0,
eDE0=y$eDE0,eNC=y$eNC,eNE=y$eNE,tol=x$tol,
variable=x$variable)
}
class(rval) <- "gsSize"
return(rval)
}
###################################################
### code chunk number 35: tEventsIA
###################################################
tEventsIA<-function(x, timing=.25, tol = .Machine$double.eps^0.25)
{ T <- x$T[length(x$T)]
z <- uniroot(f=nEventsIA, interval=c(0.0001,T-.0001), x=x,
target=timing, tol=tol,simple=TRUE)
return(nEventsIA(tIA=z$root,x=x,simple=FALSE))
}
nEventsIA <- function(tIA=5, x=NULL, target=0, simple=TRUE)
{ Qe <- x$ratio/(1+x$ratio)
eDC <- eEvents(lambda=x$lambdaC, eta=x$etaC,
gamma=x$gamma*(1-Qe), R=x$R, S=x$S, T=tIA,
Tfinal=x$T[length(x$T)], minfup=x$minfup)
eDE <- eEvents(lambda=x$lambdaC * x$hr, eta=x$etaC,
gamma=x$gamma*Qe, R=x$R, S=x$S, T=tIA,
Tfinal=x$T[length(x$T)], minfup=x$minfup)
if (simple)
{ if (class(x)[1] == "gsSize") d<-x$d
#OLD else d <- sum(x$eDC[length(x$eDC)]+x$eDE[length(x$eDE)])
else if(!is.matrix(x$eDC)) d <- sum(x$eDC[length(x$eDC)]+x$eDE[length(x$eDE)])
else d <- sum(x$eDC[nrow(x$eDC),]+x$eDE[nrow(x$eDE),])
return(sum(eDC$d+eDE$d)-target*d)
}
else return(list(T=tIA,eDC=eDC$d,eDE=eDE$d,eNC=eDC$n,eNE=eDE$n))
}
###################################################
### code chunk number 36: gsSurv
###################################################
gsSurv<-function(k=3, test.type=4, alpha=0.025, sided=1,
beta=0.1, astar=0, timing=1, sfu=sfHSD, sfupar=-4,
sfl=sfHSD, sflpar=-2, r=18,
lambdaC=log(2)/6, hr=.6, hr0=1, eta=0, etaE=NULL,
gamma=1, R=12, S=NULL, T=NULL, minfup=NULL, ratio=1,
tol = .Machine$double.eps^0.25)
{ x<-nSurv(lambdaC=lambdaC, hr=hr, hr0=hr0, eta = eta, etaE=etaE,
gamma=gamma, R=R, S=S, T=T, minfup = minfup, ratio = ratio,
alpha = alpha, beta = beta, sided = sided, tol = tol)
y<-gsDesign(k=k,test.type=test.type,alpha=alpha/sided,
beta=beta, astar=astar, n.fix=x$d, timing=timing,
sfu=sfu, sfupar=sfupar, sfl=sfl, sflpar=sflpar, tol=tol,
delta1=log(hr), delta0=log(hr0))
z<-gsnSurv(x,y$n.I[k])
eDC <- NULL
eDE <- NULL
eNC <- NULL
eNE <- NULL
T <- NULL
for(i in 1:(k-1)){
xx <- tEventsIA(z,y$timing[i],tol)
T <- c(T,xx$T)
eDC <- rbind(eDC,xx$eDC)
eDE <- rbind(eDE,xx$eDE)
eNC <- rbind(eNC,xx$eNC)
eNE <- rbind(eNE,xx$eNE)
}
y$T <- c(T,z$T)
y$eDC <- rbind(eDC,z$eDC)
y$eDE <- rbind(eDE,z$eDE)
y$eNC <- rbind(eNC,z$eNC)
y$eNE <- rbind(eNE,z$eNE)
y$hr=hr; y$hr0=hr0; y$R=z$R; y$S=z$S; y$minfup=z$minfup;
y$gamma=z$gamma; y$ratio=ratio; y$lambdaC=z$lambdaC;
y$etaC=z$etaC; y$etaE=z$etaE; y$variable=x$variable; y$tol=tol
class(y) <- c("gsSurv","gsDesign")
nameR<-nameperiod(cumsum(y$R))
stratnames <- paste("Stratum",1:ncol(y$lambdaC))
if (is.null(y$S)) nameS<-"0-Inf"
else nameS <- nameperiod(cumsum(c(y$S,Inf)))
rownames(y$lambdaC)<-nameS
colnames(y$lambdaC)<-stratnames
rownames(y$etaC)<-nameS
colnames(y$etaC)<-stratnames
rownames(y$etaE)<-nameS
colnames(y$etaE)<-stratnames
rownames(y$gamma)<-nameR
colnames(y$gamma)<-stratnames
return(y)
}
print.gsSurv<-function(x,digits=2,...){
cat("Time to event group sequential design with HR=",x$hr,"\n")
if (x$hr0 != 1) cat("Non-inferiority design with null HR=",x$hr0,"\n")
if (min(x$ratio==1)==1)
cat("Equal randomization: ratio=1\n")
else {cat("Randomization (Exp/Control): ratio=",
x$ratio, "\n")
if (length(x$ratio)>1) cat("(randomization ratios shown by strata)\n")
}
print.gsDesign(x)
if(x$test.type != 1){
y<-cbind(x$T,(x$eNC+x$eNE)%*%array(1,ncol(x$eNE)),
(x$eDC+x$eDE)%*%array(1,ncol(x$eNE)),
round(zn2hr(x$lower$bound,x$n.I,x$ratio,hr0=x$hr0,hr1=x$hr),3),
round(zn2hr(x$upper$bound,x$n.I,x$ratio,hr0=x$hr0,hr1=x$hr),3))
colnames(y)<-c("T","n","Events","HR futility","HR efficacy")
}else{
y<-cbind(x$T,(x$eNC+x$eNE)%*%array(1,ncol(x$eNE)),
(x$eDC+x$eDE)%*%array(1,ncol(x$eNE)),
round(zn2hr(x$upper$bound,x$n.I,x$ratio,hr0=x$hr0,hr1=x$hr),3))
colnames(y)<-c("T","n","Events","HR efficacy")
}
rnames<-paste("IA",1:(x$k))
rnames[length(rnames)]<-"Final"
rownames(y)<-rnames
print(y)
cat("Accrual rates:\n")
print(round(x$gamma,digits))
cat("Control event rates (H1):\n")
print(round(x$lambda,digits))
if (max(abs(x$etaC-x$etaE))==0)
{ cat("Censoring rates:\n")
print(round(x$etaC,digits))
}
else
{ cat("Control censoring rates:\n")
print(round(x$etaC,digits))
cat("Experimental censoring rates:\n")
print(round(x$etaE,digits))
}
}
xtable.gsSurv <- function(x, caption=NULL, label=NULL, align=NULL, digits=NULL,
display=NULL, auto=FALSE, footnote=NULL, fnwid="9cm", timename="months",...){
k <- x$k
stat <- c("Z-value","HR","p (1-sided)", paste("P\\{Cross\\} if HR=",x$hr0,sep=""),
paste("P\\{Cross\\} if HR=",x$hr,sep=""))
st <- stat
for (i in 2:k) stat <- c(stat,st)
an <- array(" ",5*k)
tim <- an
enrol <- an
fut <- an
eff <- an
an[5*(0:(k-1))+1]<-c(paste("IA ",as.character(1:(k-1)),": ",
as.character(round(100*x$timing[1:(k-1)],1)), "\\%",sep=""), "Final analysis")
an[5*(1:(k-1))+1] <- paste("\\hline",an[5*(1:(k-1))+1])
an[5*(0:(k-1))+2]<- paste("N:",ceiling(rowSums(x$eNC))+ceiling(rowSums(x$eNE)))
an[5*(0:(k-1))+3]<- paste("Events:",ceiling(rowSums(x$eDC+x$eDE)))
an[5*(0:(k-1))+4]<- paste(round(x$T,1),timename,sep=" ")
if (x$test.type != 1) fut[5*(0:(k-1))+1]<- as.character(round(x$lower$bound,2))
eff[5*(0:(k-1))+1]<- as.character(round(x$upper$bound,2))
if (x$test.type != 1) fut[5*(0:(k-1))+2]<- as.character(round(gsHR(z=x$lower$bound,i=1:k,x,ratio=x$ratio)*x$hr0,2))
eff[5*(0:(k-1))+2]<- as.character(round(gsHR(z=x$upper$bound,i=1:k,x,ratio=x$ratio)*x$hr0,2))
asp <- as.character(round(pnorm(-x$upper$bound),4))
asp[asp=="0"]<-"$< 0.0001$"
eff[5*(0:(k-1))+3] <- asp
asp <- as.character(round(cumsum(x$upper$prob[,1]),4))
asp[asp=="0"]<-"$< 0.0001$"
eff[5*(0:(k-1))+4] <- asp
asp <- as.character(round(cumsum(x$upper$prob[,2]),4))
asp[asp=="0"]<-"$< 0.0001$"
eff[5*(0:(k-1))+5] <- asp
if (x$test.type != 1) {
bsp <- as.character(round(pnorm(-x$lower$bound),4))
bsp[bsp=="0"]<-" $< 0.0001$"
fut[5*(0:(k-1))+3] <- bsp
bsp <- as.character(round(cumsum(x$lower$prob[,1]),4))
bsp[bsp=="0"]<-"$< 0.0001$"
fut[5*(0:(k-1))+4] <- bsp
bsp <- as.character(round(cumsum(x$lower$prob[,2]),4))
bsp[bsp=="0"]<-"$< 0.0001$"
fut[5*(0:(k-1))+5] <- bsp
}
neff <- length(eff)
if (!is.null(footnote)) eff[neff] <-
paste(eff[neff],"\\\\ \\hline \\multicolumn{4}{p{",fnwid,"}}{\\footnotesize",footnote,"}")
if (x$test.type != 1){
xxtab <- data.frame(cbind(an,stat,fut,eff))
colnames(xxtab) <- c("Analysis","Value","Futility","Efficacy")
}else{
xxtab <- data.frame(cbind(an,stat,eff))
colnames(xxtab) <- c("Analysis","Value","Efficacy")
}
return(xtable(xxtab, caption=caption, label=label, align=align, digits=digits,
display=display,auto=auto,...))
}
Try the gsDesign package in your browser
Any scripts or data that you put into this service are public.
gsDesign documentation built on May 2, 2019, 4:49 p.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 eEvents1 eEvents periods print.eEvents LFPWE print.nSurv KTZ KT nSurv gsnSurv tEventsIA nEventsIA gsSurv print.gsSurv xtable.gsSurv
Documented in eEvents gsSurv nEventsIA nSurv print.eEvents print.gsSurv print.nSurv tEventsIA xtable.gsSurv
###################################################
### code chunk number 2: eEvents1
###################################################
eEvents1<-function(lambda=1, eta=0, gamma=1, R=1, S=NULL,
T=2, Tfinal=NULL, minfup=0, simple=TRUE)
{
if (is.null(Tfinal))
{ Tfinal <- T
minfupia <- minfup
}
else minfupia <- max(0, minfup-(Tfinal - T))
nlambda <- length(lambda)
if (length(eta)==1 & nlambda > 1)
eta <- array(eta,nlambda)
T1 <- cumsum(S)
T1 <- c(T1[T1<T],T)
T2 <- T - cumsum(R)
T2[T2 < minfupia] <- minfupia
i <- 1:length(gamma)
gamma[i>length(unique(T2))] <- 0
T2 <- unique(c(T,T2[T2 > 0]))
T3 <- sort(unique(c(T1,T2)))
if (sum(R) >= T) T2 <- c(T2,0)
nperiod <- length(T3)
s <- T3-c(0,T3[1:(nperiod-1)])
lam <- array(lambda[nlambda],nperiod)
et <- array(eta[nlambda],nperiod)
gam <- array(0,nperiod)
for(i in length(T1):1)
{ indx <- T3<=T1[i]
lam[indx]<-lambda[i]
et[indx]<-eta[i]
}
for(i in min(length(gamma)+1,length(T2)):2)
gam[T3>T2[i]]<-gamma[i-1]
q <- exp(-(lam+et)*s)
Q <- cumprod(q)
indx<-1:(nperiod-1)
Qm1 <- c(1,Q[indx])
p <- lam/(lam+et)*Qm1*(1-q)
p[is.nan(p)] <- 0
P <- cumsum(p)
B <- gam/(lam+et)*lam*(s-(1-q)/(lam+et))
B[is.nan(B)]<-0
A <- c(0,P[indx])*gam*s+Qm1*B
if (!simple)
return(list(lambda=lambda, eta=eta, gamma=gamma, R=R, S=S,
T=T, Tfinal=Tfinal, minfup=minfup, d=sum(A),
n=sum(gam*s), q=q,Q=Q,p=p,P=P,B=B,A=A,T1=T1,
T2=T2,T3=T3,lam=lam,et=et,gam=gam))
else
return(list(lambda=lambda, eta=eta, gamma=gamma, R=R, S=S,
T=T, Tfinal=Tfinal, minfup=minfup, d=sum(A),
n=sum(gam*s)))
}
###################################################
### code chunk number 4: eEvents
###################################################
eEvents<-function(lambda=1, eta=0, gamma=1, R=1, S=NULL, T=2,
Tfinal=NULL, minfup=0, digits=4)
{ if (is.null(Tfinal))
{ if (minfup >= T)
stop("Minimum follow-up greater than study duration.")
Tfinal <- T
minfupia <- minfup
}
else minfupia <- max(0, minfup-(Tfinal - T))
if (!is.matrix(lambda))
lambda <- matrix(lambda, nrow=length(lambda))
if (!is.matrix(eta))
eta <- matrix(eta,nrow=nrow(lambda),ncol=ncol(lambda))
if (!is.matrix(gamma))
gamma<-matrix(gamma,nrow=length(R),ncol=ncol(lambda))
n <- array(0,ncol(lambda))
d <- n
for(i in 1:ncol(lambda))
{ a <- eEvents1(lambda=lambda[,i],eta=eta[,i],
gamma=gamma[,i],R=R,S=S,T=T,
Tfinal=Tfinal, minfup=minfup)
n[i]<-a$n
d[i]<-a$d
}
T1 <- cumsum(S)
T1 <- unique(c(0,T1[T1<T],T))
nper <- length(T1)-1
names1 <- round(T1[1:nper],digits)
namesper <- paste("-",round(T1[2:(nper+1)],digits),sep="")
namesper <- paste(names1,namesper,sep="")
if (nper < dim(lambda)[1])
lambda <- matrix(lambda[1:nper,],nrow=nper)
if (nper < dim(eta)[1])
eta <- matrix(eta[1:nper,],nrow=nper)
rownames(lambda) <- namesper
rownames(eta) <- namesper
colnames(lambda) <- paste("Stratum",1:ncol(lambda))
colnames(eta) <- paste("Stratum",1:ncol(eta))
T2 <- cumsum(R)
T2[T - T2 < minfupia] <- T - minfupia
T2 <- unique(c(0,T2))
nper <- length(T2)-1
names1 <- round(c(T2[1:nper]),digits)
namesper <- paste("-",round(T2[2:(nper+1)],digits),sep="")
namesper <- paste(names1,namesper,sep="")
if (nper < length(gamma))
gamma <- matrix(gamma[1:nper,],nrow=nper)
rownames(gamma) <- namesper
colnames(gamma) <- paste("Stratum",1:ncol(gamma))
x <- list(lambda=lambda, eta=eta, gamma=gamma, R=R,
S=S, T=T, Tfinal=Tfinal,
minfup=minfup, d=d, n=n, digits=digits)
class(x) <- "eEvents"
return(x)
}
###################################################
### code chunk number 5: periods
###################################################
periods <- function(S, T, minfup, digits)
{ periods <- cumsum(S)
if (length(periods)==0) periods <- max(0, T - minfup)
else
{ maxT <- max(0,min(T - minfup, max(periods)))
periods <- periods[periods <= maxT]
if (max(periods) < T - minfup)
periods <- c(periods, T - minfup)
}
nper <- length(periods)
names1 <- c(0, round(periods[1:(nper-1)],digits))
names <- paste("-",periods,sep="")
names <- paste(names1,names,sep="")
return(list(periods,names))
}
###################################################
### code chunk number 6: print.eEvents
###################################################
print.eEvents <- function(x,digits=4,...){
if (class(x) != "eEvents")
stop("print.eEvents: primary argument must have class eEvents")
cat("Study duration: Tfinal=",
round(x$Tfinal,digits), "\n", sep="")
cat("Analysis time: T=",
round(x$T,digits), "\n", sep="")
cat("Accrual duration: ",
round(min(x$T - max(0, x$minfup-(x$Tfinal - x$T)),
sum(x$R)),digits), "\n", sep="")
cat("Min. end-of-study follow-up: minfup=",
round(x$minfup,digits), "\n", sep="")
cat("Expected events (total): ",
round(sum(x$d),digits), "\n",sep="")
if (length(x$d)>1)
{ cat("Expected events by stratum: d=",
round(x$d[1],digits))
for(i in 2:length(x$d))
cat(paste("",round(x$d[i],digits)))
cat("\n")
}
cat("Expected sample size (total): ",
round(sum(x$n),digits), "\n", sep="")
if (length(x$n)>1)
{ cat("Sample size by stratum: n=",
round(x$n[1],digits))
for(i in 2:length(x$n))
cat(paste("",round(x$n[i],digits)))
cat("\n")
}
nstrata <- dim(x$lambda)[2]
cat("Number of strata: ",
nstrata, "\n", sep="")
cat("Accrual rates:\n")
print(round(x$gamma,digits))
cat("Event rates:\n")
print(round(x$lambda,digits))
cat("Censoring rates:\n")
print(round(x$eta,digits))
return(x)
}
###################################################
### code chunk number 12: nameperiod
###################################################
"nameperiod" <- function(R, digits=2)
{ if (length(R)==1) return(paste("0-",round(R,digits),sep=""))
R0 <- c(0,R[1:(length(R)-1)])
return(paste(round(R0,digits),"-",round(R,digits),sep=""))
}
###################################################
### code chunk number 14: LFPWE
###################################################
LFPWE <- function(alpha=.025, sided=1, beta=.1,
lambdaC=log(2) / 6, hr=.5, hr0=1, etaC=0, etaE=0,
gamma=1, ratio=1, R=18, S=NULL, T=24, minfup=NULL)
{ # set up parameters
zalpha <- -qnorm(alpha/sided)
zbeta <- -qnorm(beta)
if (is.null(minfup)) minfup <- max(0,T-sum(R))
if (length(R)==1) {R <- T-minfup
}else if (sum(R) != T-minfup)
{ cR<-cumsum(R)
nR<-length(R)
if (cR[length(cR)] < T - minfup) {cR[length(cR)]<-T-minfup
}else
{ cR[cR>T-minfup]<-T-minfup
cR <- unique(cR)
}
if (length(cR)>1) {R <- cR-c(0,cR[1:(length(cR)-1)])
}else R <- cR
if (nR != length(R))
{ if (is.vector(gamma)) {gamma <- gamma[1:length(R)]
}else gamma<-gamma[1:length(R),]
}
}
ngamma <- length(R)
if (is.null(S)) {nlambda <- 1
}else nlambda <- length(S) + 1
Qe <- ratio / (1 + ratio)
Qc <- 1 - Qe
# compute H0 failure rates as average of control, experimental
if (length(ratio)==1){
lambdaC0 <- (1 + hr * ratio) / (1 + hr0 * ratio) * lambdaC
gammaC <- gamma*Qc
gammaE <- gamma*Qe
}else{
lambdaC0 <- lambdaC %*% diag((1 + hr * ratio) / (1 + hr0 * ratio))
gammaC <- gamma%*%diag(Qc)
gammaE <- gamma%*%diag(Qe)
}
# do computations
eDC0 <- sum(eEvents(lambda=lambdaC0, eta=etaC, gamma=gammaC,
R=R, S=S, T=T, minfup=minfup)$d)
eDE0 <- sum(eEvents(lambda=lambdaC0 * hr0, eta=etaE, gamma=gammaE,
R=R, S=S, T=T, minfup=minfup)$d)
eDC <- eEvents(lambda=lambdaC, eta=etaC, gamma=gammaC,
R=R, S=S, T=T, minfup=minfup)
eDE <- eEvents(lambda=lambdaC * hr, eta=etaE, gamma=gammaE,
R=R, S=S, T=T, minfup=minfup)
n <- ((zalpha * sqrt(1 / eDC0 + 1 / eDE0) +
zbeta * sqrt(1 / sum(eDC$d) + 1 / sum(eDE$d))
) / log(hr / hr0))^2
mx <- sum(eDC$n + eDE$n)
rval <- list(alpha=alpha, sided=sided, beta=beta, power=1-beta,
lambdaC=lambdaC, etaC=etaC, etaE=etaE, gamma=n * gamma,
ratio=ratio, R=R, S=S, T=T, minfup=minfup,
hr=hr, hr0=hr0, n=n * mx, d=n * sum(eDC$d + eDE$d),
eDC=eDC$d*n, eDE=eDE$d*n, eDC0=eDC0*n, eDE0=eDE0*n,
eNC=eDC$n*n, eNE=eDE$n*n, variable="Accrual rate")
class(rval) <- "nSurv"
return(rval)
}
print.nSurv<-function(x,digits=4,...){
if (class(x) != "nSurv")
stop("Primary argument must have class nSurv")
x$digits<-digits
x$sided <- 1
cat("Fixed design, two-arm trial with time-to-event\n")
cat("outcome (Lachin and Foulkes, 1986).\n")
cat("Solving for: ",x$variable,"\n")
cat("Hazard ratio H1/H0=",
round(x$hr,digits),
"/", round(x$hr0,digits),"\n",sep="")
cat("Study duration: T=",
round(x$T,digits), "\n", sep="")
cat("Accrual duration: ",
round(x$T-x$minfup,digits),"\n",sep="")
cat("Min. end-of-study follow-up: minfup=",
round(x$minfup,digits), "\n", sep="")
cat("Expected events (total, H1): ",
round(x$d,digits), "\n",sep="")
cat("Expected sample size (total): ",
round(x$n,digits), "\n", sep="")
enrollper <- periods(x$S, x$T, x$minfup, x$digits)
cat("Accrual rates:\n")
print(round(x$gamma,digits))
cat("Control event rates (H1):\n")
print(round(x$lambda,digits))
if (max(abs(x$etaC-x$etaE))==0)
{ cat("Censoring rates:\n")
print(round(x$etaC,digits))
}
else
{ cat("Control censoring rates:\n")
print(round(x$etaC,digits))
cat("Experimental censoring rates:\n")
print(round(x$etaE,digits))
}
cat("Power: 100*(1-beta)=",
round((1-x$beta)*100,digits), "%\n",sep="")
cat("Type I error (", x$sided,
"-sided): 100*alpha=",
100*x$alpha, "%\n", sep="")
if (min(x$ratio==1)==1)
cat("Equal randomization: ratio=1\n")
else cat("Randomization (Exp/Control): ratio=",
x$ratio, "\n")
}
###################################################
### code chunk number 19: KTZ
###################################################
KTZ <- function(x=NULL, minfup=NULL, n1Target=NULL,
lambdaC=log(2) / 6, etaC=0, etaE=0,
gamma=1, ratio=1, R=18, S=NULL, beta=.1,
alpha=.025, sided=1, hr0=1, hr=.5, simple=TRUE)
{ zalpha<- -qnorm(alpha/sided)
Qc <- 1/(1+ratio)
Qe <- 1 - Qc
# set minimum follow-up to x if that is missing and x is given
if (!is.null(x) && is.null(minfup))
{ minfup <- x
if (sum(R)==Inf)
stop("If minimum follow-up is sought, enrollment duration must be finite")
T <- sum(R)+minfup
variable <- "Follow-up duration"
}
else if (!is.null(x)&&!is.null(minfup))
{ # otherwise, if x is given, set it to accrual duration
T <- x+minfup
R[length(R)]<-Inf
variable <- "Accrual duration"
}
else
{ # otherwise, set follow-up time to accrual plus follow-up
T <- sum(R) + minfup
variable <- "Power"
}
# compute H0 failure rates as average of control, experimental
if (length(ratio)==1){
lambdaC0 <- (1 + hr * ratio) / (1 + hr0 * ratio) * lambdaC
gammaC <- gamma*Qc
gammaE <- gamma*Qe
}else{
lambdaC0 <- lambdaC %*% diag((1 + hr * ratio) / (1 + hr0 * ratio))
gammaC <- gamma%*%diag(Qc)
gammaE <- gamma%*%diag(Qe)
}
# do computations
eDC <- eEvents(lambda=lambdaC, eta=etaC, gamma=gammaC,
R=R, S=S, T=T, minfup=minfup)
eDE <- eEvents(lambda=lambdaC * hr, eta=etaE, gamma=gammaE,
R=R, S=S, T=T, minfup=minfup)
# if this is all that is needed, return difference
# from targeted number of events
if (simple && !is.null(n1Target))
return(sum(eDC$d+eDE$d)-n1Target)
eDC0 <- eEvents(lambda=lambdaC0, eta=etaC, gamma=gammaC,
R=R, S=S, T=T, minfup=minfup)
eDE0 <- eEvents(lambda=lambdaC0 * hr0, eta=etaE, gamma=gammaE,
R=R, S=S, T=T, minfup=minfup)
# compute Z-value related to power from power equation
zb <- (log(hr0 / hr) -
zalpha * sqrt(1 / sum(eDC0$d) + 1 / sum(eDE0$d)))/
sqrt(1 / sum(eDC$d) + 1 / sum(eDE$d))
# if that is all that is needed, return difference from
# targeted value
if (simple)
{ if (!is.null(beta)) return(zb + qnorm(beta))
else return(pnorm(-zb))
}
# compute power
power <- pnorm(zb)
beta <- 1-power
# set accrual period durations
if (sum(R) != T-minfup)
{ if (length(R)==1) R <- T-minfup
else
{ nR <- length(R)
cR <- cumsum(R)
cR[cR>T-minfup] <- T - minfup
cR <- unique(cR)
cR[length(R)] <- T - minfup
if (length(cR)==1) R <- cR
else R <- cR - c(0,cR[1:(length(cR)-1)])
if (length(R) != nR)
{ gamma <- matrix(gamma[1:length(R),], nrow=length(R))
gdim <- dim(gamma)
}
}
}
rval <- list(alpha=alpha, sided=sided, beta=beta, power=power,
lambdaC=lambdaC, etaC=etaC, etaE=etaE,
gamma=gamma, ratio=ratio, R=R, S=S, T=T,
minfup=minfup, hr=hr, hr0=hr0, n=sum(eDC$n + eDE$n),
d=sum(eDC$d + eDE$d), tol=NULL, eDC=eDC$d, eDE=eDE$d,
eDC0=eDC0$d, eDE0=eDE0$d, eNC=eDC$n, eNE=eDE$n,
variable=variable)
class(rval)<-"nSurv"
return(rval)
}
###################################################
### code chunk number 21: KT
###################################################
KT <- function(alpha=.025, sided=1, beta=.1,
lambdaC=log(2) / 6, hr=.5, hr0=1, etaC=0, etaE=0,
gamma=1, ratio=1, R=18, S=NULL, minfup=NULL,
n1Target=NULL, tol = .Machine$double.eps^0.25)
{ # set up parameters
ngamma <- length(R)
if (is.null(S)) {nlambda <- 1
}else nlambda <- length(S) + 1
Qe <- ratio / (1 + ratio)
Qc <- 1 - Qe
if (!is.matrix(lambdaC)) lambdaC <- matrix(lambdaC)
ldim <- dim(lambdaC)
nstrata <- ldim[2]
nlambda <- ldim[1]
etaC <- matrix(etaC,nrow=nlambda,ncol=nstrata)
etaE <- matrix(etaE,nrow=nlambda,ncol=nstrata)
if (!is.matrix(gamma)) gamma <- matrix(gamma)
gdim <- dim(gamma)
eCdim <- dim(etaC)
eEdim <- dim(etaE)
# search for trial duration needed to achieve desired power
if (is.null(minfup))
{ if (sum(R)==Inf){
stop("Enrollment duration must be specified as finite")}
left <- KTZ(.01, lambdaC=lambdaC, n1Target=n1Target,
etaC=etaC, etaE=etaE, gamma=gamma, ratio=ratio,
R=R, S=S, beta=beta, alpha=alpha, sided=sided,
hr0=hr0, hr=hr)
right <- KTZ(1000, lambdaC=lambdaC, n1Target=n1Target,
etaC=etaC, etaE=etaE, gamma=gamma, ratio=ratio,
R=R, S=S, beta=beta, alpha=alpha, sided=sided,
hr0=hr0, hr=hr)
if (left>0) stop("Enrollment duration over-powers trial")
if (right<0) stop("Enrollment duration insufficient to power trial")
y <- uniroot(f=KTZ,interval=c(.01,10000), lambdaC=lambdaC,
etaC=etaC, etaE=etaE, gamma=gamma, ratio=ratio,
R=R, S=S, beta=beta, alpha=alpha, sided=sided,
hr0=hr0, hr=hr, tol=tol, n1Target=n1Target)
minfup <- y$root
xx<-KTZ(x=y$root,lambdaC=lambdaC,
etaC=etaC, etaE=etaE, gamma=gamma, ratio=ratio,
R=R, S=S, minfup=NULL, beta=beta, alpha=alpha,
sided=sided, hr0=hr0, hr=hr, simple=F)
xx$tol <- tol
return(xx)
}else
{ y <- uniroot(f=KTZ, interval=minfup+c(.01,10000), lambdaC=lambdaC,
n1Target=n1Target,
etaC=etaC, etaE=etaE, gamma=gamma, ratio=ratio,
R=R, S=S, minfup=minfup, beta=beta,
alpha=alpha, sided=sided, hr0=hr0, hr=hr, tol=tol)
xx <- KTZ(x=y$root,lambdaC=lambdaC,
etaC=etaC, etaE=etaE, gamma=gamma, ratio=ratio,
R=R, S=S, minfup=minfup, beta=beta, alpha=alpha,
sided=sided, hr0=hr0, hr=hr, simple=F)
xx$tol<-tol
return(xx)
}
}
###################################################
### code chunk number 25: nSurv
###################################################
nSurv <- function(lambdaC=log(2)/6, hr=.6, hr0=1, eta = 0, etaE=NULL,
gamma=1, R=12, S=NULL, T=NULL, minfup = NULL, ratio = 1,
alpha = 0.025, beta = 0.10, sided = 1, tol = .Machine$double.eps^0.25)
{ if (is.null(etaE)) etaE<-eta
# set up rates as matrices with row and column names
# default is 1 stratum if lambdaC not input as matrix
if (is.vector(lambdaC)) lambdaC <- matrix(lambdaC)
ldim <- dim(lambdaC)
nstrata <- ldim[2]
nlambda <- ldim[1]
rownames(lambdaC) <- paste("Period", 1:nlambda)
colnames(lambdaC) <- paste("Stratum", 1:nstrata)
etaC <- matrix(eta,nrow=nlambda,ncol=nstrata)
etaE <- matrix(etaE,nrow=nlambda,ncol=nstrata)
if (!is.matrix(gamma)) gamma <- matrix(gamma)
gdim <- dim(gamma)
eCdim <- dim(etaC)
eEdim <- dim(etaE)
if (is.null(minfup) || is.null(T))
xx<-KT(lambdaC=lambdaC, hr=hr, hr0=hr0, etaC=etaC, etaE=etaE,
gamma=gamma, R=R, S=S, minfup = minfup, ratio = ratio,
alpha=alpha, sided=sided, beta = beta, tol = tol)
else if (is.null(beta))
xx<-KTZ(lambdaC=lambdaC, hr=hr, hr0=hr0, etaC=etaC, etaE=etaE,
gamma=gamma, R=R, S=S, minfup = minfup, ratio = ratio,
alpha=alpha, sided=sided, beta = beta, simple=F)
else
xx<-LFPWE(lambdaC=lambdaC, hr=hr, hr0=hr0, etaC=etaC, etaE=etaE,
gamma=gamma, R=R, S=S, T=T, minfup = minfup, ratio = ratio,
alpha=alpha, sided=sided, beta = beta)
nameR<-nameperiod(cumsum(xx$R))
stratnames <- paste("Stratum",1:ncol(xx$lambdaC))
if (is.null(xx$S)) nameS<-"0-Inf"
else nameS <- nameperiod(cumsum(c(xx$S,Inf)))
rownames(xx$lambdaC)<-nameS
colnames(xx$lambdaC)<-stratnames
rownames(xx$etaC)<-nameS
colnames(xx$etaC)<-stratnames
rownames(xx$etaE)<-nameS
colnames(xx$etaE)<-stratnames
rownames(xx$gamma)<-nameR
colnames(xx$gamma)<-stratnames
return(xx)
}
###################################################
### code chunk number 33: gsnSurv
###################################################
gsnSurv <- function(x,nEvents)
{ if (x$variable=="Accrual rate")
{ Ifct <- nEvents/x$d
rval <- list(lambdaC=x$lambdaC, etaC=x$etaC, etaE=x$etaE,
gamma=x$gamma*Ifct, ratio=x$ratio, R=x$R, S=x$S, T=x$T,
minfup=x$minfup, hr=x$hr, hr0=x$hr0, n=x$n*Ifct, d=nEvents,
eDC=x$eDC*Ifct,eDE=x$eDE*Ifct,eDC0=x$eDC0*Ifct,
eDE0=x$eDE0*Ifct,eNC=x$eNC*Ifct,eNE=x$eNE*Ifct,
variable=x$variable)
}
else if (x$variable=="Accrual duration")
{ y<-KT(n1Target=nEvents,minfup=x$minfup,lambdaC=x$lambdaC,etaC=x$etaC,
etaE=x$etaE,R=x$R,S=x$S,hr=x$hr,hr0=x$hr0,gamma=x$gamma,
ratio=x$ratio,tol=x$tol)
rval <- list(lambdaC=x$lambdaC, etaC=x$etaC, etaE=x$etaE,
gamma=x$gamma, ratio=x$ratio, R=y$R, S=x$S, T=y$T,
minfup=y$minfup, hr=x$hr, hr0=x$hr0, n=y$n, d=nEvents,
eDC=y$eDC,eDE=y$eDE,eDC0=y$eDC0,
eDE0=y$eDE0,eNC=y$eNC,eNE=y$eNE,tol=x$tol,
variable=x$variable)
}
else
{ y<-KT(n1Target=nEvents,minfup=NULL,lambdaC=x$lambdaC,etaC=x$etaC,
etaE=x$etaE,R=x$R,S=x$S,hr=x$hr,hr0=x$hr0,gamma=x$gamma,
ratio=x$ratio,tol=x$tol)
rval <- list(lambdaC=x$lambdaC, etaC=x$etaC, etaE=x$etaE,
gamma=x$gamma, ratio=x$ratio, R=x$R, S=x$S, T=y$T,
minfup=y$minfup, hr=x$hr, hr0=x$hr0, n=y$n, d=nEvents,
eDC=y$eDC,eDE=y$eDE,eDC0=y$eDC0,
eDE0=y$eDE0,eNC=y$eNC,eNE=y$eNE,tol=x$tol,
variable=x$variable)
}
class(rval) <- "gsSize"
return(rval)
}
###################################################
### code chunk number 35: tEventsIA
###################################################
tEventsIA<-function(x, timing=.25, tol = .Machine$double.eps^0.25)
{ T <- x$T[length(x$T)]
z <- uniroot(f=nEventsIA, interval=c(0.0001,T-.0001), x=x,
target=timing, tol=tol,simple=TRUE)
return(nEventsIA(tIA=z$root,x=x,simple=FALSE))
}
nEventsIA <- function(tIA=5, x=NULL, target=0, simple=TRUE)
{ Qe <- x$ratio/(1+x$ratio)
eDC <- eEvents(lambda=x$lambdaC, eta=x$etaC,
gamma=x$gamma*(1-Qe), R=x$R, S=x$S, T=tIA,
Tfinal=x$T[length(x$T)], minfup=x$minfup)
eDE <- eEvents(lambda=x$lambdaC * x$hr, eta=x$etaC,
gamma=x$gamma*Qe, R=x$R, S=x$S, T=tIA,
Tfinal=x$T[length(x$T)], minfup=x$minfup)
if (simple)
{ if (class(x)[1] == "gsSize") d<-x$d
#OLD else d <- sum(x$eDC[length(x$eDC)]+x$eDE[length(x$eDE)])
else if(!is.matrix(x$eDC)) d <- sum(x$eDC[length(x$eDC)]+x$eDE[length(x$eDE)])
else d <- sum(x$eDC[nrow(x$eDC),]+x$eDE[nrow(x$eDE),])
return(sum(eDC$d+eDE$d)-target*d)
}
else return(list(T=tIA,eDC=eDC$d,eDE=eDE$d,eNC=eDC$n,eNE=eDE$n))
}
###################################################
### code chunk number 36: gsSurv
###################################################
gsSurv<-function(k=3, test.type=4, alpha=0.025, sided=1,
beta=0.1, astar=0, timing=1, sfu=sfHSD, sfupar=-4,
sfl=sfHSD, sflpar=-2, r=18,
lambdaC=log(2)/6, hr=.6, hr0=1, eta=0, etaE=NULL,
gamma=1, R=12, S=NULL, T=NULL, minfup=NULL, ratio=1,
tol = .Machine$double.eps^0.25)
{ x<-nSurv(lambdaC=lambdaC, hr=hr, hr0=hr0, eta = eta, etaE=etaE,
gamma=gamma, R=R, S=S, T=T, minfup = minfup, ratio = ratio,
alpha = alpha, beta = beta, sided = sided, tol = tol)
y<-gsDesign(k=k,test.type=test.type,alpha=alpha/sided,
beta=beta, astar=astar, n.fix=x$d, timing=timing,
sfu=sfu, sfupar=sfupar, sfl=sfl, sflpar=sflpar, tol=tol,
delta1=log(hr), delta0=log(hr0))
z<-gsnSurv(x,y$n.I[k])
eDC <- NULL
eDE <- NULL
eNC <- NULL
eNE <- NULL
T <- NULL
for(i in 1:(k-1)){
xx <- tEventsIA(z,y$timing[i],tol)
T <- c(T,xx$T)
eDC <- rbind(eDC,xx$eDC)
eDE <- rbind(eDE,xx$eDE)
eNC <- rbind(eNC,xx$eNC)
eNE <- rbind(eNE,xx$eNE)
}
y$T <- c(T,z$T)
y$eDC <- rbind(eDC,z$eDC)
y$eDE <- rbind(eDE,z$eDE)
y$eNC <- rbind(eNC,z$eNC)
y$eNE <- rbind(eNE,z$eNE)
y$hr=hr; y$hr0=hr0; y$R=z$R; y$S=z$S; y$minfup=z$minfup;
y$gamma=z$gamma; y$ratio=ratio; y$lambdaC=z$lambdaC;
y$etaC=z$etaC; y$etaE=z$etaE; y$variable=x$variable; y$tol=tol
class(y) <- c("gsSurv","gsDesign")
nameR<-nameperiod(cumsum(y$R))
stratnames <- paste("Stratum",1:ncol(y$lambdaC))
if (is.null(y$S)) nameS<-"0-Inf"
else nameS <- nameperiod(cumsum(c(y$S,Inf)))
rownames(y$lambdaC)<-nameS
colnames(y$lambdaC)<-stratnames
rownames(y$etaC)<-nameS
colnames(y$etaC)<-stratnames
rownames(y$etaE)<-nameS
colnames(y$etaE)<-stratnames
rownames(y$gamma)<-nameR
colnames(y$gamma)<-stratnames
return(y)
}
print.gsSurv<-function(x,digits=2,...){
cat("Time to event group sequential design with HR=",x$hr,"\n")
if (x$hr0 != 1) cat("Non-inferiority design with null HR=",x$hr0,"\n")
if (min(x$ratio==1)==1)
cat("Equal randomization: ratio=1\n")
else {cat("Randomization (Exp/Control): ratio=",
x$ratio, "\n")
if (length(x$ratio)>1) cat("(randomization ratios shown by strata)\n")
}
print.gsDesign(x)
if(x$test.type != 1){
y<-cbind(x$T,(x$eNC+x$eNE)%*%array(1,ncol(x$eNE)),
(x$eDC+x$eDE)%*%array(1,ncol(x$eNE)),
round(zn2hr(x$lower$bound,x$n.I,x$ratio,hr0=x$hr0,hr1=x$hr),3),
round(zn2hr(x$upper$bound,x$n.I,x$ratio,hr0=x$hr0,hr1=x$hr),3))
colnames(y)<-c("T","n","Events","HR futility","HR efficacy")
}else{
y<-cbind(x$T,(x$eNC+x$eNE)%*%array(1,ncol(x$eNE)),
(x$eDC+x$eDE)%*%array(1,ncol(x$eNE)),
round(zn2hr(x$upper$bound,x$n.I,x$ratio,hr0=x$hr0,hr1=x$hr),3))
colnames(y)<-c("T","n","Events","HR efficacy")
}
rnames<-paste("IA",1:(x$k))
rnames[length(rnames)]<-"Final"
rownames(y)<-rnames
print(y)
cat("Accrual rates:\n")
print(round(x$gamma,digits))
cat("Control event rates (H1):\n")
print(round(x$lambda,digits))
if (max(abs(x$etaC-x$etaE))==0)
{ cat("Censoring rates:\n")
print(round(x$etaC,digits))
}
else
{ cat("Control censoring rates:\n")
print(round(x$etaC,digits))
cat("Experimental censoring rates:\n")
print(round(x$etaE,digits))
}
}
xtable.gsSurv <- function(x, caption=NULL, label=NULL, align=NULL, digits=NULL,
display=NULL, auto=FALSE, footnote=NULL, fnwid="9cm", timename="months",...){
k <- x$k
stat <- c("Z-value","HR","p (1-sided)", paste("P\\{Cross\\} if HR=",x$hr0,sep=""),
paste("P\\{Cross\\} if HR=",x$hr,sep=""))
st <- stat
for (i in 2:k) stat <- c(stat,st)
an <- array(" ",5*k)
tim <- an
enrol <- an
fut <- an
eff <- an
an[5*(0:(k-1))+1]<-c(paste("IA ",as.character(1:(k-1)),": ",
as.character(round(100*x$timing[1:(k-1)],1)), "\\%",sep=""), "Final analysis")
an[5*(1:(k-1))+1] <- paste("\\hline",an[5*(1:(k-1))+1])
an[5*(0:(k-1))+2]<- paste("N:",ceiling(rowSums(x$eNC))+ceiling(rowSums(x$eNE)))
an[5*(0:(k-1))+3]<- paste("Events:",ceiling(rowSums(x$eDC+x$eDE)))
an[5*(0:(k-1))+4]<- paste(round(x$T,1),timename,sep=" ")
if (x$test.type != 1) fut[5*(0:(k-1))+1]<- as.character(round(x$lower$bound,2))
eff[5*(0:(k-1))+1]<- as.character(round(x$upper$bound,2))
if (x$test.type != 1) fut[5*(0:(k-1))+2]<- as.character(round(gsHR(z=x$lower$bound,i=1:k,x,ratio=x$ratio)*x$hr0,2))
eff[5*(0:(k-1))+2]<- as.character(round(gsHR(z=x$upper$bound,i=1:k,x,ratio=x$ratio)*x$hr0,2))
asp <- as.character(round(pnorm(-x$upper$bound),4))
asp[asp=="0"]<-"$< 0.0001$"
eff[5*(0:(k-1))+3] <- asp
asp <- as.character(round(cumsum(x$upper$prob[,1]),4))
asp[asp=="0"]<-"$< 0.0001$"
eff[5*(0:(k-1))+4] <- asp
asp <- as.character(round(cumsum(x$upper$prob[,2]),4))
asp[asp=="0"]<-"$< 0.0001$"
eff[5*(0:(k-1))+5] <- asp
if (x$test.type != 1) {
bsp <- as.character(round(pnorm(-x$lower$bound),4))
bsp[bsp=="0"]<-" $< 0.0001$"
fut[5*(0:(k-1))+3] <- bsp
bsp <- as.character(round(cumsum(x$lower$prob[,1]),4))
bsp[bsp=="0"]<-"$< 0.0001$"
fut[5*(0:(k-1))+4] <- bsp
bsp <- as.character(round(cumsum(x$lower$prob[,2]),4))
bsp[bsp=="0"]<-"$< 0.0001$"
fut[5*(0:(k-1))+5] <- bsp
}
neff <- length(eff)
if (!is.null(footnote)) eff[neff] <-
paste(eff[neff],"\\\\ \\hline \\multicolumn{4}{p{",fnwid,"}}{\\footnotesize",footnote,"}")
if (x$test.type != 1){
xxtab <- data.frame(cbind(an,stat,fut,eff))
colnames(xxtab) <- c("Analysis","Value","Futility","Efficacy")
}else{
xxtab <- data.frame(cbind(an,stat,eff))
colnames(xxtab) <- c("Analysis","Value","Efficacy")
}
return(xtable(xxtab, caption=caption, label=label, align=align, digits=digits,
display=display,auto=auto,...))
}
Try the gsDesign package in your browser
Any scripts or data that you put into this service are public.
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.