ssrCP: Sample size re-estimation based on conditional power in gsDesign: Group Sequential Design (2024)

In gsDesign: Group Sequential Design

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/ssrCP.R

Description

ssrCP() adapts 2-stage group sequential designs to 2-stage sample size re-estimation designs based on interim analysis conditional power.This is a simple case of designs developed by Lehmacher and Wassmer, Biometrics (1999). The conditional power designs of Bauer and Kohne (1994), Proschan and Hunsberger (199x), Cui, Hung and Wang (199x) and Liu and Chi (), Gao, Ware and Mehta (), and Mehta and Poco*ck (2011). Either the estimated treatment effect at the interim analysis or any chosen effect size can be used for sample size re-estimation.If not done carefully, these designs can be very inefficient. It is probably a good idea to compare any design to a simpler group sequential design; see, for example, Jennison and Turnbull (2003).The a assumes a small Type I error is included with the interim analysis and that the design is an adaptation from a 2-stage group sequential design Related functions include 3 pre-defined combination test functions (z2NC, z2Z, z2Fisher) that represent the inverse normal combination test (Lehmacher and Wassmer, 1999), the sufficient statistic for the complete data, and Fisher's combination test. Power.ssrCP computes unconditional power for a conditional power design derived by ssrCP.

condPower is a supportive routine that also is interesting in its own right; it computes conditional power of a combination test given an interim test statistic, stage 2 sample size and combindation test statistic.While the returned data frame should make general plotting easy, the function plot.ssrCP() prints a plot of study sample size by stage 1 outcome with multiple x-axis labels for stage 1 z-value, conditional power, and stage 1 effect size relative to the effect size for which the underlying group sequential design was powered.

Usage

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ssrCP(z1, theta=NULL, maxinc=2, overrun=0, beta = x$beta, cpadj=c(.5,1-beta), x=gsDesign(k=2, timing=.5), z2=z2NC,...)## S3 method for class 'ssrCP'plot(x, z1ticks=NULL, mar=c(7, 4, 4, 4)+.1, ylab="Adapted sample size", xlaboffset=-.2, lty=1, col=1,...)Power.ssrCP(x, theta=NULL, delta=NULL, r=18) condPower(z1, n2, z2=z2NC, theta=NULL, x=gsDesign(k=2, timing=.5, beta=beta), ...)z2NC(z1,x,...)z2Z(z1,x,n2=x$n.I[2]-x$n.I[1],...)z2Fisher(z1,x,...)

Arguments

Arguments for ssrCP()

Additional arguments for Power.ssrCP():

Additional argument for z2Z() and condPower:

Additional arguments for plot.ssrCP() are all graphical parameters:

Details

Sample size re-estimation using conditional power and an interim estimate of treatment effect was proposed by several authors in the 1990's (see references below). Statistical testing for these original methods was based on combination tests since Type I error could be inflated by using a sufficient statistic for testing at the end of the trial. Since 2000, more efficient variations of these conditional power designs have been developed. Fully optimized designs have also been derived (Posch et all, 2003, Lokhnygina and Tsiatis, 2008). Some of the later conditional power methods allow use of sufficient statistics for testing (Chen, DeMets and Lan, 2004, Gao, Ware and Mehta, 2008, and Mehta and Poco*ck, 2011).

The methods considered here are extensions of 2-stage group sequential designs that include both an efficacy and a futility bound at the planned interim analysis. A maximum fold-increase in sample size (maxinc)from the supplied group sequential design (x) is specified by the user, as well as a range of conditional power (cpadj) where sample size should be re-estimated at the interim analysis, 1-the targeted conditional power to be used for sample size re-estimation (beta) and a combination test statistic (z2) to be used for testing at the end of the trial.The input value overrun represents incremental enrollment not included in the interim analysis that is not included in the analysis; this is used for calculating the required number of patients enrolled to complete the trial.

Whereas most of the methods proposed have been based on using the interim estimated treatment effect size (default for ssrCP), the variable theta allows the user to specify an alternative; Liu and Chi (2001) suggest that using the parameter value for which the trial was originally powered is a good choice.

Value

ssrCP returns a list with the following items:

Author(s)

Keaven Anderson keaven\_anderson@merck.

References

Bauer, Peter and Kohne, F., Evaluation of experiments with adaptive interim analyses, Biometrics, 50:1029-1041, 1994.

Chen, YHJ, DeMets, DL and Lan, KKG. Increasing the sample size when the unblinded interim result is promising, Statistics in Medicine,23:1023-1038, 2004.

Gao, P, Ware, JH and Mehta, C, Sample size re-estimation for adaptive sequential design in clinical trials, Journal of Biopharmaceutical Statistics", 18:1184-1196, 2008.

Jennison, C and Turnbull, BW. Mid-course sample size modification in clinical trials based on the observed treatment effect. Statistics in Medicine, 22:971-993", 2003.

Lehmacher, W and Wassmer, G. Adaptive sample size calculations in group sequential trials, Biometrics, 55:1286-1290, 1999.

Liu, Q and Chi, GY., On sample size and inference for two-stage adaptive designs, Biometrics, 57:172-177, 2001.

Mehta, C and Poco*ck, S. Adaptive increase in sample size when interim results are promising: A practical guide with examples, Statistics in Medicine, 30:3267-3284, 2011.

See Also

gsDesign

Examples

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# Following is a template for entering parameters for ssrCP# Natural parameter value null and alternate hypothesis valuesdelta0 <- 0delta1 <- 1# timing of interim analysis for underlying group sequential designtiming <- .5# upper spending function sfu <- sfHSD# upper spending function paramatersfupar <- -12# maximum sample size inflationmaxinflation <- 2# assumed enrollment overrrun at IAoverrun <- 25# interim z-values for plottingz <- seq(0,4,.025)# Type I error (1-sided)alpha <- .025# Type II error for designbeta <- .1# Fixed design sample sizen.fix <- 100# conditional power interval where sample # size is to be adjustedcpadj <- c(.3,.9)# targeted Type II error when adapting sample sizebetastar <- beta# combination test (built-in options are: z2Z, z2NC, z2Fisher)z2 <- z2NC# use the above parameters to generate design# generate a 2-stage group sequential design with x<-gsDesign(k=2,n.fix=n.fix,timing=timing,sfu=sfu,sfupar=sfupar, alpha=alpha,beta=beta,delta0=delta0,delta1=delta1)# extend this to a conditional power designxx <- ssrCP(x=x,z1=z,overrun=overrun,beta=betastar,cpadj=cpadj, maxinc=maxinflation, z2=z2)# plot the stage 2 sample sizeplot(xx)# demonstrate overlays on this plot# overlay with densities for z1 under different hypotheseslines(z,80+240*dnorm(z,mean=0),col=2)lines(z,80+240*dnorm(z,mean=sqrt(x$n.I[1])*x$theta[2]),col=3)lines(z,80+240*dnorm(z,mean=sqrt(x$n.I[1])*x$theta[2]/2),col=4)lines(z,80+240*dnorm(z,mean=sqrt(x$n.I[1])*x$theta[2]*.75),col=5)axis(side=4, at=80+240*seq(0,.4,.1), labels=as.character(seq(0,.4,.1))) mtext(side=4,expression(paste("Density for ",z[1])),line=2)text(x=1.5,y=90,col=2,labels=expression(paste("Density for ",theta,"=0")))text(x=3.00,y=180,col=3,labels=expression(paste("Density for ",theta,"=", theta[1])))text(x=1.00,y=180,col=4,labels=expression(paste("Density for ",theta,"=", theta[1],"/2")))text(x=2.5,y=140,col=5,labels=expression(paste("Density for ",theta,"=", theta[1],"*.75")))# overall line for max sample sizenalt <- xx$maxinc*x$n.I[2]lines(x=par("usr")[1:2],y=c(nalt,nalt),lty=2)# compare above design with different combination tests# use sufficient statistic for final testingxxZ <- ssrCP(x=x,z1=z,overrun=overrun,beta=betastar,cpadj=cpadj, maxinc=maxinflation, z2=z2Z)# use Fisher combination test for final testingxxFisher <- ssrCP(x=x,z1=z,overrun=overrun,beta=betastar,cpadj=cpadj, maxinc=maxinflation, z2=z2Fisher)# combine data frames from these designsy <- rbind( data.frame(cbind(xx$dat,Test="Normal combination")), data.frame(cbind(xxZ$dat,Test="Sufficient statistic")), data.frame(cbind(xxFisher$dat,Test="Fisher combination")))# plot stage 2 statistic required for positive combination testggplot(data=y,aes(x=z1,y=z2,col=Test))+geom_line()# plot total sample size versus stage 1 test statisticggplot(data=y,aes(x=z1,y=n2,col=Test))+geom_line()# check achieved Type I error for sufficient statistic designPower.ssrCP(x=xxZ, theta=0)# compare designs using observed vs planned theta for conditional powerxxtheta1 <- ssrCP(x=x,z1=z,overrun=overrun,beta=betastar,cpadj=cpadj, maxinc=maxinflation, z2=z2, theta=x$delta)# combine data frames for the 2 designsy <- rbind( data.frame(cbind(xx$dat,"CP effect size"="Obs. at IA")), data.frame(cbind(xxtheta1$dat,"CP effect size"="Alt. hypothesis")))# plot stage 2 sample size by designggplot(data=y,aes(x=z1,y=n2,col=CP.effect.size))+geom_line()# compare power and expected sample sizey1 <- Power.ssrCP(x=xx)y2 <- Power.ssrCP(x=xxtheta1)# combine data frames for the 2 designsy3 <- rbind( data.frame(cbind(y1,"CP effect size"="Obs. at IA")), data.frame(cbind(y2,"CP effect size"="Alt. hypothesis")))# plot expected sample size by design and effect sizeggplot(data=y3,aes(x=delta,y=en,col=CP.effect.size))+geom_line() + xlab(expression(delta)) + ylab("Expected sample size")# plot power by design and effect sizeggplot(data=y3,aes(x=delta,y=Power,col=CP.effect.size))+geom_line() + xlab(expression(delta))

Loading required package: xtableLoading required package: ggplot2 theta delta Power en1 0 0 0.0220804 95.11565

gsDesign documentation built on May 2, 2019, 4:49 p.m.