# Estimation in adaptive group sequential trials

### Description

The package allows to compute repeated confidence intervals as well as confidence intervals based on the stage-wise ordering in groug sequential designs (GSD; see Jennison and Turnbull, 1989; Tsiatis, Rosner, Mehta, 1984) and adaptive groug sequential designs (Mehta, Bauer, Posch, Brannath, 2007; Brannath, Mehta, Posch, 2008). For adaptive group sequential designs the confidence intervals are based on the conditional rejection probability principle of Mueller and Schaefer (2001). This principle allows us to perform data dependent changes to the sample size, the spending function, and the number and spacing of interim looks while preserving the overall type I error rate. Currently the procedures do not support the use of futility boundaries as well as more than one adaptive interim analysis. Furthermore, the package is currently restricted to the computation of lower one-sided confidence intervals.

### Details

Package: AGSDest

Type: Package Version: 2.2 Date: 2015-01-12 License: GPL Version 2 or later

Main functions:
`adapt`

: Performs adaptations at an interim analysis of a GSD to the sample size, number of interim stages and spending function based on the conditional power in a GSD at an interim analysis; the result is a secondary trial
`plan.GST`

: Plans a group sequential trial
`cer`

: Computes the conditional type I error rate (also called conditional rejection probability) of a GSD at an interim analysis
`typeIerr`

: Computes the type I error rate of a GSD
`pvalue`

: Computes the repeated or stage-wise adjusted p-value for a classical GSD or for a GSD with design adaptations
`seqconfint`

: Computes the repeated confidence bound and confidence bound based on the stage-wise ordering for a GSD or for a GSD with design adaptations

Subfunctions:
`as.GST`

: Builds a group sequential trial object
`as.AGST`

: Builds an adaptive group sequential trial object

### Author(s)

Niklas Hack niklas.hack@meduniwien.ac.at and Werner Brannath werner.brannath@meduniwien.ac.at

### References

Brannath, W, Mehta, CR, Posch, M (2008) ”Exact confidence bounds following adaptive group sequential tests”, *Biometrics* accepted.

Jennison, C, Turnbull, BW (1989) ”Repeated confidence intervals for group sequential clinical trials”, *Contr. Clin. Trials*, 5, 33-45.

Mehta, CR, Bauer, P, Posch, M, Brannath, W (2007) ”Repeated confidence intervals for adaptive group sequential trials”, *Statistics in Medicine*, 26, 5422-5433.

Mueller, HH, Schaefer, H (2001) ”Adaptive group sequential design for clinical trials: Combining the advantages of adaptive and of classical group sequential approaches”, *Biometrics*, 57, 886-891.

O'Brien, PC, Fleming, TR (1979) ”A multiple testing procedure for clinical trials”, *Biometrics*, 35 , 549-556

Schoenfeld, D (2001) ”A simple Algorithm for Designing Group Sequential Clinical Trials”, *Biometrics*, 27, 972-974

Tsiatis,AA, Rosner,GL, Mehta,CR (1984) ”Exact confidence intervals following a group sequential test”, *Biometrics*, 40, 797-804.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | ```
pT=plan.GST(K=3,SF=4,phi=-4,alpha=0.05,delta=6,pow=0.9,compute.alab=TRUE,compute.als=TRUE)
iD=list(T=1, z=1.090728)
swImax=0.0625
I2min=3*swImax
I2max=3*swImax
sT=adapt(pT=pT,iD=iD,SF=1,phi=0,cp=0.8,theta=5,I2min,I2max,swImax)
sTo=list(T=2, z=2.393)
AGST <- as.AGST(pT=pT,iD=iD,sT=sT,sTo=sTo)
##The following calculates the stage-wise adjusted p-value
##of a group sequential trial after a design adaptation
pvalue(AGST,type="so")
##and the corresponding confidence bound based on the stage-wise ordering.
seqconfint(AGST,type="so")
##Both, the p-value and the confidence interval can be calculated by
##the summary function
## Not run:
summary(AGST,ctype="so",ptype="so")
## End(Not run)
``` |