Comparing Sample Size and Power Calculation Results for a Group Sequential Trial with a Survival Endpoint: rpact vs. gsDesign

Planning

Survival

This document provides an example that illustrates how to compare sample size and power calculation results of the two different R packages rpact and gsDesign.

Author

Gernot Wassmer, Friedrich Pahlke, and Marcel Wolbers

Published

March 8, 2023

The design

1:1 randomized

Two-sided log-rank test; 80% power at the 5% significance level (or one-sided at 2.5%)

Target HR for primary endpoint (PFS) is 0.75

PFS in the control arm follows a piece-wise exponential distribution, with the hazard rate h(t) estimated using historical controls as follows:

h(t) = 0.025 for t between 0 and 6 months;

h(t) = 0.04 for t between 6 and 9 months;

h(t) = 0.015 for t between 9 and 15 months;

h(t) = 0.01 for t between 15 and 21 months;

h(t) = 0.007 for t beyond 21 months.

An annual dropout probability of 20%

Interim analyses at 33% and 70% of total information

Alpha-spending version of O’Brien-Fleming boundary for efficacy

No futility interim

1405 subjects recruited in total

Staggered recruitment:

15 pt/month during first 12 months;

subsequently, increase of # of sites and ramp up of recruitment by +6 pt/month each month until a maximum of 45 pt/month

Sequential analysis with a maximum of 3 looks (group sequential design), overall significance level 2.5% (one-sided). The results were calculated for a two-sample logrank test, H0: hazard ratio = 1, power directed towards smaller values, H1: hazard ratio = 0.75, piecewise survival distribution, piecewise survival time = c(0, 6, 9, 15, 21), control lambda(2) = c(0.025, 0.04, 0.015, 0.01, 0.007), maximum number of subjects = 1405, maximum number of events = 386, accrual time = c(12, 13, 14, 15, 16, 40.556), accrual intensity = c(15, 21, 27, 33, 39, 45), dropout rate(1) = 0.2, dropout rate(2) = 0.2, dropout time = 12.

is not exactly equal to getPowerSurvival from above. This, however, has definitely no consequences in practice but explains the slight differences in rpact and gsDesign.

System: rpact 3.3.4, R version 4.2.2 (2022-10-31 ucrt), platform: x86_64-w64-mingw32

To cite R in publications use:

R Core Team (2022). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.

To cite package ‘rpact’ in publications use:

Wassmer G, Pahlke F (2023). rpact: Confirmatory Adaptive Clinical Trial Design and Analysis. https://www.rpact.org, https://www.rpact.com, https://github.com/rpact-com/rpact.