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
July 6, 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.
Stage
1
2
3
Information rate
33%
70%
100%
Efficacy boundary (z-value scale)
3.731
2.440
2.000
Overall power
0.0175
0.4702
0.8009
Expected number of subjects
1354.8
Number of subjects
785.4
1318.1
1405.0
Expected number of events
328.9
Cumulative number of events
127.3
270.1
385.9
Analysis time
26.8
38.6
50.8
Expected study duration
44.9
Cumulative alpha spent
<0.0001
0.0074
0.0250
One-sided local significance level
<0.0001
0.0074
0.0227
Efficacy boundary (t)
0.516
0.743
0.816
Exit probability for efficacy (under H0)
<0.0001
0.0073
Exit probability for efficacy (under H1)
0.0175
0.4526
Legend:
(t): treatment effect scale
Design plan parameters and output for survival data
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 3.4.0, 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, https://rpact-com.github.io/rpact/.