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/.