Sample size determination in superiority or non-inferiority clinical trials with time-to-event data under exponential, Weibull and Gompertz distributions

TL;DR

This paper develops and compares sample size formulas for clinical trials with time-to-event data under exponential, Weibull, and Gompertz distributions, highlighting the robustness of Weibull-based calculations.

Contribution

It introduces new sample size formulas for Weibull and Gompertz distributions and demonstrates the superiority of Weibull-based formulas through simulations.

Findings

Weibull-based formula is most robust for sample size estimation.

Assuming Weibull distribution improves trial planning accuracy.

Current exponential formula is less reliable under varied distributions.

Abstract

To examine the effect of exponential, Weibull and Gompertz distributions on sample size determination for superiority trials (STs) or non-inferiority trials (NTs) with time-to-event data, we present two sample size formulas for STs or NTs based on Weibull and Gompertz distributions, respectively. The formulas are compared with the current exponential formula to examine their performance. The simulation results show that the sample size formula based on the Weibull distribution is the most robust among the three formulas in STs or NTs. We suggest that recognizing the appropriate distribution in advance is beneficial for proper project planning and that assuming a Weibull distributed survival time is most advantageous in STs or NTs.