Sample size reestimation and Bayesian predictive probability for single-arm clinical trials with a time-to-event endpoint using Weibull distribution with unknown shape parameter

ABSTRACT

This manuscript consists of two topics. Firstly, we explore the utility of internal pilot study (IPS) approach for reestimating sample size at an interim stage when a reliable estimate of the nuisance shape parameter of the Weibull distribution for modeling survival data is unavailable during the planning phase of a study. Although IPS approach can help rescue the study power, it is noted that the adjusted sample size can be as much as twice the initially planned sample size, which may put substantial practical constraints to continue the study. Secondly, we discuss Bayesian predictive probability for conducting interim analyses to obtain preliminary evidence of efficacy or futility of an experimental treatment warranting early termination of a clinical trial. In the context of single-arm clinical trials with time-to-event endpoints following Weibull distribution, we present the calculation of the Bayesian predictive probability when the shape parameter of the Weibull distribution is unknown. Based on the data accumulated at the interim, we propose two approaches which rely on the posterior mode or the entire posterior distribution of the shape parameter. To account for uncertainty in the shape parameter, it is recommended to incorporate its entire posterior distribution in our calculation.

KEYWORDS:

• Interim analysis
• prior elicitation
• sample size re-estimation
• stochastic curtailment
• Weibull distribution

Acknowledgements

The authors would like to thank the associate editor and two reviewers for their constructive comments and suggestions which led to significant improvement of this manuscript. The authors would also like to thank Byron J. Gajeswski, Matthew S. Mayo, and Scott Weir for providing valuable feedback which improved the presentation of this manuscript.

This work was supported by the K-INBRE Bioinformatics Core that is supported in part by the National Institute of General Medical Science award (P20 GM103418), the Biostatistics and Informatics Shared Resource, supported by the National Cancer Institute Cancer Center Support Grant (P30 CA168524), and the Kansas Institute for Precision Medicine COBRE, supported by the National Institute of General Medical Science award (P20 GM130423).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Supplementary data

Supplemental data for this article can be accessed online at https://doi.org/10.1080/10543406.2023.2234998.

Additional information

Funding

The author(s) reported that there is no funding associated with the work featured in this article.