Power and Sample Size Calculations for Bayes Factors in two-arm clinical Phase II Trials with binary Endpoints

TL;DR

This paper introduces a computationally efficient method for power and sample size calculations for Bayes factors in two-arm phase II clinical trials with binary endpoints, avoiding Monte Carlo simulations.

Contribution

It derives closed-form Bayes factors for binomial hypotheses and proposes a numerical approach for sample size determination with Bayesian power and error bounds.

Findings

Method avoids Monte Carlo simulations for Bayesian sample size calculation.

Provides real-world examples demonstrating the approach's advantages.

Implemented in R package bfbin2arm.

Abstract

Bayesian sample size calculations in clinical trials usually rely on complex Monte Carlo simulations in practice. Obtaining bounds on Bayesian notions of the false-positive rate and power often lack closed-form or approximate numerical solutions. In this paper, we focus on power and sample size calculations for Bayes factors in the two-arm binomial setting of phase II trials. We cover point-null versus composite and directional hypothesis tests, derive the corresponding Bayes factors, and discuss relevant aspects to consider when pursuing Bayesian design of experiments with the introduced approach. Based on these Bayes factors, we propose a numerical approach which allows to determine the necessary sample size to obtain prespecified bounds of Bayesian power and type-I-error rate in a computationally efficient way. Our method does not rely on Monte Carlo simulations and instead solely relies on standard numerical methods. Real-world examples of phase II trials from oncology and autoimmune diseases illustrate the advantage of the proposed calibration method. In summary, our approach allows for a Bayes-frequentist compromise by providing a Bayesian analogue to a frequentist power analysis for various Bayes factors in the two-arm binomial setting of a phase II clinical trial. The methods are implemented in our R package bfbin2arm.