Bayes Factor Group Sequential Designs

TL;DR

This paper introduces a fast, simulation-free method for designing sequential Bayes factor experiments, making it easier to plan efficient studies with early stopping rules across various scientific fields.

Contribution

It extends classical group sequential design theory to Bayes factor-based designs, enabling quick and accurate calculation of stopping probabilities without intensive simulations.

Findings

Method is fast and simulation-free

Applicable to clinical, animal, and psychological studies

Open-source implementation available in R package

Abstract

The Bayes factor, the data-based updating factor from prior to posterior odds, is a principled measure of relative evidence for two competing hypotheses. It is naturally suited to sequential data analysis in settings such as clinical trials and animal experiments, where early stopping for efficacy or futility is desirable. However, designing such studies is challenging because computing design characteristics, such as the probability of obtaining conclusive evidence or the expected sample size, typically requires computationally intensive Monte Carlo simulations, as no closed-form or efficient numerical methods exist. To address this issue, we extend results from classical group sequential design theory to sequential Bayes factor designs. The key idea is to derive Bayes factor stopping regions in terms of the z-statistic and use the known distribution of the cumulative z-statistics to compute stopping probabilities through multivariate normal integration. The resulting method is fast, accurate, and simulation-free. We illustrate it with examples from clinical trials, animal experiments, and psychological studies. We also provide an open-source implementation in the bfpwr R package. Our method makes exploring sequential Bayes factor designs as straightforward as classical group sequential designs, enabling experiments to rapidly design informative and efficient experiments.