An Economical Approach to Design Posterior Analyses

TL;DR

This paper introduces a cost-effective method for designing Bayesian studies by modeling posterior probabilities to optimize sample sizes and decision criteria, reducing the need for extensive simulations.

Contribution

It presents a theoretical framework that estimates operating characteristics across sample sizes from limited simulations, enabling efficient Bayesian study design.

Findings

The method accurately estimates optimal sample sizes and decision criteria.

Bootstrap confidence intervals reflect the stochastic variability in design.

Application to clinical examples demonstrates broad utility.

Abstract

To design Bayesian studies, criteria for the operating characteristics of posterior analyses - such as power and the type I error rate - are often assessed by estimating sampling distributions of posterior probabilities via simulation. In this paper, we propose an economical method to determine optimal sample sizes and decision criteria for such studies. Using our theoretical results that model posterior probabilities as a function of the sample size, we assess operating characteristics throughout the sample size space given simulations conducted at only two sample sizes. These theoretical results are used to construct bootstrap confidence intervals for the optimal sample sizes and decision criteria that reflect the stochastic nature of simulation-based design. We also repurpose the simulations conducted in our approach to efficiently investigate various sample sizes and decision criteria using contour plots. The broad applicability and wide impact of our methodology is illustrated using two clinical examples.