An Economical Approach to Design Posterior Analyses

• 成果类型: Article; Early Access
• 署名作者: Hagar, Luke; Stevens, Nathaniel T.
• 署名单位: McGill University; University of Waterloo
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2025.2476221
• 发表日期: 2025
• 关键词: sample-size determination; clinical-trials

摘要

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 article, 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. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.