Economical Experimental Design with Generalized Posteriors

TL;DR

This paper introduces an efficient method for experimental design using generalized posteriors to improve robustness and reduce computational costs, demonstrated through adaptive clinical trial redesign.

Contribution

It develops a novel, economical approach to determine sample sizes and decision criteria with generalized posteriors in hybrid Bayesian experimental design.

Findings

Efficient assessment of operating characteristics across sample sizes using only two simulation points.

Redesign of an adaptive clinical trial with time-to-event outcomes demonstrating the method's effectiveness.

Framework applicable to experiments involving Bayesian analogues to M-estimation.

Abstract

The hybrid approach to experimental design aims to control frequentist operating characteristics of Bayesian decision procedures. These operating characteristics are assessed by simulating sampling distributions of posterior summaries under assumed data-generation processes that also define posterior distributions. Model misspecification can distort effect estimation and compromise control over operating characteristics. Generalized posterior distributions are defined using generalized likelihoods that characterize data generation under fewer assumptions, enhancing the robustness of Bayesian analysis and study design. However, widely applicable and computationally efficient design methodology with generalized posteriors is lacking. We propose an economical method to determine suitable sample sizes and decision criteria associated with generalized posteriors under the hybrid approach. Using theoretical results to model posterior summaries as functions of the sample size, we efficiently assess operating characteristics throughout the sample size space given simulations conducted at only two sample sizes. While the benefits of the proposed methodology are emphasized by redesigning an adaptive clinical trial with time-to-event outcomes, we overview our framework's broader applicability to experiments involving Bayesian analogues to M-estimation.