Calibrated Bayes analysis of cluster-randomized trials

TL;DR

This paper introduces a calibrated Bayesian approach for analyzing cluster-randomized trials, focusing on estimands like cluster-ATE and individual-ATE, ensuring robustness even with model misspecification and informative cluster sizes.

Contribution

It proposes a novel calibrated Bayesian methodology for CRTs that targets specific estimands and maintains coverage guarantees under model misspecification.

Findings

Bayesian estimators are robust to model misspecification.

Posterior summarization strategies achieve frequentist coverage.

Flexible Bayesian models improve analysis robustness.

Abstract

In cluster-randomized trials (CRTs), entire clusters of individuals are randomized to treatment, and outcomes within a cluster are typically correlated. While frequentist approaches are standard practice for CRT analysis, Bayesian methods have emerged as a strong alternative. Previous work has investigated the use of Bayesian hierarchical models for continuous, binary, and count outcomes in CRTs, but these approaches focus on model-based treatment effect coefficients as the target estimands, which may have ambiguous interpretation under model misspecification and informative cluster size. In this article, we introduce a calibrated Bayesian procedure for estimand-aligned analysis of CRTs even in the presence of potentially misspecified models. We propose estimators targeting both the cluster-average treatment effect (cluster-ATE) and individual-average treatment effect (individual-ATE), particularly in scenarios with informative cluster sizes. We additionally explore strategies for summarizing the posterior samples that can achieve the frequentist coverage guarantee even under working model misspecification. We provide simulation evidence to demonstrate the model-robustness property of the proposed Bayesian estimators in CRTs, and further investigate the impact of covariate adjustment as well as the use of more flexible Bayesian nonparametric working models.