On finite-population Bayesian inferences for $2^K$ factorial designs with binary outcomes

TL;DR

This paper develops a finite-population Bayesian causal inference method for $2^K$ factorial designs with binary outcomes, addressing variance over-estimation issues in classical approaches, especially relevant in medical research.

Contribution

It introduces a Bayesian framework based on potential outcomes for factorial designs, improving variance estimation over traditional Neymanian methods.

Findings

Corrects variance over-estimation in classical inference

Validated through simulated and empirical examples

Applicable to medical research with binary outcomes

Abstract

Inspired by the pioneering work of Rubin (1978), we employ the potential outcomes framework to develop a finite-population Bayesian causal inference framework for randomized controlled $2^K$ factorial designs with binary outcomes, which are common in medical research. As demonstrated by simulated and empirical examples, the proposed framework corrects the well-known variance over-estimation issue of the classic "Neymanian" inference framework, under various settings.