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

ABSTRACT

Inspired by the pioneering work of Rubin [Bayesian inference for causal effects: the role of randomization. Ann Stat. 1978;6:34–58], 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.

KEYWORDS:

• Factorial effect
• frequentist-Bayes reconciliation
• potential outcome
• randomization-based inference
• sensitivity analysis

Acknowledgments

The author thanks the Editor, Associate Editor and five anonymous reviewers for their valuable comments, which improve the quality of this paper significantly. The author benefits from early discussions with Professor Tirthankar Dasgupta at Rutgers and Professor Peng Ding at Berkeley.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Jiannan Lu  http://orcid.org/0000-0002-8839-6024