Causally Sound Priors for Binary Experiments.

Area of Science:

• Biostatistics
• Causal Inference
• Clinical Trial Analysis

Background:

• Bayesian analysis of randomized controlled trials (RCTs) is crucial for evaluating treatment effectiveness.
• Current methods often lack interpretability and flexibility in parameterization.
• A need exists for robust Bayesian frameworks that incorporate clinical relevance.

Purpose of the Study:

• To introduce the BREASE (Baseline Risk, Efficacy, and Adverse Side Effects) framework for Bayesian analysis of RCTs.
• To provide a flexible and interpretable Bayesian approach for binary treatment and outcome data.
• To offer a generalized prior distribution that enhances causal inference in clinical trials.

Main Methods:

• Parameterizing the likelihood using baseline risk, efficacy, and adverse side effects.
• Utilizing a flexible, jointly independent beta prior distribution, a generalization of the Dirichlet prior.
• Developing analytical formulae for marginal likelihood and Bayes factors.
• Implementing an exact posterior sampling algorithm and a data-augmented Gibbs sampler.

Main Results:

• The BREASE framework naturally induces prior dependence between treatment and control group outcomes.
• Prior hyperparameters are directly interpretable, aiding prior knowledge elicitation and sensitivity analysis.
• Analytical solutions and efficient MCMC algorithms are provided for complex cases.
• Empirical examples demonstrate utility in estimation, hypothesis testing, and sensitivity analysis.

Conclusions:

• The BREASE framework offers a powerful and interpretable Bayesian approach for RCT analysis.
• It enhances causal inference by providing clinically relevant parameterizations and flexible priors.
• The framework facilitates robust estimation, hypothesis testing, and sensitivity analysis of treatment effects.