Model-based Bayesian inference under computer assisted balance-improving designs.

Area of Science:

• Statistics
• Biostatistics
• Experimental Design

Background:

• Complete randomization can lead to covariate imbalance.
• Covariate-balanced designs improve precision but complicate inference.
• Existing methods for inference in covariate-balanced designs are often asymptotic.

Purpose of the Study:

• To propose model-based Bayesian inference as a general method for analyzing covariate-balanced randomized experiments.
• To compare the finite sample performance of Bayesian inference with existing methods.
• To address challenges in inference with arbitrary covariate balancing criteria and complex estimands.

Main Methods:

• Developed a model-based Bayesian inference framework for covariate-balanced designs.
• Focused on linear outcome models and the Sample Average Treatment Effect (SATE) as an estimand.
• Conducted a large Monte Carlo simulation study to compare methods.

Main Results:

• Bayesian inference demonstrated superior finite sample performance compared to previous methods in small to moderate sample sizes.
• Regression adjustment with small-sample adjusted standard errors also showed improved performance.
• The proposed Bayesian method handles arbitrary balancing criteria and complex estimands effectively.

Conclusions:

• Model-based Bayesian inference is a preferred method for analyzing covariate-balanced randomized experiments, especially with limited sample sizes.
• The Bayesian approach provides a flexible and robust framework for treatment effect estimation.
• Regression adjustment offers a viable alternative when Bayesian methods are not feasible.