Bayesian Model Averaging for Propensity Score Analysis.

Area of Science:

• Statistics
• Biostatistics
• Causal Inference

Background:

• Propensity score methods are crucial for causal inference in observational studies.
• Uncertainty in propensity score model selection can bias causal effect estimates.
• Bayesian model averaging (BMA) offers a framework to handle model uncertainty.

Purpose of the Study:

• To investigate Bayesian model averaging (BMA) for propensity score variable selection.
• To compare approximate and fully Bayesian BMA approaches.
• To assess the impact of priors and Occam's window size on causal estimates and prediction.

Main Methods:

• Implemented an approximate BMA approach using the R package BMA.
• Developed a fully Bayesian BMA approach using Markov chain Monte Carlo (MCMC) sampling.
• Evaluated methods with varying prior specifications and Occam's window sizes.

Main Results:

• Both BMA approaches recovered treatment effect estimates well.
• BMA generally yielded larger uncertainty estimates compared to single-model approaches.
• BMA approaches showed improved propensity score prediction and covariate balance.

Conclusions:

• Bayesian model averaging is a robust strategy for propensity score model selection.
• The fully Bayesian approach provides posterior intervals for balance indices.
• BMA enhances the reliability of causal inference from observational data.