Bayesian nonparametric generative models for causal inference with missing at random covariates.

Area of Science:

• Statistics
• Biostatistics
• Epidemiology

Background:

• Causal inference in observational studies is challenging due to unobserved confounding.
• Existing methods often rely on restrictive parametric assumptions.
• Handling missing covariate data requires separate imputation steps, potentially introducing bias.

Purpose of the Study:

• To propose a general Bayesian nonparametric (BNP) approach for causal inference in the point treatment setting.
• To develop a method that flexibly models the joint distribution of outcomes, treatments, and confounders.
• To enable robust estimation of various causal effects (differences, ratios, quantile effects) and handle missing covariates.

Main Methods:

• Utilized an enriched Dirichlet process to model the joint distribution of observed data.
• Integrated causal assumptions to identify causal effects.
• Employed Gibbs sampling for computational efficiency.
• Incorporated data augmentation for imputing missing covariates under ignorable missingness.

Main Results:

• The proposed BNP model avoids parametric assumptions on confounder distributions.
• The method allows for flexible estimation of marginal and subpopulation causal effects.
• Integrated covariate imputation guarantees congeniality between imputation and analysis models.
• Simulation studies demonstrated the method's performance.

Conclusions:

• The developed BNP approach provides a powerful and flexible framework for causal inference.
• It effectively addresses challenges of complex data structures and missing covariate information.
• The method is applicable to real-world observational studies, such as those involving co-infected patients.