A New Multilevel Bayesian Nonparametric Algorithm and Its Application in Causal Inference

Abstract

Propensity score methods (PSM) has become one of the most advanced and popular strategies for casual analysis in observational studies. However, there are substantial challenges that PSM face, such as biased estimation when lacking common support and model misspecification. Recently, the Bayesian Additive regression trees (BART) algorithms has shown its great potentials for both robust and accurate estimation in causal inference. The proposed Multilevel BART (M-BART) estimated the fixed-effect components and random-effect component using a Single-level BART (S-BART) and Linear Mixed Effect model, respective under the Expectation-Maximization Framework. The M-BART could handle both continuous and dichotomous outcome and could be used to estimate the propensity scores (PS_(M-BART)) or to model the potential outcomes directly (DE_(M-BART)). In the first study, the use of M-BART algorithm was demonstrated using a well-known multilevel public dataset. A follow-up simulation study that mimics the empirical dataset was conducted. Results suggested, DE_(M-BART) is a highly efficient alternative approach to the PS_(M-BART) and generates more accurate ATE estimation, better confidence interval coverage, and eliminates the complexity of PSM implementation. In the second study, the performance of PS_(M-BART) and DE_(M-BART) were investigate in a full-scale simulation study and compared with S-BART methods (DE_(S-BART) and PS_(S-BART)) and PSM using logistic regression models (PS_FE and PS_ME). The results suggested that M-BART methods, especially PS_(M-BART) generated more desirable treatment effect estimation compared to S-BART methods and PSM using logits regression models and show great capacities in dealing with nonlinearity, cluster effects and treatment effect heterogeneity.