Data_Sheet_1_GPMatch: A Bayesian causal inference approach using Gaussian process covariance function as a matching tool.PDF

A Gaussian process (GP) covariance function is proposed as a matching tool for causal inference within a full Bayesian framework under relatively weaker causal assumptions. We demonstrate that matching can be accomplished by utilizing GP prior covariance function to define matching distance. The matching properties of GPMatch is presented analytically under the setting of categorical covariates. Under the conditions of either (1) GP mean function is correctly specified; or (2) the GP covariance function is correctly specified, we suggest GPMatch possesses doubly robust properties asymptotically. Simulation studies were carried out without assuming any a priori knowledge of the functional forms of neither the outcome nor the treatment assignment. The results demonstrate that GPMatch enjoys well-calibrated frequentist properties and outperforms many widely used methods including Bayesian Additive Regression Trees. The case study compares the effectiveness of early aggressive use of biological medication in treating children with newly diagnosed Juvenile Idiopathic Arthritis, using data extracted from electronic medical records. Discussions and future directions are presented.