  Gaussian process (GP) covariance function is proposed as a matching tool in
GPMatch within a full Bayesian framework under relatively weaker causal
assumptions. The matching is accomplished by utilizing GP prior covariance
function to define matching distance. We show that GPMatch provides a doubly
robust estimate of the averaged treatment effect (ATE) much like the
G-estimation, the ATE is correctly estimated when either conditions are
satisfied: 1) the GP mean function correctly specifies potential outcome
\(Y^{(0)}\); or 2) the GP covariance function correctly specifies matching
structure. Simulation studies were carried out without assuming any known
matching structure nor functional form of the outcomes. 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 effectiveness of early aggressive use of biological medication
in treating children with newly diagnosed Juvenile Idiopathic Arthritis, using
data extracted from electronic medical records.
