Keywords: Causal Inference, Double Robustness, Time Dependent Confounders, Rubin’s Causal Model
Observational studies lack randomized treatment assignment; thus valid inference about causal e?ects requires controlling for confounders. When time dependent confounders are present that serve as mediators of treatment e?ects and a?ect future treatment assignment – “confounding by indication” - standard regression methods to control for confounders fail. We propose a robust Bayesian approach to causal inference in this setting called Penalized Spline of Propensity Methods for Treatment Comparison (PENCOMP). It relies on the balancing property of propensity score to achieve double robustness by modeling the relationship between propensity scores and potential outcomes as a penalized spline regression. PENCOMP imputes missing potential outcomes with ?exible spline models, and draws inference based on imputed and observed outcomes. We demonstrate that PENCOMP has a double robustness property for causal e?ects, and simulations suggest that it tends to outperform doubly-robust marginal structural modeling when the weights are variable. We estimate the e?ect of antiretroviral treatment on CD4 counts in HIV infected patients using data from the Multicenter AIDS Cohort study (MACS).