Enhanced Doubly Robust Procedure for Causal Inference

In the last two decades, doubly robust estimators (DREs) have been developed for causal inference on various target parameters derived from different study designs. The approach combines propensity score and outcome models of the confounding variables. It yields unbiased estimator of the target parameter if at least one of the two models is correctly specified, a desirable property and an improvement on the inverse propensity score weighted estimate. However, in practice it is difficult to know what the correct model could be and both propensity score and outcome models may be incorrectly specified. Furthermore, it is known that DRE may fail and give estimates with large bias and variance, even when the propensity and/or outcome models are mildly misspecified. To reduce such risk and increase robustness in inference, we propose an enhanced DRE method utilizing semiparametric models with nonparametric monotone link functions for both the propensity score and the outcome models. The models are estimated using an iterative procedure incorporating the pool adjacent violators algorithm. We then study the asymptotic properties of the enhanced DREs. Simulation studies, performed to evaluate their finite sample performance, demonstrated clear superiority to several commonly used doubly robust procedures with reduced bias and increased efficiency even with both models are misspecified, thus enhancing the robustness of DRE. The method is then applied to analyzing a clinical trial from the AIDS Clinical Trials Group and the National Epidemiology Follow-up Study.