Doubly Robust Semiparametric Estimation for Multi-group Causal Comparisons

In biomedical research, especially in epidemiological studies, we often need to compare nonrandomized groups, as randomization is only sometimes feasible. Even in randomized clinical trials, the actual treatment assignments may not be completely random, or the covariates may be imbalanced between treatment and control groups. It is known that naive estimates of treatment effects are biased if treatments are not randomized or covariates not balanced. Various causal inference methods have been proposed to debias or correct the bias. The doubly robust (DR) method is a more recent development that aims to ensure the robustness of the causal estimates to model assumptions. However, the DR method may still be significantly biased even when the model is only mildly misspecified. Motivated by the need to increase the robustness of multi-group causal estimates, e.g., treatments in multiarm clinical trials, and the effects of multiple levels of smoking intensity on health outcomes in epidemiological studies, this article proposes a semiparametric doubly robust estimator for multigroup causal effects, in which both the propensity score and the outcome models are specified semiparametrically with link functions estimated by shape-restricted maximum likelihood. The approach is shown to be highly robust against model assumptions, enhancing the double robustness. After deriving the asymptotic properties of the proposed DR estimators, we perform simulations to demonstrate the finite sample properties of the proposed estimators and compare them with parametric and naive estimators. We then apply the method to analyzing the effect of smoking intensity on health outcomes in the National Epidemiology Follow-up Study.