Model Selection for Causal Modeling in Missing Exposure Problems

In causal inference, properly selecting the propensity score (PS) model is a popular topic and has been widely investigated in observational studies. In addition, there is a large literature concerning the missing data problem. However, there are very few studies investigating the model selection issue for causal inference when the exposure is missing at random (MAR). In this paper, we discuss how to select both imputation and PS models, which can result in the smallest RMSE of the estimated causal effect. Then, we provide a new criterion, called the ``rank score" for evaluating the overall performance of both models. The simulation studies show that the full imputation plus the outcome-related PS models lead to the smallest RMSE and the rank score can also pick the best models. An application study is conducted to study the causal effect of CVD on the mortality of COVID-19 patients.