Model selection for causal inference in missing exposure problems

In causal inference, properly selecting the propensity score (PS) model is an important topic and has been widely investigated in observational studies. However, there are very few studies investigating the model selection issue for causal inference when the exposure is missing at random (MAR). When the exposure variable contains missing data, an intuitive approach is to impute the missing exposure values first and perform a PS analysis on the imputed dataset under MAR assumption. In this article, we discuss how to select both imputation and PS models. We then propose a new criterion, termed the “rank score,” for evaluating the overall performance of both models. Simulation studies show that the full imputation plus the outcome‐related PS models leads to the smallest root mean squared error, and the rank score can help select the best models. An application study is conducted to quantify the causal effect of cardiovascular disease on the mortality of COVID‐19 patients.