Doubly robust criterion for causal inference

In causal inference, semiparametric estimation using propensity scores has rapidly developed in various directions. At the same time, although model selection is indispensable in statistical analysis, an information criterion for selecting the regression structure between the potential outcome and explanatory variables has not been well developed. Here, based on the original definition of AIC, we derive an AIC-type criterion for propensity score analysis. A risk based on the Kullback–Leibler divergence is defined as the cornerstone, and general causal inference models and general causal effects are treated. Considering the high importance of doubly robust estimation, we make the information criterion itself doubly robust so that it is an asymptotically unbiased estimator of the risk even under some model misspecification. In simulation studies, we compare the derived criterion with an existing weighted quasi-likelihood information criterion and confirm that the former outperforms the latter. Real data analyses indicate that results using the two criteria can differ significantly.