Information projection approach to smoothed propensity score weighting for handling selection bias under missing at random

Propensity score weighting is widely used to correct the selection bias in the sample with missing data. The propensity score function is often developed using a model for the response probability, which completely ignores the outcome regression model. In this paper, we explore an alternative approach by developing smoothed propensity score weights that provide a more efficient estimation by removing unnecessary auxiliary variables in the propensity score model. The smoothed propensity score function is obtained by applying the information projection of the original propensity score function to the space that satisfies the moment conditions on the balancing scores obtained from the outcome regression model. By including the covariates for the outcome regression models only in the density ratio model, we can achieve an efficiency gain. Penalized regression is used to identify important covariates. Some limited simulation studies are presented to compare with the existing methods.