Using link-preserving imputation for logistic partially linear models with missing covariates

To handle missing data one needs to specify auxiliary models such as the probability of observation or imputation model. Doubly robust (DR) method uses both auxiliary models and produces consistent estimation when either of the model is correctly specified. While the DR method in estimating equation approaches could be easy to implement in the case of missing outcomes, it is computationally cumbersome in the case of missing covariates especially in the context of semiparametric regression models. In this paper, we propose a new kernel-assisted estimating equation method for logistic partially linear models with missing covariates. We replace the conditional expectation in the DR estimating function with an unbiased estimating function constructed using the conditional mean of the outcome given the observed data, and impute the missing covariates using the so called link-preserving imputation models to simplify the estimation. The proposed method is valid when the response model is correctly specified and is more efficient than the kernel-assisted inverse probability weighting estimator by Liang (2008). The proposed estimator is consistent and asymptotically normal. We evaluate the finite sample performance in terms of efficiency and robustness, and illustrate the application of the proposed method to the health insurance data using the 2011-2012 National Health and Nutrition Examination Survey, in which data were collected in two phases and some covariates were partially missing in the second phase.