Doubly robust augmented-estimating-equations estimation with nonignorable nonresponse data

The problem of nonignorable nonresponse data is ubiquitous in medical and social science studies. Analyses focused only on the missing-at-random assumption may lead to biased results. Various debias methods have been extensively studied in the literature, particularly the doubly robust (DR) estimators. We propose DR augmented-estimating-equations (AEE) estimators of the mean response which enjoy the double-robustness property under correct specification of the log odds ratio model. An advantage of DR AEE estimators is that they can efficiently use the completely observed covariates to improve estimation efficiency of existing DR estimators with nonignorable nonresponse data. We propose a model selection criterion that can consistently select the correct parametric model of the log odds ratio model from a group of candidate models. Moreover, the correctness of the required working models can be evaluated via straightforward goodness-of-fit tests. Simulation results indicate that doubly robust augmented-estimating-equations estimators are very robust to a misspecification of the baseline outcome density model or the baseline response model and dominate other competitors in the sense of having smaller mean-square errors. The analysis of a real dataset illustrates the flexibility and usefulness of the proposed methods.