Multiply Robust Estimation in Regression Analysis With Missing Data

Doubly robust estimators are widely used in missing-data analysis. They provide double protection on estimation consistency against model misspecifications. However, they allow only a single model for the missingness mechanism and a single model for the data distribution, and the assumption that one of these two models is correctly specified is restrictive in practice. For regression analysis with possibly missing outcome, we propose an estimation method that allows multiple models for both the missingness mechanism and the data distribution. The resulting estimator is consistent if any one of those multiple models is correctly specified, and thus provides multiple protection on consistency. This estimator is also robust against extreme values of the fitted missingness probability, which, for most doubly robust estimators, can lead to erroneously large inverse probability weights that may jeopardize the numerical performance. The numerical implementation of the proposed method through a modified Newton–Raphson algorithm is discussed. The asymptotic distribution of the resulting estimator is derived, based on which we study the estimation efficiency and provide ways to improve the efficiency. As an application, we analyze the data collected from the AIDS Clinical Trials Group Protocol 175.