On aspects of robustness and sensitivity in missing data methods

Missing data are common wherever statistical methods are applied in practice. They present a problem by demanding that additional untestable assumptions be made about the mechanism leading to the incompleteness of the data. Minimising the strength of these assumptions and assessing the sensitivity of conclusions to their possible violation constitute two important aspects of current research in this area. One attractive approach is the doubly robust (DR) weighting-based method proposed by Robins and colleagues. By incorporating two models for the missing data process, inferences are valid when at least one model is correctly specified. The balance between robustness, efficiency and analytical complexity is one which is difficult to strike, resulting in a split between the likelihood and multiple imputation (MI) school on one hand and the weighting and DR school on the other. We propose a new method, doubly robust multiple imputation (DRMI), combining the convenience of MI with the robustness of the DR approach, and explore the use of our new estimator for non-monotone missing at random data, a setting in which, hitherto, estimators with the DR property have not been implemented. We apply the method to data from a clinical trial comparing type II diabetes drugs, where we also use MI as a tool to explore sensitivity to the missing at random assumption. Finally, we study DRMI in the longitudinal binary data setting and find that it compares favourably with existing methods