Multiply Robust Weighted Generalized Estimating Equations for Incomplete Longitudinal Binary Data Using Empirical Likelihood

In clinical trials, missing data may lead to serious misinterpretation of trial results. To address this issue, it is important to collect post-randomization data (such as efficacy measurement data and adverse event onset data). Such post-randomization data are called auxiliary variables and they can be useful for constructing missingness and imputation models. A multiply robust estimator using an empirical likelihood method was previously proposed by Han and Wang and by Han. However, that estimator was developed for cross-sectional data and situations in which no auxiliary variables are missing. This is contrary to actual clinical trial settings, in which some auxiliary variables will invariably be missing. Consequently, to apply Han’s method to longitudinal data, missing auxiliary variables need to be imputed. This article proposes a new method that extends Han’s method to a longitudinal outcome model by applying weighted generalized estimating equations with new weights. Monte Carlo simulations of a repeated binary response with missing at random dropouts demonstrated that the proposed estimator is multiply robust and exhibits better performance than that of augmented inverse probability weighted complete-case estimating equations under several simulation scenarios. We also successfully applied the proposed method to plaque psoriasis study data.