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

Abstract

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.

Keywords:

• Auxiliary variables
• Imputation model
• Missing at random
• Monte Carlo simulation
• Plaque psoriasis

Supplementary Materials

Additional supporting information for the web appendices and tables referenced in Sections 2.6, 3.3, and 5 may be found online in supplementary materials section at the end of the article.

Acknowledgments

We thank Maruho Co., Ltd., Japan, for providing the plaque psoriasis phase III trial data. We are deeply grateful to Dr. Katsuhiro Omae for invaluable advice provided.

Disclosure Statement

Hiroshi Komazaki is an employee of Maruho Co., Ltd. Masaaki Doi is an employee of Ono Pharmaceutical Co., Ltd. Naohiro Yonemoto is an employee of Pfizer Japan Inc.

Additional information

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Japan Agency for Medical Research and Development10.13039/100009619 [grant number JP16lk0201061].