Assessing treatment effect heterogeneity in the presence of missing effect modifier data in cluster-randomized trials

Understanding whether and how treatment effects vary across individuals is crucial to inform clinical practice and recommendations. Accordingly, the assessment of heterogeneous treatment effects (HTE) based on pre-specified potential effect modifiers has become a common goal in modern randomized trials. However, when one or more potential effect modifiers are missing, complete-case analysis may lead to bias, under-coverage, inflated type I error, or low power. While statistical methods for handling missing data have been proposed and compared for individually randomized trials with missing effect modifier data, few guidelines exist for the cluster-randomized setting, where intracluster correlations in the effect modifiers, outcomes, or even missingness mechanisms may introduce further threats to accurate assessment of HTE. In this paper, the performance of various commonly-used missing data methods (complete case analysis, single imputation, multiple imputation, multilevel multiple imputation [MMI], and Bayesian MMI) are neutrally compared in a simulation study of cluster-randomized trials with missing effect modifier data. Thereafter, we impose controlled missing data scenarios to a potential effect modifier from the Work, Family, and Health Study to further compare the available methods using real data. Our simulations and data application suggest that MMI and Bayesian MMI have better performance than other available methods, and that Bayesian MMI has improved bias and coverage over standard MMI when there are model specification or compatibility issues. We also provide recommendations for practitioners and outline future research areas.