Protective estimation of mixed-effects logistic regression when data are not missing at random

Abstract

We consider estimation of mixed-effects logistic regression models for longitudinal data when missing outcomes are not missing at random. A typology of missingness mechanisms is presented that includes missingness dependent on observed or missing current outcomes, observed or missing lagged outcomes and subject-specific effects. When data are not missing at random, consistent estimation by maximum marginal likelihood generally requires correct parametric modelling of the missingness mechanism, which hinges on unverifiable assumptions. We show that standard maximum conditional likelihood estimators are protective in the sense that they are consistent for monotone or intermittent missing data under a wide range of missingness mechanisms. Our approach requires neither specification of parametric models for the missingness mechanism nor refreshment samples and is straightforward to implement in standard software.