Mixed Effects Logistic Regression Models for Longitudinal Binary Response Data with Informative Drop-Out

Abstract

A shared parameter model with logistic link is presented for longitudinal binary response data to accommodate informative drop-out. The model consists of observed longitudinal and missing response components that share random effects parameters. To our knowledge, this is the first presentation of such a model for longitudinal binary response data. Comparisons are made to an approximate conditional logit model in terms of a clinical trial dataset and simulations. The naive mixed effects logit model that does not account for informative drop-out is also compared. The simulation-based differences among the models with respect to coverage of confidence intervals, bias, and mean squared error (MSE) depend on at least two factors: whether an effect is a between- or within-subject effect and the amount of between-subject variation as exhibited by variance components of the random effects distributions. When the shared parameter model holds, the approximate conditional model provides confidence intervals with good coverage for within-cluster factors but not for between-cluster factors. The converse is true for the naive model. Under a different drop-out mechanism, when the probability of drop-out is dependent only on the current unobserved observation, all three models behave similarly by providing between-subject confidence intervals with good coverage and comparable MSE and bias but poor within-subject confidence intervals, MSE, and bias. The naive model does more poorly with respect to the within-subject effects than do the shared parameter and approximate conditional models. The data analysis, which entails a comparison of two pain relievers and a placebo with respect to pain relief, conforms to the simulation results based on the shared parameter model but not on the simulation based on the outcome-driven drop-out process. This comparison between the data analysis and simulation results may provide evidence that the shared parameter model holds for the pain data.