A Random Effects Transition Model For Longitudinal Binary Data With Informative Missingness

Understanding the transitions between disease states is often the goal in studying chronic disease. These studies, however, are typically subject to a large amount of missingness either due to patient dropout or intermittent missed visits. The missing data is often informative since missingness and dropout are usually related to either an individual's underlying disease process or the actual value of the missed observation. Our motivating example is a study of opiate addiction that examined the effect of a new treatment on thrice‐weekly binary urine tests to assess opiate use over follow‐up. The interest in this opiate addiction clinical trial was to characterize the transition pattern of opiate use (in each treatment arm) as well as to compare both the marginal probability of a positive urine test over follow‐up and the time until the first positive urine test between the treatment arms. We develop a shared random effects model that links together the propensity of transition between states and the probability of either an intermittent missed observation or dropout. This approach allows for heterogeneous transition and missing data patterns between individuals as well as incorporating informative intermittent missing data and dropout. We compare this new approach with other approaches proposed for the analysis of longitudinal binary data with informative missingness.