A Likelihood-Based Approach with Shared Latent Random Parameters for the Longitudinal Binary and Informative Censoring Processes

Longitudinal studies with binary outcomes characterized by informative right censoring are commonly encountered in clinical, basic, behavioral, and health sciences. Approaches developed to analyze data with binary outcomes were mainly tailored to clustered or longitudinal data with missing completely at random or at random. Studies that focused on informative right censoring with binary outcomes are characterized by their imbedded computational complexity and difficulty of implementation. Here we present a new maximum likelihood-based approach with repeated binary measures modeled in a generalized linear mixed model as a function of time and other covariates. The longitudinal binary outcome and the censoring process determined by the number of times a subject is observed share latent random variables (random intercept and slope) where these subject-specific random effects are common to both models. A simulation study and sensitivity analysis were conducted to test the model under different assumptions and censoring settings. Our results showed accuracy of the estimates generated under this model when censoring was fully informative or partially informative with dependence on the slopes. A successful implementation was undertaken on a cohort of renal transplant patients with blood urea nitrogen as a binary outcome measured over time to indicate normal and abnormal kidney function until the emanation of graft rejection that eventuated in informative right censoring. In addition to its novelty and accuracy, an additional key feature and advantage of the proposed model is its viability of implementation on available analytical tools and widespread application on any other longitudinal dataset with informative censoring.