The New England Journal of Statistics in Data Science

The timing of longitudinal measurements may depend upon outcome or disease severity. In biomedical studies relying on clinical encounter data, patients often have dense, irregular collections of visit data when suffering a worse health condition. In parallel, the longitudinal measurements may be impacted by the period of irregular visiting. Ignoring the impact of the outcome-dependent visiting process when constructing a longitudinal disease progression model can produce biased results. We propose a Bayesian joint model linking a mixed-effects model for the longitudinal marker and Weibull proportional hazards model with a log frailty for the visiting process, adjusting both longitudinal marker and event processes with covariates. We examine different random effect structures and performance characterizing disease trajectory. Motivated by clinical data on cystic fibrosis lung disease, we estimate the longitudinal process for lung function decline. Individuals with lower lung function tend to have more frequent clinical visits than those with higher lung function. Simulation studies suggest that incorporating a time-dependent Gaussian process is more important for model fit than adding the survival model via joint modeling; the random intercepts model exhibits maximum bias, especially when there is an outcome-dependent visiting process.