Joint Modeling of Longitudinal Data and Potentially Informative Visiting Process to Dynamically Predict Future Visit Times.

Frequent visits in cohort studies are important as they enable, among others, the assessment of disease progression and treatment effectiveness. In HIV studies, extended intervals between visits have been shown to be associated with adverse outcomes (e.g., antiretroviral therapy interruption). Prediction of the next visit time can be a useful tool in identifying those more prone to (temporarily) disengage from care. Since visit times are to a large extent individually driven, patient characteristics such as longitudinal markers history and past visit patterns have to be taken into account when dealing with the prediction of future visit times. The topic of dynamic prediction has been developed greatly, especially within the framework of joint models of longitudinal and survival data. While joint models have been extended to account for an informative visiting process, little attention has been given in the dynamic prediction of the next visit time. In this study we propose a model for the joint analysis of a longitudinal continuous marker and the visiting process. A gap time mechanism is employed for the visiting process, while a linear mixed model is used for the marker. The two submodels are linked via correlated normally distributed random effects. The resulting form of the marginal likelihood requires only uni-dimensional integration, irrespective of the dimension of the random effects in the longitudinal model, a property that holds with multiple continuous markers. The model is used to derive dynamic predictions for the time to the next visit, conditioning on patient's previous gap times and marker history. The performance of the proposed methodology is assessed through simulation. Finally, we apply the proposed model to data of people living with HIV from the Athens Multicenter AIDS Cohort Study.