Joint modelling of longitudinal biomarker and gap time between recurrent events: copula-based dependence

In this paper, we will extend the joint model of longitudinal biomarker and recurrent event via copula function for accounting the dependence between the two processes. The general idea of joining separate processes by allowing model-specific random effect may come from different families distribution. It is a main advantage of the proposed method that a copula construction does not constrain the choice of marginal distributions of random effects. A maximum likelihood estimation with importance sampling technique as a simple and easy understanding method is employed to model inference. To evaluate and verify the validation of the proposed joint model, a bootstrapping method as a model-based resampling is developed. Our proposed joint model is also applied to pemphigus disease data for assessing the effect of biomarker trajectory on risk of recurrence.