A time‐varying Bayesian joint hierarchical copula model for analysing recurrent events and a terminal event: an application to the Cardiovascular Health Study

Recurrent events could be stopped by a terminal event, which commonly occurs in biomedical and clinical studies. Taking the Cardiovascular Health Study as a motivating example, patients can experience recurrent events of myocardial infarction (MI) or stroke during follow‐up, which, however, can be truncated by death. Since death could be a devastating complication of MI or stroke recurrences, ignoring dependent censoring when analysing recurrent events may lead to invalid inference. The joint shared frailty model is widely used but with several limitations: two event processes are conditionally independent given the subject level frailty, which could be violated because the dependence may rely on unknown covariates varying across recurrences; the correlation between recurrent events and death is constant over time because of the same frailty within subject, but MI or stroke recurrences could have a time‐varying influence on death due to higher risk of another event of MI or stroke after the first. We propose a time‐varying joint hierarchical copula model under the Bayesian framework to accommodate correlation between recurrent events and dependence between two event processes which may change over time. The performance of our method is extensively evaluated by simulation studies, and lastly by the Cardiovascular Health Study for illustration.