Myocardial infarction (MI) and stroke are the most common acute life-threatening cardiovascular disease (CVD) events and are triggered by the rupture of lipid-rich plaques in the arterial wall during the progression of atherosclerosis. Thus, they share a common pathology and preventive interventions. However, the association between the recurrent events of MI and stroke among CVD patients as the disease progresses remains unclear. In this study, we propose a bivariate Markov model to describe the multistate of recurrent events of MI and stroke. A partial likelihood approach was adopted by using the Sarkar's absolutely continuous bivariate exponential distribution (ACBVE) separately for the transitions among different states. The parametric model estimates the hazard function at each state and thus takes more information than an alternative semiparametric approach. As an illustrative example, we analyzed recurrent events of MI and stroke in individuals from the Taiwan National Health Insurance Research Database. Comparisons with the nonparametric Aalen-Johansen estimator for each state showed that the parametric ACBVE explained the data well. The correlation coefficients between the first recurrent MI and stroke tended to increase as the state of disease status progresses. The proposed two-dimensional multistate Markov model may be employed to describe the progressive comorbidity of two associated diseases.
