Nonparametric inference for the joint distribution of recurrent marked variables and recurrent survival time

Time between recurrent medical events may be correlated with the cost incurred at each event. As a result, it may be of interest to describe the relationship between recurrent events and recurrent medical costs by estimating a joint distribution. In this paper, we propose a nonparametric estimator for the joint distribution of recurrent events and recurrent medical costs in right-censored data. We also derive the asymptotic variance of our estimator, a test for equality of recurrent marker distributions, and present simulation studies to demonstrate the performance of our point and variance estimators. Our estimator is shown to perform well for a wide range of levels of correlation, demonstrating that our estimators can be employed in a variety of situations when the correlation structure may be unknown in advance. We apply our methods to hospitalization events and their corresponding costs in the second Multicenter Automatic Defibrillator Implantation Trial (MADIT-II), which was a randomized clinical trial studying the effect of implantable cardioverter-defibrillators in preventing ventricular arrhythmia.