Lifetime Data Analysis

, Volume 23, Issue 2, pp 207–222 | Cite as

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.


Induced informative censoring Marked variables Medical cost data Nonparametric estimation Recurrent events 



The authors would like to thank Dr. Arthur Moss and Dr. Hongwei Zhao for access to the MADIT-II data. The authors would also like to thank the editor, an associate editor and three reviewers for their constructive comments that greatly improved the paper. Kwun Chuen Gary Chan is partially supported by US National Institutes of Health Grant R01 HL 122212.

Supplementary material

10985_2015_9347_MOESM1_ESM.pdf (38 kb)
Supplementary material 1 (pdf 38 KB)


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Copyright information

© Springer Science+Business Media New York (outside the USA) 2015

Authors and Affiliations

  1. 1.Center for Devices and Radiological HealthU.S. Food and Drug AdministrationSilver SpringUSA
  2. 2.Department of BiostatisticsUniversity of WashingtonSeattleUSA

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