Joint Scale-Change Models for Recurrent Events and Failure Time

ABSTRACT

Recurrent event data arise frequently in various fields such as biomedical sciences, public health, engineering, and social sciences. In many instances, the observation of the recurrent event process can be stopped by the occurrence of a correlated failure event, such as treatment failure and death. In this article, we propose a joint scale-change model for the recurrent event process and the failure time, where a shared frailty variable is used to model the association between the two types of outcomes. In contrast to the popular Cox-type joint modeling approaches, the regression parameters in the proposed joint scale-change model have marginal interpretations. The proposed approach is robust in the sense that no parametric assumption is imposed on the distribution of the unobserved frailty and that we do not need the strong Poisson-type assumption for the recurrent event process. We establish consistency and asymptotic normality of the proposed semiparametric estimators under suitable regularity conditions. To estimate the corresponding variances of the estimators, we develop a computationally efficient resampling-based procedure. Simulation studies and an analysis of hospitalization data from the Danish Psychiatric Central Register illustrate the performance of the proposed method. Supplementary materials for this article are available online.

KEYWORDS:

• Accelerated failure time model
• Frailty
• Informative censoring
• Marginal models
• Semiparametric methods

Supplement Materials

The supplementary materials contain additional simulation results and the proof of the main theorem.

Acknowledgment

The authors thank the editors and referees for their helpful comments. The authors also thank Drs. Preben Bo Mortensen and William Eaton for kindly sharing the anonymous Denmark schizophrenia data.

Funding

Xu's work was partially supported by IES grant R305D160010 and NSA grant H98230-16-1-0299. Chiou's work was supported in part by the Harvard NeuroDiscovery Center and NIH T32NS048005. Huang and Wang's work was sponsored by National Institutes of Health grant R01CA193888. Yan's research was partially supported by National Science Foundation grant DMS1209022.