title: Two-stage estimation for multivariate recurrent event data with a dependent terminal event.
abstract: Recurrent event data arise in longitudinal follow-up studies, where each subject may experience the same type of events repeatedly. The work in this article is motivated by the data from a study of repeated peritonitis for patients on peritoneal dialysis. Due to the aspects of medicine and cost, the peritonitis cases were classified into two types: Gram-positive and non-Gram-positive peritonitis. Further, since the death and hemodialysis therapy preclude the occurrence of recurrent events, we face multivariate recurrent event data with a dependent terminal event. We propose a flexible marginal model, which has three characteristics: first, we assume marginal proportional hazard and proportional rates models for terminal event time and recurrent event processes, respectively; second, the inter-recurrences dependence and the correlation between the multivariate recurrent event processes and terminal event time are modeled through three multiplicative frailties corresponding to the specified marginal models; third, the rate model with frailties for recurrent events is specified only on the time before the terminal event. We propose a two-stage estimation procedure for estimating unknown parameters. We also establish the consistency of the two-stage estimator. Simulation studies show that the proposed approach is appropriate for practical use. The methodology is applied to the peritonitis cohort data that motivated this study.
authors.affiliation: Department of Statistics and Informatics Science, Providence University, Taichung, 43301, Taiwan, Republic of China; Department of Financial and Computational Mathematics, Providence University, Taichung, 43301, Taiwan, Republic of China.
authors.forename: Chyong-Mei
authors.initials: CM
authors.lastname: Chen
authors.forename: Ya-Wen
authors.initials: YW
authors.lastname: Chuang
authors.forename: Pao-Sheng
authors.initials: PS
authors.lastname: Shen
mesh_terms: D001699:Biometry / Q000379:methods*; D005260:Female; D005500:Follow-Up Studies; D006801:Humans; D008297:Male; D015233:Models, Statistical; D015999:Multivariate Analysis; D010530:Peritoneal Dialysis / Q000009:adverse effects; D010538:Peritonitis / Q000209:etiology; D012008:Recurrence; D016896:Treatment Outcome
keywords: Dependent terminal event; Frailty; Multivariate recurrent event data; Proportional hazards model; Two-stage estimation