Semiparametric Modeling and Estimation of the Terminal Behavior of Recurrent Marker Processes Before Failure Events

Kwun Chuen Gary Chan, Mei Cheng Wang

Research output: Contribution to journalArticlepeer-review


Recurrent event processes with marker measurements are mostly and largely studied with forward time models starting from an initial event. Interestingly, the processes could exhibit important terminal behavior during a time period before occurrence of the failure event. A natural and direct way to study recurrent events prior to a failure event is to align the processes using the failure event as the time origin and to examine the terminal behavior by a backward time model. This article studies regression models for backward recurrent marker processes by counting time backward from the failure event. A three-level semiparametric regression model is proposed for jointly modeling the time to a failure event, the backward recurrent event process, and the marker observed at the time of each backward recurrent event. The first level is a proportional hazards model for the failure time, the second level is a proportional rate model for the recurrent events occurring before the failure event, and the third level is a proportional mean model for the marker given the occurrence of a recurrent event backward in time. By jointly modeling the three components, estimating equations can be constructed for marked counting processes to estimate the target parameters in the three-level regression models. Large sample properties of the proposed estimators are studied and established. The proposed models and methods are illustrated by a community-based AIDS clinical trial to examine the terminal behavior of frequencies and severities of opportunistic infections among HIV-infected individuals in the last 6 months of life.

Original languageEnglish (US)
Pages (from-to)351-362
Number of pages12
JournalJournal of the American Statistical Association
Issue number517
StatePublished - Jan 2 2017


  • Marked counting process
  • Partial likelihood
  • Recurrent event process
  • Semiparametric models

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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