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

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  • Kwun Chuen Gary Chan
  • Mei-Cheng Wang

Abstract

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.

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  • Kwun Chuen Gary Chan & Mei-Cheng Wang, 2017. "Semiparametric Modeling and Estimation of the Terminal Behavior of Recurrent Marker Processes Before Failure Events," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 351-362, January.
  • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:517:p:351-362
    DOI: 10.1080/01621459.2016.1140051
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    1. Kwun Chuen Gary Chan, 2018. "Commentary: Alignment of time scales and joint models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(4), pages 601-604, October.
    2. Jie Zhou & Xin Chen & Xinyuan Song & Liuquan Sun, 2021. "A joint modeling approach for analyzing marker data in the presence of a terminal event," Biometrics, The International Biometric Society, vol. 77(1), pages 150-161, March.

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