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Statistical inference methods for recurrent event processes with shape and size parameters

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  • Mei-Cheng Wang
  • Chiung-Yu Huang

Abstract

This paper proposes a unified framework to characterize the rate function of a recurrent event process through shape and size parameters. In contrast to the intensity function, which is the event occurrence rate conditional on the event history, the rate function is the occurrence rate unconditional on the event history, and thus it can be interpreted as a population-averaged count of events in unit time. In this paper, shape and size parameters are introduced and used to characterize the association between the rate function λ(⋅) and a random variable X. Measures of association between X and λ(⋅) are defined via shape- and size-based coefficients. Rate-independence of X and λ(⋅) is studied through tests of shape-independence and size-independence, where the shape- and size-based test statistics can be used separately or in combination. These tests can be applied when X is a covariable possibly correlated with the recurrent event process through λ(⋅) or, in the one-sample setting, when X is the censoring time at which the observation of N(⋅) is terminated. The proposed tests are shape- and size-based, so when a null hypothesis is rejected, the test results can serve to distinguish the source of violation.

Suggested Citation

  • Mei-Cheng Wang & Chiung-Yu Huang, 2014. "Statistical inference methods for recurrent event processes with shape and size parameters," Biometrika, Biometrika Trust, vol. 101(3), pages 553-566.
    • Handle: RePEc:oup:biomet:v:101:y:2014:i:3:p:553-566.
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    File URL: http://hdl.handle.net/10.1093/biomet/asu016
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    Citations

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    Cited by:

    1. Yifei Sun & Chiung-Yu Huang & Mei-Cheng Wang, 2017. "Nonparametric Benefit–Risk Assessment Using Marker Process in the Presence of a Terminal Event," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 826-836, April.
    2. Xiaoyu Wang & Liuquan Sun, 2023. "Joint modeling of generalized scale-change models for recurrent event and failure time data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(1), pages 1-33, January.
    3. Gongjun Xu & Sy Han Chiou & Chiung-Yu Huang & Mei-Cheng Wang & Jun Yan, 2017. "Joint Scale-Change Models for Recurrent Events and Failure Time," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 794-805, April.
    4. Xin Chen & Jieli Ding & Liuquan Sun, 2018. "A semiparametric additive rate model for a modulated renewal process," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(4), pages 675-698, October.

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