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A flexible parametric approach for analyzing arbitrarily censored data that are potentially subject to left truncation under the proportional hazards model

Author

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  • Prabhashi W. Withana Gamage

    (James Madison University)

  • Christopher S. McMahan

    (Clemson University)

  • Lianming Wang

    (University of South Carolina)

Abstract

The proportional hazards (PH) model is, arguably, the most popular model for the analysis of lifetime data arising from epidemiological studies, among many others. In such applications, analysts may be faced with censored outcomes and/or studies which institute enrollment criterion leading to left truncation. Censored outcomes arise when the event of interest is not observed but rather is known relevant to an observation time(s). Left truncated data occur in studies that exclude participants who have experienced the event prior to being enrolled in the study. If not accounted for, both of these features can lead to inaccurate inferences about the population under study. Thus, to overcome this challenge, herein we propose a novel unified PH model that can be used to accommodate both of these features. In particular, our approach can seamlessly analyze exactly observed failure times along with interval-censored observations, while aptly accounting for left truncation. To facilitate model fitting, an expectation–maximization algorithm is developed through the introduction of carefully structured latent random variables. To provide modeling flexibility, a monotone spline representation is used to approximate the cumulative baseline hazard function. The performance of our methodology is evaluated through a simulation study and is further illustrated through the analysis of two motivating data sets; one that involves child mortality in Nigeria and the other prostate cancer.

Suggested Citation

  • Prabhashi W. Withana Gamage & Christopher S. McMahan & Lianming Wang, 2023. "A flexible parametric approach for analyzing arbitrarily censored data that are potentially subject to left truncation under the proportional hazards model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(1), pages 188-212, January.
    • Handle: RePEc:spr:lifeda:v:29:y:2023:i:1:d:10.1007_s10985-022-09579-z
    DOI: 10.1007/s10985-022-09579-z
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    References listed on IDEAS

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    Cited by:

    1. Mengyue Zhang & Shishun Zhao & Tao Hu & Da Xu & Jianguo Sun, 2023. "Regression Analysis of Dependent Current Status Data with Left Truncation," Mathematics, MDPI, vol. 11(16), pages 1-13, August.
    2. Fan Feng & Guanghui Cheng & Jianguo Sun, 2023. "Variable Selection for Length-Biased and Interval-Censored Failure Time Data," Mathematics, MDPI, vol. 11(22), pages 1-20, November.
    3. Sisi Chen & Fengkai Yang, 2023. "Expectation-Maximization Algorithm for the Weibull Proportional Hazard Model under Current Status Data," Mathematics, MDPI, vol. 11(23), pages 1-23, November.

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