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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

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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.

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Acknowledgements

Dr. McMahan acknowledges support of Grant R01 AI121351 from the National Institutes of Health, Grant OIA-1826715 from the National Science Foundation, and Grant N00014-19-1-2295 from the Office of Naval Research. Dr. Wang acknowledges support of R01CA218578 from the National Institutes of Health.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, James Madison University, Harrisonburg, VA, 22807, USA

    Prabhashi W. Withana Gamage

  2. School of Mathematical and Statistical Sciences, Clemson University, Clemson, SC, 29634, USA

    Christopher S. McMahan

  3. Department of Statistics, University of South Carolina, Columbia, SC, 29208, USA

    Lianming Wang

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  1. Prabhashi W. Withana Gamage
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  2. Christopher S. McMahan
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  3. Lianming Wang
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Correspondence to Prabhashi W. Withana Gamage.

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Withana Gamage, P.W., McMahan, C.S. & Wang, L. A flexible parametric approach for analyzing arbitrarily censored data that are potentially subject to left truncation under the proportional hazards model. Lifetime Data Anal 29, 188–212 (2023). https://doi.org/10.1007/s10985-022-09579-z

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