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Longitudinal Survival Analysis Using First Hitting Time Threshold Regression: With Applications to Wiener Processes

Author

Listed:
  • Ya-Shan Cheng

    (Institute of Statistics, National Tsing Hua University, Hsinchu 300044, Taiwan)

  • Yiming Chen

    (Food and Drug Administration, Silver Spring, MD 20993, USA)

  • Mei-Ling Ting Lee

    (Epidemiology and Biostatistics Department, University of Maryland, College Park, MD 20742, USA)

Abstract

First-hitting time threshold regression (TR) is well-known for analyzing event time data without the proportional hazards assumption. To date, most applications and software are developed for cross-sectional data. In this paper, using the Markov property of processes with stationary independent increments, we present methods and procedures for conducting longitudinal threshold regression (LTR) for event time data with or without covariates. We demonstrate the usage of LTR in two case scenarios, namely, analyzing laser reliability data without covariates, and cardiovascular health data with time-dependent covariates. Moreover, we provide a simple-to-use R function for LTR estimation for applications using Wiener processes.

Suggested Citation

  • Ya-Shan Cheng & Yiming Chen & Mei-Ling Ting Lee, 2025. "Longitudinal Survival Analysis Using First Hitting Time Threshold Regression: With Applications to Wiener Processes," Stats, MDPI, vol. 8(2), pages 1-16, April.
    • Handle: RePEc:gam:jstats:v:8:y:2025:i:2:p:32-:d:1644920
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    References listed on IDEAS

    as
    1. Chrys Caroni, 2022. "Regression Models for Lifetime Data: An Overview," Stats, MDPI, vol. 5(4), pages 1-11, December.
    2. Mei-Ling Ting Lee & G. A. Whitmore, 2023. "Semiparametric predictive inference for failure data using first-hitting-time threshold regression," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(3), pages 508-536, July.
    3. Yiming Chen & Paul J. Smith & Mei-Ling Ting Lee, 2023. "Causal Inference in Threshold Regression and the Neural Network Extension (TRNN)," Stats, MDPI, vol. 6(2), pages 1-24, April.
    4. Fernando Alvarez & Katarína Borovičková & Robert Shimer, 2024. "Decomposing Duration Dependence in a Stopping Time Model," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 91(6), pages 3151-3189.
    5. Jonathan A. Race & Michael L. Pennell, 2021. "Semi-parametric survival analysis via Dirichlet process mixtures of the First Hitting Time model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(1), pages 177-194, January.
    6. Liqun Wang & Klaus Pötzelberger, 2007. "Crossing Probabilities for Diffusion Processes with Piecewise Continuous Boundaries," Methodology and Computing in Applied Probability, Springer, vol. 9(1), pages 21-40, March.
    Full references (including those not matched with items on IDEAS)

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