IDEAS home Printed from https://ideas.repec.org/a/gam/jstats/v8y2025i2p32-d1644920.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2571-905X/8/2/32/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2571-905X/8/2/32/
    Download Restriction: no
    ---><---

    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. 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.
    3. 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.
    4. 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.
    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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Arne F. Lyshol & Plamen T. Nenov & Thea Wevelstad, 2021. "Duration Dependence and Labor Market Experience," LABOUR, CEIS, vol. 35(1), pages 105-134, March.
    2. Escanciano, Juan Carlos, 2023. "Irregular identification of structural models with nonparametric unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 234(1), pages 106-127.
    3. Qinglai Dong & Lirong Cui, 2019. "First Hitting Time Distributions for Brownian Motion and Regions with Piecewise Linear Boundaries," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 1-23, March.
    4. Hangsuck Lee & Hongjun Ha & Minha Lee, 2022. "Piecewise linear boundary crossing probabilities, barrier options, and variable annuities," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(12), pages 2248-2272, December.
    5. Ioannis Kospentaris, 2021. "Unobserved Heterogeneity and Skill Loss in a Structural Model of Duration Dependence," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 39, pages 280-303, January.
    6. Lee, Taeho, 2023. "Exact simulation for the first hitting time of Brownian motion and Brownian bridge," Statistics & Probability Letters, Elsevier, vol. 193(C).
    7. Carl Singleton, 2018. "Long‐Term Unemployment and the Great Recession: Evidence from UK Stocks and Flows," Scottish Journal of Political Economy, Scottish Economic Society, vol. 65(2), pages 105-126, May.
    8. Lee, Hangsuck & Lee, Minha & Ha, Hongjun, 2025. "Multi-piecewise linear double barrier options," Finance Research Letters, Elsevier, vol. 75(C).
    9. Ruixuan Liu, 2020. "A competing risks model with time‐varying heterogeneity and simultaneous failure," Quantitative Economics, Econometric Society, vol. 11(2), pages 535-577, May.
    10. Zhiyong Jin & Liqun Wang, 2017. "First Passage Time for Brownian Motion and Piecewise Linear Boundaries," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 237-253, March.
    11. Tiago Chandiona Ernesto Franque & Marcílio Ramos Pereira Cardial & Eduardo Yoshio Nakano, 2025. "Proportional Log Survival Model for Discrete Time-to-Event Data," Mathematics, MDPI, vol. 13(5), pages 1-14, February.
    12. Felder, Rahel & Frings, Hanna & Mittag, Nikolas, 2024. "How Does Potential Unemployment Insurance Benefit Duration Affect Reemployment Timing and Wages?," IZA Discussion Papers 17348, Institute of Labor Economics (IZA).
    13. Andrew N. Downes & Konstantin Borovkov, 2008. "First Passage Densities and Boundary Crossing Probabilities for Diffusion Processes," Methodology and Computing in Applied Probability, Springer, vol. 10(4), pages 621-644, December.
    14. Schmidpeter, Bernhard & Winter-Ebmer, Rudolf, 2021. "Automation, unemployment, and the role of labor market training," European Economic Review, Elsevier, vol. 137(C).
    15. Felder, Rahel & Frings, Hanna & Mittag, Nikolas, 2024. "How does potential unemployment insurance benefit duration affect reemployment timing and wages?," Ruhr Economic Papers 1111, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    16. Andreas Hornstein & Marianna Kudlyak, 2015. "Estimating Matching Efficiency with Variable Search Effort," Working Paper Series 2016-24, Federal Reserve Bank of San Francisco.
    17. Lee, Hangsuck & Ha, Hongjun & Kong, Byungdoo, 2024. "Pricing first-touch digitals with a multi-step double boundary and American barrier options," Finance Research Letters, Elsevier, vol. 59(C).
    18. Güell, Maia & Lafuente, Cristina, 2019. "Unemployment Duration Variance Decomposition a la ABS: Evidence from Spain," CEPR Discussion Papers 13610, C.E.P.R. Discussion Papers.
    19. 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.
    20. Mr. Ippei Shibata, 2019. "Labor Market Dynamics: A Hidden Markov Approach," IMF Working Papers 2019/282, International Monetary Fund.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jstats:v:8:y:2025:i:2:p:32-:d:1644920. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.