IDEAS home Printed from https://ideas.repec.org/a/bla/biomet/v79y2023i3p1646-1656.html
   My bibliography  Save this article

Maximum likelihood estimation in the additive hazards model

Author

Listed:
  • Chengyuan Lu
  • Jelle Goeman
  • Hein Putter

Abstract

The additive hazards model specifies the effect of covariates on the hazard in an additive way, in contrast to the popular Cox model, in which it is multiplicative. As the non‐parametric model, additive hazards offer a very flexible way of modeling time‐varying covariate effects. It is most commonly estimated by ordinary least squares. In this paper, we consider the case where covariates are bounded, and derive the maximum likelihood estimator under the constraint that the hazard is non‐negative for all covariate values in their domain. We show that the maximum likelihood estimator may be obtained by separately maximizing the log‐likelihood contribution of each event time point, and we show that the maximizing problem is equivalent to fitting a series of Poisson regression models with an identity link under non‐negativity constraints. We derive an analytic solution to the maximum likelihood estimator. We contrast the maximum likelihood estimator with the ordinary least‐squares estimator in a simulation study and show that the maximum likelihood estimator has smaller mean squared error than the ordinary least‐squares estimator. An illustration with data on patients with carcinoma of the oropharynx is provided.

Suggested Citation

  • Chengyuan Lu & Jelle Goeman & Hein Putter, 2023. "Maximum likelihood estimation in the additive hazards model," Biometrics, The International Biometric Society, vol. 79(3), pages 1646-1656, September.
    • Handle: RePEc:bla:biomet:v:79:y:2023:i:3:p:1646-1656
    DOI: 10.1111/biom.13764
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/biom.13764
    Download Restriction: no
    File URL: https://libkey.io/10.1111/biom.13764?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Marschner, Ian C. & Gillett, Alexandra C. & O’Connell, Rachel L., 2012. "Stratified additive Poisson models: Computational methods and applications in clinical epidemiology," Computational Statistics & Data Analysis, Elsevier, vol. 56(5), pages 1115-1130.
    2. Sheila M. Gore & Stuart J. Pocock & Gillian R. Kerr, 1984. "Regression Models and Non‐Proportional Hazards in the Analysis of Breast Cancer Survival," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(2), pages 176-195, June.
    3. Torben Martinussen & Stijn Vansteelandt & Per Kragh Andersen, 2020. "Subtleties in the interpretation of hazard contrasts," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(4), pages 833-855, October.
    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. Rachel Axelrod & Daniel Nevo, 2023. "A sensitivity analysis approach for the causal hazard ratio in randomized and observational studies," Biometrics, The International Biometric Society, vol. 79(3), pages 2743-2756, September.
    2. Paul Frédéric Blanche & Anders Holt & Thomas Scheike, 2023. "On logistic regression with right censored data, with or without competing risks, and its use for estimating treatment effects," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(2), pages 441-482, April.
    3. Benjamin R. Baer & Robert L. Strawderman & Ashkan Ertefaie, 2023. "Discussion on “Instrumental variable estimation of the causal hazard ratio,” by Linbo Wang, Eric Tchetgen Tchetgen, Torben Martinussen, and Stijn Vansteelandt," Biometrics, The International Biometric Society, vol. 79(2), pages 554-558, June.
    4. Ian W. McKeague & Mourad Tighiouart, 2000. "Bayesian Estimators for Conditional Hazard Functions," Biometrics, The International Biometric Society, vol. 56(4), pages 1007-1015, December.
    5. repec:ilo:ilowps:292067 is not listed on IDEAS
    6. D. Stogiannis & C. Caroni & C. E. Anagnostopoulos & I. K. Toumpoulis, 2011. "Comparing first hitting time and proportional hazards regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(7), pages 1483-1492, June.
    7. Gupta, Ramesh C. & Gupta, Pushpa L., 2000. "On the crossings of reliability measures," Statistics & Probability Letters, Elsevier, vol. 46(3), pages 301-305, February.
    8. Ross L. Prentice, 2022. "On the targets of inference with multivariate failure time data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(4), pages 546-559, October.
    9. Lu Mao, 2023. "Study design for restricted mean time analysis of recurrent events and death," Biometrics, The International Biometric Society, vol. 79(4), pages 3701-3714, December.
    10. Congdon, Peter, 2008. "A bivariate frailty model for events with a permanent survivor fraction and non-monotonic hazards; with an application to age at first maternity," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4346-4356, May.
    11. Mats J. Stensrud & Miguel A. Hernán & Eric J Tchetgen Tchetgen & James M. Robins & Vanessa Didelez & Jessica G. Young, 2021. "A generalized theory of separable effects in competing event settings," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(4), pages 588-631, October.
    12. Donoghoe Mark W. & Marschner Ian C., 2015. "Flexible Regression Models for Rate Differences, Risk Differences and Relative Risks," The International Journal of Biostatistics, De Gruyter, vol. 11(1), pages 91-108, May.
    13. Devarajan, Karthik & Ebrahimi, Nader, 2011. "A semi-parametric generalization of the Cox proportional hazards regression model: Inference and applications," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 667-676, January.
    14. Ofosu, Yaw., 1993. "Socio-economic change and evolution of cultural models of reproduction in Ghana: implications for population policy," ILO Working Papers 992920673402676, International Labour Organization.
    15. Qin, Fei, 2015. "Global talent, local careers: Circular migration of top Indian engineers and professionals," Research Policy, Elsevier, vol. 44(2), pages 405-420.
    16. Colubi, Ana & Domínguez-Menchero, J. Santos & González-Rodríguez, Gil, 2014. "Testing constancy in monotone response models," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 45-56.
    17. Tat-Thang Vo & Hilary Davies-Kershaw & Ruth Hackett & Stijn Vansteelandt, 2022. "Longitudinal mediation analysis of time-to-event endpoints in the presence of competing risks," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(3), pages 380-400, July.
    18. Mariam O. Adeleke & Gianluca Baio & Aidan G. O'Keeffe, 2022. "Regression discontinuity designs for time‐to‐event outcomes: An approach using accelerated failure time models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(3), pages 1216-1246, July.

    More about this item

    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:bla:biomet:v:79:y:2023:i:3:p:1646-1656. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0006-341X .

    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.