IDEAS home Printed from https://ideas.repec.org/a/bla/biomet/v76y2020i3p722-733.html
   My bibliography  Save this article

One‐step targeted maximum likelihood estimation for time‐to‐event outcomes

Author

Listed:
  • Weixin Cai
  • Mark J. van der Laan

Abstract

Researchers in observational survival analysis are interested in not only estimating survival curve nonparametrically but also having statistical inference for the parameter. We consider right‐censored failure time data where we observe n independent and identically distributed observations of a vector random variable consisting of baseline covariates, a binary treatment at baseline, a survival time subject to right censoring, and the censoring indicator. We assume the baseline covariates are allowed to affect the treatment and censoring so that an estimator that ignores covariate information would be inconsistent. The goal is to use these data to estimate the counterfactual average survival curve of the population if all subjects are assigned the same treatment at baseline. Existing observational survival analysis methods do not result in monotone survival curve estimators, which is undesirable and may lose efficiency by not constraining the shape of the estimator using the prior knowledge of the estimand. In this paper, we present a one‐step Targeted Maximum Likelihood Estimator (TMLE) for estimating the counterfactual average survival curve. We show that this new TMLE can be executed via recursion in small local updates. We demonstrate the finite sample performance of this one‐step TMLE in simulations and an application to a monoclonal gammopathy data.

Suggested Citation

  • Weixin Cai & Mark J. van der Laan, 2020. "One‐step targeted maximum likelihood estimation for time‐to‐event outcomes," Biometrics, The International Biometric Society, vol. 76(3), pages 722-733, September.
    • Handle: RePEc:bla:biomet:v:76:y:2020:i:3:p:722-733
    DOI: 10.1111/biom.13172
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/biom.13172
    Download Restriction: no
    File URL: https://libkey.io/10.1111/biom.13172?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. D Benkeser & M Carone & M J Van Der Laan & P B Gilbert, 2017. "Doubly robust nonparametric inference on the average treatment effect," Biometrika, Biometrika Trust, vol. 104(4), pages 863-880.
    2. Stitelman Ori M & van der Laan Mark J., 2010. "Collaborative Targeted Maximum Likelihood for Time to Event Data," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-46, June.
    3. van der Laan Mark J. & Gruber Susan, 2010. "Collaborative Double Robust Targeted Maximum Likelihood Estimation," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-71, May.
    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. Rose Sherri & van der Laan Mark J., 2011. "A Targeted Maximum Likelihood Estimator for Two-Stage Designs," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-21, March.
    2. Gruber, Susan & Laan, Mark van der, 2012. "tmle: An R Package for Targeted Maximum Likelihood Estimation," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i13).
    3. Stitelman Ori M. & De Gruttola Victor & van der Laan Mark J., 2012. "A General Implementation of TMLE for Longitudinal Data Applied to Causal Inference in Survival Analysis," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-39, September.
    4. Stitelman Ori M & Wester C. William & De Gruttola Victor & van der Laan Mark J., 2011. "Targeted Maximum Likelihood Estimation of Effect Modification Parameters in Survival Analysis," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-34, March.
    5. van der Laan Mark J. & Gruber Susan, 2012. "Targeted Minimum Loss Based Estimation of Causal Effects of Multiple Time Point Interventions," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-41, May.
    6. Stitelman Ori M & van der Laan Mark J., 2010. "Collaborative Targeted Maximum Likelihood for Time to Event Data," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-46, June.
    7. Gruber Susan & van der Laan Mark J., 2010. "A Targeted Maximum Likelihood Estimator of a Causal Effect on a Bounded Continuous Outcome," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-18, August.
    8. Kara E. Rudolph & Jonathan Levy & Mark J. van der Laan, 2021. "Transporting stochastic direct and indirect effects to new populations," Biometrics, The International Biometric Society, vol. 77(1), pages 197-211, March.
    9. David Cheng & Abhishek Chakrabortty & Ashwin N. Ananthakrishnan & Tianxi Cai, 2020. "Estimating average treatment effects with a double‐index propensity score," Biometrics, The International Biometric Society, vol. 76(3), pages 767-777, September.
    10. Gruber Susan & van der Laan Mark J., 2010. "An Application of Collaborative Targeted Maximum Likelihood Estimation in Causal Inference and Genomics," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-31, May.
    11. Agboola, Oluwagbenga David & Yu, Han, 2023. "Neighborhood-based cross fitting approach to treatment effects with high-dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 186(C).
    12. Heejun Shin & Joseph Antonelli, 2023. "Improved inference for doubly robust estimators of heterogeneous treatment effects," Biometrics, The International Biometric Society, vol. 79(4), pages 3140-3152, December.
    13. Zheng Wenjing & van der Laan Mark J., 2012. "Targeted Maximum Likelihood Estimation of Natural Direct Effects," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-40, January.
    14. Wei Luo & Yeying Zhu & Debashis Ghosh, 2017. "On estimating regression-based causal effects using sufficient dimension reduction," Biometrika, Biometrika Trust, vol. 104(1), pages 51-65.
    15. Karel Vermeulen & Stijn Vansteelandt, 2015. "Bias-Reduced Doubly Robust Estimation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1024-1036, September.
    16. van der Laan Mark J. & Petersen Maya & Zheng Wenjing, 2013. "Estimating the Effect of a Community-Based Intervention with Two Communities," Journal of Causal Inference, De Gruyter, vol. 1(1), pages 83-106, June.
    17. Torben Martinussen & Mats Julius Stensrud, 2023. "Estimation of separable direct and indirect effects in continuous time," Biometrics, The International Biometric Society, vol. 79(1), pages 127-139, March.
    18. David Cheng & Ashwin N. Ananthakrishnan & Tianxi Cai, 2021. "Robust and efficient semi‐supervised estimation of average treatment effects with application to electronic health records data," Biometrics, The International Biometric Society, vol. 77(2), pages 413-423, June.
    19. Jiaming Mao & Jingzhi Xu, 2020. "Ensemble Learning with Statistical and Structural Models," Papers 2006.05308, arXiv.org.
    20. Yunda Huang & Lily Zhang & Shelly Karuna & Philip Andrew & Michal Juraska & Joshua A. Weiner & Heather Angier & Evgenii Morgan & Yasmin Azzam & Edith Swann & Srilatha Edupuganti & Nyaradzo M. Mgodi & , 2023. "Adults on pre-exposure prophylaxis (tenofovir-emtricitabine) have faster clearance of anti-HIV monoclonal antibody VRC01," Nature Communications, Nature, vol. 14(1), pages 1-19, December.

    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:76:y:2020:i:3:p:722-733. 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.