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

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  • 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
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    References listed on IDEAS

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    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.
    4. van der Laan Mark & Gruber Susan, 2016. "One-Step Targeted Minimum Loss-based Estimation Based on Universal Least Favorable One-Dimensional Submodels," The International Journal of Biostatistics, De Gruyter, vol. 12(1), pages 351-378, May.
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    Cited by:

    1. Lan Wen & Jon A. Steingrimsson & Sarah E. Robertson & Issa J. Dahabreh, 2025. "Multi-source analyses of average treatment effects with failure time outcomes," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 31(4), pages 869-897, October.

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