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Targeted maximum likelihood estimation for causal inference in survival and competing risks analysis

Author

Listed:
  • Helene C. W. Rytgaard

    (University of Copenhagen)

  • Mark J. Laan

    (Center for Targeted Machine)

Abstract

Targeted maximum likelihood estimation (TMLE) provides a general methodology for estimation of causal parameters in presence of high-dimensional nuisance parameters. Generally, TMLE consists of a two-step procedure that combines data-adaptive nuisance parameter estimation with semiparametric efficiency and rigorous statistical inference obtained via a targeted update step. In this paper, we demonstrate the practical applicability of TMLE based causal inference in survival and competing risks settings where event times are not confined to take place on a discrete and finite grid. We focus on estimation of causal effects of time-fixed treatment decisions on survival and absolute risk probabilities, considering different univariate and multidimensional parameters. Besides providing a general guidance to using TMLE for survival and competing risks analysis, we further describe how the previous work can be extended with the use of loss-based cross-validated estimation, also known as super learning, of the conditional hazards. We illustrate the usage of the considered methods using publicly available data from a trial on adjuvant chemotherapy for colon cancer. R software code to implement all considered algorithms and to reproduce all analyses is available in an accompanying online appendix on Github.

Suggested Citation

  • Helene C. W. Rytgaard & Mark J. Laan, 2024. "Targeted maximum likelihood estimation for causal inference in survival and competing risks analysis," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 30(1), pages 4-33, January.
    • Handle: RePEc:spr:lifeda:v:30:y:2024:i:1:d:10.1007_s10985-022-09576-2
    DOI: 10.1007/s10985-022-09576-2
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    References listed on IDEAS

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    1. van der Laan Mark J. & Dudoit Sandrine & Keles Sunduz, 2004. "Asymptotic Optimality of Likelihood-Based Cross-Validation," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-25, March.
    2. van der Laan Mark J., 2006. "Statistical Inference for Variable Importance," The International Journal of Biostatistics, De Gruyter, vol. 2(1), pages 1-33, February.
    3. 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.
    4. 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.
    5. Gruber Susan & van der Laan Mark J., 2012. "Targeted Minimum Loss Based Estimation of a Causal Effect on an Outcome with Known Conditional Bounds," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-18, July.
    6. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    7. van der Laan Mark J. & Rubin Daniel, 2006. "Targeted Maximum Likelihood Learning," The International Journal of Biostatistics, De Gruyter, vol. 2(1), pages 1-40, December.
    8. Simon, Noah & Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2011. "Regularization Paths for Cox's Proportional Hazards Model via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 39(i05).
    9. 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.
    10. van der Laan Mark, 2017. "A Generally Efficient Targeted Minimum Loss Based Estimator based on the Highly Adaptive Lasso," The International Journal of Biostatistics, De Gruyter, vol. 13(2), pages 1-35, November.
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