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Targeted Minimum Loss Based Estimation of a Causal Effect on an Outcome with Known Conditional Bounds

Author

Listed:
  • Gruber Susan

    (Harvard University)

  • van der Laan Mark J.

    (University of California, Berkeley)

Abstract

This paper presents a targeted minimum loss based estimator (TMLE) that incorporates known conditional bounds on a continuous outcome. Subject matter knowledge regarding the bounds of a continuous outcome within strata defined by a subset of covariates, X, translates into statistical knowledge that constrains the model space of the true joint distribution of the data. In settings where there is low Fisher Information in the data for estimating the desired parameter, as is common when X is high dimensional relative to sample size, incorporating this domain knowledge can improve the fit of the targeted outcome regression, thereby improving bias and variance of the parameter estimate. We show that TMLE, a substitution estimator defined as a mapping from a density to a (possibly d-dimensional) real number, readily incorporates this global knowledge, resulting in improved finite sample performance.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:ijbist:v:8:y:2012:i:1:n:21
    DOI: 10.1515/1557-4679.1413
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    References listed on IDEAS

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    1. 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.
    2. Heejung Bang & James M. Robins, 2005. "Doubly Robust Estimation in Missing Data and Causal Inference Models," Biometrics, The International Biometric Society, vol. 61(4), pages 962-973, December.
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    Citations

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    Cited by:

    1. Sapp Stephanie & van der Laan Mark J. & Page Kimberly, 2014. "Targeted Estimation of Binary Variable Importance Measures with Interval-Censored Outcomes," The International Journal of Biostatistics, De Gruyter, vol. 10(1), pages 77-97, May.
    2. Matthew Blackwell & Anton Strezhnev, 2022. "Telescope matching for reducing model dependence in the estimation of the effects of time‐varying treatments: An application to negative advertising," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(1), pages 377-399, January.
    3. 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.
    4. 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.
    5. Susan Gruber & Mark J. van der Laan, 2013. "An Application of Targeted Maximum Likelihood Estimation to the Meta-Analysis of Safety Data," Biometrics, The International Biometric Society, vol. 69(1), pages 254-262, March.
    6. Audrey Renson & Michael G. Hudgens & Alexander P. Keil & Paul N. Zivich & Allison E. Aiello, 2023. "Identifying and estimating effects of sustained interventions under parallel trends assumptions," Biometrics, The International Biometric Society, vol. 79(4), pages 2998-3009, December.
    7. Lina M. Montoya & Michael R. Kosorok & Elvin H. Geng & Joshua Schwab & Thomas A. Odeny & Maya L. Petersen, 2023. "Efficient and robust approaches for analysis of sequential multiple assignment randomized trials: Illustration using the ADAPT‐R trial," Biometrics, The International Biometric Society, vol. 79(3), pages 2577-2591, September.
    8. Philipp Baumann & Enzo Rossi & Michael Schomaker, 2022. "Estimating the effect of central bank independence on inflation using longitudinal targeted maximum likelihood estimation," IFC Bulletins chapters, in: Bank for International Settlements (ed.), Machine learning in central banking, volume 57, Bank for International Settlements.
    9. David Benkeser & Keith Horvath & Cathy J. Reback & Joshua Rusow & Michael Hudgens, 2020. "Design and Analysis Considerations for a Sequentially Randomized HIV Prevention Trial," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 12(3), pages 446-467, December.
    10. Adel Hussein Elduma & Kourosh Holakouie-Naieni & Amir Almasi-Hashiani & Abbas Rahimi Foroushani & Hamdan Mustafa Hamdan Ali & Muatsim Ahmed Mohammed Adam & Asma Elsony & Mohammad Ali Mansournia, 2023. "The Targeted Maximum Likelihood estimation to estimate the causal effects of the previous tuberculosis treatment in Multidrug-resistant tuberculosis in Sudan," PLOS ONE, Public Library of Science, vol. 18(1), pages 1-12, January.

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