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Targeted Minimum Loss Based Estimation of Causal Effects of Multiple Time Point Interventions

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  • van der Laan Mark J.

    (University of California - Berkeley)

  • Gruber Susan

    (Harvard University)

Abstract

We consider estimation of the effect of a multiple time point intervention on an outcome of interest, where the intervention nodes are subject to time-dependent confounding by intermediate covariates.In previous work van der Laan (2010) and Stitelman and van der Laan (2011a) developed and implemented a closed form targeted maximum likelihood estimator (TMLE) relying on the log-likelihood loss function, and demonstrated important gains relative to inverse probability of treatment weighted estimators and estimating equation based estimators. This TMLE relies on an initial estimator of the entire probability distribution of the longitudinal data structure. To enhance the finite sample performance of the TMLE of the target parameter it is of interest to select the smallest possible relevant part of the data generating distribution, which is estimated and updated by TMLE. Inspired by this goal, we develop a new closed form TMLE of an intervention specific mean outcome based on general longitudinal data structures. The target parameter is represented as an iterative sequence of conditional expectations of the outcome of interest. This collection of conditional means represents the relevant part, which is estimated and updated using the general TMLE algorithm. We also develop this new TMLE for other causal parameters, such as parameters defined by working marginal structural models. The theoretical properties of the TMLE are also practically demonstrated with a small scale simulation study.The proposed TMLE is building upon a previously proposed estimator Bang and Robins (2005) by integrating some of its key and innovative ideas into the TMLE framework.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:ijbist:v:8:y:2012:i:1:n:9
    DOI: 10.1515/1557-4679.1370
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    References listed on IDEAS

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    1. 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.
    2. Wang, Hui & Rose, Sherri & van der Laan, Mark J., 2011. "Finding quantitative trait loci genes with collaborative targeted maximum likelihood learning," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 792-796, July.
    3. 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.
    4. 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.
    5. van der Laan Mark J. & Polley Eric C & Hubbard Alan E., 2007. "Super Learner," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 6(1), pages 1-23, September.
    6. Porter Kristin E. & Gruber Susan & van der Laan Mark J. & Sekhon Jasjeet S., 2011. "The Relative Performance of Targeted Maximum Likelihood Estimators," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-34, August.
    7. 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.
    8. 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.
    9. van der Laan Mark J., 2008. "Estimation Based on Case-Control Designs with Known Prevalence Probability," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-57, September.
    10. Rose Sherri & van der Laan Mark J., 2008. "Simple Optimal Weighting of Cases and Controls in Case-Control Studies," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-24, September.
    11. Rosenblum Michael & van der Laan Mark J., 2010. "Targeted Maximum Likelihood Estimation of the Parameter of a Marginal Structural Model," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-30, April.
    12. Rose Sherri & van der Laan Mark J., 2009. "Why Match? Investigating Matched Case-Control Study Designs with Causal Effect Estimation," The International Journal of Biostatistics, De Gruyter, vol. 5(1), pages 1-26, January.
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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 1-21, May.
    2. Helene C. W. Rytgaard & Frank Eriksson & Mark J. van der Laan, 2023. "Estimation of time‐specific intervention effects on continuously distributed time‐to‐event outcomes by targeted maximum likelihood estimation," Biometrics, The International Biometric Society, vol. 79(4), pages 3038-3049, December.
    3. 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.
    4. Mireille E. Schnitzer & Erica E.M. Moodie & Mark J. van der Laan & Robert W. Platt & Marina B. Klein, 2014. "Modeling the impact of hepatitis C viral clearance on end-stage liver disease in an HIV co-infected cohort with targeted maximum likelihood estimation," Biometrics, The International Biometric Society, vol. 70(1), pages 144-152, March.
    5. 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.
    6. 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.
    7. Hugo Bodory & Martin Huber & Lukáš Lafférs, 2022. "Evaluating (weighted) dynamic treatment effects by double machine learning [Identification of causal effects using instrumental variables]," The Econometrics Journal, Royal Economic Society, vol. 25(3), pages 628-648.
    8. 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.
    9. 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.
    10. 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.
    11. Rahul Singh & Liyuan Xu & Arthur Gretton, 2021. "Sequential Kernel Embedding for Mediated and Time-Varying Dose Response Curves," Papers 2111.03950, arXiv.org, revised Jul 2023.
    12. 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.

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