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History-Adjusted Marginal Structural Models and Statically-Optimal Dynamic Treatment Regimens

Author

Listed:
  • van der Laan Mark J.

    (Division of Biostatistics, School of Public Health, University of California, Berkeley)

  • Petersen Maya L

    (Division of Biostatistics, School of Public Health, University of California, Berkeley)

  • Joffe Marshall M

    (Department of Biostatistics and Epidemiology, University of Pennsylvania School of Medicine)

Abstract

Marginal structural models (MSM) provide a powerful tool for estimating the causal effect of a treatment. These models, introduced by Robins, model the marginal distributions of treatment-specific counterfactual outcomes, possibly conditional on a subset of the baseline covariates. Marginal structural models are particularly useful in the context of longitudinal data structures, in which each subject's treatment and covariate history are measured over time, and an outcome is recorded at a final time point. However, the utility of these models for some applications has been limited by their inability to incorporate modification of the causal effect of treatment by time-varying covariates. Particularly in the context of clinical decision making, such time-varying effect modifiers are often of considerable or even primary interest, as they are used in practice to guide treatment decisions for an individual. In this article we propose a generalization of marginal structural models, which we call history-adjusted marginal structural models (HA-MSM). These models allow estimation of adjusted causal effects of treatment, given the observed past, and are therefore more suitable for making treatment decisions at the individual level and for identification of time-dependent effect modifiers. Specifically, a HA-MSM models the conditional distribution of treatment-specific counterfactual outcomes, conditional on the whole or a subset of the observed past up till a time-point, simultaneously for all time-points. Double robust inverse probability of treatment weighted estimators have been developed and studied in detail for standard MSM. We extend these results by proposing a class of double robust inverse probability of treatment weighted estimators for the unknown parameters of the HA-MSM. In addition, we show that HA-MSM provide a natural approach to identifying the dynamic treatment regimen which follows, at each time-point, the history-adjusted (up till the most recent time point) optimal static treatment regimen. We illustrate our results using an example drawn from the treatment of HIV infection.

Suggested Citation

  • van der Laan Mark J. & Petersen Maya L & Joffe Marshall M, 2005. "History-Adjusted Marginal Structural Models and Statically-Optimal Dynamic Treatment Regimens," The International Journal of Biostatistics, De Gruyter, vol. 1(1), pages 1-41, November.
    • Handle: RePEc:bpj:ijbist:v:1:y:2005:i:1:n:4
    DOI: 10.2202/1557-4679.1003
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    Citations

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    Cited by:

    1. Biernot Peter & Moodie Erica E. M., 2010. "A Comparison of Variable Selection Approaches for Dynamic Treatment Regimes," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-20, January.
    2. Q. Clairon & R. Henderson & N. J. Young & E. D. Wilson & C. J. Taylor, 2021. "Adaptive treatment and robust control," Biometrics, The International Biometric Society, vol. 77(1), pages 223-236, March.
    3. Marshall M. Joffe & Wei Peter Yang & Harold Feldman, 2012. "G-Estimation and Artificial Censoring: Problems, Challenges, and Applications," Biometrics, The International Biometric Society, vol. 68(1), pages 275-286, March.
    4. Kristin A. Linn & Eric B. Laber & Leonard A. Stefanski, 2017. "Interactive -Learning for Quantiles," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 638-649, April.
    5. van der Laan Mark J., 2010. "Targeted Maximum Likelihood Based Causal Inference: Part I," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-45, February.
    6. Neugebauer Romain & Chandra Malini & Paredes Antonio & J. Graham David & McCloskey Carolyn & S. Go Alan, 2013. "A Marginal Structural Modeling Approach with Super Learning for a Study on Oral Bisphosphonate Therapy and Atrial Fibrillation," Journal of Causal Inference, De Gruyter, vol. 1(1), pages 21-50, June.
    7. Jelena Bradic & Weijie Ji & Yuqian Zhang, 2021. "High-dimensional Inference for Dynamic Treatment Effects," Papers 2110.04924, arXiv.org, revised May 2023.
    8. Victor Chernozhukov & Whitney Newey & Rahul Singh & Vasilis Syrgkanis, 2022. "Automatic Debiased Machine Learning for Dynamic Treatment Effects and General Nested Functionals," Papers 2203.13887, arXiv.org, revised Jun 2023.
    9. 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.
    10. Isaac Meza & Rahul Singh, 2021. "Nested Nonparametric Instrumental Variable Regression: Long Term, Mediated, and Time Varying Treatment Effects," Papers 2112.14249, arXiv.org, revised Mar 2024.

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