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Bayesian Index Models for Heterogeneous Treatment Effects on a Binary Outcome

Author

Listed:
  • Hyung G. Park

    (New York University School of Medicine)

  • Danni Wu

    (New York University School of Medicine)

  • Eva Petkova

    (New York University School of Medicine)

  • Thaddeus Tarpey

    (New York University School of Medicine)

  • R. Todd Ogden

    (Columbia University)

Abstract

This paper develops a Bayesian model with a flexible link function connecting a binary treatment response to a linear combination of covariates and a treatment indicator and the interaction between the two. Generalized linear models allowing data-driven link functions are often called “single-index models” and are among popular semi-parametric modeling methods. In this paper, we focus on modeling heterogeneous treatment effects, with the goal of developing a treatment benefit index (TBI) incorporating prior information from historical data. The model makes inference on a composite moderator of treatment effects, summarizing the effect of the predictors within a single variable through a linear projection of the predictors. This treatment benefit index can be useful for stratifying patients according to their predicted treatment benefit levels and can be especially useful for precision health applications. The proposed method is applied to a COVID-19 treatment study.

Suggested Citation

  • Hyung G. Park & Danni Wu & Eva Petkova & Thaddeus Tarpey & R. Todd Ogden, 2023. "Bayesian Index Models for Heterogeneous Treatment Effects on a Binary Outcome," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(2), pages 397-418, July.
    • Handle: RePEc:spr:stabio:v:15:y:2023:i:2:d:10.1007_s12561-023-09370-0
    DOI: 10.1007/s12561-023-09370-0
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    References listed on IDEAS

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    1. E. B. Laber & Y. Q. Zhao, 2015. "Tree-based methods for individualized treatment regimes," Biometrika, Biometrika Trust, vol. 102(3), pages 501-514.
    2. Wang, Hai-Bin, 2009. "Bayesian estimation and variable selection for single index models," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2617-2627, May.
    3. Thomas A. Murray & Ying Yuan & Peter F. Thall, 2018. "A Bayesian Machine Learning Approach for Optimizing Dynamic Treatment Regimes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1255-1267, July.
    4. Stefan Wager & Susan Athey, 2018. "Estimation and Inference of Heterogeneous Treatment Effects using Random Forests," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1228-1242, July.
    5. X Nie & S Wager, 2021. "Quasi-oracle estimation of heterogeneous treatment effects [TensorFlow: A system for large-scale machine learning]," Biometrika, Biometrika Trust, vol. 108(2), pages 299-319.
    6. Stoker, Thomas M, 1986. "Consistent Estimation of Scaled Coefficients," Econometrica, Econometric Society, vol. 54(6), pages 1461-1481, November.
    7. Lu Tian & Ash A. Alizadeh & Andrew J. Gentles & Robert Tibshirani, 2014. "A Simple Method for Estimating Interactions Between a Treatment and a Large Number of Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1517-1532, December.
    8. Wai-Yin Poon & Hai-Bin Wang, 2014. "Multivariate partially linear single-index models: Bayesian analysis," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(4), pages 755-768, December.
    9. Yingqi Zhao & Donglin Zeng & A. John Rush & Michael R. Kosorok, 2012. "Estimating Individualized Treatment Rules Using Outcome Weighted Learning," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1106-1118, September.
    10. S. A. Murphy, 2003. "Optimal dynamic treatment regimes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 331-355, May.
    11. Ying-Qi Zhao & Donglin Zeng & Eric B. Laber & Michael R. Kosorok, 2015. "New Statistical Learning Methods for Estimating Optimal Dynamic Treatment Regimes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 583-598, June.
    12. Donald B. Rubin, 2005. "Causal Inference Using Potential Outcomes: Design, Modeling, Decisions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 322-331, March.
    13. Eric B. Laber & Ana-Maria Staicu, 2018. "Functional Feature Construction for Individualized Treatment Regimes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1219-1227, July.
    14. Shi, Chengchun & Song, Rui & Lu, Wenbin, 2016. "Robust learning for optimal treatment decision with NP-dimensionality," LSE Research Online Documents on Economics 102114, London School of Economics and Political Science, LSE Library.
    15. Alberto Caron & Gianluca Baio & Ioanna Manolopoulou, 2022. "Estimating individual treatment effects using non‐parametric regression models: A review," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(3), pages 1115-1149, July.
    16. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881.
    17. Taeryon Choi & Jian Shi & Bo Wang, 2011. "A Gaussian process regression approach to a single-index model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 21-36.
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