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A high-dimensional single-index regression for interactions between treatment and covariates

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Abstract

This paper explores a methodology for dimension reduction in regression models for a treatment outcome, specifically to capture covariates’ moderating impact on the treatment-outcome association. The motivation behind this stems from the field of precision medicine, where a comprehensive understanding of the interactions between a treatment variable and pretreatment covariates is essential for developing individualized treatment regimes (ITRs). We provide a review of sufficient dimension reduction methods suitable for capturing treatment-covariate interactions and establish connections with linear model-based approaches for the proposed model. Within the framework of single-index regression models, we introduce a sparse estimation method for a dimension reduction vector to tackle the challenges posed by high-dimensional covariate data. Our methods offer insights into dimension reduction techniques specifically for interaction analysis, by providing a semiparametric framework for approximating the minimally sufficient subspace for interactions.

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Acknowledgements

This work was supported by National Institute of Health (NIH) grant 5 R01 MH099003. The first author thanks Dr. Peter Radchenko of the University of Sydney for his comments and providing the code to implement his regression model.

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Authors and Affiliations

  1. Division of Biostatistics, Department of Population Health, New York University School of Medicine, New York, NY, 10016, USA

    Hyung Park, Thaddeus Tarpey & Eva Petkova

  2. Department of Biostatistics, Columbia University, New York, NY, 10032, USA

    R. Todd Ogden

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  1. Hyung Park
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  2. Thaddeus Tarpey
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  3. Eva Petkova
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  4. R. Todd Ogden
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Correspondence to Hyung Park.

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Park, H., Tarpey, T., Petkova, E. et al. A high-dimensional single-index regression for interactions between treatment and covariates. Stat Papers (2024). https://doi.org/10.1007/s00362-024-01546-0

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