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

Author

Listed:
  • Hyung Park

    (New York University School of Medicine)

  • Thaddeus Tarpey

    (New York University School of Medicine)

  • Eva Petkova

    (New York University School of Medicine)

  • R. Todd Ogden

    (Columbia University)

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.

Suggested Citation

  • Hyung Park & Thaddeus Tarpey & Eva Petkova & R. Todd Ogden, 2024. "A high-dimensional single-index regression for interactions between treatment and covariates," Statistical Papers, Springer, vol. 65(7), pages 4025-4056, September.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:7:d:10.1007_s00362-024-01546-0
    DOI: 10.1007/s00362-024-01546-0
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