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

Hyung Park (), Thaddeus Tarpey, Eva Petkova and R. Todd Ogden
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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

Statistical Papers, 2024, vol. 65, issue 7, No 2, 4025-4056

Abstract: 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.

Keywords: Precision medicine; Modified covariate method; Single-index model; Sufficient reduction; Central mean subspace (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-024-01546-0

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