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A constrained single‐index regression for estimating interactions between a treatment and covariates

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  • Hyung Park
  • Eva Petkova
  • Thaddeus Tarpey
  • R. Todd Ogden

Abstract

We consider a single‐index regression model, uniquely constrained to estimate interactions between a set of pretreatment covariates and a treatment variable on their effects on a response variable, in the context of analyzing data from randomized clinical trials. We represent interaction effect terms of the model through a set of treatment‐specific flexible link functions on a linear combination of the covariates (a single index), subject to the constraint that the expected value given the covariates equals 0, while leaving the main effects of the covariates unspecified. We show that the proposed semiparametric estimator is consistent for the interaction term of the model, and that the efficiency of the estimator can be improved with an augmentation procedure. The proposed single‐index regression provides a flexible and interpretable modeling approach to optimizing individualized treatment rules based on patients' data measured at baseline, as illustrated by simulation examples and an application to data from a depression clinical trial.

Suggested Citation

  • Hyung Park & Eva Petkova & Thaddeus Tarpey & R. Todd Ogden, 2021. "A constrained single‐index regression for estimating interactions between a treatment and covariates," Biometrics, The International Biometric Society, vol. 77(2), pages 506-518, June.
    • Handle: RePEc:bla:biomet:v:77:y:2021:i:2:p:506-518
    DOI: 10.1111/biom.13320
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    References listed on IDEAS

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    1. 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.

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