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

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.

SUBMITTER: Park H

PROVIDER: S-EPMC7755672 | biostudies-literature | 2021 Jun

REPOSITORIES: biostudies-literature

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

Park Hyung H Petkova Eva E Tarpey Thaddeus T Ogden R Todd RT

Biometrics 20200703 2

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 covar ...[more]

PMID: 32573759

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Project description:BackgroundIn cohort studies with time-to-event outcomes, covariates of interest often have values that change over time. The classical Cox regression model can handle time-dependent covariates but assumes linear effects on the log hazard function, which can be limiting in practice. Furthermore, when multiple correlated covariates are studied, it is of great interest to model their joint effects by allowing a flexible functional form and to delineate their relative contributions to survival risk.MethodsMotivated by the World Trade Center (WTC)-exposed Fire Department of New York cohort study, we proposed a partial-linear single-index Cox (PLSI-Cox) model to investigate the effects of repeatedly measured metabolic syndrome indicators on the risk of developing WTC lung injury associated with particulate matter exposure. The PLSI-Cox model reduces the dimensionality of covariates while providing interpretable estimates of their effects. The model's flexible link function accommodates nonlinear effects on the log hazard function. We developed an iterative estimation algorithm using spline techniques to model the nonparametric single-index component for potential nonlinear effects, followed by maximum partial likelihood estimation of the parameters.ResultsExtensive simulations showed that the proposed PLSI-Cox model outperformed the classical time-dependent Cox regression model when the true relationship was nonlinear. When the relationship was linear, both the PLSI-Cox model and classical time-dependent Cox regression model performed similarly. In the data application, we found a possible nonlinear joint effect of metabolic syndrome indicators on survival risk. Among the different indicators, BMI had the largest positive effect on the risk of developing lung injury, followed by triglycerides.ConclusionThe PLSI-Cox models allow for the evaluation of nonlinear effects of covariates and offer insights into their relative importance and direction. These methods provide a powerful set of tools for analyzing data with multiple time-dependent covariates and survival outcomes, potentially offering valuable insights for both current and future studies.

Dataset Information

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

Publications

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

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