A single-index model with multiple-links
Hyung Park, Eva Petkova, Thaddeus Tarpey, R Todd Ogden, Hyung Park, Eva Petkova, Thaddeus Tarpey, R Todd Ogden
Abstract
In a regression model for treatment outcome in a randomized clinical trial, a treatment effect modifier is a covariate that has an interaction with the treatment variable, implying that the treatment efficacies vary across values of such a covariate. In this paper, we present a method for determining a composite variable from a set of baseline covariates, that can have a nonlinear association with the treatment outcome, and acts as a composite treatment effect modifier. We introduce a parsimonious generalization of the single-index models that targets the effect of the interaction between the treatment conditions and the vector of covariates on the outcome, a single-index model with multiple-links (SIMML) that estimates a single linear combination of the covariates (i.e., a single-index), with treatment-specific nonparametric link functions. The approach emphasizes a focus on the treatment-by-covariates interaction effects on the treatment outcome that are relevant for making optimal treatment decisions. Asymptotic results for estimator are obtained under possible model misspecification. A treatment decision rule based on the derived single-index is defined, and it is compared to other methods for estimating optimal treatment decision rules. An application to a clinical trial for the treatment of depression is presented.
Keywords: Biosignature; Single-index models; Treatment effect modifier.
Figures
![Figure 1:](https://www.ncbi.nlm.nih.gov/pmc/articles/instance/7441812/bin/nihms-1533650-f0001.jpg)
![Figure 2:](https://www.ncbi.nlm.nih.gov/pmc/articles/instance/7441812/bin/nihms-1533650-f0002.jpg)
![Figure 3:. Depression randomized clinical trial:](https://www.ncbi.nlm.nih.gov/pmc/articles/instance/7441812/bin/nihms-1533650-f0003.jpg)
![Figure 4:. Depression randomized clinical trial:](https://www.ncbi.nlm.nih.gov/pmc/articles/instance/7441812/bin/nihms-1533650-f0004.jpg)
![Figure 5:. Depression randomized clinical trial:](https://www.ncbi.nlm.nih.gov/pmc/articles/instance/7441812/bin/nihms-1533650-f0005.jpg)
![Figure 6:. Depression randomized clinical trial:](https://www.ncbi.nlm.nih.gov/pmc/articles/instance/7441812/bin/nihms-1533650-f0006.jpg)
Source: PubMed