Variable Selection for Generalized Single-Index Varying-Coefficient Models with Applications to Synergistic G × E Interactions

Shunjie Guan, Xu Liu and Yuehua Cui ()
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Shunjie Guan: Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA
Xu Liu: School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China
Yuehua Cui: Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA

Mathematics, 2025, vol. 13, issue 3, 1-23

Abstract: Complex diseases such as type 2 diabetes are influenced by both environmental and genetic risk factors, leading to a growing interest in identifying gene–environment (G × E) interactions. A three-step variable selection method for single-index varying-coefficients models was proposed in recent research. This method selects varying and constant-effect genetic predictors, as well as non-zero loading parameters, to identify genetic factors that interact linearly or nonlinearly with a mixture of environmental factors to influence disease risk. In this paper, we extend this approach to a binary response setting given that many complex human diseases are binary traits. We also establish the oracle property for our variable selection method, demonstrating that it performs as well as if the correct sub-model were known in advance. Additionally, we assess the performance of our method through finite-sample simulations with both continuous and discrete gene variables. Finally, we apply our approach to a type 2 diabetes dataset, identifying potential genetic factors that interact with a combination of environmental variables, both linearly and nonlinearly, to influence the risk of developing type 2 diabetes.

Keywords: gene–environment interaction (G × E); generalized single-index varying-coefficient models (gSIVCM); mixture of exposures; nonlinear G × E; synergistic G × E (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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