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

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 resea...

Full description

Saved in:
Bibliographic Details
Main Authors: Shunjie Guan, Xu Liu, Yuehua Cui
Format: Article
Language:English
Published: MDPI AG 2025-01-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/13/3/469
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1850199884473303040
author Shunjie Guan
Xu Liu
Yuehua Cui
author_facet Shunjie Guan
Xu Liu
Yuehua Cui
author_sort Shunjie Guan
collection DOAJ
description 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.
format Article
id doaj-art-28404281995f490db94fa0e44ef31506
institution OA Journals
issn 2227-7390
language English
publishDate 2025-01-01
publisher MDPI AG
record_format Article
series Mathematics
spelling doaj-art-28404281995f490db94fa0e44ef315062025-08-20T02:12:30ZengMDPI AGMathematics2227-73902025-01-0113346910.3390/math13030469Variable Selection for Generalized Single-Index Varying-Coefficient Models with Applications to Synergistic G × E InteractionsShunjie Guan0Xu Liu1Yuehua Cui2Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USASchool of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, ChinaDepartment of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USAComplex 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.https://www.mdpi.com/2227-7390/13/3/469gene–environment interaction (G × E)generalized single-index varying-coefficient models (gSIVCM)mixture of exposuresnonlinear G × Esynergistic G × E
spellingShingle Shunjie Guan
Xu Liu
Yuehua Cui
Variable Selection for Generalized Single-Index Varying-Coefficient Models with Applications to Synergistic G × E Interactions
Mathematics
gene–environment interaction (G × E)
generalized single-index varying-coefficient models (gSIVCM)
mixture of exposures
nonlinear G × E
synergistic G × E
title Variable Selection for Generalized Single-Index Varying-Coefficient Models with Applications to Synergistic G × E Interactions
title_full Variable Selection for Generalized Single-Index Varying-Coefficient Models with Applications to Synergistic G × E Interactions
title_fullStr Variable Selection for Generalized Single-Index Varying-Coefficient Models with Applications to Synergistic G × E Interactions
title_full_unstemmed Variable Selection for Generalized Single-Index Varying-Coefficient Models with Applications to Synergistic G × E Interactions
title_short Variable Selection for Generalized Single-Index Varying-Coefficient Models with Applications to Synergistic G × E Interactions
title_sort variable selection for generalized single index varying coefficient models with applications to synergistic g e interactions
topic gene–environment interaction (G × E)
generalized single-index varying-coefficient models (gSIVCM)
mixture of exposures
nonlinear G × E
synergistic G × E
url https://www.mdpi.com/2227-7390/13/3/469
work_keys_str_mv AT shunjieguan variableselectionforgeneralizedsingleindexvaryingcoefficientmodelswithapplicationstosynergisticgeinteractions
AT xuliu variableselectionforgeneralizedsingleindexvaryingcoefficientmodelswithapplicationstosynergisticgeinteractions
AT yuehuacui variableselectionforgeneralizedsingleindexvaryingcoefficientmodelswithapplicationstosynergisticgeinteractions