Gene-gene and gene-environment interactions are widely believed to play significant roles in explaining the variability of complex traits. While substantial research exists in this area, a comprehensive statistical framework that addresses multiple sources of uncertainty simultaneously remains lacking. In this article, we synthesize and propose extension of a novel class of Bayesian nonparametric approaches that account for interactions among genes, loci, and environmental factors while accommodating uncertainty about population substructure. Our contribution is threefold: (1) We provide a unified exposition of hierarchical Bayesian models driven by Dirichlet processes for genetic interactions, clarifying their conceptual advantages over traditional regression approaches; (2) We shed light on new computational strategies that combine transformation-based MCMC with parallel processing for scalable inference; and (3) We present enhanced hypothesis testing procedures for identifying disease-predisposing loci.Through applications to myocardial infarction data, we demonstrate how these methods offer biological insights not readily obtainable from standard approaches. Our synthesis highlights the advantages of Bayesian nonparametric thinking in genetic epidemiology while providing practical guidance for implementation.
Complex diseases such as cardiovascular disorders, diabetes, and psychiatric conditions result from intricate networks of genetic and environmental factors. While genome-wide association studies (GWAS) have identified numerous single nucleotide polymorphisms (SNPs) associated with disease risk, these explain only a small fraction of heritability (Larson and Schaid, 2013). The "missing heritability" problem has spurred interest in gene-gene (epistasis) and gene-environment interactions as potential explanations. Traditional approaches to studying these interactions face several significant limitations that our work aims to address. Most existing methods rely on linear or additive models that may not adequately capture the complex biological pathways through which genetic factors interact (Wang et al., 2010). These simplified modeling assumptions often fail to represent the intricate biochemical networks that characterize many complex diseases. Furthermore, the failure to properly account for population stratification-the presence of genetic substructure within study populations-can lead to inflated false positive rates in association studies (Bhattacharjee et al., 2010). This issue is particularly problematic in genetically diverse populations where different subgroups may have distinct allele frequencies unrelated to disease risk.
The computational burden represents another substantial challenge in studying genetic interactions. Testing all possible pairwise SNP-SNP interactions becomes infeasible for genome-wide data, leading researchers to adopt heuristic screening methods that may miss important interactions or identify spurious ones. Additionally, many current approaches provide point estimates without adequately characterizing the uncertainty in model structure, particularly regarding the number of underlying sub-populations or the complexity of interaction networks. This lack of comprehensive uncertainty quantification limits the reliability and interpretability of findings from genetic interaction studies.
This article synthesizes and extends a series of Bayesian nonparametric models developed to address these challenges. Unlike previous works that presented these models in isolation (Bhattacharya and Bhattacharya 2018, 2020, 2024), we provide a unified framework connecting gene-gene interaction models, gene-environment extensions, and hierarchical Dirichlet process formulations. Our synthesis represents a comprehensive overview of this methodological approach, highlighting both theoretical foundations and practical implementation considerations.
We develop enhanced computational strategies that leverage parallel processing and transformationbased MCMC (Dutta and Bhattacharya, 2014) for practical implementation of these complex models. These computational innovations make it feasible to apply Bayesian nonparametric methods to realistic genetic datasets of meaningful size. Additionally, we present new hypothesis testing procedures for identifying disease-predisposing loci in the presence of population stratification, offering more robust alternatives to traditional association tests. Finally, we provide comprehensive applications demonstrating biological insights from myocardial infarction data, showing how these methods can uncover relationships not readily apparent using standard approaches.
Our approach fundamentally departs from standard logistic regression by modeling genotypes conditional on disease status using Dirichlet process mixtures. This inversion of the typical modeling relationship allows us to capture several important features simultaneously. We can model uncertainty in population substructure nonparametrically, allowing the data to inform about the number and characteristics of genetic subgroups. We capture gene-gene interactions through covariance structures rather than regression coefficients, providing a more flexible representation of genetic dependencies. Furthermore, we accommodate subject-specific environmental effects through hierarchical modeling, enabling personalized assessment of genetic risk factors.
The remainder of this article is organized as follows. Section 2 introduces our modeling philosophy and contrasts it with traditional approaches, explaining the conceptual shift from regression-based to conditional genotype modeling. Section 3 presents the gene-gene interaction model with computational details, including our parallel implementation strategy. Section 4 extends this framework to incorporate gene-environment interactions, discussing both modeling extensions and enhanced hypothesis testing procedures. Section 5 introduces the hierarchical Dirichlet process formulation, which addresses limitations of previous models by allowing more flexible sharing patterns. Section 6 presents comprehensive applications to myocardial infarction data, demonstrating the practical utility of our methods. Section 7 provides extensive sensitivity analyses to assess the robustnes
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