Complete Effect‐Profile Assessment in Association Studies With Multiple Genetic and Multiple Environmental Factors

Abstract

Studying complex diseases in the post GWAS era has led to developing methods that consider factor-sets rather than individual genetic/environmental factors (i.e., Multi-G-Multi-E studies), and mining for potential gene-environment (GxE) interactions has proven to be an invaluable aid in both discovery and deciphering underlying biological mechanisms. Current approaches for examining effect profiles in Multi-G-Multi-E analyses are either underpowered due to large degrees of freedom, ill-suited for detecting GxE interactions due to imprecise modeling of the G and E effects, or lack of capacity for modeling interactions between two factor sets (e.g., existing methods focus primarily on a single E factor). In this work, we illustrate the issues encountered in constructing kernels for investigating interactions between two factor-sets, and propose a simple yet intuitive solution to construct the GxE kernel that retains the ease-of-interpretation of classic regression. We also construct a series of KM score tests to evaluate the complete effect profile (i.e., the G, E, and GxE effects individually or in combination). We show, via simulations and a data application, that the proposed KM methods outperform the classic and PC regressions across a range of scenarios, including varying effect size, effect structure, and interaction complexity. The largest power gain was observed when the underlying effect structure involved complex GxE interactions; however, the proposed methods have consistent, powerful performance when the effect profile is simple or complex, suggesting that the proposed method could be a useful tool for exploratory or confirmatory GxE analysis.

A Fast Multiple‐Kernel Method With Applications to Detect Gene‐Environment Interaction

“…The proposed low‐rank KM framework has broad impact on KM modeling and beyond. It greatly enhances the computational efficiency of KM tests that contain multiple kernel components and involve high‐dimensional nuisance parameters, e.g., the G× G kernel tests [Larson and Schaid, ] and the conditional kernel tests [Wang et al., ,b]. It can be generalized to study copy‐number variants (CNVs) s, for example, to extend burden‐based CNV tests [Raychaudhuri et al., ], which simultaneously model multiple CNV features, to the framework of KM tests (e.g., testing for a CNV dosage effect while adjusting for length and gene interruption status; Tzeng et al., 2015).…”

“…Given the genetic main effect kernel , one possible way to construct the interaction kernel is to take the element‐wise product of the genetic main effect kernel and the environmental kernel , as described in Larson and Schaid [] and Wang et al. [2014, ,b]. When the environmental covariate is a scalar, this simplifies to , where is a diagonal matrix with elements E [Tzeng et al., ].…”

“…When the environmental covariate is a scalar, this simplifies to , where is a diagonal matrix with elements E [Tzeng et al., ]. However, caution must be taken when using this direct product kernel to avoid duplicating the main effect terms in the G× E kernel [Wang et al., ].…”

“…Although the popular KM methods, for example, the Sequence Kernel Association Test (SKAT) [Wu et al., ], focus on single‐kernel analysis (i.e., using one kernel function to model a single variable set), analyses involving multiple kernels (i.e., using separate kernels to simultaneously model multiple variable sets) are also frequently encountered in genomic research. Multikernel approaches include tests for gene‐environment (G× E) interactions [Lin et al., ; Tzeng et al., ; Wang et al., 2015b; Zhao et al., ], tests for gene‐gene interactions [Larson and Schaid, ; Wang et al., ], conditional tests for evaluating the effect of a single variable set adjusting for other variable sets [Pang et al., ; Wang et al., ,b], and SKAT analysis coupled with a variance component method [Kang et al., ] to account for population substructure. The number of explanatory variables in these analyses is much higher than in a single marker‐set analysis.…”

“…For example, performing a KM G× E test, even under the null hypothesis of no G× E effects, requires the estimation of nuisance genetic main effects. Current attempts to overcome the dimensionality challenges include treating the n ‐dimensional parameters as random and using the EM algorithm to estimate its variance component [Tzeng et al., ; Wang et al., , ,b; Zhao et al., ], or imposing penalization on these parameters [Lin et al., ]. While both techniques have proven to be valid, the estimation procedures are usually phenotype‐specific (e.g., the algorithms developed for quantitative traits cannot be applied to binary or survival traits) and computationally intensive (e.g., requiring the inversion of a n ‐dimensional matrix at each iteration of the EM algorithm or the tuning of a regularization parameter), making them not scalable to the large samples considered in rare variant studies.…”