Gene-environment Independence Research Articles

Misclassification Bias in the Assessment of Gene-by-Environment Interactions.

Misclassification bias is a common concern in epidemiologic studies. Despite strong bias on main effects, gene-environment interactions have been shown to be biased towards the null under gene-environment independence. In the context of a recent article examining the interaction between nerve agent exposure and paraoxonase-1 gene on Gulf War Illness, we aimed to assess the impact of recall bias-a common misclassfication bias-on the identification of gene-environment interactions when the independence assumption is violated. We derive equations to quantify the bias of the interaction, and numerically illustrate these results by simulating a case-control study of 1000 cases and 1000 controls. Simulation input parameters included exposure prevalence, strength of gene-environment dependence, strength of the main effect, exposure specificity among cases, and strength of the gene-environment interaction. We show that, even if gene-environment independence is violated, we can bound possible gene-environment interactions by knowing the strength and direction of the gene-environment dependence ( ) and the observed gene-environment interaction ( )-thus often still allowing for the identification of such interactions. Depending on whether is larger or smaller than the inverse of , is a lower (if ) or upper (if ) bound for the true interaction. In addition, the bias magnitude is somewhat predictable by examining other characteristics such as exposure prevalence, the strength of the exposure main effect, and directions of the recall bias and gene-environment dependence. Even if gene-environment dependence exists, we may still be able to identify gene-environment interactions even when misclassification bias is present.

The hidden factor: accounting for covariate effects in power and sample size computation for a binary trait.

Accurate power and sample size estimation is crucial to the design and analysis of genetic association studies. When analyzing a binary trait via logistic regression, important covariates such as age and sex are typically included in the model. However, their effects are rarely properly considered in power or sample size computation during study planning. Unlike when analyzing a continuous trait, the power of association testing between a binary trait and a genetic variant depends, explicitly, on covariate effects, even under the assumption of gene-environment independence. Earlier work recognizes this hidden factor but the implemented methods are not flexible. We thus propose and implement a generalized method for estimating power and sample size for (discovery or replication) association studies of binary traits that (i) accommodates different types of nongenetic covariates E, (ii) deals with different types of G-E relationships, and (iii) is computationally efficient. Extensive simulation studies show that the proposed method is accurate and computationally efficient for both prospective and retrospective sampling designs with various covariate structures. A proof-of-principle application focused on the understudied African sample in the UK Biobank data. Results show that, in contrast to studying the continuous blood pressure trait, when analyzing the binary hypertension trait ignoring covariate effects of age and sex leads to overestimated power and underestimated replication sample size. The simulated datasets can be found on the online web-page of this manuscript, and the UK Biobank application data can be accessed at https://www.ukbiobank.ac.uk. The R package SPCompute that implements the proposed method is available at CRAN. The genome-wide association studies are carried out using the software PLINK 2.0 [Purcell et al. (Plink: a tool set for whole-genome association and population-based linkage analyses. Am J Hum Genet 2007;81:559-75.)].

Using potential variable to study gene-gene and gene-environment interaction effects with genetic model uncertainty.

One of the critical issues in genetic association studies is to evaluate the risk of a disease associated with gene-gene or gene-environment interactions. The commonly employed procedures are derived by assigning a particular set of scores to genotypes. However, the underlying genetic models of inheritance are rarely known in practice. Misspecifying a genetic model may result in power loss. By using some potential genetic variables to separate the genotype coding and genetic model parameter, we construct a model-embedded score test (MEST). Our test is free of assumption of gene-environment independence and allows for covariates in the model. An effective sequential optimization algorithm is developed. Extensive simulations show the proposed MEST is robust and powerful in most of scenarios. Finally, we apply the proposed method to rheumatoid arthritis data from the Genetic Analysis Workshop 16 to further investigate the potential interaction effects.

Evaluation of a Gene–Environment Interaction of PON1 and Low-Level Nerve Agent Exposure with Gulf War Illness: A Prevalence Case–Control Study Drawn from the U.S. Military Health Survey’s National Population Sample

Background:Consensus on the etiology of 1991 Gulf War illness (GWI) has been limited by lack of objective individual-level environmental exposure information and assumed recall bias.Objectives:We investigated a prestated hypothesis of the association of GWI with a gene–environment (GxE) interaction of the paraoxonase-1 (PON1) Q192R polymorphism and low-level nerve agent exposure.Methods:A prevalence sample of 508 GWI cases and 508 nonpaired controls was drawn from the 8,020 participants in the U.S. Military Health Survey, a representative sample survey of military veterans who served during the Gulf War. The PON1 Q192R genotype was measured by real-time polymerase chain reaction (RT-PCR), and the serum Q and R isoenzyme activity levels were measured with PON1-specific substrates. Low-level nerve agent exposure was estimated by survey questions on having heard nerve agent alarms during deployment.Results:The GxE interaction of the Q192R genotype and hearing alarms was strongly associated with GWI on both the multiplicative [prevalence odds ratio (POR) of the ; 95% confidence interval (CI): 1.20, 9.72] and additive (synergy ; 95% CI: 1.82, 12.19) scales, adjusted for measured confounders. The Q192R genotype and the alarms variable were independent (adjusted POR in the ; 95% CI: 0.81, 1.73; ), and the associations of GWI with the number of R alleles and quartiles of Q isoenzyme were monotonic. The adjusted relative excess risk due to interaction (aRERI) was 7.69 (95% CI: 2.71, 19.13). Substituting Q isoenzyme activity for the genotype in the analyses corroborated the findings. Sensitivity analyses suggested that recall bias had forced the estimate of the GxE interaction toward the null and that unmeasured confounding is unlikely to account for the findings. We found a GxE interaction involving the Q-correlated PON1 diazoxonase activity and a weak possible GxE involving the Khamisiyah plume model, but none involving the PON1 R isoenzyme activity, arylesterase activity, paraoxonase activity, butyrylcholinesterase genotypes or enzyme activity, or pyridostigmine.Discussion:Given gene–environment independence and monotonicity, the unconfounded supports a mechanistic interaction. Together with the direct evidence of exposure to fallout from bombing of chemical weapon storage facilities and the extensive toxicologic evidence of biochemical protection from organophosphates by the Q isoenzyme, the findings provide strong evidence for an etiologic role of low-level nerve agent in GWI. https://doi.org/10.1289/EHP9009

A Robust Test for Additive Gene-Environment Interaction Under the Trend Effect of Genotype Using an Empirical Bayes-Type Shrinkage Estimator.

Evaluating gene by environment (G×E) interaction under an additive risk model (i.e., additive interaction) has gained wider attention. Recently, statistical tests have been proposed for detecting additive interaction, utilizing an assumption on gene-environment (G-E) independence to boost power, that do not rely on restrictive genetic models such as dominant or recessive models. However, a major limitation of these methods is a sharp increase in type I error when this assumption is violated. Our goal was to develop a robust test for additive G×E interaction under the trend effect of genotype, applying an empirical Bayes-type shrinkage estimator of the relative excess risk due to interaction. The proposed method uses a set of constraints to impose the trend effect of genotype and builds an estimator that data-adaptively shrinks an estimator of relative excess risk due to interaction obtained under a general model for G-E dependence using a retrospective likelihood framework. Numerical study under varying levels of departures from G-E independence shows that the proposed method is robust against the violation of the independence assumption while providing an adequate balance between bias and efficiency compared with existing methods. We applied the proposed method to the genetic data of Alzheimer disease and lung cancer.

A Likelihood Ratio Test for Gene-Environment Interaction Based on the Trend Effect of Genotype Under an Additive Risk Model Using the Gene-Environment Independence Assumption.

Several statistical methods have been proposed for testing gene-environment (G-E) interactions under additive risk models using data from genome-wide association studies. However, these approaches have strong assumptions from underlying genetic models, such as dominant or recessive effects that are known to be less robust when the true genetic model is unknown. We aimed to develop a robust trend test employing a likelihood ratio test for detecting G-E interaction under an additive risk model, while incorporating the G-E independence assumption to increase power. We used a constrained likelihood to impose 2 sets of constraints for: 1) the linear trend effect of genotype and 2) the additive joint effects of gene and environment. To incorporate the G-E independence assumption, a retrospective likelihood was used versus a standard prospective likelihood. Numerical investigation suggests that the proposed tests are more powerful than tests assuming dominant, recessive, or general models under various parameter settings and under both likelihoods. Incorporation of the independence assumption enhances efficiency by 2.5-fold. We applied the proposed methods to examine the gene-smoking interaction for lung cancer and gene-apolipoprotein E $\varepsilon$4 interaction for Alzheimer disease, which identified 2 interactions between apolipoprotein E $\varepsilon$4 and loci membrane-spanning 4-domains subfamily A (MS4A) and bridging integrator 1 (BIN1) genes at genome-wide significance that were replicated using independent data.

Abstract 1213: Genome-wide interaction scan identifies gene by smoking interaction at 2q21.3 for pancreatic cancer risk

Abstract Introduction: Pancreatic cancer is the seventh leading cause of cancer death worldwide with pancreatic ductal adenocarcinoma (PDAC) being the most common subtype (>90%). Inherited genetic changes and cigarette smoking are established independent risk factors of PDAC. Methods: We conducted a genome-wide gene by smoking interaction analysis of PDAC risk among 7,937 PDAC cases and 12,389 controls of European ancestry from the Pancreatic Cancer Cohort (PanScan) and Pancreatic Cancer Case-Control Consortia (PanC4) with complete genotyping and smoking data. Over 6,769,447 SNPs met our inclusion criteria of imputation score >0.5 and MAF >0.05 after imputation to phase 3 1000G and were included in our analysis. We evaluated the gene-environment interactions using the empirical Bayes method which allows data-adaptive relaxation of the gene-environment independence assumption. The logistic regression model was adjusted for age, sex, top principal components for each phase, study and study region (PanScan only). The analysis was conducted separately for the PanScan and PanC4 GWAS studies, using a score test to efficiently incorporate expected SNP dosages. The estimates were then combined using a fixed-effect meta-analysis. We examined expression quantitative trait locus using data from the NIH Genotype-Tissue Expression (GTEx) database. We considered a P-value < 5.0 × 10−8 statistically significant. Results: We found a genome-wide significant qualitative interaction with the SNP rs1818613 by smoking status (P-value <5 × 10−9) where, compared to the G allele, the T allele was associated with a reduced risk PDAC in never smokers (per T allele OR, 0.87; 95% CI, 0.82-0.93), had no association in former smokers (OR, 1.00; 95% CI, 0.91-1.07) and was associated with an increased risk in current smokers (OR, 1.25; 95% CI, 1.12-1.40). This SNP is located on chromosome 2q21.3 in intron 5 of the transmembrane protein 163 (TMEM163) gene and upstream of the cyclin T2 (CCNT2) gene. More than 40 additional SNPs within 100Kbp and in high LD (r2 > 0.8) with rs1818613 provided significant evidence of interaction by smoking status for PDAC risk. rs1818613 was associated with differential expression of TMEM163 in several tissues: for T allele compared with the G allele there was increased expression in the heart, pituitary, whole blood, and esophagus-muscularis and decreased expression in the testis tissues (P-value < 3 × 10−11). It was also associated with decreased CCNT2 expression in the tibial nerve tissue (P-value = 1.9 × 10−9). Conclusions: Our work supports that the genetic variation in the region, in conjunction with cigarette smoking, influences PDAC risk. Future studies are needed to explore this association in other smoking-related cancers and to understand the biological mechanism of such association. Citation Format: Prosenjit Kundu, Evelina Mocci, William Wheeler, Laufey T. Amundadottir, Donghui Li, Eric J. Jacobs, Gloria M. Petersen, Brian M. Wolpin, Harvey A. Risch, Peter Kraft, Nilanjan Chatterjee, Alison P. Klein, Rachael Z. Stolzenberg-Solomon, The PanScan and Panc4 consortia. Genome-wide interaction scan identifies gene by smoking interaction at 2q21.3 for pancreatic cancer risk [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr 1213.

Exploiting gene-environment independence in haplotype-based inferences for population-based case-control studies with complex sampling.

The use of complex sampling in population-based case-control studies is becoming more common. Although most single nucleotide polymorphism-based association studies with complex sampling account for the design complications, many of haplotype-based genetic association studies with complex sampling tend to ignore them when estimating haplotype frequencies, regression coefficients, or both. In this article, we develop innovative one-step and two-step statistical methods that account for the design complications in haplotype-based association studies when cases and/or controls are sampled with complex sampling. Attracted by the efficiency advantage of the retrospective method, we explore the assumptions of Hardy-Weinberg equilibrium and gene-environment independence in the underlying population. Results of our simulation studies demonstrate superior performance of the proposed methods over selected existing methods under various complex sampling designs. An application of the proposed methods is illustrated using a population-based case-control study of kidney cancer.

New perspective on the benefits of the gene–environment independence in case–control studies

AbstractWe study the benefit of exploiting the gene–environment independence (GEI) assumption for inferring the joint effect of genotype and environmental exposure on disease risk in a case–control study. By transforming the problem into a constrained maximum likelihood estimation problem we derive the asymptotic distribution of the maximum likelihood estimator (MLE) under the GEI assumption (MLE‐GEI) in a closed form. Our approach uncovers a transparent explanation of the efficiency gained by exploiting the GEI assumption in more general settings, thus bridging an important gap in the existing literature. Moreover, we propose an easy‐to‐implement numerical algorithm for estimating the model parameters in practice. Finally, we conduct simulation studies to compare the proposed method with the traditional prospective logistic regression method and the case‐only estimator. The Canadian Journal of Statistics 47: 473–486; 2019 © 2019 Statistical Society of Canada

Review of Statistical Methods for Gene-Environment Interaction Analysis

Complex diseases are caused by a combination of genetic and environmental factors, creating a challenge for understanding the disease mechanisms. Understanding the interplay between genes and environmental factors is important, as genes do not operate in isolation but rather in complex networks and pathways influenced by environmental factors. The advent of new technologies has made a massive amount of genetic data available, and various statistical methods have been developed to analyze genetic data and to identify interactions between genes and the environment, i.e., gene-environment (G-E) interactions. In this review article, we introduce various statistical methods for identifying G-E interactions using case-control designs. We review a range of disease risk models for modeling the joint effects of genetic and environmental factors such as multiplicative and additive models. We then introduce various inference methods under these disease risk models, which include a standard prospective likelihood, case-only designs, a retrospective likelihood that exploits a gene-environment independence assumption to boost power, and an empirical Bayes type approach that uses the independence assumption in a data-adaptive way. Several tests for detecting genetic associations in the presence of G-E interactions are also introduced, which include a joint test and a maximum score test that provides a unified approach by integrating a class of disease risk models to maximize over a class of score tests. There are several challenges of G-E interaction analysis that include replication issues. While more powerful statistical methods for detecting interactions are helpful, ultimately studies with larger sample sizes are needed to identify interactions through consortium-based studies to achieve adequate power for G-E analysis.

Using imputed genotype data in the joint score tests for genetic association and gene-environment interactions in case-control studies.

Genome-wide association studies (GWAS) are now routinely imputed for untyped single nucleotide polymorphisms (SNPs) based on various powerful statistical algorithms for imputation trained on reference datasets. The use of predicted allele counts for imputed SNPs as the dosage variable is known to produce valid score test for genetic association. In this paper, we investigate how to best handle imputed SNPs in various modern complex tests for genetic associations incorporating gene-environment interactions. We focus on case-control association studies where inference for an underlying logistic regression model can be performed using alternative methods that rely on varying degree on an assumption of gene-environment independence in the underlying population. As increasingly large-scale GWAS are being performed through consortia effort where it is preferable to share only summary-level information across studies, we also describe simple mechanisms for implementing score tests based on standard meta-analysis of "one-step" maximum-likelihood estimates across studies. Applications of the methods in simulation studies and a dataset from GWAS of lung cancer illustrate ability of the proposed methods to maintain type-I error rates for the underlying testing procedures. For analysis of imputed SNPs, similar to typed SNPs, the retrospective methods can lead to considerable efficiency gain for modeling of gene-environment interactions under the assumption of gene-environment independence. Methods are made available for public use through CGEN R software package.

Testing for gene-environment interaction under exposure misspecification.

Complex interplay between genetic and environmental factors characterizes the etiology of many diseases. Modeling gene-environment (GxE) interactions is often challenged by the unknown functional form of the environment term in the true data-generating mechanism. We study the impact of misspecification of the environmental exposure effect on inference for the GxE interaction term in linear and logistic regression models. We first examine the asymptotic bias of the GxE interaction regression coefficient, allowing for confounders as well as arbitrary misspecification of the exposure and confounder effects. For linear regression, we show that under gene-environment independence and some confounder-dependent conditions, when the environment effect is misspecified, the regression coefficient of the GxE interaction can be unbiased. However, inference on the GxE interaction is still often incorrect. In logistic regression, we show that the regression coefficient is generally biased if the genetic factor is associated with the outcome directly or indirectly. Further, we show that the standard robust sandwich variance estimator for the GxE interaction does not perform well in practical GxE studies, and we provide an alternative testing procedure that has better finite sample properties.

Semiparametric analysis of complex polygenic gene-environment interactions in case-control studies.

Many methods have recently been proposed for efficient analysis of case-control studies of gene-environment interactions using a retrospective likelihood framework that exploits the natural assumption of gene-environment independence in the underlying population. However, for polygenic modelling of gene-environment interactions, which is a topic of increasing scientific interest, applications of retrospective methods have been limited due to a requirement in the literature for parametric modelling of the distribution of the genetic factors. We propose a general, computationally simple, semiparametric method for analysis of case-control studies that allows exploitation of the assumption of gene-environment independence without any further parametric modelling assumptions about the marginal distributions of any of the two sets of factors. The method relies on the key observation that an underlying efficient profile likelihood depends on the distribution of genetic factors only through certain expectation terms that can be evaluated empirically. We develop asymptotic inferential theory for the estimator and evaluate its numerical performance via simulation studies. An application of the method is presented.

Meta-analysis of gene-environment interaction exploiting gene-environment independence across multiple case-control studies.

Multiple papers have studied the use of gene-environment (G-E) independence to enhance power for testing gene-environment interaction in case-control studies. However, studies that evaluate the role of G-E independence in a meta-analysis framework are limited. In this paper, we extend the single-study empirical Bayes type shrinkage estimators proposed by Mukherjee and Chatterjee (2008) to a meta-analysis setting that adjusts for uncertainty regarding the assumption of G-E independence across studies. We use the retrospective likelihood framework to derive an adaptive combination of estimators obtained under the constrained model (assuming G-E independence) and unconstrained model (without assumptions of G-E independence) with weights determined by measures of G-E association derived from multiple studies. Our simulation studies indicate that this newly proposed estimator has improved average performance across different simulation scenarios than the standard alternative of using inverse variance (covariance) weighted estimators that combines study-specific constrained, unconstrained, or empirical Bayes estimators. The results are illustrated by meta-analyzing 6 different studies of type 2 diabetes investigating interactions between genetic markers on the obesity related FTO gene and environmental factors body mass index and age.

Robust Tests for Additive Gene-Environment Interaction in Case-Control Studies Using Gene-Environment Independence.

There have been recent proposals advocating the use of additive gene-environment interaction instead of the widely used multiplicative scale, as a more relevant public health measure. Using gene-environment independence enhances statistical power for testing multiplicative interaction in case-control studies. However, under departure from this assumption, substantial bias in the estimates and inflated type I error in the corresponding tests can occur. In this paper, we extend the empirical Bayes (EB) approach previously developed for multiplicative interaction, which trades off between bias and efficiency in a data-adaptive way, to the additive scale. An EB estimator of the relative excess risk due to interaction is derived, and the corresponding Wald test is proposed with a general regression setting under a retrospective likelihood framework. We study the impact of gene-environment association on the resultant test with case-control data. Our simulation studies suggest that the EB approach uses the gene-environment independence assumption in a data-adaptive way and provides a gain in power compared with the standard logistic regression analysis and better control of type I error when compared with the analysis assuming gene-environment independence. We illustrate the methods with data from the Ovarian Cancer Association Consortium.

In the Wrong Place with the Wrong SNP: The Association Between Stressful Neighborhoods and Cardiac Arrest Within Beta-2-adrenergic Receptor Variants.

Sudden cardiac arrest has been linked independently both to stressful neighborhood conditions and to polymorphisms in the ADRB2 gene. The ADRB2 gene mediates sympathetic activation in response to stress. Therefore, if neighborhood conditions cause cardiac arrest through the stress pathway, the ADRB2 variant may modify the association between neighborhood conditions, such as socioeconomic deprivation and incidence of cardiac arrest. The Cardiac Arrest Blood Study Repository is a population-based repository of specimens and other data from adult cardiac arrest patients residing in King County, Washington. Cases (n = 1,539) were 25- to 100-year-old individuals of European descent who experienced out-of-hospital cardiac arrest from 1988 to 2004. Interactions between neighborhood conditions and the ADRB2 genotype on cardiac arrest risk were assessed in a case-only study design. Gene-environment independence was assessed in blood samples obtained from King County residents initially contacted by random-digit dialing. Fewer than 4% of study subjects resided in socioeconomically deprived neighborhoods. Nonetheless, the case-only analysis indicated the presence of supramultiplicative interaction of socioeconomic deprivation and the homozygous Gln27Glu variant (case-only odds ratio: 1.8 [95% confidence interval: 1.0, 2.9]). Interactions between population density and the homozygous Gln27Glu variant were weaker (case-only odds ratio: 1.2 [95% confidence interval: 0.97, 1.5]). Findings support a supramultiplicative interaction between the Gln27Glu ADRB2 variant and socioeconomic deprivation among individuals of European descent. This result is consistent with the hypothesis that the elevation in cardiac arrest risk associated with socioeconomic deprivation operates through the stress pathway.

False Appearance of Gene-Environment Interactions in Genetic Association Studies.

Under the assumption of gene-environment independence, unknown/unmeasured environmental factors, irrespective of what they may be, cannot confound the genetic effects. This may lead many people to believe that genetic heterogeneity across different levels of the studied environmental exposure should only mean gene-environment interaction--even though other environmental factors are not adjusted for. However, this is not true if the odds ratio is the effect measure used for quantifying genetic effects. This is because the odds ratio is a "noncollapsible" measure--a marginal odds ratio is not a weighted average of the conditional odds ratios, but instead has a tendency toward the null. In this study, the authors derive formulae for gene-environment interaction bias due to noncollapsibility. They use computer simulation and real data example to show that the bias can be substantial for common diseases. For genetic association study of nonrare diseases, researchers are advised to use collapsible measures, such as risk ratio or peril ratio.

Gene-Environment Independence in Case–Control Studies: Issues of Parameterization and Bayesian Inference

We consider the problem of exploiting the gene–environment independence (GEI) assumption in a case–control study inferring the joint effect of genotype and environmental exposure on disease risk. Specifically, we focus on the special case that both genotype and environmental exposure are binary. We note that the prospective intercept can sometimes be identified as a pair of “twin” values. Also, the GEI and general maximum-likelihood estimators of the gene–environment interaction coincide if the data cell proportions are directly compatible with the GEI assumption. Further, we approach the problem in a Bayesian framework by reweighing the general posterior subject to the prior specified over the subset of parameter space that is consistent with the GEI assumption. Some simulation studies have been conducted to compare the proposed method to its general counterpart. Finally, we have also extended the proposed method to address the concern that the GEI assumption may sometimes be violated.

Genome-Wide Analysis of Gene-Gene and Gene-Environment Interactions Using Closed-Form Wald Tests.

Despite the successful discovery of hundreds of variants for complex human traits using genome-wide association studies, the degree to which genes and environmental risk factors jointly affect disease risk is largely unknown. One obstacle toward this goal is that the computational effort required for testing gene-gene and gene-environment interactions is enormous. As a result, numerous computationally efficient tests were recently proposed. However, the validity of these methods often relies on unrealistic assumptions such as additive main effects, main effects at only one variable, no linkage disequilibrium between the two single-nucleotide polymorphisms (SNPs) in a pair or gene-environment independence. Here, we derive closed-form and consistent estimates for interaction parameters and propose to use Wald tests for testing interactions. The Wald tests are asymptotically equivalent to the likelihood ratio tests (LRTs), largely considered to be the gold standard tests but generally too computationally demanding for genome-wide interaction analysis. Simulation studies show that the proposed Wald tests have very similar performances with the LRTs but are much more computationally efficient. Applying the proposed tests to a genome-wide study of multiple sclerosis, we identify interactions within the major histocompatibility complex region. In this application, we find that (1) focusing on pairs where both SNPs are marginally significant leads to more significant interactions when compared to focusing on pairs where at least one SNP is marginally significant; and (2) parsimonious parameterization of interaction effects might decrease, rather than increase, statistical power.

Testing for Sufficient-Cause Gene-Environment Interactions Under the Assumptions of Independence and Hardy-Weinberg Equilibrium.

To detect gene-environment interactions, a logistic regression model is typically fitted to a set of case-control data, and the focus is on testing of the cross-product terms (gene × environment) in the model. A significant result is indicative of a gene-environment interaction under a multiplicative model for disease odds. Based on the sufficient-cause model for rates, in this paper we put forward a general approach to testing for sufficient-cause gene-environment interactions in case-control studies. The proposed tests can be tailored to detect a particular type of sufficient-cause gene-environment interaction with greater sensitivity. These tests include testing for autosomal dominant, autosomal recessive, and gene-dosage interactions. The tests can also detect trend interactions (e.g., a larger gene-environment interaction with a higher level of environmental exposure) and threshold interactions (e.g., gene-environment interaction occurs only when environmental exposure reaches a certain threshold level). Two assumptions are necessary for the validity of the tests: 1) the rare-disease assumption and 2) the no-redundancy assumption. Another 2 assumptions are optional but, if imposed correctly, can boost the statistical powers of the tests: 3) the gene-environment independence assumption and 4) the Hardy-Weinberg equilibrium assumption. SAS code (SAS Institute, Inc., Cary, North Carolina) for implementing the methods is provided.