Assumption Of Gene-environment Independence Research Articles

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.

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.

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.

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.

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.

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.

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.

Investigations of Gene–Disease Associations

Environmental exposure data may improve statistical power in genetic studies when gene-environment interaction is present. However, resources invested in obtaining exposure data could instead be applied to measure disease status and genotype on more subjects. In a cohort-study setting, we consider the tradeoff between measuring only disease status and genotype for a larger study sample and measuring disease status, genotype, and environmental exposure for a smaller sample, under the gene-environment independence assumption in the study population. We focus on the power of tests for gene-disease association, applied in situations where a gene modifies risk of disease due to environmental exposure. Our results are equally applicable to exploratory genome-wide association studies and to more hypothesis-driven candidate gene investigations. We further consider the impact of misclassification for environmental exposures. We identify circumstances under which higher power is achieved via the larger study sample without measurements of environmental exposure.

Using shared genetic controls in studies of gene-environment interactions.

With the advent of modern genomic methods to adjust for population stratification, the use of external or publicly available controls has become an attractive option for reducing the cost of large-scale case-control genetic association studies. In this article, we study the estimation of joint effects of genetic and environmental exposures from a case-control study where data on genome-wide markers are available on the cases and a set of external controls while data on environmental exposures are available on the cases and a set of internal controls. We show that under such a design, one can exploit an assumption of gene-environment independence in the underlying population to estimate the gene-environment joint effects, after adjustment for population stratification. We develop a semiparametric profile likelihood method and related pseudolikelihood and working likelihood methods that are easy to implement in practice. We propose variance estimators for the methods based on asymptotic theory. Simulation is used to study the performance of the methods, and data from a multi-centre genome-wide association study of bladder cancer is further used to illustrate their application.

Testing Gene-Environment Interaction in Large-Scale Case-Control Association Studies: Possible Choices and Comparisons

Several methods for screening gene-environment interaction have recently been proposed that address the issue of using gene-environment independence in a data-adaptive way. In this report, the authors present a comparative simulation study of power and type I error properties of 3 classes of procedures: 1) the standard 1-step case-control method; 2) the case-only method that requires an assumption of gene-environment independence for the underlying population; and 3) a variety of hybrid methods, including empirical-Bayes, 2-step, and model averaging, that aim at gaining power by exploiting the assumption of gene-environment independence and yet can protect against false positives when the independence assumption is violated. These studies suggest that, although the case-only method generally has maximum power, it has the potential to create substantial false positives in large-scale studies even when a small fraction of markers are associated with the exposure under study in the underlying population. All the hybrid methods perform well in protecting against such false positives and yet can retain substantial power advantages over standard case-control tests. The authors conclude that, for future genome-wide scans for gene-environment interactions, major power gain is possible by using alternatives to standard case-control analysis. Whether a case-only type scan or one of the hybrid methods should be used depends on the strength and direction of gene-environment interaction and association, the level of tolerance for false positives, and the nature of replication strategies.

Invited Commentary: GE-Whiz! Ratcheting Gene-Environment Studies up to the Whole Genome and the Whole Exposome

One goal in the post-genome-wide association study era is characterizing gene-environment interactions, including scanning for interactions with all available polymorphisms, not just those showing significant main effects. In recent years, several approaches to such "gene-environment-wide interaction studies" have been proposed. Two contributions in this issue of the American Journal of Epidemiology provide systematic comparisons of the performance of these various approaches, one based on simulation and one based on application to 2 real genome-wide association study scans for type 2 diabetes. The authors discuss some of the broader issues raised by these contributions, including the plausibility of the gene-environment independence assumption that some of these approaches rely upon, the need for replication, and various generalizations of these approaches.

Robust Discovery of Genetic Associations Incorporating Gene-Environment Interaction and Independence

This article considers the detection and evaluation of genetic effects incorporating gene-environment interaction and independence. Whereas ordinary logistic regression cannot exploit the assumption of gene-environment independence, the proposed approach makes explicit use of the independence assumption to improve estimation efficiency. This method, which uses both cases and controls, fits a constrained retrospective regression in which the genetic variant plays the role of the response variable, and the disease indicator and the environmental exposure are the independent variables. The regression model constrains the association of the environmental exposure with the genetic variant among the controls to be null, thus explicitly encoding the gene-environment independence assumption, which yields substantial gain in accuracy in the evaluation of genetic effects. The proposed retrospective regression approach has several advantages. It is easy to implement with standard software, and it readily accounts for multiple environmental exposures of a polytomous or of a continuous nature, while easily incorporating extraneous covariates. Unlike the profile likelihood approach of Chatterjee and Carroll (Biometrika. 2005;92:399-418), the proposed method does not require a model for the association of a polytomous or continuous exposure with the disease outcome, and, therefore, it is agnostic to the functional form of such a model and completely robust to its possible misspecification.

Genetic modifiers of the effect of menopausal hormone therapy on breast cancer risk – A meta-analysis of four genome-wide association studies

Hormone therapy (HT) is associated with an elevated risk of breast cancer (BC) in postmenopausal women. Only limited studies have examined whether BC risk after HT exposure varies by individual susceptibility. To identify loci that modify HT related BC risk, four genome-wide case-only studies were analysed separately and combined in a meta-analysis. We included data from the genome-wide association studies HEBCS (Finland), MARIE (Germany), NHS (USA) and SASBAC (Sweden) which yielded 344, 742, 1,090 and 773 female, postmenopausal BC cases, respectively. Recruitment was hospital-based for HEBCS and population-based for MARIE, SASBAC and NHS. The available SNPs (genotyped using the Illumina 370k array in MARIE and 550 k in HEBCS, NHS and SASBAC) were used to impute additional SNPs (software: MACH) which resulted in up to 2,800,000 SNPs in total per study. The case-only approach is more powerful to detect gene-environment interactions than the case-control approach if the assumption of gene-environment independence is valid. We performed case-only logistic regression analysis for each study separately (outcome: current versus never/past HT use) using the software ProbABEL that takes into account the uncertainty introduced by imputation, i.e. the probabilities of each genotype per SNP and individual are used rather than the most likely genotype. A log-additive mode of inheritance is employed. The meta-analyses will be conducted assuming fixed effects (software: Plink). Our study has 80% power to detect an interaction effect of 1.25 assuming genetic and environmental main effects of 1.15, a moderate risk allele frequency of 0.10 and a prevalence of the environmental exposure of 0.50, Currently, analyses are ongoing and results will be presented at the conference. The most significant results will be replicated in independent case-control studies from the Breast Cancer Association Consortium (BCAC). We will thus rule out false positives due to possible gene-HT dependencies.

Case–Control Studies of Gene–Environment Interaction: Bayesian Design and Analysis

With increasing frequency, epidemiologic studies are addressing hypotheses regarding gene-environment interaction. In many well-studied candidate genes and for standard dietary and behavioral epidemiologic exposures, there is often substantial prior information available that may be used to analyze current data as well as for designing a new study. In this article, first, we propose a proper full Bayesian approach for analyzing studies of gene-environment interaction. The Bayesian approach provides a natural way to incorporate uncertainties around the assumption of gene-environment independence, often used in such an analysis. We then consider Bayesian sample size determination criteria for both estimation and hypothesis testing regarding the multiplicative gene-environment interaction parameter. We illustrate our proposed methods using data from a large ongoing case-control study of colorectal cancer investigating the interaction of N-acetyl transferase type 2 (NAT2) with smoking and red meat consumption. We use the existing data to elicit a design prior and show how to use this information in allocating cases and controls in planning a future study that investigates the same interaction parameters. The Bayesian design and analysis strategies are compared with their corresponding frequentist counterparts.

Two‐stage analysis for gene‐environment interaction utilizing both case‐only and family‐based analysis

The case-only study and family-based study are two popular study designs for detecting gene-environment interactions. It is well known that the case-only analysis is efficient, but its validity relies crucially on the assumption of gene-environment independence in the study population. In contrast, the family-based analysis is robust to the violation of such an assumption, but is less efficient. We propose a two-stage study design for detecting gene-environment interactions, where a case-only study is performed at the first stage, and a case-parent/case-sibling study is performed at the second stage on a random subsample of the first-stage case sample as well as their parents/unaffected siblings. Statistical inference procedures are developed for the proposed two-stage study designs, which not only preserve the robustness property of the family-based analysis, but also utilize information from the case-only analysis to enhance estimation efficiency and testing power. Simulation results reveal both the robustness and efficiency of the proposed strategies.

Tests for gene‐environment interaction from case‐control data: a novel study of type I error, power and designs

To evaluate the risk of a disease associated with the joint effects of genetic susceptibility and environmental exposures, epidemiologic researchers often test for non-multiplicative gene-environment effects from case-control studies. In this article, we present a comparative study of four alternative tests for interactions: (i) the standard case-control method; (ii) the case-only method, which requires an assumption of gene-environment independence for the underlying population; (iii) a two-step method that decides between the case-only and case-control estimators depending on a statistical test for the gene-environment independence assumption and (iv) a novel empirical-Bayes (EB) method that combines the case-control and case-only estimators depending on the sample size and strength of the gene-environment association in the data. We evaluate the methods in terms of integrated Type I error and power, averaged with respect to varying scenarios for gene-environment association that are likely to appear in practice. These unique studies suggest that the novel EB procedure overall is a promising approach for detection of gene-environment interactions from case-control studies. In particular, the EB procedure, unlike the case-only or two-step methods, can closely maintain a desired Type I error under realistic scenarios of gene-environment dependence and yet can be substantially more powerful than the traditional case-control analysis when the gene-environment independence assumption is satisfied, exactly or approximately. Our studies also reveal potential utility of some non-traditional case-control designs that samples controls at a smaller rate than the cases. Apart from the simulation studies, we also illustrate the different methods by analyzing interactions of two commonly studied genes, N-acetyl transferase type 2 and glutathione s-transferase M1, with smoking and dietary exposures, in a large case-control study of colorectal cancer.