The use of hierarchical models for estimating relative risks of individual genetic variants: an application to a study of melanoma

For major genes known to influence the risk of cancer, an important task is to determine the risks conferred by individual variants, so that one can appropriately counsel carriers of these mutations. This is a challenging task, since new mutations are continually being identified, and there is typically relatively little empirical evidence available about each individual mutation. Hierarchical modeling offers a natural strategy to leverage the collective evidence from these rare variants with sparse data. This can be accomplished when there are available higher-level covariates that characterize the variants in terms of attributes that could distinguish their association with disease. In this article, we explore the use of hierarchical modeling for this purpose using data from a large population-based study of the risks of melanoma conferred by variants in the CDKN2A gene. We employ both a pseudo-likelihood approach and a Bayesian approach using Gibbs sampling. The results indicate that relative risk estimates tend to be primarily influenced by the individual case-control frequencies when several cases and/or controls are observed with the variant under study, but that relative risk estimates for variants with very sparse data are more influenced by the higher-level covariate values, as one would expect. The analysis offers encouragement that we can draw strength from the aggregating power of hierarchical models to provide guidance to medical geneticists when they offer counseling to patients with rare or even hitherto unobserved variants. However, further research is needed to validate the application of asymptotic methods to such sparse data.     

Hierarchical Modeling of the Relation Between Sequence Variants and a Quantitative Trait: Addressing Multiple Comparison and Population Stratification Issues

When analyzing the relation between genetic sequence information and disease traits, false‐positive associations can arise due to multiple comparisons and population stratification. In an attempt to address these issues, we incorporate into a conventional analytic model higher‐level—or “prior”—models that use additional information to improve estimates while allowing for differing population structures. We apply this hierarchical model to simulated data from the Genetic Analysis Workshop 12. We focus on the effects of common candidate gene sequence variants on quantitative risk factor 5 (Q5) levels. In particular, we compare the regression coefficients (and 95% confidence intervals) obtained from conventional (one‐stage) analyses versus the corresponding results from the hierarchical analyses. When examining either the marry‐ins or all subjects in the general and isolate populations, the conventional model detected numerous sites in candidate genes 1–5 and 7 that had statistically significant regression coefficients (alpha level = 0.05). In contrast, our hierarchical model primarily only detected associations for variants in candidate gene 2, which is the casual gene for Q5. © 2001 Wiley‐Liss, Inc.     

Mendelian Randomization Analysis With Multiple Genetic Variants Using Summarized Data

Genome‐wide association studies, which typically report regression coefficients summarizing the associations of many genetic variants with various traits, are potentially a powerful source of data for Mendelian randomization investigations. We demonstrate how such coefficients from multiple variants can be combined in a Mendelian randomization analysis to estimate the causal effect of a risk factor on an outcome. The bias and efficiency of estimates based on summarized data are compared to those based on individual‐level data in simulation studies. We investigate the impact of gene–gene interactions, linkage disequilibrium, and ‘weak instruments’ on these estimates. Both an inverse‐variance weighted average of variant‐specific associations and a likelihood‐based approach for summarized data give similar estimates and precision to the two‐stage least squares method for individual‐level data, even when there are gene–gene interactions. However, these summarized data methods overstate precision when variants are in linkage disequilibrium. If the P‐value in a linear regression of the risk factor for each variant is less than , then weak instrument bias will be small. We use these methods to estimate the causal association of low‐density lipoprotein cholesterol (LDL‐C) on coronary artery disease using published data on five genetic variants. A 30% reduction in LDL‐C is estimated to reduce coronary artery disease risk by 67% (95% CI: 54% to 76%). We conclude that Mendelian randomization investigations using summarized data from uncorrelated variants are similarly efficient to those using individual‐level data, although the necessary assumptions cannot be so fully assessed.     

Does the addition of information on genotype improve prediction of the risk of melanoma and nonmelanoma skin cancer beyond that obtained from skin phenotype?

The authors quantified improvement in predicting cutaneous malignant melanoma, basal cell carcinoma, and squamous cell carcinoma of the skin made possible by information on common variants of the melanocortin-1 receptor gene (MC1R) in a 1998-1999 population-based case-control study of subjects aged 20-59 years of northern European ancestry in Tasmania, Australia. Melanin density at the upper inner arm was estimated by spectrophotometry. DNA samples were genotyped for five MC1R variants: Val60Leu, Asp84Glu, Arg151Cys, Arg160Trp, and Asp294His. Among controls (n = 267), variant carriers, versus noncarriers, had lower (p < 0.01) mean melanin concentrations. Increased risk conferred by genotype was restricted mainly to those with the darkest skins: for subjects with at least 2% melanin, the odds of carrying each additional variant were higher for cutaneous malignant melanoma (n = 39; odds ratio = 1.45, 95% confidence interval: 0.87, 2.44), basal cell carcinoma (n = 35; odds ratio = 1.86, 95% confidence interval: 1.14, 3.02), and squamous cell carcinoma (n = 42; odds ratio = 2.67, 95% confidence interval: 1.50, 4.74) cases than for controls (n = 135). Adding MC1R information to prediction based on age, sex, and cutaneous melanin increased the area under the receiver operating characteristic curve by 1.4% (cutaneous malignant melanoma), 3.2% (basal cell carcinoma), or 2.0% (squamous cell carcinoma). The improvement in prediction was probably too small to be valuable in a clinical setting.     

Risk factors for skin melanoma: genetic factors probably more important than exposure to sunlight

Pigmented naevi (moles) are increasingly regarded as risk factors for the development of melanoma. The probability of melanoma developing from congenital naevi is proportional to the volume of the naevi. The risk of melanoma development from large naevi (diameter > 20 cm) is already present in the early years of childhood. The most important risk factor is the higher number of acquired naevi. This applies particularly to dysplastic (also called clinically atypical) naevi that not only represent the highest risk group but are also considered potential melanoma precursors. The development of acquired naevi (including dysplastic naevi) is dependant on the degree of skin pigmentation. The role of sunlight (ultraviolet radiation) in the development of melanoma is less significant than is generally assumed. The indirect effect of sunlight on melanoma development is to stimulate naevogenesis. One of the risk-modifying genes is the gene coding for melanocortin-1-receptor (MC1R). The presence of some gene variants has been found to lead to changes in melanin synthesis and is associated with a higher risk of melanoma. Recent research has shown that dysplastic naevi synthesise more phaeomelanin. There are also strong indications that dysplastic naevus cells suffer from chronic oxidative stress. This situation can lead to hypermutability and genetical instability.     

Mendelian randomization with fine‐mapped genetic data: Choosing from large numbers of correlated instrumental variables

Mendelian randomization uses genetic variants to make causal inferences about the effect of a risk factor on an outcome. With fine‐mapped genetic data, there may be hundreds of genetic variants in a single gene region any of which could be used to assess this causal relationship. However, using too many genetic variants in the analysis can lead to spurious estimates and inflated Type 1 error rates. But if only a few genetic variants are used, then the majority of the data is ignored and estimates are highly sensitive to the particular choice of variants. We propose an approach based on summarized data only (genetic association and correlation estimates) that uses principal components analysis to form instruments. This approach has desirable theoretical properties: it takes the totality of data into account and does not suffer from numerical instabilities. It also has good properties in simulation studies: it is not particularly sensitive to varying the genetic variants included in the analysis or the genetic correlation matrix, and it does not have greatly inflated Type 1 error rates. Overall, the method gives estimates that are less precise than those from variable selection approaches (such as using a conditional analysis or pruning approach to select variants), but are more robust to seemingly arbitrary choices in the variable selection step. Methods are illustrated by an example using genetic associations with testosterone for 320 genetic variants to assess the effect of sex hormone related pathways on coronary artery disease risk, in which variable selection approaches give inconsistent inferences.     

Genetic associations with childhood brain growth,defined in two longitudinal cohorts

Genome‐wide association studies (GWASs) are unraveling the genetics of adult brain neuroanatomy as measured by cross‐sectional anatomic magnetic resonance imaging (aMRI). However, the genetic mechanisms that shape childhood brain development are, as yet, largely unexplored. In this study we identify common genetic variants associated with childhood brain development as defined by longitudinal aMRI. Genome‐wide single nucleotide polymorphism (SNP) data were determined in two cohorts: one enriched for attention‐deficit/hyperactivity disorder (ADHD) (LONG cohort: 458 participants; 119 with ADHD) and the other from a population‐based cohort (Generation R: 257 participants). The growth of the brain's major regions (cerebral cortex, white matter, basal ganglia, and cerebellum) and one region of interest (the right lateral prefrontal cortex) were defined on all individuals from two aMRIs, and a GWAS and a pathway analysis were performed. In addition, association between polygenic risk for ADHD and brain growth was determined for the LONG cohort. For white matter growth, GWAS meta‐analysis identified a genome‐wide significant intergenic SNP (rs12386571, P = 9.09 × 10^?9), near AKR1B10. This gene is part of the aldo‐keto reductase superfamily and shows neural expression. No enrichment of neural pathways was detected and polygenic risk for ADHD was not associated with the brain growth phenotypes in the LONG cohort that was enriched for the diagnosis of ADHD. The study illustrates the use of a novel brain growth phenotype defined in vivo for further study.     

Burden of malignancy after a primary skin cancer: recurrence, multiple skin cancers and second primary cancers

The current paper summarizes relevant recent research on the high risk of recurrence, multiple skin cancers and second primary cancers in the growing number of people with a history of skin cancer; the ultimate purpose is to better assess the burden of malignancy following skin cancer. A number of challenges exist in identifying and tracking both melanoma and non-melanoma skin cancer (NMSC) cases. Most jurisdictions do not routinely track NMSC cases and, even if they do, it is customary to only include the first diagnosis. There are variable rules for counting multiple melanoma cancers, and recurrences are not considered for either major type of skin cancer. Applying insights from recent studies of this issue to Canadian cancer statistics would increase reported diagnoses of NMSC by about 26% and melanoma by 10% in this country. This approach to a fuller assessment of the burden of skin cancers has been called a "diagnosis-based incidence approach" as compared with a "patient-based incidence approach". A further issue that is not usually taken into account when assessing the burden of skin cancers is the 20% to 30% elevated risk of noncutaneous second primary cancers following a primary skin tumour. In summary, individuals with skin cancer are subject to a high risk of recurrence, multiple skin cancers and second primary cancers. This burden should be a special concern in the large and growing pool of individuals with a history of skin cancer, as well as among prevention planners.     

Explicit Modeling of Ancestry Improves Polygenic Risk Scores and BLUP Prediction

Polygenic prediction using genome‐wide SNPs can provide high prediction accuracy for complex traits. Here, we investigate the question of how to account for genetic ancestry when conducting polygenic prediction. We show that the accuracy of polygenic prediction in structured populations may be partly due to genetic ancestry. However, we hypothesized that explicitly modeling ancestry could improve polygenic prediction accuracy. We analyzed three GWAS of hair color (HC), tanning ability (TA), and basal cell carcinoma (BCC) in European Americans (sample size from 7,440 to 9,822) and considered two widely used polygenic prediction approaches: polygenic risk scores (PRSs) and best linear unbiased prediction (BLUP). We compared polygenic prediction without correction for ancestry to polygenic prediction with ancestry as a separate component in the model. In 10‐fold cross‐validation using the PRS approach, the R² for HC increased by 66% (0.0456–0.0755; P < 10⁻¹⁶), the R² for TA increased by 123% (0.0154 to 0.0344; P < 10⁻¹⁶), and the liability‐scale R² for BCC increased by 68% (0.0138–0.0232; P < 10⁻¹⁶) when explicitly modeling ancestry, which prevents ancestry effects from entering into each SNP effect and being overweighted. Surprisingly, explicitly modeling ancestry produces a similar improvement when using the BLUP approach, which fits all SNPs simultaneously in a single variance component and causes ancestry to be underweighted. We validate our findings via simulations, which show that the differences in prediction accuracy will increase in magnitude as sample sizes increase. In summary, our results show that explicitly modeling ancestry can be important in both PRS and BLUP prediction.     

Prognostic and Predictive Values and Statistical Interactions in the Era of Targeted Treatment

The current era of targeted treatment has accelerated the interest in studying gene‐treatment, gene‐gene, and gene‐environment interactions using statistical models in the health sciences. Interactions are incorporated into models as product terms of risk factors. The statistical significance of interactions is traditionally examined using a likelihood ratio test (LRT). Epidemiological and clinical studies also evaluate interactions in order to understand the prognostic and predictive values of genetic factors. However, it is not clear how different types and magnitudes of interaction effects are related to prognostic and predictive values. The contribution of interaction to prognostic values can be examined via improvements in the area under the receiver operating characteristic curve due to the inclusion of interaction terms in the model (). We develop a resampling based approach to test the significance of this improvement and show that it is equivalent to LRT. Predictive values provide insights into whether carriers of genetic factors benefit from specific treatment or preventive interventions relative to noncarriers, under some definition of treatment benefit. However, there is no unique definition of the term treatment benefit. We show that and relative excess risk due to interaction (RERI) measure predictive values under two specific definitions of treatment benefit. We investigate the properties of LRT, , and RERI using simulations. We illustrate these approaches using published melanoma data to understand the benefits of possible intervention on sun exposure in relation to the MC1R gene. The goal is to evaluate possible interventions on sun exposure in relation to MC1R.     

Surveillance of cancer risks for firefighters,police, and armed forces among men in a Canadian census cohort

Background

Firefighters, police, and armed services may be exposed to hazards such as combustion by‐products and shift work.

Methods

The CanCHEC cohort linked 1991 census data to the Canadian cancer registry for follow up. Cox proportional hazards modeling was used to estimate hazard ratios (HRs) and 95% confidence intervals (CIs) to estimate risks for firefighter, police, or armed forces compared to workers in other occupations.

Results

The cohort of 1 108 410 men included 4535 firefighters, 10 055 police, and 9165 armed forces. For firefighters, elevated risks were noted for Hodgkin's lymphoma (HR: 2.89, 95%CI: 1.29‐6.46), melanoma (HR: 1.67, 95%CI: 1.17‐2.37), and prostate cancer (HR: 1.18, 95%CI: 1.01‐1.37). Police had elevated risks for melanoma (HR:1.69, 95%CI: 1.32‐2.16) and prostate cancer (HR:1.28, 95%CI: 1.14‐1.42). No significant associations were found for armed forces workers.

Conclusions

Canadian firefighters, police, and armed services, may be at an increased risk of developing certain cancers. Results suggested that a healthy worker effect may influence risk estimates.

     

UN Scientific Agency collaborating with scientists involved in sabotaging UN Rotterdam Convention

Abstract

The published information about work-related carpal tunnel syndrome (CTS) was surveyed to identify risk estimates and possible biases influencing the risk estimates. Seventeen studies from the English-language literature were identified and study characteristics were coded for univariate and regression analysis. Country of publication, study population, force, and repetitive motion were significant predictors or risk, with R² = 0.57, adjusted R² = 0.43, Cp = 5.79, and AIC = 19.6 using the best-subset method of variable selection. Using the forward variable selection method, country, study population, study type, and repetitive motion were, significant predictors, with R² = 0.57, Cp = 6.24, p = 0.033. Excess risks of work-related CTS were consistent in the studies reviewed. Studies published in the United States reported higher risk estimates than did those published elsewhere. Some industrial populations were found to have higher risk estimates than others. Cross-sectional designs were the most common epidemiologic approach, but are not without methodologic concerns.     

Estimating cancer incidence in Indigenous Australians

Objective: To assess data quality of cancer registrations for Indigenous Australians and produce reliable national Indigenous cancer incidence statistics. Methods: Completeness of Indigenous identification was assessed for the eight Australian cancer registries using an innovative indirect assessment method based on registry‐specific registration rates for smoking‐related cancers. National age‐standardised incidence rates and rate ratios (Indigenous:non‐Indigenous) were calculated for all cancers combined and 26 individual cancer sites. Multivariate regression analysis was used to investigate trends in Indigenous cancer incidence by time or remoteness of residence, and whether the incidence rate ratio (Indigenous:non‐Indigenous) was different in younger than older age‐groups. Results: Four registries covering 84% of the Indigenous population had sufficiently complete Indigenous identification to be included in analysis. Compared to other Australians, Indigenous Australians had much higher incidence of lung and other smoking‐related cancers, cervix, uterus and liver cancer, but much lower incidence of breast, prostate, testis, colorectal and brain cancer, melanoma of skin, lymphoma and leukaemia. Incidence was higher in remote areas for some cancers (including several smoking‐related cancers) but lower for others. The incidence rate ratios (IRRs) for smoking‐related cancers were higher in younger than older people. Conclusions: Indigenous Australians have a different pattern of incidence of specific cancers than other Australians and large geographical variations for several cancers. Implications: All cancer registries need to further improve Indigenous identification, but national Indigenous cancer incidence statistics can, and should, be regularly reported. Tobacco control is a critical cancer‐control issue for Indigenous Australians.     

TARV: Tree‐based Analysis of Rare Variants Identifying Risk Modifying Variants in CTNNA2 and CNTNAP2 for Alcohol Addiction

Since the development of next generation sequencing (NGS) technology, researchers have been extending their efforts on genome‐wide association studies (GWAS) from common variants to rare variants to find the missing inheritance. Although various statistical methods have been proposed to analyze rare variants data, they generally face difficulties for complex disease models involving multiple genes. In this paper, we propose a tree‐based analysis of rare variants (TARV) that adopts a nonparametric disease model and is capable of exploring gene–gene interactions. We found that TARV outperforms the sequence kernel association test (SKAT) in most of our simulation scenarios, and by notable margins in some cases. By applying TARV to the study of addiction: genetics and environment (SAGE) data, we successfully detected gene CTNNA2 and its 43 specific variants that increase the risk of alcoholism in women, with an odds ratio (OR) of 1.94. This gene has not been detected in the SAGE data. Post hoc literature search also supports the role of CTNNA2 as a likely risk gene for alcohol addiction. In addition, we also detected a plausible protective gene CNTNAP2, whose 97 rare variants can reduce the risk of alcoholism in women, with an OR of 0.55. These findings suggest that TARV can be effective in dissecting genetic variants for complex diseases using rare variants data.     

Empirical Bayes ranking and selection methods via semiparametric hierarchical mixture models in microarray studies

The main purpose of microarray studies is screening of differentially expressed genes as candidates for further investigation. Because of limited resources in this stage, prioritizing genes are relevant statistical tasks in microarray studies. For effective gene selections, parametric empirical Bayes methods for ranking and selection of genes with largest effect sizes have been proposed (Noma et al., 2010; Biostatistics 11 : 281–289). The hierarchical mixture model incorporates the differential and non‐differential components and allows information borrowing across differential genes with separation from nuisance, non‐differential genes. In this article, we develop empirical Bayes ranking methods via a semiparametric hierarchical mixture model. A nonparametric prior distribution, rather than parametric prior distributions, for effect sizes is specified and estimated using the “smoothing by roughening” approach of Laird and Louis (1991; Computational Statistics and Data Analysis 12 : 27–37). We present applications to childhood and infant leukemia clinical studies with microarrays for exploring genes related to prognosis or disease progression. Copyright © 2012 John Wiley & Sons, Ltd.     

Influence of common variants in <Emphasis Type="Italic">FTO</Emphasis> and near <Emphasis Type="Italic">INSIG2</Emphasis> and <Emphasis Type="Italic">MC4R</Emphasis> on growth curves for adiposity in African– and European–American youth

Recent genome-wide association (GWA) studies identified several common variants for obesity: rs9939609 in FTO, rs7566605 near INSIG2 and both rs17782313 and rs17700633 near the MC4R gene. This study aimed to assess the influence of these polymorphisms on development of adiposity in European– (EA) and African–American (AA) youth in two ongoing longitudinal studies including 986 and 606 participants with age ranges of 10–25.8 and 4.0–23.9 years, respectively. Individual growth curve modeling was conducted separately in the two studies. We tested the effect of the SNPs on levels and increase with age (i.e., slope) of weight, body mass index (BMI), waist circumference and skinfolds from childhood to adulthood, and potential moderation by ethnicity or gender. Beta coefficients computed in the two studies were pooled using meta-analysis. Rs9939609 was associated with logtransformed levels of BMI (β = 0.021, P = 0.01), weight (β = 0.019, P = 0.04) and waist circumference (β = 0.012, P = 0.04). Rs17782313 was associated with triceps (β = 0.05, P = 0.02). Significant interactions of rs17700633 with gender were observed on subscapular-, suprailiac- and sum of skinfolds, with significant associations limited to males (P < 0.05). No significant interactions with ethnicity were found. Only one effect on the slope was observed, rs17700633 showed a significant interaction with age on triceps (β = 0.004, P = 0.04). In two longitudinal studies of EA and AA youth, we replicated the effect of FTO and common variants near MC4R on general and central adiposity. These variants did not affect the increase with age of adiposity from childhood to adulthood with one exception. Common variants for obesity identified in GWA studies have detectable but modest effects on growth curves for adiposity in EA and AA youth.     

Detecting pleiotropy in Mendelian randomisation studies with summary data and a continuous outcome

Mendelian randomisation (MR) estimates causal effects of modifiable phenotypes on an outcome by using genetic variants as instrumental variables, but its validity relies on the assumption of no pleiotropy, that is, genes influence the outcome only through the given phenotype. Excluding pleiotropy is difficult, but the use of multiple instruments can indirectly address the issue: if all genes represent valid instruments, their MR estimates should vary only by chance. The Sargan test detects pleiotropy when individual phenotype, outcome and genotype data are measured in the same subjects. We propose an alternative approach to be used when only summary genetic data are available or data on gene‐phenotype and gene‐outcome come from different subjects. The presence of pleiotropy is investigated using the between‐instrument heterogeneity Q test (together with the I² index) in a meta‐analysis of MR Wald estimates, derived separately from each instrument. For a continuous outcome, we evaluate the approach through simulations and illustrate it using published data. For the scenario where all data come from the same subjects, we compare it with the Sargan test. The Q test tends to be conservative in small samples. Its power increases with the degree of pleiotropy and the sample size, as does the precision of the I² index, in which case results are similar to those of the Sargan test. In MR studies with large sample sizes based on summary data, the between‐instrument Q test represents a useful tool to explore the presence of heterogeneity due to pleiotropy or other causes. Copyright © 2015 John Wiley & Sons, Ltd.     

基因-基因间交互作用对学龄儿童腹型肥胖的影响

目的 探讨我国学龄儿童6个肥胖相关基因多态性位点（SNPs）及其交互作用与腹型肥胖的关联。方法 以"北京市儿童青少年代谢综合征（BCAMS）研究"中1 196名肥胖儿童和2 306名非肥胖儿童为研究对象。采用盐析法从外周血白细胞中提取DNA。使用ABI Prisms^TM-7900实时荧光定量PCR仪对6个SNPs（FTO rs9939609、MC4R rs17782313、BDNF rs6265、PCSK1 rs6235、SH2B1 rs4788102和CSK rs1378942）进行分型检测。采用BCAMS基线总人群腰围的性别年龄别第90百分位值判定腹型肥胖。运用logistic回归模型分析6个SNPs与腹型肥胖的关联。采用广义多因子降维法（GMDR）模型检测6个SNPs之间的基因-基因交互作用,并使用多因素logistic回归模型验证。结果 在加性遗传模型下,调整性别、年龄、Tanner分期、体力活动和肥胖家族史后,FTO rs9939609-A、MC4R rs17782313-C和BDNF rs6265-G等位基因增加儿童腹型肥胖罹患风险（OR=1.24,95%CI：1.06~1.45,P=0.008;OR=1.26,95%CI：1.11~1.43,P=2.98×10^-4;OR=1.18,95%CI：1.06~1.32,P=0.003）。GMDR模型分析显示,在调整同样的影响因素后,MC4R rs17782313和BDNF rs6265之间交互作用的差异有统计学意义（P=0.001）,交叉验证一致性为10/10,平均检验准确度为0.539,为最优模型;logistic回归分析显示,MC4R rs17782313-C和BDNF rs6265-G可能存在正交互作用。结论 FTO rs9939609-A、MC4R rs17782313-C和BDNF rs6265-G增加儿童腹型肥胖罹患风险;MC4R rs17782313与BDNF rs6265可能存在交互作用,对学龄儿童腹型肥胖的罹患风险存在影响。     

Meta-analysis of gene-environment interaction: joint estimation of SNP and SNP × environment regression coefficients

Introduction: Genetic discoveries are validated through the meta‐analysis of genome‐wide association scans in large international consortia. Because environmental variables may interact with genetic factors, investigation of differing genetic effects for distinct levels of an environmental exposure in these large consortia may yield additional susceptibility loci undetected by main effects analysis. We describe a method of joint meta‐analysis (JMA) of SNP and SNP by Environment (SNP × E) regression coefficients for use in gene‐environment interaction studies. Methods: In testing SNP × E interactions, one approach uses a two degree of freedom test to identify genetic variants that influence the trait of interest. This approach detects both main and interaction effects between the trait and the SNP. We propose a method to jointly meta‐analyze the SNP and SNP × E coefficients using multivariate generalized least squares. This approach provides confidence intervals of the two estimates, a joint significance test for SNP and SNP × E terms, and a test of homogeneity across samples. Results: We present a simulation study comparing this method to four other methods of meta‐analysis and demonstrate that the JMA performs better than the others when both main and interaction effects are present. Additionally, we implemented our methods in a meta‐analysis of the association between SNPs from the type 2 diabetes‐associated gene PPARG and log‐transformed fasting insulin levels and interaction by body mass index in a combined sample of 19,466 individuals from five cohorts. Genet. Epidemiol. 35:11–18, 2011. © 2010 Wiley‐Liss, Inc.