Adjusted Sequence Kernel Association Test for Rare Variants Controlling for Cryptic and Family Relatedness

Recent progress in sequencing technologies makes it possible to identify rare and unique variants that may be associated with complex traits. However, the results of such efforts depend crucially on the use of efficient statistical methods and study designs. Although family‐based designs might enrich a data set for familial rare disease variants, most existing rare variant association approaches assume independence of all individuals. We introduce here a framework for association testing of rare variants in family‐based designs. This framework is an adaptation of the sequence kernel association test (SKAT) which allows us to control for family structure. Our adjusted SKAT (ASKAT) combines the SKAT approach and the factored spectrally transformed linear mixed models (FaST‐LMMs) algorithm to capture family effects based on a LMM incorporating the realized proportion of the genome that is identical by descent between pairs of individuals, and using restricted maximum likelihood methods for estimation. In simulation studies, we evaluated type I error and power of this proposed method and we showed that regardless of the level of the trait heritability, our approach has good control of type I error and good power. Since our approach uses FaST‐LMM to calculate variance components for the proposed mixed model, ASKAT is reasonably fast and can analyze hundreds of thousands of markers. Data from the UK twins consortium are presented to illustrate the ASKAT methodology.     

Combining Family‐ and Population‐Based Imputation Data for Association Analysis of Rare and Common Variants in Large Pedigrees

In the last two decades, complex traits have become the main focus of genetic studies. The hypothesis that both rare and common variants are associated with complex traits is increasingly being discussed. Family‐based association studies using relatively large pedigrees are suitable for both rare and common variant identification. Because of the high cost of sequencing technologies, imputation methods are important for increasing the amount of information at low cost. A recent family‐based imputation method, Genotype Imputation Given Inheritance (GIGI), is able to handle large pedigrees and accurately impute rare variants, but does less well for common variants where population‐based methods perform better. Here, we propose a flexible approach to combine imputation data from both family‐ and population‐based methods. We also extend the Sequence Kernel Association Test for Rare and Common variants (SKAT‐RC), originally proposed for data from unrelated subjects, to family data in order to make use of such imputed data. We call this extension “famSKAT‐RC.” We compare the performance of famSKAT‐RC and several other existing burden and kernel association tests. In simulated pedigree sequence data, our results show an increase of imputation accuracy from use of our combining approach. Also, they show an increase of power of the association tests with this approach over the use of either family‐ or population‐based imputation methods alone, in the context of rare and common variants. Moreover, our results show better performance of famSKAT‐RC compared to the other considered tests, in most scenarios investigated here.     

Robust Rare Variant Association Testing for Quantitative Traits in Samples With Related Individuals

The recent development of high‐throughput sequencing technologies calls for powerful statistical tests to detect rare genetic variants associated with complex human traits. Sampling related individuals in sequencing studies offers advantages over sampling unrelated individuals only, including improved protection against sequencing error, the ability to use imputation to make more efficient use of sequence data, and the possibility of power boost due to more observed copies of extremely rare alleles among relatives. With related individuals, familial correlation needs to be accounted for to ensure correct control over type I error and to improve power. Recognizing the limitations of existing rare‐variant association tests for family data, we propose MONSTER (Minimum P‐value Optimized Nuisance parameter Score Test Extended to Relatives), a robust rare‐variant association test, which generalizes the SKAT‐O method for independent samples. MONSTER uses a mixed effects model that accounts for covariates and additive polygenic effects. To obtain a powerful test, MONSTER adaptively adjusts to the unknown configuration of effects of rare‐variant sites. MONSTER also offers an analytical way of assessing P‐values, which is desirable because permutation is not straightforward to conduct in related samples. In simulation studies, we demonstrate that MONSTER effectively accounts for family structure, is computationally efficient and compares very favorably, in terms of power, to previously proposed tests that allow related individuals. We apply MONSTER to an analysis of high‐density lipoprotein cholesterol in the Framingham Heart Study, where we are able to replicate association with three genes.     

A Comparison Study of Fixed and Mixed Effect Models for Gene Level Association Studies of Complex Traits

In association studies of complex traits, fixed‐effect regression models are usually used to test for association between traits and major gene loci. In recent years, variance‐component tests based on mixed models were developed for region‐based genetic variant association tests. In the mixed models, the association is tested by a null hypothesis of zero variance via a sequence kernel association test (SKAT), its optimal unified test (SKAT‐O), and a combined sum test of rare and common variant effect (SKAT‐C). Although there are some comparison studies to evaluate the performance of mixed and fixed models, there is no systematic analysis to determine when the mixed models perform better and when the fixed models perform better. Here we evaluated, based on extensive simulations, the performance of the fixed and mixed model statistics, using genetic variants located in 3, 6, 9, 12, and 15 kb simulated regions. We compared the performance of three models: (i) mixed models that lead to SKAT, SKAT‐O, and SKAT‐C, (ii) traditional fixed‐effect additive models, and (iii) fixed‐effect functional regression models. To evaluate the type I error rates of the tests of fixed models, we generated genotype data by two methods: (i) using all variants, (ii) using only rare variants. We found that the fixed‐effect tests accurately control or have low false positive rates. We performed simulation analyses to compare power for two scenarios: (i) all causal variants are rare, (ii) some causal variants are rare and some are common. Either one or both of the fixed‐effect models performed better than or similar to the mixed models except when (1) the region sizes are 12 and 15 kb and (2) effect sizes are small. Therefore, the assumption of mixed models could be satisfied and SKAT/SKAT‐O/SKAT‐C could perform better if the number of causal variants is large and each causal variant contributes a small amount to the traits (i.e., polygenes). In major gene association studies, we argue that the fixed‐effect models perform better or similarly to mixed models in most cases because some variants should affect the traits relatively large. In practice, it makes sense to perform analysis by both the fixed and mixed effect models and to make a comparison, and this can be readily done using our R codes and the SKAT packages.     

Rare variant association test with multiple phenotypes

Although genome‐wide association studies (GWAS) have now discovered thousands of genetic variants associated with common traits, such variants cannot explain the large degree of “missing heritability,” likely due to rare variants. The advent of next generation sequencing technology has allowed rare variant detection and association with common traits, often by investigating specific genomic regions for rare variant effects on a trait. Although multiple correlated phenotypes are often concurrently observed in GWAS, most studies analyze only single phenotypes, which may lessen statistical power. To increase power, multivariate analyses, which consider correlations between multiple phenotypes, can be used. However, few existing multivariant analyses can identify rare variants for assessing multiple phenotypes. Here, we propose Multivariate Association Analysis using Score Statistics (MAAUSS), to identify rare variants associated with multiple phenotypes, based on the widely used sequence kernel association test (SKAT) for a single phenotype. We applied MAAUSS to whole exome sequencing (WES) data from a Korean population of 1,058 subjects to discover genes associated with multiple traits of liver function. We then assessed validation of those genes by a replication study, using an independent dataset of 3,445 individuals. Notably, we detected the gene ZNF620 among five significant genes. We then performed a simulation study to compare MAAUSS's performance with existing methods. Overall, MAAUSS successfully conserved type 1 error rates and in many cases had a higher power than the existing methods. This study illustrates a feasible and straightforward approach for identifying rare variants correlated with multiple phenotypes, with likely relevance to missing heritability.     

On the substructure controls in rare variant analysis: Principal components or variance components?

Recent studies showed that population substructure (PS) can have more complex impact on rare variant tests and that similarity‐based collapsing tests (e.g., SKAT) may suffer more severely by PS than burden‐based tests. In this work, we evaluate the performance of SKAT coupling with principal components (PC) or variance components (VC) based PS correction methods. We consider confounding effects caused by PS including stratified populations, admixed populations, and spatially distributed nongenetic risk; we investigate which types of variants (e.g., common, less frequent, rare, or all variants) should be used to effectively control for confounding effects. We found that (i) PC‐based methods can account for confounding effects in most scenarios except for admixture, although the number of sufficient PCs depends on the PS complexity and the type of variants used. (ii) PCs based on all variants (i.e., common + less frequent + rare) tend to require equal or fewer sufficient PCs and often achieve higher power than PCs based on other variant types. (iii) VC‐based methods can effectively adjust for confounding in all scenarios (even for admixture), though the type of variants should be used to construct VC may vary. (iv) VC based on all variants works consistently in all scenarios, though its power may be sometimes lower than VC based on other variant types. Given that the best‐performed method and which variants to use depend on the underlying unknown confounding mechanisms, a robust strategy is to perform SKAT analyses using VC‐based methods based on all variants.     

Hierarchical Bayesian Model for Rare Variant Association Analysis Integrating Genotype Uncertainty in Human Sequence Data

Next‐generation sequencing (NGS) has led to the study of rare genetic variants, which possibly explain the missing heritability for complex diseases. Most existing methods for rare variant (RV) association detection do not account for the common presence of sequencing errors in NGS data. The errors can largely affect the power and perturb the accuracy of association tests due to rare observations of minor alleles. We developed a hierarchical Bayesian approach to estimate the association between RVs and complex diseases. Our integrated framework combines the misclassification probability with shrinkage‐based Bayesian variable selection. It allows for flexibility in handling neutral and protective RVs with measurement error, and is robust enough for detecting causal RVs with a wide spectrum of minor allele frequency (MAF). Imputation uncertainty and MAF are incorporated into the integrated framework to achieve the optimal statistical power. We demonstrate that sequencing error does significantly affect the findings, and our proposed model can take advantage of it to improve statistical power in both simulated and real data. We further show that our model outperforms existing methods, such as sequence kernel association test (SKAT). Finally, we illustrate the behavior of the proposed method using a Finnish low‐density lipoprotein cholesterol study, and show that it identifies an RV known as FH North Karelia in LDLR gene with three carriers in 1,155 individuals, which is missed by both SKAT and Granvil.     

Sequence Kernel Association Analysis of Rare Variant Set Based on the Marginal Regression Model for Binary Traits

Recent sequencing efforts have focused on exploring the influence of rare variants on the complex diseases. Gene level based tests by aggregating information across rare variants within a gene have become attractive to enrich the rare variant association signal. Among them, the sequence kernel association test (SKAT) has proved to be a very powerful method for jointly testing multiple rare variants within a gene. In this article, we explore an alternative SKAT. We propose to use the univariate likelihood ratio statistics from the marginal model for individual variants as input into the kernel association test. We show how to compute its significance P‐value efficiently based on the asymptotic chi‐square mixture distribution. We demonstrate through extensive numerical studies that the proposed method has competitive performance. Its usefulness is further illustrated with application to associations between rare exonic variants and type 2 diabetes (T2D) in the Atherosclerosis Risk in Communities (ARIC) study. We identified an exome‐wide significant rare variant set in the gene ZZZ3 worthy of further investigations.     

Two adaptive weighting methods to test for rare variant associations in family-based designs

Although next-generation DNA sequencing technologies have made rare variant association studies feasible and affordable, the development of powerful statistical methods for rare variant association studies is still under way. Most of the existing methods for rare variant association studies compare the number of rare mutations in a group of rare variants (in a gene or a pathway) between cases and controls. However, these methods assume that all causal variants are risk to diseases. Recently, several methods that are robust to the direction and magnitude of effects of causal variants have been proposed. However, they are applicable to unrelated individuals only, whereas family data have been shown to improve power to detect rare variants. In this article, we propose two adaptive weighting methods for rare variant association studies based on family data for quantitative traits. Using extensive simulation studies, we evaluate and compare our proposed methods with two methods based on the weights proposed by Madsen and Browning. Our results show that both proposed methods are robust to population stratification, robust to the direction and magnitude of the effects of causal variants, and more powerful than the methods using weights suggested by Madsen and Browning, especially when both risk and protective variants are present.     

Gene‐Based Association Analysis for Censored Traits Via Fixed Effect Functional Regressions

Genetic studies of survival outcomes have been proposed and conducted recently, but statistical methods for identifying genetic variants that affect disease progression are rarely developed. Motivated by our ongoing real studies, here we develop Cox proportional hazard models using functional regression (FR) to perform gene‐based association analysis of survival traits while adjusting for covariates. The proposed Cox models are fixed effect models where the genetic effects of multiple genetic variants are assumed to be fixed. We introduce likelihood ratio test (LRT) statistics to test for associations between the survival traits and multiple genetic variants in a genetic region. Extensive simulation studies demonstrate that the proposed Cox RF LRT statistics have well‐controlled type I error rates. To evaluate power, we compare the Cox FR LRT with the previously developed burden test (BT) in a Cox model and sequence kernel association test (SKAT), which is based on mixed effect Cox models. The Cox FR LRT statistics have higher power than or similar power as Cox SKAT LRT except when 50%/50% causal variants had negative/positive effects and all causal variants are rare. In addition, the Cox FR LRT statistics have higher power than Cox BT LRT. The models and related test statistics can be useful in the whole genome and whole exome association studies. An age‐related macular degeneration dataset was analyzed as an example.     

Rare‐variant association tests in longitudinal studies,with an application to the Multi‐Ethnic Study of Atherosclerosis (MESA)

Over the past few years, an increasing number of studies have identified rare variants that contribute to trait heritability. Due to the extreme rarity of some individual variants, gene‐based association tests have been proposed to aggregate the genetic variants within a gene, pathway, or specific genomic region as opposed to a one‐at‐a‐time single variant analysis. In addition, in longitudinal studies, statistical power to detect disease susceptibility rare variants can be improved through jointly testing repeatedly measured outcomes, which better describes the temporal development of the trait of interest. However, usual sandwich/model‐based inference for sequencing studies with longitudinal outcomes and rare variants can produce deflated/inflated type I error rate without further corrections. In this paper, we develop a group of tests for rare‐variant association based on outcomes with repeated measures. We propose new perturbation methods such that the type I error rate of the new tests is not only robust to misspecification of within‐subject correlation, but also significantly improved for variants with extreme rarity in a study with small or moderate sample size. Through extensive simulation studies, we illustrate that substantially higher power can be achieved by utilizing longitudinal outcomes and our proposed finite sample adjustment. We illustrate our methods using data from the Multi‐Ethnic Study of Atherosclerosis for exploring association of repeated measures of blood pressure with rare and common variants based on exome sequencing data on 6,361 individuals.     

Functional Linear Models for Association Analysis of Quantitative Traits

Functional linear models are developed in this paper for testing associations between quantitative traits and genetic variants, which can be rare variants or common variants or the combination of the two. By treating multiple genetic variants of an individual in a human population as a realization of a stochastic process, the genome of an individual in a chromosome region is a continuum of sequence data rather than discrete observations. The genome of an individual is viewed as a stochastic function that contains both linkage and linkage disequilibrium (LD) information of the genetic markers. By using techniques of functional data analysis, both fixed and mixed effect functional linear models are built to test the association between quantitative traits and genetic variants adjusting for covariates. After extensive simulation analysis, it is shown that the F‐distributed tests of the proposed fixed effect functional linear models have higher power than that of sequence kernel association test (SKAT) and its optimal unified test (SKAT‐O) for three scenarios in most cases: (1) the causal variants are all rare, (2) the causal variants are both rare and common, and (3) the causal variants are common. The superior performance of the fixed effect functional linear models is most likely due to its optimal utilization of both genetic linkage and LD information of multiple genetic variants in a genome and similarity among different individuals, while SKAT and SKAT‐O only model the similarities and pairwise LD but do not model linkage and higher order LD information sufficiently. In addition, the proposed fixed effect models generate accurate type I error rates in simulation studies. We also show that the functional kernel score tests of the proposed mixed effect functional linear models are preferable in candidate gene analysis and small sample problems. The methods are applied to analyze three biochemical traits in data from the Trinity Students Study.     

Sequence Kernel Association Test of Multiple Continuous Phenotypes

Genetic studies often collect multiple correlated traits, which could be analyzed jointly to increase power by aggregating multiple weak effects and provide additional insights into the etiology of complex human diseases. Existing methods for multiple trait association tests have primarily focused on common variants. There is a surprising dearth of published methods for testing the association of rare variants with multiple correlated traits. In this paper, we extend the commonly used sequence kernel association test (SKAT) for single‐trait analysis to test for the joint association of rare variant sets with multiple traits. We investigate the performance of the proposed method through extensive simulation studies. We further illustrate its usefulness with application to the analysis of diabetes‐related traits in the Atherosclerosis Risk in Communities (ARIC) Study. We identified an exome‐wide significant rare variant set in the gene YAP1 worthy of further investigations.     

A Fast and Noise‐Resilient Approach to Detect Rare‐Variant Associations With Deep Sequencing Data for Complex Disorders

Next generation sequencing technology has enabled the paradigm shift in genetic association studies from the common disease/common variant to common disease/rare‐variant hypothesis. Analyzing individual rare variants is known to be underpowered; therefore association methods have been developed that aggregate variants across a genetic region, which for exome sequencing is usually a gene. The foreseeable widespread use of whole genome sequencing poses new challenges in statistical analysis. It calls for new rare‐variant association methods that are statistically powerful, robust against high levels of noise due to inclusion of noncausal variants, and yet computationally efficient. We propose a simple and powerful statistic that combines the disease‐associated P‐values of individual variants using a weight that is the inverse of the expected standard deviation of the allele frequencies under the null. This approach, dubbed as Sigma‐P method, is extremely robust to the inclusion of a high proportion of noncausal variants and is also powerful when both detrimental and protective variants are present within a genetic region. The performance of the Sigma‐P method was tested using simulated data based on realistic population demographic and disease models and its power was compared to several previously published methods. The results demonstrate that this method generally outperforms other rare‐variant association methods over a wide range of models. Additionally, sequence data on the ANGPTL family of genes from the Dallas Heart Study were tested for associations with nine metabolic traits and both known and novel putative associations were uncovered using the Sigma‐P method.     

A Generalized Genetic Random Field Method for the Genetic Association Analysis of Sequencing Data

With the advance of high‐throughput sequencing technologies, it has become feasible to investigate the influence of the entire spectrum of sequencing variations on complex human diseases. Although association studies utilizing the new sequencing technologies hold great promise to unravel novel genetic variants, especially rare genetic variants that contribute to human diseases, the statistical analysis of high‐dimensional sequencing data remains a challenge. Advanced analytical methods are in great need to facilitate high‐dimensional sequencing data analyses. In this article, we propose a generalized genetic random field (GGRF) method for association analyses of sequencing data. Like other similarity‐based methods (e.g., SIMreg and SKAT), the new method has the advantages of avoiding the need to specify thresholds for rare variants and allowing for testing multiple variants acting in different directions and magnitude of effects. The method is built on the generalized estimating equation framework and thus accommodates a variety of disease phenotypes (e.g., quantitative and binary phenotypes). Moreover, it has a nice asymptotic property, and can be applied to small‐scale sequencing data without need for small‐sample adjustment. Through simulations, we demonstrate that the proposed GGRF attains an improved or comparable power over a commonly used method, SKAT, under various disease scenarios, especially when rare variants play a significant role in disease etiology. We further illustrate GGRF with an application to a real dataset from the Dallas Heart Study. By using GGRF, we were able to detect the association of two candidate genes, ANGPTL3 and ANGPTL4, with serum triglyceride.     

Generalized Functional Linear Models for Gene‐Based Case‐Control Association Studies

By using functional data analysis techniques, we developed generalized functional linear models for testing association between a dichotomous trait and multiple genetic variants in a genetic region while adjusting for covariates. Both fixed and mixed effect models are developed and compared. Extensive simulations show that Rao's efficient score tests of the fixed effect models are very conservative since they generate lower type I errors than nominal levels, and global tests of the mixed effect models generate accurate type I errors. Furthermore, we found that the Rao's efficient score test statistics of the fixed effect models have higher power than the sequence kernel association test (SKAT) and its optimal unified version (SKAT‐O) in most cases when the causal variants are both rare and common. When the causal variants are all rare (i.e., minor allele frequencies less than 0.03), the Rao's efficient score test statistics and the global tests have similar or slightly lower power than SKAT and SKAT‐O. In practice, it is not known whether rare variants or common variants in a gene region are disease related. All we can assume is that a combination of rare and common variants influences disease susceptibility. Thus, the improved performance of our models when the causal variants are both rare and common shows that the proposed models can be very useful in dissecting complex traits. We compare the performance of our methods with SKAT and SKAT‐O on real neural tube defects and Hirschsprung's disease datasets. The Rao's efficient score test statistics and the global tests are more sensitive than SKAT and SKAT‐O in the real data analysis. Our methods can be used in either gene‐disease genome‐wide/exome‐wide association studies or candidate gene analyses.     

A powerful association test of multiple genetic variants using a random‐effects model

There is an emerging interest in sequencing‐based association studies of multiple rare variants. Most association tests suggested in the literature involve collapsing rare variants with or without weighting. Recently, a variance‐component score test [sequence kernel association test (SKAT)] was proposed to address the limitations of collapsing method. Although SKAT was shown to outperform most of the alternative tests, its applications and power might be restricted and influenced by missing genotypes. In this paper, we suggest a new method based on testing whether the fraction of causal variants in a region is zero. The new association test, T _REM, is derived from a random‐effects model and allows for missing genotypes, and the choice of weighting function is not required when common and rare variants are analyzed simultaneously. We performed simulations to study the type I error rates and power of four competing tests under various conditions on the sample size, genotype missing rate, variant frequency, effect directionality, and the number of non‐causal rare variant and/or causal common variant. The simulation results showed that T _REM was a valid test and less sensitive to the inclusion of non‐causal rare variants and/or low effect common variants or to the presence of missing genotypes. When the effects were more consistent in the same direction, T _REM also had better power performance. Finally, an application to the Shanghai Breast Cancer Study showed that rare causal variants at the FGFR2 gene were detected by T _REM and SKAT, but T _REM produced more consistent results for different sets of rare and common variants. Copyright © 2013 John Wiley & Sons, Ltd.     

Sequence Kernel Association Test for Survival Traits

Rare variant tests have been of great interest in testing genetic associations with diseases and disease‐related quantitative traits in recent years. Among these tests, the sequence kernel association test (SKAT) is an omnibus test for effects of rare genetic variants, in a linear or logistic regression framework. It is often described as a variance component test treating the genotypic effects as random. When the linear kernel is used, its test statistic can be expressed as a weighted sum of single‐marker score test statistics. In this paper, we extend the test to survival phenotypes in a Cox regression framework. Because of the anticonservative small‐sample performance of the score test in a Cox model, we substitute signed square‐root likelihood ratio statistics for the score statistics, and confirm that the small‐sample control of type I error is greatly improved. This test can also be applied in meta‐analysis. We show in our simulation studies that this test has superior statistical power except in a few specific scenarios, as compared to burden tests in a Cox model. We also present results in an application to time‐to‐obesity using genotypes from Framingham Heart Study SNP Health Association Resource.     

Region‐based association tests for sequencing data on survival traits

Family‐based designs enriched with affected subjects and disease associated variants can increase statistical power for identifying functional rare variants. However, few rare variant analysis approaches are available for time‐to‐event traits in family designs and none of them applicable to the X chromosome. We developed novel pedigree‐based burden and kernel association tests for time‐to‐event outcomes with right censoring for pedigree data, referred to FamRATS (family‐based rare variant association tests for survival traits). Cox proportional hazard models were employed to relate a time‐to‐event trait with rare variants with flexibility to encompass all ranges and collapsing of multiple variants. In addition, the robustness of violating proportional hazard assumptions was investigated for the proposed and four current existing tests, including the conventional population‐based Cox proportional model and the burden, kernel, and sum of squares statistic (SSQ) tests for family data. The proposed tests can be applied to large‐scale whole‐genome sequencing data. They are appropriate for the practical use under a wide range of misspecified Cox models, as well as for population‐based, pedigree‐based, or hybrid designs. In our extensive simulation study and data example, we showed that the proposed kernel test is the most powerful and robust choice among the proposed burden test and the existing four rare variant survival association tests. When applied to the Diabetes Heart Study, the proposed tests found exome variants of the JAK1 gene on chromosome 1 showed the most significant association with age at onset of type 2 diabetes from the exome‐wide analysis.     

A unified method for rare variant analysis of gene-environment interactions

Advanced technology in whole-genome sequencing has offered the opportunity to comprehensively investigate the genetic contribution, particularly rare variants, to complex traits. Several region-based tests have been developed to jointly model the marginal effect of rare variants, but methods to detect gene-environment (GE) interactions are underdeveloped. Identifying the modification effects of environmental factors on genetic risk poses a considerable challenge. To tackle this challenge, we develop a method to detect GE interactions for rare variants using generalized linear mixed effect model. The proposed method can accommodate either binary or continuous traits in related or unrelated samples. Under this model, genetic main effects, GE interactions, and sample relatedness are modeled as random effects. We adopt a kernel-based method to leverage the joint information across rare variants and implement variance component score tests to reduce the computational burden. Our simulation studies of continuous and binary traits show that the proposed method maintains correct type I error rates and appropriate power under various scenarios, such as genotype main effects and GE interaction effects in opposite directions and varying the proportion of causal variants in the model. We apply our method in the Framingham Heart Study to test GE interaction of smoking on body mass index or overweight status and replicate the Cholinergic Receptor Nicotinic Beta 4 gene association reported in previous large consortium meta-analysis of single nucleotide polymorphism-smoking interaction. Our proposed set-based GE test is computationally efficient and is applicable to both binary and continuous phenotypes, while appropriately accounting for familial or cryptic relatedness.