A unified approach for quantifying, testing and correcting population stratification in case-control association studies

The HapMap project has given case-control association studies a unique opportunity to uncover the genetic basis of complex diseases. However, persistent issues in such studies remain the proper quantification of, testing for, and correction for population stratification (PS). In this paper, we present the first unified paradigm that addresses all three fundamental issues within one statistical framework. Our unified approach makes use of an omnibus quantity (delta), which can be estimated in a case-control study from suitable null loci. We show how this estimated value can be used to quantify PS, to statistically test for PS, and to correct for PS, all in the context of case-control studies. Moreover, we provide guidelines for interpreting values of delta in association studies (e.g., at alpha = 0.05, a delta of size 0.416 is small, a delta of size 0.653 is medium, and a delta of size 1.115 is large). A novel feature of our testing procedure is its ability to test for either strictly any PS or only 'practically important' PS. We also performed simulations to compare our correction procedure with Genomic Control (GC). Our results show that, unlike GC, it maintains good Type I error rates and power across all levels of PS.     

Two-stage design of sequencing studies for testing association with rare variants

Multiple rare variants have been suggested as accounting for some of the associations with common single nucleotide polymorphisms identified in genome-wide association studies or possibly some of the as yet undiscovered heritability. We consider the power of various approaches to designing substudies aimed at using next-generation sequencing technologies to discover novel variants and to select some subsets that are possibly causal for genotyping in the original case-control study and testing for association using various weighted sum indices. We find that the selection of variants based on the statistical significance of the case-control difference in the subsample yields good power for testing rare variant indices in the main study, and that multivariate models including both the summary index of rare variants and the associated common single nucleotide polymorphisms can distinguish which is the causal factor. By simulation, we explore the effects of varying the size of the discovery subsample, choice of index, and true causal model.     

Optimal tests for rare variant effects in sequencing association studies

With development of massively parallel sequencing technologies, there is a substantial need for developing powerful rare variant association tests. Common approaches include burden and non-burden tests. Burden tests assume all rare variants in the target region have effects on the phenotype in the same direction and of similar magnitude. The recently proposed sequence kernel association test (SKAT) (Wu, M. C., and others, 2011. Rare-variant association testing for sequencing data with the SKAT. The American Journal of Human Genetics 89, 82-93], an extension of the C-alpha test (Neale, B. M., and others, 2011. Testing for an unusual distribution of rare variants. PLoS Genetics 7, 161-165], provides a robust test that is particularly powerful in the presence of protective and deleterious variants and null variants, but is less powerful than burden tests when a large number of variants in a region are causal and in the same direction. As the underlying biological mechanisms are unknown in practice and vary from one gene to another across the genome, it is of substantial practical interest to develop a test that is optimal for both scenarios. In this paper, we propose a class of tests that include burden tests and SKAT as special cases, and derive an optimal test within this class that maximizes power. We show that this optimal test outperforms burden tests and SKAT in a wide range of scenarios. The results are illustrated using simulation studies and triglyceride data from the Dallas Heart Study. In addition, we have derived sample size/power calculation formula for SKAT with a new family of kernels to facilitate designing new sequence association studies.     

Optimal DNA pooling-based two-stage designs in case-control association studies

Study cost remains the major limiting factor for genome-wide association studies due to the necessity of genotyping a large number of SNPs for a large number of subjects. Both DNA pooling strategies and two-stage designs have been proposed to reduce genotyping costs. In this study, we propose a cost-effective, two-stage approach with a DNA pooling strategy. During stage I, all markers are evaluated on a subset of individuals using DNA pooling. The most promising set of markers is then evaluated with individual genotyping for all individuals during stage II. The goal is to determine the optimal parameters (pi(p)(sample ), the proportion of samples used during stage I with DNA pooling; and pi(p)(marker ), the proportion of markers evaluated during stage II with individual genotyping) that minimize the cost of a two-stage DNA pooling design while maintaining a desired overall significance level and achieving a level of power similar to that of a one-stage individual genotyping design. We considered the effects of three factors on optimal two-stage DNA pooling designs. Our results suggest that, under most scenarios considered, the optimal two-stage DNA pooling design may be much more cost-effective than the optimal two-stage individual genotyping design, which use individual genotyping during both stages.     

A general framework for two-stage analysis of genome-wide association studies and its application to case-control studies

Two-stage analyses of genome-wide association studies have been proposed as a means to improving power for designs including family-based association and gene-environment interaction testing. In these analyses, all markers are first screened via a statistic that may not be robust to an underlying assumption, and the markers thus selected are then analyzed in a second stage with a test that is independent from the first stage and is robust to the assumption in question. We give a general formulation of two-stage designs and show how one can use this formulation both to derive existing methods and to improve upon them, opening up a range of possible further applications. We show how using simple regression models in conjunction with external data such as average trait values can improve the power of genome-wide association studies. We focus on case-control studies and show how it is possible to use allele frequencies derived from an external reference to derive a powerful two-stage analysis. An illustration involving the Wellcome Trust Case-Control Consortium data shows several genome-wide-significant associations, subsequently validated, that were not significant in the standard analysis. We give some analytic properties of the methods and discuss some underlying principles.     

Rare-variant association testing for sequencing data with the sequence kernel association test

Sequencing studies are increasingly being conducted to identify rare variants associated with complex traits. The limited power of classical single-marker association analysis for rare variants poses a central challenge in such studies. We propose the sequence kernel association test (SKAT), a supervised, flexible, computationally efficient regression method to test for association between genetic variants (common and rare) in a region and a continuous or dichotomous trait while easily adjusting for covariates. As a score-based variance-component test, SKAT can quickly calculate p values analytically by fitting the null model containing only the covariates, and so can easily be applied to genome-wide data. Using SKAT to analyze a genome-wide sequencing study of 1000 individuals, by segmenting the whole genome into 30 kb regions, requires only 7 hr on a laptop. Through analysis of simulated data across a wide range of practical scenarios and triglyceride data from the Dallas Heart Study, we show that SKAT can substantially outperform several alternative rare-variant association tests. We also provide analytic power and sample-size calculations to help design candidate-gene, whole-exome, and whole-genome sequence association studies.     

Family-based association studies for next-generation sequencing

An individual's disease risk is determined by the compounded action of both common variants, inherited from remote ancestors, that segregated within the population and rare variants, inherited from recent ancestors, that segregated mainly within pedigrees. Next-generation sequencing (NGS) technologies generate high-dimensional data that allow a nearly complete evaluation of genetic variation. Despite their promise, NGS technologies also suffer from remarkable limitations: high error rates, enrichment of rare variants, and a large proportion of missing values, as well as the fact that most current analytical methods are designed for population-based association studies. To meet the analytical challenges raised by NGS, we propose a general framework for sequence-based association studies that can use various types of family and unrelated-individual data sampled from any population structure and a universal procedure that can transform any population-based association test statistic for use in family-based association tests. We develop family-based functional principal-component analysis (FPCA) with or without smoothing, a generalized T(2), combined multivariate and collapsing (CMC) method, and single-marker association test statistics. Through intensive simulations, we demonstrate that the family-based smoothed FPCA (SFPCA) has the correct type I error rates and much more power to detect association of (1) common variants, (2) rare variants, (3) both common and rare variants, and (4) variants with opposite directions of effect from other population-based or family-based association analysis methods. The proposed statistics are applied to two data sets with pedigree structures. The results show that the smoothed FPCA has a much smaller p value than other statistics.     

A new expectation-maximization statistical test for case-control association studies considering rare variants obtained by high-throughput sequencing

Genome-wide association studies (GWAS) have been successful in identifying common genetic variation reproducibly associated with disease. However, most associated variants confer very small risk and after meta-analysis of large cohorts a large fraction of expected heritability still remains unexplained. A possible explanation is that rare variants currently undetected by GWAS with SNP arrays could contribute a large fraction of risk when present in cases. This concept has spurred great interest in exploring the role of rare variants in disease. As the cost of sequencing continue to plummet, it is becoming feasible to directly sequence case-control samples for testing disease association including rare variants. We have developed a test statistic that allows for association testing among cases and controls using data directly from sequencing reads. In addition, our method allows for random errors in reads. We determine the probability of a true genotype call based on the observed base pair reads using the expectation-maximization algorithm. We apply the SumStat procedure to obtain a single statistic for a group of multiple rare variant loci. We document the validity of our method through simulations. Our results suggest that our statistic maintains the correct type I error rate, even in the presence of differential misclassification for sequence reads, and that it has good power under a number of scenarios. Finally, our SumStat results show power at least as good as the maximum single locus results.     

Admixture-matched case-control study: a practical approach for genetic association studies in admixed populations

Case-control genetic association studies in admixed populations are known to be susceptible to genetic confounding due to population stratification. The transmission/disequilibrium test (TDT) approach can avoid this problem. However, the TDT is expensive and impractical for late-onset diseases. Case-control study designs, in which, cases and controls are matched by admixture, can be an appealing and a suitable alternative for genetic association studies in admixed populations. In this study, we applied this matching strategy when recruiting our African American participants in the Study of African American, Asthma, Genes and Environments. Group admixture in this cohort consists of 83% African ancestry and 17% European ancestry, which was consistent with reports from other studies. By carrying out several complementary analyses, our results show that there is a substructure in the cohort, but that the admixture distributions are almost identical in cases and controls, and also in cases only. We performed association tests for asthma-related traits with ancestry, and only found that FEV(1), a measure for baseline pulmonary function, was associated with ancestry after adjusting for socio-economic and environmental risk factors (P=0.01). We did not observe an excess of type I error rate in our association tests for ancestry informative markers and asthma-related phenotypes when ancestry was not adjusted in the analyses. Furthermore, using the association tests between genetic variants in a known asthma candidate gene, beta(2) adrenergic receptor (beta(2)AR) and DeltaFEF(25-75), an asthma-related phenotype, as an example, we demonstrated population stratification was not a confounder in our genetic association. Our present work demonstrates that admixture-matched case-control strategies can efficiently control population stratification confounding in admixed populations.     

Detection of genes for ordinal traits in nuclear families and a unified approach for association studies

There is growing interest in genomewide association analysis using single-nucleotide polymorphisms (SNPs), because traditional linkage studies are not as powerful in identifying genes for common, complex diseases. Tests for linkage disequilibrium have been developed for binary and quantitative traits. However, since many human conditions and diseases are measured in an ordinal scale, methods need to be developed to investigate the association of genes and ordinal traits. Thus, in the current report we propose and derive a score test statistic that identifies genes that are associated with ordinal traits when gametic disequilibrium between a marker and trait loci exists. Through simulation, the performance of this new test is examined for both ordinal traits and quantitative traits. The proposed statistic not only accommodates and is more powerful for ordinal traits, but also has similar power to that of existing tests when the trait is quantitative. Therefore, our proposed statistic has the potential to serve as a unified approach to identifying genes that are associated with any trait, regardless of how the trait is measured. We further demonstrated the advantage of our test by revealing a significant association (P = 0.00067) between alcohol dependence and a SNP in the growth-associated protein 43.     

A Bayesian approach to case-control studies with errors in covariables

We develop Bayesian methodology for the analysis of case-control data with covariate imprecision. The pretense that the distribution of the imprecisely measured covariate is discrete on a heuristically chosen support set leads to a method which is reasonably simple to implement, and can be applied to different study designs. The methodological development emphasizes the interplay between retrospective and prospective analysis. We illustrate the method on simulated data, and on data from a cancer study where smoking history is the imprecisely measured covariate.     

Robust tests for matched case-control genetic association studies

Background

Infectious disease of livestock continues to be a cause of substantial economic loss and has adverse welfare consequences in both the developing and developed world. New solutions to control disease are needed and research focused on the genetic loci determining variation in immune-related traits has the potential to deliver solutions. However, identifying selectable markers and the causal genes involved in disease resistance and vaccine response is not straightforward. The aims of this study were to locate regions of the bovine genome that control the immune response post immunisation. 195 F2 and backcross Holstein Charolais cattle were immunised with a 40-mer peptide derived from foot-and-mouth disease virus (FMDV). T cell and antibody (IgG1 and IgG2) responses were measured at several time points post immunisation. All experimental animals (F0, F1 and F2, n = 982) were genotyped with 165 microsatellite markers for the genome scan.

Results

Considerable variability in the immune responses across time was observed and sire, dam and age had significant effects on responses at specific time points. There were significant correlations within traits across time, and between IgG1 and IgG2 traits, also some weak correlations were detected between T cell and IgG2 responses. The whole genome scan detected 77 quantitative trait loci (QTL), on 22 chromosomes, including clusters of QTL on BTA 4, 5, 6, 20, 23 and 25. Two QTL reached 5% genome wide significance (on BTA 6 and 24) and one on BTA 20 reached 1% genome wide significance.

Conclusions

A proportion of the variance in the T cell and antibody response post immunisation with an FDMV peptide has a genetic component. Even though the antigen was relatively simple, the humoral and cell mediated responses were clearly under complex genetic control, with the majority of QTL located outside the MHC locus. The results suggest that there may be specific genes or loci that impact on variation in both the primary and secondary immune responses, whereas other loci may be specifically important for early or later phases of the immune response. Future fine mapping of the QTL clusters identified has the potential to reveal the causal variations underlying the variation in immune response observed.     

A Gaussian copula approach for the analysis of secondary phenotypes in case-control genetic association studies

In many case-control genetic association studies, a set of correlated secondary phenotypes that may share common genetic factors with disease status are collected. Examination of these secondary phenotypes can yield valuable insights about the disease etiology and supplement the main studies. However, due to unequal sampling probabilities between cases and controls, standard regression analysis that assesses the effect of SNPs (single nucleotide polymorphisms) on secondary phenotypes using cases only, controls only, or combined samples of cases and controls can yield inflated type I error rates when the test SNP is associated with the disease. To solve this issue, we propose a Gaussian copula-based approach that efficiently models the dependence between disease status and secondary phenotypes. Through simulations, we show that our method yields correct type I error rates for the analysis of secondary phenotypes under a wide range of situations. To illustrate the effectiveness of our method in the analysis of real data, we applied our method to a genome-wide association study on high-density lipoprotein cholesterol (HDL-C), where "cases" are defined as individuals with extremely high HDL-C level and "controls" are defined as those with low HDL-C level. We treated 4 quantitative traits with varying degrees of correlation with HDL-C as secondary phenotypes and tested for association with SNPs in LIPG, a gene that is well known to be associated with HDL-C. We show that when the correlation between the primary and secondary phenotypes is >0.2, the P values from case-control combined unadjusted analysis are much more significant than methods that aim to correct for ascertainment bias. Our results suggest that to avoid false-positive associations, it is important to appropriately model secondary phenotypes in case-control genetic association studies.     

A robust method for testing association in genome-wide association studies

In genetic association studies, due to the varying underlying genetic models, no single statistical test can be the most powerful test under all situations. Current studies show that if the underlying genetic models are known, trend-based tests, which outperform the classical Pearson χ2 test, can be constructed. However, when the underlying genetic models are unknown, the χ2 test is usually more robust than trend-based tests. In this paper, we propose a new association test based on a generalized genetic model, namely the generalized order-restricted relative risks model. Through a Monte Carlo simulation study, we show that the proposed association test is generally more powerful than the χ2 test, and more robust than those trend-based tests. The proposed methodologies are also illustrated by some real SNP datasets.     

A new powerful non-parametric two-stage approach for testing multiple phenotypes in family-based association studies

We introduce a new powerful nonparametric testing strategy for family-based association studies in which multiple quantitative traits are recorded and the phenotype with the strongest genetic component is not known prior to the analysis. In the first stage, using a population-based test based on the generalized estimating equation approach, we test all recorded phenotypes for association with the marker locus without biasing the nominal significance level of the later family-based analysis. In the second stage the phenotype with the smallest p value is selected and tested by a family-based association test for association with the marker locus. This strategy is robust against population admixture and stratification and does not require any adjustment for multiple testing. We demonstrate the advantages of this testing strategy over standard methodology in a simulation study. The practical importance of our testing strategy is illustrated by applications to the Childhood Asthma Management Program asthma data sets.     

Genomewide weighted hypothesis testing in family-based association studies, with an application to a 100K scan

For genomewide association (GWA) studies in family-based designs, we propose a novel two-stage strategy that weighs the association P values with the use of independently estimated weights. The association information contained in the family sample is partitioned into two orthogonal components--namely, the between-family information and the within-family information. The between-family component is used in the first (i.e., screening) stage to obtain a relative ranking of all the markers. The within-family component is used in the second (i.e., testing) stage in the framework of the standard family-based association test, and the resulting P values are weighted using the estimated marker ranking from the screening step. The approach is appealing, in that it ensures that all the markers are tested in the testing step and, at the same time, also uses information from the screening step. Through simulation studies, we show that testing all the markers is more powerful than testing only the most promising ones from the screening step, which was the method suggested by Van Steen et al. A comparison with a population-based approach shows that the approach achieves comparable power. In the presence of a reasonable level of population stratification, our approach is only slightly affected in terms of power and, since it is a family-based method, is completely robust to spurious effects. An application to a 100K scan in the Framingham Heart Study illustrates the practical advantages of our approach. The proposed method is of general applicability; it extends to any setting in which prior, independent ranking of hypotheses is available.     

A constrained-likelihood approach to marker-trait association studies

Marker-trait association analysis is an important statistical tool for detecting DNA variants responsible for genetic traits. In such analyses, an analysis model of the mean genetic effects of the genotypes is often specified. For instance, the effect of the disease allele on the trait is often specified to be dominant, recessive, additive, or multiplicative. Although this model-based approach is powerful when the analysis model is correctly specified, it has been found to have low power sometimes when the specified model is incorrect. We introduce an approach that does not require the specification of a particular genetic model. This approach is built upon a constrained maximum likelihood in which the mean genetic effect of the heterozygous genotype is required to not exceed those of the two homozygous genotypes. The asymptotic distribution of the likelihood-ratio statistic is derived for two special cases. A simulation study suggests that this new approach has power comparable to that of the model-based method when the analysis model is correctly specified. This approach uses one marker at a time (i.e., it is a single-marker analysis). However, given the latest findings that powerful inferential procedures for haplotype analyses can be constructed from single-marker analyses, we expect this approach to be useful for haplotype analyses.     

A gene-centric approach to genome-wide association studies

Genic variants are more likely to alter gene function and affect disease risk than those that occur outside genes. Variants in genes, however, might not be sufficiently covered by the existing approaches to genome-wide association studies. Our analysis of the HapMap ENCODE data indicates that this concern is valid, and that an alternative approach that focuses on genic variants provides a more complete coverage of functionally important regions and a greater genotyping efficiency. We therefore argue that resources should be developed to make gene-centric genome-wide association studies feasible.