Design of association studies with pooled or un‐pooled next‐generation sequencing data

Most common hereditary diseases in humans are complex and multifactorial. Large‐scale genome‐wide association studies based on SNP genotyping have only identified a small fraction of the heritable variation of these diseases. One explanation may be that many rare variants (a minor allele frequency, MAF <5%), which are not included in the common genotyping platforms, may contribute substantially to the genetic variation of these diseases. Next‐generation sequencing, which would allow the analysis of rare variants, is now becoming so cheap that it provides a viable alternative to SNP genotyping. In this paper, we present cost‐effective protocols for using next‐generation sequencing in association mapping studies based on pooled and un‐pooled samples, and identify optimal designs with respect to total number of individuals, number of individuals per pool, and the sequencing coverage. We perform a small empirical study to evaluate the pooling variance in a realistic setting where pooling is combined with exon‐capturing. To test for associations, we develop a likelihood ratio statistic that accounts for the high error rate of next‐generation sequencing data. We also perform extensive simulations to determine the power and accuracy of this method. Overall, our findings suggest that with a fixed cost, sequencing many individuals at a more shallow depth with larger pool size achieves higher power than sequencing a small number of individuals in higher depth with smaller pool size, even in the presence of high error rates. Our results provide guidelines for researchers who are developing association mapping studies based on next‐generation sequencing. Genet. Epidemiol. 34: 479–491, 2010. © 2010 Wiley‐Liss, Inc.     

On optimal pooling designs to identify rare variants through massive resequencing

The advent of next‐generation sequencing technologies has facilitated the detection of rare variants. Despite the significant cost reduction, sequencing cost is still high for large‐scale studies. In this article, we examine DNA pooling as a cost‐effective strategy for rare variant detection. We consider the optimal number of individuals in a DNA pool to detect an allele with a specific minor allele frequency (MAF) under a given coverage depth and detection threshold. We found that the optimal number of individuals in a pool is indifferent to the MAF at the same coverage depth and detection threshold. In addition, when the individual contributions to each pool are equal, the total number of individuals across different pools required in an optimal design to detect a variant with a desired power is similar at different coverage depths. When the contributions are more variable, more individuals tend to be needed for higher coverage depths. Our study provides general guidelines on using DNA pooling for more cost‐effective identifications of rare variants. Genet. Epidemiol. 35:139‐147, 2011. © 2011 Wiley‐Liss, Inc.     

Identifying Rare Variants With Optimal Depth of Coverage and Cost‐Effective Overlapping Pool Sequencing

Genome‐wide association studies have identified hundreds of genetic variants associated with complex diseases although most variants identified so far explain only a small proportion of heritability, suggesting that rare variants are responsible for missing heritability. Identification of rare variants through large‐scale resequencing becomes increasing important but still prohibitively expensive despite the rapid decline in the sequencing costs. Nevertheless, group testing based overlapping pool sequencing in which pooled rather than individual samples are sequenced will greatly reduces the efforts of sample preparation as well as the costs to screen for rare variants. Here, we proposed an overlapping pool sequencing to screen rare variants with optimal sequencing depth and a corresponding cost model. We formulated a model to compute the optimal depth for sufficient observations of variants in pooled sequencing. Utilizing shifted transversal design algorithm, appropriate parameters for overlapping pool sequencing could be selected to minimize cost and guarantee accuracy. Due to the mixing constraint and high depth for pooled sequencing, results showed that it was more cost‐effective to divide a large population into smaller blocks which were tested using optimized strategies independently. Finally, we conducted an experiment to screen variant carriers with frequency equaled 1%. With simulated pools and publicly available human exome sequencing data, the experiment achieved 99.93% accuracy. Utilizing overlapping pool sequencing, the cost for screening variant carriers with frequency equaled 1% in 200 diploid individuals dropped to at least 66% at which target sequencing region was set to 30 Mb.     

Efficient study design for next generation sequencing

Next Generation Sequencing represents a powerful tool for detecting genetic variation associated with human disease. Because of the high cost of this technology, it is critical that we develop efficient study designs that consider the trade‐off between the number of subjects (n) and the coverage depth (µ). How we divide our resources between the two can greatly impact study success, particularly in pilot studies. We propose a strategy for selecting the optimal combination of n and µ for studies aimed at detecting rare variants and for studies aimed at detecting associations between rare or uncommon variants and disease. For detecting rare variants, we find the optimal coverage depth to be between 2 and 8 reads when using the likelihood ratio test. For association studies, we find the strategy of sequencing all available subjects to be preferable. In deriving these combinations, we provide a detailed analysis describing the distribution of depth across a genome and the depth needed to identify a minor allele in an individual. The optimal coverage depth depends on the aims of the study, and the chosen depth can have a large impact on study success. Genet. Epidemiol. 35: 269‐277, 2011. © 2011 Wiley‐Liss, Inc.     

Recommended Joint and Meta‐Analysis Strategies for Case‐Control Association Testing of Single Low‐Count Variants

In genome‐wide association studies of binary traits, investigators typically use logistic regression to test common variants for disease association within studies, and combine association results across studies using meta‐analysis. For common variants, logistic regression tests are well calibrated, and meta‐analysis of study‐specific association results is only slightly less powerful than joint analysis of the combined individual‐level data. In recent sequencing and dense chip based association studies, investigators increasingly test low‐frequency variants for disease association. In this paper, we seek to (1) identify the association test with maximal power among tests with well controlled type I error rate and (2) compare the relative power of joint and meta‐analysis tests. We use analytic calculation and simulation to compare the empirical type I error rate and power of four logistic regression based tests: Wald, score, likelihood ratio, and Firth bias‐corrected. We demonstrate for low‐count variants (roughly minor allele count [MAC] < 400) that: (1) for joint analysis, the Firth test has the best combination of type I error and power; (2) for meta‐analysis of balanced studies (equal numbers of cases and controls), the score test is best, but is less powerful than Firth test based joint analysis; and (3) for meta‐analysis of sufficiently unbalanced studies, all four tests can be anti‐conservative, particularly the score test. We also establish MAC as the key parameter determining test calibration for joint and meta‐analysis.     

G‐STRATEGY: Optimal Selection of Individuals for Sequencing in Genetic Association Studies

In a large‐scale genetic association study, the number of phenotyped individuals available for sequencing may, in some cases, be greater than the study's sequencing budget will allow. In that case, it can be important to prioritize individuals for sequencing in a way that optimizes power for association with the trait. Suppose a cohort of phenotyped individuals is available, with some subset of them possibly already sequenced, and one wants to choose an additional fixed‐size subset of individuals to sequence in such a way that the power to detect association is maximized. When the phenotyped sample includes related individuals, power for association can be gained by including partial information, such as phenotype data of ungenotyped relatives, in the analysis, and this should be taken into account when assessing whom to sequence. We propose G‐STRATEGY, which uses simulated annealing to choose a subset of individuals for sequencing that maximizes the expected power for association. In simulations, G‐STRATEGY performs extremely well for a range of complex disease models and outperforms other strategies with, in many cases, relative power increases of 20–40% over the next best strategy, while maintaining correct type 1 error. G‐STRATEGY is computationally feasible even for large datasets and complex pedigrees. We apply G‐STRATEGY to data on high‐density lipoprotein and low‐density lipoprotein from the AGES‐Reykjavik and REFINE‐Reykjavik studies, in which G‐STRATEGY is able to closely approximate the power of sequencing the full sample by selecting for sequencing a only small subset of the individuals.     

Confounded by sequencing depth in association studies of rare alleles

Next‐generation DNA sequencing technologies are facilitating large‐scale association studies of rare genetic variants. The depth of the sequence read coverage is an important experimental variable in the next‐generation technologies and it is a major determinant of the quality of genotype calls generated from sequence data. When case and control samples are sequenced separately or in different proportions across batches, they are unlikely to be matched on sequencing read depth and a differential misclassification of genotypes can result, causing confounding and an increased false‐positive rate. Data from Pilot Study 3 of the 1000 Genomes project was used to demonstrate that a difference between the mean sequencing read depth of case and control samples can result in false‐positive association for rare and uncommon variants, even when the mean coverage depth exceeds 30× in both groups. The degree of the confounding and inflation in the false‐positive rate depended on the extent to which the mean depth was different in the case and control groups. A logistic regression model was used to test for association between case‐control status and the cumulative number of alleles in a collapsed set of rare and uncommon variants. Including each individual's mean sequence read depth across the variant sites in the logistic regression model nearly eliminated the confounding effect and the inflated false‐positive rate. Furthermore, accounting for the potential error by modeling the probability of the heterozygote genotype calls in the regression analysis had a relatively minor but beneficial effect on the statistical results. Genet. Epidemiol. 35: 261‐268, 2011. © 2011 Wiley‐Liss, Inc.     

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.     

Resetting the bar: Statistical significance in whole‐genome sequencing‐based association studies of global populations

Genome‐wide association studies (GWAS) of common disease have been hugely successful in implicating loci that modify disease risk. The bulk of these associations have proven robust and reproducible, in part due to community adoption of statistical criteria for claiming significant genotype‐phenotype associations. As the cost of sequencing continues to drop, assembling large samples in global populations is becoming increasingly feasible. Sequencing studies interrogate not only common variants, as was true for genotyping‐based GWAS, but variation across the full allele frequency spectrum, yielding many more (independent) statistical tests. We sought to empirically determine genome‐wide significance thresholds for various analysis scenarios. Using whole‐genome sequence data, we simulated sequencing‐based disease studies of varying sample size and ancestry. We determined that future sequencing efforts in >2,000 samples of European, Asian, or admixed ancestry should set genome‐wide significance at approximately P = 5 × 10^?9, and studies of African samples should apply a more stringent genome‐wide significance threshold of P = 1 × 10^?9. Adoption of a revised multiple test correction will be crucial in avoiding irreproducible claims of association.     

Simple method to analyze SNP-based association studies using DNA pools

Association studies using DNA pools are in principle powerful and efficient to detect association between a marker allele and disease status, e.g., in a case-control design. A common observation with the use of DNA pools is that the two alleles at a polymorphic SNP locus are not amplified in equal amounts in heterozygous individuals. In addition, there are pool-specific experimental errors so that there is variation in the estimates of allele frequencies from different pools that are from the same individuals. As a result of these additional sources of variation, the outcome of an experiment is an estimated count of alleles rather than the usual outcome in terms of observed counts. In this study, we show analytically and by computer simulation that unequal amplification should be taken into account when testing for differences in allele frequencies between pools, and suggest a simple modification of the standard chi(2) test to control the type I error rate in the presence of experimental error variation. The impact of experimental errors on the power of association studies is shown.     

Two‐phase designs for joint quantitative‐trait‐dependent and genotype‐dependent sampling in post‐GWAS regional sequencing

We evaluate two‐phase designs to follow‐up findings from genome‐wide association study (GWAS) when the cost of regional sequencing in the entire cohort is prohibitive. We develop novel expectation‐maximization‐based inference under a semiparametric maximum likelihood formulation tailored for post‐GWAS inference. A GWAS‐SNP (where SNP is single nucleotide polymorphism) serves as a surrogate covariate in inferring association between a sequence variant and a normally distributed quantitative trait (QT). We assess test validity and quantify efficiency and power of joint QT‐SNP‐dependent sampling and analysis under alternative sample allocations by simulations. Joint allocation balanced on SNP genotype and extreme‐QT strata yields significant power improvements compared to marginal QT‐ or SNP‐based allocations. We illustrate the proposed method and evaluate the sensitivity of sample allocation to sampling variation using data from a sequencing study of systolic blood pressure.     

Evaluating the Calibration and Power of Three Gene‐Based Association Tests of Rare Variants for the X Chromosome

Although genome‐wide association studies (GWAS) have identified thousands of trait‐associated genetic variants, there are relatively few findings on the X chromosome. For analysis of low‐frequency variants (minor allele frequency <5%), investigators can use region‐ or gene‐based tests where multiple variants are analyzed jointly to increase power. To date, there are no gene‐based tests designed for association testing of low‐frequency variants on the X chromosome. Here we propose three gene‐based tests for the X chromosome: burden, sequence kernel association test (SKAT), and optimal unified SKAT (SKAT‐O). Using simulated case‐control and quantitative trait (QT) data, we evaluate the calibration and power of these tests as a function of (1) male:female sample size ratio; and (2) coding of haploid male genotypes for variants under X‐inactivation. For case‐control studies, all three tests are reasonably well‐calibrated for all scenarios we evaluated. As expected, power for gene‐based tests depends on the underlying genetic architecture of the genomic region analyzed. Studies with more (haploid) males are generally less powerful due to decreased number of chromosomes. Power generally is slightly greater when the coding scheme for male genotypes matches the true underlying model, but the power loss for misspecifying the (generally unknown) model is small. For QT studies, type I error and power results largely mirror those for binary traits. We demonstrate the use of these three gene‐based tests for X‐chromosome association analysis in simulated data and sequencing data from the Genetics of Type 2 Diabetes (GoT2D) study.     

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.     

Pooled versus individual genotyping in a breast cancer genome‐wide association study

We examine the measurement properties of pooled DNA odds ratio estimates for 7,357 single nucleotide polymorphisms (SNPs) genotyped in a genome‐wide association study of postmenopausal breast cancer. This study involved DNA pools formed from 125 cases or125 matched controls. Individual genotyping for these SNPs subsequently came available for a substantial majority of women included in seven pool pairs, providing the opportunity for a comparison of pooled DNA and individual odds ratio estimates and their variances. We find that the “per minor allele” odds ratio estimates from the pooled DNA comparisons agree fairly well with those from individual genotyping. Furthermore, the log‐odds ratio variance estimates support a pooled DNA measurement model that we previously described, although with somewhat greater extra‐binomial variation than was hypothesized in project design. Implications for the role of pooled DNA comparisons in the future genetic epidemiology research agenda are discussed. Genet. Epidemiol. 34: 603–612, 2010. © 2010 Wiley‐Liss, Inc.     

Kernel‐Machine Testing Coupled with a Rank‐Truncation Method for Genetic Pathway Analysis

Traditional genome‐wide association studies (GWASs) usually focus on single‐marker analysis, which only accesses marginal effects. Pathway analysis, on the other hand, considers biological pathway gene marker hierarchical structure and therefore provides additional insights into the genetic architecture underlining complex diseases. Recently, a number of methods for pathway analysis have been proposed to assess the significance of a biological pathway from a collection of single‐nucleotide polymorphisms. In this study, we propose a novel approach for pathway analysis that assesses the effects of genes using the sequence kernel association test and the effects of pathways using an extended adaptive rank truncated product statistic. It has been increasingly recognized that complex diseases are caused by both common and rare variants. We propose a new weighting scheme for genetic variants across the whole allelic frequency spectrum to be analyzed together without any form of frequency cutoff for defining rare variants. The proposed approach is flexible. It is applicable to both binary and continuous traits, and incorporating covariates is easy. Furthermore, it can be readily applied to GWAS data, exome‐sequencing data, and deep resequencing data. We evaluate the new approach on data simulated under comprehensive scenarios and show that it has the highest power in most of the scenarios while maintaining the correct type I error rate. We also apply our proposed methodology to data from a study of the association between bipolar disorder and candidate pathways from Wellcome Trust Case Control Consortium (WTCCC) to show its utility.     

Biases and errors on allele frequency estimation and disease association tests of next-generation sequencing of pooled samples

Next-generation sequencing is widely used to study complex diseases because of its ability to identify both common and rare variants without prior single nucleotide polymorphism (SNP) information. Pooled sequencing of implicated target regions can lower costs and allow more samples to be analyzed, thus improving statistical power for disease-associated variant detection. Several methods for disease association tests of pooled data and for optimal pooling designs have been developed under certain assumptions of the pooling process, for example, equal/unequal contributions to the pool, sequencing depth variation, and error rate. However, these simplified assumptions may not portray the many factors affecting pooled sequencing data quality, such as PCR amplification during target capture and sequencing, reference allele preferential bias, and others. As a result, the properties of the observed data may differ substantially from those expected under the simplified assumptions. Here, we use real datasets from targeted sequencing of pooled samples, together with microarray SNP genotypes of the same subjects, to identify and quantify factors (biases and errors) affecting the observed sequencing data. Through simulations, we find that these factors have a significant impact on the accuracy of allele frequency estimation and the power of association tests. Furthermore, we develop a workflow protocol to incorporate these factors in data analysis to reduce the potential biases and errors in pooled sequencing data and to gain better estimation of allele frequencies. The workflow, Psafe, is available at http://bioinformatics.med.yale.edu/group/.     

Gene‐based segregation method for identifying rare variants in family‐based sequencing studies

Whole‐exome sequencing using family data has identified rare coding variants in Mendelian diseases or complex diseases with Mendelian subtypes, using filters based on variant novelty, functionality, and segregation with the phenotype within families. However, formal statistical approaches are limited. We propose a gene‐based segregation test (GESE) that quantifies the uncertainty of the filtering approach. It is constructed using the probability of segregation events under the null hypothesis of Mendelian transmission. This test takes into account different degrees of relatedness in families, the number of functional rare variants in the gene, and their minor allele frequencies in the corresponding population. In addition, a weighted version of this test allows incorporating additional subject phenotypes to improve statistical power. We show via simulations that the GESE and weighted GESE tests maintain appropriate type I error rate, and have greater power than several commonly used region‐based methods. We apply our method to whole‐exome sequencing data from 49 extended pedigrees with severe, early‐onset chronic obstructive pulmonary disease (COPD) in the Boston Early‐Onset COPD study (BEOCOPD) and identify several promising candidate genes. Our proposed methods show great potential for identifying rare coding variants of large effect and high penetrance for family‐based sequencing data. The proposed tests are implemented in an R package that is available on CRAN ( https://cran.r-project.org/web/packages/GESE/ ).     

Rare variants association testing for a binary outcome when pooling individual level data from heterogeneous studies

Whole genome sequencing (WGS) and whole exome sequencing studies are used to test the association of rare genetic variants with health traits. Many existing WGS efforts now aggregate data from heterogeneous groups, for example, combining sets of individuals of European and African ancestries. We here investigate the statistical implications on rare variant association testing with a binary trait when combining together heterogeneous studies, defined as studies with potentially different disease proportion and different frequency of variant carriers. We study and compare in simulations the Type 1 error control and power of the naïve score test, the saddlepoint approximation to the score test, and the BinomiRare test in a range of settings, focusing on low numbers of variant carriers. We show that Type 1 error control and power patterns depend on both the number of carriers of the rare allele and on disease prevalence in each of the studies. We develop recommendations for association analysis of rare genetic variants. (1) The Score test is preferred when the case proportion in the sample is 50%. (2) Do not down‐sample controls to balance case–control ratio, because it reduces power. Rather, use a test that controls the Type 1 error. (3) Conduct stratified analysis in parallel with combined analysis. Aggregated testing may have lower power when the variant effect size differs between strata.     

What SNP genotyping errors are most costly for genetic association studies?

Which genotype misclassification errors are most costly, in terms of increased sample size necessary (SSN) to maintain constant asymptotic power and significance level, when performing case/control studies of genetic association? We answer this question for single‐nucleotide polymorphisms (SNPs), using the 2×3 χ² test of independence. Our strategy is to expand the noncentrality parameter of the asymptotic distribution of the χ² test under a specified alternative hypothesis to approximate SSN, using a linear Taylor series in the error parameters. We consider two scenarios: the first assumes Hardy‐Weinberg equilibrium (HWE) for the true genotypes in both cases and controls, and the second assumes HWE only in controls. The Taylor series approximation has a relative error of less than 1% when each error rate is less than 2%. The most costly error is recording the more common homozygote as the less common homozygote, with indefinitely increasing cost coefficient as minor SNP allele frequencies approach 0 in both scenarios. The cost of misclassifying the more common homozygote to the heterozygote also becomes indefinitely large as the minor SNP allele frequency goes to 0 under both scenarios. For the violation of HWE modeled here, the cost of misclassifying a heterozygote to the less common homozygote becomes large, although bounded. Therefore, the use of SNPs with a small minor allele frequency requires careful attention to the frequency of genotyping errors to ensure that power specifications are met. Furthermore, the design of automated genotyping should minimize those errors whose cost coefficients can become indefinitely large. Genet Epidemiol 26:132–141, 2004. © 2004 Wiley‐Liss, Inc.