Local Joint Testing Improves Power and Identifies Hidden ... · *Department of Computer Science, University of California, Berkeley, California 94720, †Harvard T. H. Chan School

| 4TH RECOMB SATELLITE ON COMPUTATIONAL METHODS IN GENETICS

Local Joint Testing Improves Power and IdentifiesHidden Heritability in Association Studies

Brielin C. Brown,*,1 Alkes L. Price,† Nikolaos A. Patsopoulos,‡,§,**,2 and Noah Zaitlen††,2

*Department of Computer Science, University of California, Berkeley, California 94720, †Harvard T. H. Chan School of PublicHealth, Harvard University, Boston, Massachusetts 02115, ‡Department of Neurology and §Division of Genetics, Department ofMedicine, Brigham & Women’s Hospital, Boston, Massachusetts 02115, **Broad Institute, Cambridge, Massachusetts 02142, and

††Department of Medicine, University of California, San Francisco, California 94158

ABSTRACT There is mounting evidence that complex human phenotypes are highly polygenic, with many loci harboring multiplecausal variants, yet most genetic association studies examine each SNP in isolation. While this has led to the discovery of thousands ofdisease associations, discovered variants account for only a small fraction of disease heritability. Alternative multi-SNP methods havebeen proposed, but issues such as multiple-testing correction, sensitivity to genotyping error, and optimization for the underlyinggenetic architectures remain. Here we describe a local joint-testing procedure, complete with multiple-testing correction, that leveragesa genetic phenomenon we call linkage masking wherein linkage disequilibrium between SNPs hides their signal under standardassociation methods. We show that local joint testing on the original Wellcome Trust Case Control Consortium (WTCCC) data set leadsto the discovery of 22 associated loci, 5 more than the marginal approach. These loci were later found in follow-up studies containingthousands of additional individuals. We find that these loci significantly increase the heritability explained by genome-wide significantassociations in the WTCCC data set. Furthermore, we show that local joint testing in a cis-expression QTL (eQTL) study of thegEUVADIS data set increases the number of genes containing significant eQTL by 10.7% over marginal analyses. Our multiple-hypothesis correction and joint-testing framework are available in a python software package called Jester, available at github.com/brielin/Jester.

KEYWORDS statistical genetics; heritability; epistasis; polygenicity; joint testing

GENETIC association studies typically take a marginalapproach to analysis, investigating each SNP in isolation

of all other SNPs for association with a phenotype of interest.While thismethodhas led to the discovery of thousands of lociassociated with hundreds of phenotypes (Welter et al. 2014;Eicher et al. 2015), it fails to capture the additional signalavailable when multiple SNPs representing independent ge-netic signals are examined simultaneously (Yang et al. 2012)or when SNPs are imperfectly imputed (Wood et al. 2011).Furthermore, the hidden heritability, the difference betweenthe heritability due to genome-wide significant associationsand heritability due to genotyped variants, remains substan-

tial (Eichler et al. 2010). In this work we investigate a localjoint-testing approach to analysis of genetic data sets inwhich pairs of variants from the same locus are examinedsimultaneously for association with a phenotype. The moti-vation for our approach comes from the mounting evidencethat complex traits are highly polygenic (Visscher et al.2012), that causal variants are not evenly distributed acrossthe genome (Gusev et al. 2013), that known associated locioften harbor multiple causal variants (Udler et al. 2009;Fellay et al. 2010; Trynka et al. 2011; Wood et al. 2011; Liuet al. 2012; Patsopoulos et al. 2013; Pickrell 2014), and thatthe underlying causal variants can be in linkage disequilib-rium (LD) with each other (Corradin et al. 2014).

In fact, LD betweenunderlying causal variants can result inadditiveassociations thatwouldbenearly impossible todetectusing standard marginal methods. Consider the case of twoSNPs: one increasing risk for a disease and the other pro-tective. If these SNPs are correlated in the study population,thenmarginal associationmethodswill fail todetect the signal

Copyright © 2016 by the Genetics Society of Americadoi: 10.1534/genetics.116.188292Manuscript received February 17, 2016; accepted for publication April 27, 2016;published Early Online May 4, 2016.Supplemental material is available online at www.genetics.org/lookup/suppl/doi:10.1534/genetics.116.188292/-/DC1.1Corresponding author: 378G Stanley Hall, University of California, Berkeley, Berkeley,CA 94709. E-mail: [email protected]

2These authors contributed equally to this work.

Genetics, Vol. 203, 1105–1116 July 2016 1105

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mailto:[email protected]

due to the large number of individuals carrying both variants(and therefore having little or no increased risk for thedisease). The same effect can occur when the variants havethe same effect direction but are anticorrelated in the studypopulation. In the context of this article, we refer to these SNPpairs as linkage masked. Note that in practice linkagemaskingmay present in two distinct and important ways. The first oneis multiple correlated genotyped causal variants with oppo-site effect direction, which may occur due to the Bulmereffect (Bulmer 1971) (see Discussion). The second one iscorrelated genotyped variants with opposite tagging of anuntyped causal variant. Lappalainen et al. (2011) give evi-dence that linkage masking between regulatory and codingvariation may be common due to balancing selection. Whilelinkage-masked SNPs are difficult to uncover using standardmarginal association methods, mixed-model heritability isdetermined by a simultaneous fit of all SNPs while account-ing for LD and therefore includes signal from linkage-maskedSNPs, implicating them as a source of hidden heritability thathas not been widely considered (Eichler et al. 2010).

Pairwise (joint) testing for additive effects without a sta-tistical interaction term may help unmask these associationsand, more generally, improve power in the presence of geneinteractions, multiple causal variants, or multiple variantsdifferentially tagging an untyped causal SNP. However, ap-plying joint tests in practice has several problems. Becauseexact multiple-testing correction is usually unknown, severalstudies have used joint testing for follow-up and finemappingofknownassociated loci, often revealingadditional associatedvariants (Wood et al. 2011; Yang et al. 2012) and demonstrat-ing the merits of joint testing in practice. Studies such as theseare able to ignore multiple-hypothesis correction issues due totheir focus on known associated regions but do not have thepotential to reveal novel loci. Other studies examining genome-wide joint testing of all pairs of SNPs, including those withstatistical interaction terms, pay such severemultiple-hypothesiscorrection penalties that many loci found via standard mar-ginal approaches would not reach genome-wide significance(Prabhu and Pe’er 2012; Arkin et al. 2014) and are computa-tionally expensive, although effect methods for reducing thecomputational burden have been explored (Prabhu and Pe’er2012; Wang et al. 2015). Slavin and Elston (Slavin et al. 2011)proposed testing all adjacent pairs and applied their approach inthe Wellcome Trust Case Control Consortium (WTCCC) sevendisease study. Howey and Cordell (2014) (SnipSnip) proposedusing a conditional test on 10 adjacent SNPs to choose a partnerSNP for inclusion in the linear model. While these approachesreduce themultiple-hypothesis correction penalty,we show thatthey do not capture much of the available power gain. Further-more, prior approaches have not accounted for a known issuewith genotyping error and joint tests (Lee et al. 2010),whichweshow affects these methods.

By testing pairs of SNPs for additive effects, rather thanindividual SNPs, we improve power to detect loci containingmultiple independent causal variants, including those containinglinkage-masked SNPs. Through local testing, we substantially

reduce the multiple-hypothesis correction penalty, while si-multaneously enriching for situations in which joint tests aremore powerful, i.e., when there are independent additivegenetic signals contained in each of the SNPs in the test.Rather than employing the overly conservative Bonferroniprocedure to account for multiple testing, we extend thework of Han et al. (2009) to provide a method for samplingfrom the null distribution of joint tests orders of magnitudefaster than a permutation test, making application computa-tionally efficient. We applied our method to the WTCCC(WTCC Consortium 2007) cohorts for bipolar disorder, coro-nary artery disease, Crohn’s disease, hypertension, rheuma-toid arthritis, type-1 diabetes, and type-2 diabetes. We definesignificant locus as any 1-Mb region containing a statisticallysignificant association at family-wise error rate (FWER) 5%and compare the number of significant loci discovered fromthe National Human Genome Research Institute (NHGRI)database of replicated associations to the standard marginalmethod. We compare our approach to SnipSnip (Howey andCordell 2014) and marginal analysis of imputed WTCCC ge-notypes. We also estimate the phenotypic variance explainedby associated SNPs discovered in the marginal and joint ap-proaches. Finally, we apply our method to gene expressiondata from the Genetic European Variation in Health and Disease(gEUVADIS) project, comparing the number of genes contain-ing cis-expression QTL (eQTL) at various false discovery rate(FDR) thresholds undermarginal- and joint-testing approaches.

We find the following:

1. Local joint testing provides significant power gains whenmultiple-risk variants are proximal, reaching as high as41% when they are linkage masked.

2. Local joint testing in the original WTCCC cohort discoversseven loci not found via the standard marginal approach,all of which were later replicated in more powerful follow-up studies. Marginal analysis of imputed genotypes dis-covers only two of these loci, as well as one locus notdetectable in either genotype-based method.

3. New SNPs and loci discovered via local joint testing ex-plain a significant amount of the phenotypic variance ofthese diseases.

4. Joint testing all pairs of cis-SNPs in gEUVADIS reveals 607more genes at FDR 5%, an increase of 10.7% over themarginal approach.

Methods

Webegin by describing thenull distributions of the tests in ourprocedure to motivate the sampling approach used to de-termine the multiple-testing correction. We then show thatgiven the marginal Z scores at two SNPs the joint x2-teststatistic can be exactly determined. In most cases, determin-ing the significance level of a pairwise test of correlated var-iables requires a computationally expensive permutation test.However, we build upon a framework for generating marginal

1106 B. C. Brown et al.

test statistics under the null efficiently, using a conditional sam-pling approach (Han et al. 2009), which has also been used forgenome-wide interaction effect power calculations (Wang et al.2015). This implies that we are able to efficiently sample fromthe null distribution of the joint test, allowing for a dramaticimprovement in speed over a permutation test. Finally, we de-scribe the local joint-testing procedure. For simplicity, we as-sume the phenotype and genotypes have been standardized.

Asymptotic distribution of the marginal and joint tests

For many widely used statistical tests, the vector of teststatistics over many markers asymptotically follows a multi-variate normal distribution (MVN) under the null hypothesisof no association (Lin 2005; Seaman and Muller-Myhsok2005). In particular, let Y be the phenotype of interest andG thegenotypematrix,withGi thegenotypeatSNP i in a studywithN individuals; then theWald testZi ¼ b̂i = sb̂i

¼ ffiffiffiffiN

pCorðGi; YÞ is

asymptoticallyNð0; 1Þ: From this, one can derive the correlationstructure for two tests under the null (Han et al. 2009),CorðZi; ZjÞ ¼ CorðGi;GjÞ :¼ rij; so that the vector of marginaltest statistics is asymptotically MVN with mean 0

!and co-

variance matrix S ¼ fSijgN;Ni¼1;j¼1 ¼ frijgN;Ni¼1; j¼1:

Next, we consider the value of the likelihood-ratio test(LRT) statistic for a linear or logistic two-SNP association test.In the Appendix we prove that it is possible to compute thevalue of this test statistic directly from the marginal associa-

tion statistics, without fitting the joint model. Specifically, weprove the following:

Observation 1. Let Zi; Zj be the Z values of test statistics forthe SNPs ði; jÞ against a phenotype Y. Let the correlation be-tween SNPs Gi and Gj be ri;j: Then the likelihood-ratio teststatistic for the model Y � 1þ Gi þ Gj against the null Y � 1 is

x2J ¼ 112 r2i; j

�Z2i þ Z2j 22rijZiZj

�(1)

and is asymptotically x22 distributed.

We verified computationally by simulating pairs of SNPs atall correlation levels that this equation is exact (not shown).

Estimating the significance threshold and localjoint testing

Weuse a conditional samplingmethod to sample themarginaltest statistics under the null from the multivariate normal distri-bution.SincedistalSNPsare likely tobe independent,wechooseawindow sizeWz and “slide” along the genome, sampling null teststatistics at SNP i conditional on the correlationwith the previousWz SNPs (Han et al. 2009). Specifically, the MVN factors as

fðZ1; . . . ; ZLÞ ¼ fðZ1Þ fðZ2jZ1Þ . . . f ðZLjZL21 . . . Z1Þ� fðZ1Þ fðZ2jZ1Þ . . . f ðZLjZL21 . . . ZL2WzÞ

and we can sample ZijZi21 . . . Zi2Wz via the standard condi-tional MVN

Figure 1 Comparison of the density of the maximum test statistic from local joint testing on the first 1000 SNPs of chromosome 1 in the WT controlsbetween Jester and permutation approaches. In each case 100,000 samples were used. The significance level a corresponding to an FWER of 5% forJester in this experiment was ajester ¼ 4:37e-06 and for the permutation test was apermutation ¼ 4:66e-06: For the purposes of this plot, marginal teststatistics (Z values) and joint test statistics (x2

2) were transformed to x21:

Local Joint Testing 1107

ZijZi21 . . . Zi2Wz ¼ ZijZp � N�Si;pS

21p;pZp; 12Si;pS

21p;pS

⊤i;p

�;

where Si;p is the vector of correlations between SNP i and theconditional SNPs, Sp;p is the Wz 3Wz correlation matrix forthe conditional SNPs, and Zp represents their sampled values.

Each set of sampled marginal null test statistics roughlycorresponds to one genome-wide marginal permutation test.Given these marginal null test statistics, we define a joint-testing window sizeWj and compute the joint null test statis-tics for every pair of SNPs within distance Wj via Equation 1.These inferred joint null test statistics similarly correspond toa permutation test of all SNP pairs within distanceWj of eachother. With these sampled null test statistics in hand, com-puting the significance threshold is straightforward. Formoredetails, see Algorithm 1 (Appendix), which takes as an input adesired FWER and number of samples (roughly analogous tothe number of permutations), a window size, and a set ofjoint tests T and outputs a multiple-testing corrected signifi-cance level corresponding to the desired FWER. To verify thatour method produced results equivalent to those of a permu-tation test, we performed a permutation test of local jointtesting with a window size of 100 SNPs on the first 1000SNPs of chromosome 1 (�10 Mb) in the wild-type (WT)control group. We find that the distributions of test statisticsunder the null for Jester and permutation approaches areconcordant and that the significance thresholds correspond-ing to an FWER of 5% are nearly identical (Figure 1).

With the multiple-testing correction in hand, the localjoint-testing procedure is a straightforward modification tothe standard genome-wide association studies (GWAS) pro-cedure. We choose a window size Wj and correlation cutoffr2min and fit the two-SNP LRT for every pair of SNPs exceedingcorrelation r2min within Wj markers of each other (Algorithm2, Appendix). This procedure is implemented in a pythonpackage called Jester (github.com/brielin/Jester).

Filtering false positives

Lee et al. (2010) describe an issue where genotyping errorsthat would go unnoticed in standard quality control (QC)procedures can cause inflation in joint and conditional testsof association. When SNPs are highly correlated, miscalledbases in only the cases or controls induce rare haplotypes. Asthese haplotypes are present only in the cases or controls, thisincreases the association signal in the joint test (Lee et al. 2010).

While performing our analysis, we found many highlycorrelated ðjrj. 0:9Þ pairs of SNPs where neither SNP hadsubstantial marginal signal but together they showed an ex-tremely strong association. We accounted for this in twoways: first, we considered only associations arising from pairswith correlation ,0.9, and second, we used imputationagainst 1000 genomes to reanalyze jointly significant geno-typed SNPs. Specifically, for each pair of potentially signifi-cant SNPs, we used the -pgs flag of Impute2 to hold out thegenotyped SNPs and replace them with values imputed fromthe surrounding SNPs. We then recomputed the test statistic,

using the imputed values of the SNPs. When the signal was atrue association, the joint test statistic remained significantafter pgs imputation (Supplemental Material, Table S2).However, when the association appeared to be driven bygenotyping error, the joint test statistic became insignificantafter pgs imputation (Table S7). In this way, we overcome thefalse positive error identified by Lee et al. (2010).

Data sets

We analyzed the WTCCC phenotypes bipolar disorder (BD),Crohn’s disease (CD), coronary artery disease (CAD), hyper-tension (HT), rheumatoid arthritis (RA), type-1 diabetes(T1D), and type-2 diabetes (T2D). We chose this data setbecause it was one of the first GWAS performed and thephenotypes have been subsequently studied in independentlarge-scale GWAS. Thus, we emphasize the potential of earlydiscovery of true effect leveraging nonstandard GWAS meth-ods. We used a window size of Wz ¼ Wj ¼ 100 SNPs for es-timating the null distribution and a correlation cutoff ofr2min ¼ 0 (all pairs in the window). We performed standardQC on the data, removing individuals with missingness. 0:1; SNPs with missingness . 0:1; markers failing aHardy–Heinberg equilibrium (HWE) test at significance level0.001, and SNPs with minor allele frequency , 0:05: Thenumbers of cases, controls, and SNPs left after QC for eachdata set are presented in Table S8. To impute the WTCCCcohort, genotypes were split into 1-Mb regions and pre-phased against the 1000 Genomes EUR reference panel, us-ing HAPI-UR, and then imputed using Impute2 against thesame reference panel. Nonbiallelic SNPs and SNPs with ref-erence panel frequency ,5% were not imputed. All imputedSNPs with information score ,0.5 were excluded from furtheranalysis.

We also analyzed gene expression data for 16,155 genes ofthe the gEUVADIS European data set. Raw RNA-sequencingreads obtained from the European Nucleotide Archive werealigned to the transcriptome, using UCSC annotations match-ing hg19 coordinates. RSEM (software tool) was used toestimate the abundances of each annotated isoform and totalgene abundance is calculated as the sum of all isoform abun-dances normalized to 1 million total counts or transcripts permillion (TPM). Genotyping datawere obtained from the 1000Genomes Phase III public release. eQTL mapping was per-formed on a per-gene basis. The cis region of each eQTL wasdefined as all SNPs with minor allele frequency .5% within200 kb of the transcription start site (TSS), which was chosenbecause the vast majority of eQTL are known to be containedin this region (Stranger et al. 2012). Joint tests were per-formed between all pairs of SNPs in the cis region. In eachanalysis, 30 genotype principal components were in-cluded as covariates. Approximate permutation tests fromour sampling procedure with 2500 samples were used toinfer permuted P-values separately for the marginal andjoint approaches, which were then independently ana-lyzed to determine the number of significant genes atFDR 1–25%.


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Data availability

All genotypes andphenotypes used in the analysis are publiclyavailable. Software used to analyze genetic data are availableat github.com/brielin/Jester. Table S1 contains details ofeach locus discovered in the marginal analysis. Table S2 isthe same for Jester with window size 100. Table S3 is thesame for Jester with window size 50 and correlation cutoffof 0.04. Table S4 contains SnipSnip results. Table S5 containsresults of a marginal analysis of imputed WT genotypes. Ta-ble S6 contains imputation analysis as described in the Fil-tering false positives section for pairs reported in the Slavinet al. paper (2011) that passed QC. Table S7 is a sampling offalse positives. Table S8 describes the SNP and sample num-bers remaining in our data sets after QC. Figure S1 containsthe distribution of correlations of significant SNPs discoveredusing Jester. Figure S2 contains the results of running FaST-LMM set on the WTCCC cohort. Scripts used in simulationsare available upon request.

Results

Multiple-testing penalties for WTCCC and power

We computed the multiple-testing correction for local jointtesting in theWTCCC cohort, using Jester for various windowsizes and r2min cutoffs. We define the effective number of tests

(ENT) as the number of independent tests that would corre-spond to a corrected significance level of aC for correspond-ing FWER a. That is, ENT ¼ a=aC: We found that thesignificance level of genome-wide marginal testing at FWER5% was aM ¼ 2:33 1027: We chose to use a window size of100 and r2min cutoff of 0 for our main analysis, increasing theENT by a factor of 19.55 over the marginal test, even thoughwe perform 100 times as many tests ðaJ ¼ 1:1831028Þ: Wechose the window size based on the work of Han et al. (2009)and used no correlation cutoff because our power simulationsshowed an increase in power even in the absence of LD(Figure 2, right). For smaller window sizes and larger cutoffs,the multiple-testing burden decreases substantially. Using amodest r2min cutoff of 0.004, for example, increases the num-ber of tests by a factor of 8.90 over the marginal testðaJ;0:004 ¼ 2:53 1028Þ:

We sought to determine the relative power of local jointtesting vs. marginal testing in the case of (1) two correlatedvariants in LD and (2) a single causal variant. We simulatedpairs of genotypes for 5000 individuals with allele frequency50% and correlation r 2 ½21; 1�:We simulated phenotypes ina linearmodelwith standard normally distributed environmen-tal noise where (1) both SNPs had an effect size of b ¼ 0:1 or(2) only SNP 1 had an effect size of b ¼ 0:1: We used thesignificance thresholds computed above to incorporate the

Figure 2 (Left) Joint testing genome-wide shows a power loss for all correlation structures when only one SNP affects the trait. (Right) Joint testinggenome-wide shows a substantial power gain for anticorrelated SNPs that both affect the trait.











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effect of testing pairs of correlated variants genome-wide. Wefound a substantial increase in power for modest windowsizes and small correlation cutoffs (Figure 2, right) whenthere were multiple causal variants. Using a window size of50 and cutoff of 0.004 led to an increase in power of up to41.0% when there were multiple correlated causal variants,while a window size of 100 and cutoff of 0.0 resulted in anincrease in power of 35.4%. In the absence of multiple causalvariants, the increase in multiple-testing burden and degree-of-freedom penalty gave a decrease in power of 15% and20%, respectively, for the two testing contitions, for all cor-relation levels. Note that while our method shows its mostsubstantial gain when SNPs are linkage masked, we also seeup to a 25% increase in power when the causal variants areuncorrelated.

Significant loci in WTCCC

We analyzed the WTCCC phenotypes, using four differentmethods: (1) marginal tests at an FWER of 5% ð2:33 1027Þ;(2) joint tests with window size 100 and r2min ¼ 0 at thesignificance level estimated by Jester corresponding to anFWER of 5% ð1:183 1028Þ; (3) SnipSnip (Howey and Cordell2014) with window size of 10 SNPs at significance level53 1028; and (4) marginal tests of imputed genotypes atsignificance level 53 1028: Since SnipSnip does not includean analysis of the multiple-testing correction, we chose to useHowey and Cordel’s (2014) suggested significance threshold.

Local joint testing resulted in the discovery of 2.3 times asmanyassociatedSNPsover themarginalmethod, summarizedin Table 1. In Figure S1 we provide a plot of the density of thecorrelation between the pair of SNPs that are genome-widesignificant at FWER 5%, using Jester. These SNP pairs have arange of correlations, but SNP pairs where neither SNP wasdiscovered in marginal testing have higher correlation(signed with respect to opposite-effect directions) than theaverage (Figure S1). The marginal test of genotyped SNPsrevealed 17 significant loci. Jester discovered 7 additional lociwhile missing 2 of the original due to the increased multiple-testing burden, for a total of 22 significant loci. For each ofthese 7 newly significant loci, we searched the NHGRI GWAS

database (Welter et al. 2014) for reported associations andfound that each one had been reported in more powerfuldisease-specific follow-up studies. The significant SNP pairsin 4 of these 7 novel loci were linkage masked, with corre-lations ranging from 0.26 to 0.74 (signed with respect toopposite-direction SNP effects). Interestingly, SnipSnip dis-covered fewer SNPs and loci than the marginal method, butwe emphasize that the set of loci it uncovered is not a strictsubset of those discovered via the marginal method (TableS4). That is, it discovers some new loci while missing somethat are marginally significant and thus remains useful as asecondary analysis tool.

We also compared our method to a GWAS of imputedgenotypes, the current gold standard method. This allows ustodetermine bothhowourmethodcompares in thenumber ofdiscovered loci and whether the linkage-masked loci thatJester uncovered were due to correlated SNPs with oppositetagging of an untyped causal variant. The imputed GWASdiscovered 20 loci in total: the 17 marginally discovered loci,2 of the 7 linkage-masked loci (Table 2), and 1 locus found bySnipSnip but not Jester or themarginal GWAS (CD 18p11.21,Table S4 and Table S5). The 2 loci discovered by both Jesterand imputation (CD 5q31.1 and T1D 10p15.1) were linkagemasked, but the discovery of a significant SNP after imputa-tion implies this was due to opposite tagging of an untypedcausal. Of the remaining 5 loci, 3 (CD 10q21.3, RA 1p36.32,and RA 10p15.1) were uncorrelated, supporting the presenceof multiple causal variants. The final 2 loci (CD 6p21.32 andT2D 9p21.3) were correlated (r ¼ 0:26 and r ¼ 0:51, respec-tively) but did not contain a significant SNP after imputation.We conclude that these loci are strong candidates for follow-up study to validate the presence of linkage masking. Forcomplete details of all associations discovered in eachmethod, see Table S1, Table S2, Table S3, Table S4, andTable S5.

Phenotypic variance explained by two new genome-wide significant associations

We sought to quantify the effect of newly significant SNPs onthe phenotypic variance explained by genome-wide signifi-cant associations. We used GCTA to compute the genetic re-lationship matrix (GRM) for each phenotype, using onlySNPs identified as significant using either the classic marginal-or local joint-testingmethod.We used theGCTA -mgrmmodeto fit a mixed model containing both marginal and jointGRMs and performed a likelihood-ratio test of the full modelagainst a reduced model containing only the marginal GRMto assess statistical significance. We were unable to fit themodel for RA because of numerical issues. For the fourremaining disease phenotypes with genome-wide significantassociations, three (CD, T1D, and T2D) show a statisticallysignificant increase in the phenotypic variance explained,while one (CAD) shows no increase in the phenotypicvariance explained. The increase in phenotypic varianceexplained varies by phenotype, with CD showing a 74%

Table 1 Signficant SNPs and loci for the considered testing methods

Pheno Marg Jester SS Imp Marg Jester SS Imp

BD 0 0 0 0 0 0 0 0CAD 1 1 0 1 16 24 0 96CD 7 8 5 8 58 89 56 587HT 0 0 0 0 0 0 0 0RA 2 4 3 3 6 29 6 88T1D 5 6 3 6 14 82 14 264T2D 2 3 2 2 16 25 24 76Total 17 22 13 20 110 249 100 1111

The left side shows the total number of loci containing genome-wide significantSNPs discovered using standard marginal (Marg), local joint (Jester), SnipSnip (SS),and genome-wide imputation (Imp) testing methods. The right side shows the totalnumber of genome-wide significant SNPs discovered using Marg, Jester, SS, andImp testing methods. For our analysis of T1D and RA, we removed chromosome 6because of the large-effect HLA locus.













increase, T1D showing a 12% increase, and T2D showing a75% increase (Figure 3).

However, the winner’s curse may disproportionally affectjoint testing due to the increased number of tests relative tothe marginal approach. To quantify the effect of the winner’scurse we estimated the out-of-sample phenotypic varianceexplained by genome-wide significant associations for T2D,using European individuals from the Genetic EpidemiologyResearch on Adult Health and Aging (GERA) cohort (detaileddescription of the cohort and study design can be found indbGaP, study accession no. phs000674.v1.p1). Of the 16marginally significant SNPs present in WTCCC, 5 were alsopresent in GERA. Of the 250 joint significant SNPs present inWTCCC, 65 were also present in GERA. In the GERA analysis,we estimated the phenotypic variance explained by those setsof SNPs as the coefficient of determination (R2) in a linearregression of the marginal and joint SNP sets against the T2Dphenotype. We found that the variance in liability explainedin GERA for the marginally significant SNPs was 1.03%(0.07%), and the variance in liability explained in GERA forthe joint significant SNPs was 1.52% (0.11%), an increase of46.6% (P ¼ 0:0049 for an LRT of the joint andmarginal SNPsagainst just the maginal SNPs). Therefore we conclude thatthe winner’s curse does affect in-sample estimates, but theincrease in variance explained due to linkage-masked vari-ants remains substantial.

gEUVADIS eQTL analysis

We compared the number of genes containing an eQTL at anFDR of 1–25%, using standard marginal linear regression ofall cis-SNPs against joint tests of all cis-SNPs (Table 3). Atan FDR of 5%, we find that 5641 of 16,155 genes containan eQTL using the marginal test, and 6248 genes contain aneQTL using the joint test, an increase of 10.7%. As in ouranalysis of the Wellcome Trust data, the genes discoveredusing the marginal approach are not a strict subset of thosediscovered using the joint approach. For each level of FDR,we determined the proportion of genes uncovered in the jointbut not marginal approach that appear to be linkage masked.At FDR 5%, the joint-testing approach discovers 908 newgenes. In 381 of those 908 genes the significant SNP pairshave a correlation of .0.2 signed with respect to opposite-direction SNP effects (Table 3). In Figure S1we provide a plot

of the density of the correlation between the pair of SNPs inthe most significant pair for each gene containing an eQTL atFDR 5%, using Jester. These SNP pairs have a range of corre-lations, but SNP pairs in genes without an eQTL discovered inmarginal testing have higher correlation (signed with respectto opposite-effect directions) than the average (Figure S1).

Discussion

In this work we described a local joint-testing procedure, itsmultiple-testing correction, the genetic architecture forwhichit is well powered, a system for reducing susceptibility togenotyping error, and implications for phenotypic varianceexplained from GWAS SNPs. We have shown that when lociharbor multiple causal variants, the joint test can outperformthe marginal test substantially. We observed that our methodoutperforms the standard marginal association method, pro-viding further evidence that disease loci frequently harbormultiple causalmutations. In our simulations,wefind that thelargest power gains come from linkage-masked SNPs: whenSNPs have opposite-effect direction but are correlated in thestudy population. Furthermore, 4 of the 7 (57%) newlysignificant WT loci have the aforementioned property and381of the 908 (42%)newly discovered eQTL at FDR5%showevidence of linkage masking. This finding is weakened onlysomewhat by the fact that 2 of the 4 linkage-masked loci inWTCCC appear to be type 2 linkagemasking, correlated SNPswith opposite tagging of an untyped causal, while the remain-ing 2 appear to be type 1 linkage masking. Still, we observeincreased power due to detection of linkage masking in allaspects of our analysis. The Bulmer effect implies linkagemasking should be common; high-fitness haplotypes are ableto resist selective pressures andmay acquire fitness-decreasingmutations without being eliminated from the population.SNPs of this kind are hypothesized as a source of missingheritability by Haig (2011) and Lappalainen et al. (2011)argue that gene expression data support widespread linkagemasking due to balancing selection.

We find more evidence for linkage masking in the regula-tion of gene expression that in the complex disease pheno-types we consider. However, it is not surprising that sucheffects are more difficult to find in a genotyped cohort. Asthe effects of such SNPs are already masked, the tagging SNP

Table 2 Loci that were not significant in the standard marginal approach but became significant using Jester

Marginal Jester Imputation

Disease Locus SNP PV SNP1 SNP2 r PV SNP PV

CD 5q31.1 rs6596075 5.97E-07 rs6596075 rs273913 0.32 9.34E-09* rs6897597 3.22E-8*6p21.32 rs9469220 9.09E-07 rs9469220 rs12524063 0.26 2.81E-10* rs210194 3.359E-610q21.3 rs10761659 2.82E-07 rs10995271 rs10995271 0.01 3.02E-09* rs10761659 1.88e-07

RA 1p36.32 rs10910099 3.09E-06 rs12027041 rs10910099 0.0 1.02E-09* rs867436 4.795e-0710p15.1 rs2104286 7.31E-06 rs1570527 rs2104286 0.03 3.71E-09* rs2181623 5.182e-05

T1D 10p15.1 rs2104286 8.28E-06 rs12722489 rs2104286 0.74 1.17E-08* rs12722563 6.39E-09*T2D 9p21.3 rs523096 2.49E-04 rs10757283 rs10811661 0.51 3.36E-09* rs12555274 1.877e-07

r indicates correlation of SNPs signed with respect to opposite-effect direction. Results at these loci from imputation against 1000 genomes are also reported. P-values (PV)that are significant for a particular testing method are denoted by an asterisk. References for articles reporting significant associations at these loci can be found in Table S2.





pair must be in tight LD with the causal SNP pair to preventsevere power loss. On top of this, the tagging SNPpairmust behighly correlated to achieve the increased signal necessary tofind linkage-masked SNP pairs. Hemani et al. (2013) make asimilar argument, showing that small reductions in LD canresult in dramatic underestimation of epistatic effects. Whilelinkage-masked SNPs are difficult to uncover using standardmarginal association methods, their signal is included inmixed-model SNP heritability estimates. These SNPs aretherefore a source of hidden heritability: the difference be-tween the phenotypic variance explained by genome-widesignificant associations and the phenotypic variance explainedby genotyped variation. This is in contrast to the missingheritability, the difference between the variance explained bygenotyped variation and the total narrow-sense heritability,which is unaffected by linkage masking. Our result narrowsthe hidden heritability gap by discovering new associationsthat increase the variance explained due to statistically sig-nificant associations.

Our approach is not without drawbacks. When causalvariants are sparse, we see a reduction in power due to thedegree-of-freedom and multiple-test correction that reapsbenefits only in the presence of multiple signals. While ourresults indicate this is a less common situation, there are two

loci discovered by a marginal GWAS but not by Jester (TableS1). Additionally, it can be difficult to distinguish heavy link-age masking from genotyping error. In our analysis of theWTdisease associations, we used a window size of 100 SNPs,chosen based on results from Han et al. (2009). A logicalquestion is whether a larger or smaller window size wouldlead to more results. We repeated the analysis with a windowsize of 50 and a correlation cutoff of 0.04 and discovered thesame number of loci and slightly more SNPs than presentedhere (Table S3).

The relationship between joint testing and set testing(Ionita-Laza et al. 2013; Listgarten et al. 2013) remains aninteresting avenue for further investigation. Set testing and

Figure 3 The heritability of liability due to genome-wide significant marginal associations (dark blue) plus additional heritability explained by genome-wide significant joint associations (light blue). Error bars correspond to the standard error of the heritability estimates. In all cases but the T2D GERA,P-values correspond to the likelihood-ratio test of the linear mixed-model fit with both marginal and joint GRMs against the linear mixed-model fit onlywith the marginal GRM. In the T2D GERA case, the P-value corresponds to a likelihood-ratio test of the linear model fit with joint and marginalsignificant SNPs against the model fit with only marginally significant SNPs.

Table 3 Joint testing pairs of cis-SNPs improves the number ofeQTL detected at FDR 5% by 10.7%

FDR 1% 2% 3% 4% 5% 10% 15% 20% 25%

Marg 4528 4936 5240 5458 5641 6432 7072 7600 8123Joint 4884 5376 5726 6015 6248 7206 7947 8625 9277New 597 698 781 850 908 1113 1263 1431 1565LM 276 303 334 358 381 473 566 634 701

Many of the new genes (row “New”) discovered using the joint test appear to belinkage masked (row “LM”), with correlation between the significant SNP pair.0.2.





joint testing are similar in that they (1) both improve powerto detect associations in the presence of multiple causal var-iants, (2) both are susceptible to false positives due to geno-typing error and population structure, and (3) both requirean explicit estimation of the multiple-testing correction tomaintain the desired FWER. We consider one recent set test,FaST-LMM-set (Factored Spectrally Transformed LinearMixed Models), which has shown desirable properties withrespect to previous set tests (Casale et al. 2015). FaST-LMM-set without a background kernel is equivalent to a likelihood-ratio test of the SNPs in the set against a null model, while ourtest is a likelihood-ratio test of pairs of SNPs. We used FaST-LMM-set to analyze the WTCCC data set, using 100-SNPwindows, the same size used in our analysis, but found con-cerning levels of inflation in the test statistics that we wereunable to resolve (Figure S2). In addition, set tests currentlyrequire expensive permutation tests to control the FWER,making genome-wide application computationally intensive(Casale et al. 2015). We view approximating the multipletesting correction of set testing without resorting to permu-tations as an interesting open problem and believe that it maybe possible to extend the MVN framework to set tests in thesame way we have done for joint tests. We hope to explorethis connection thoroughly in future work.

Yang et al. (2012) propose a mathematically similar ap-proach to ours, determining joint test statistics frommarginalsummary test statistics (albeit only at genome-wide signifi-cant marginal loci), while using an external reference panelto estimate the pairwise LD. This approach in combinationwith our multiple-hypothesis correction threshold could pro-vide a way to apply our local method without access to ge-notype data. We caution that our proposed imputation-basedgenotyping error correction method will not be applicablehere and thus high-LD SNPs should be avoided in such ananalysis. Furthermore, the variance of the correlation coeffi-cient estimates can be large even when many hundreds ofindividuals are available in the reference panel (Zaitlen et al.2009), which could lead to false positives. While the refer-ence panel correlations may still be relatively accurate forcontrols from the same population, case individuals are morelikely to harbor many disease-associated mutations and thuswill not match the reference panels as well (Zaitlen et al.2012a,b). Even with these caveats, however, the vast gainin power possible with the increased sample size of summarydata makes this a tempting proposition, and we have imple-mented this method in our software package.

Acknowledgments

We thank Lior Pachter, Ingileif Hallgrímsdóttir, and SangHong Lee for valuable discussion; Anne Biton, Joel Mefford,and Brunilda Balliu for helpful comments on the manu-script; and Nick Furlotte for permission to use SNP toolsfrom pylmm in our software. B.C.B. is supported by theNational Science Foundation Graduate Research FellowshipProgram. N.Z. is supported by National Institutes of Health

(NIH) grant K25HL121295. A.L.P. is supported by NIH grantR03 HG006731. N.A.P. is supported by a Career Indepen-dence Award by the National Multiple Sclerosis Society. Theauthors declare no conflicts of interest.

Literature Cited

Arkin, Y., E. Rahmani, M. E. Kleber, R. Laaksonen, W. März et al.,2014 Epiq—efficient detection of SNP–SNP epistatic interac-tions for quantitative traits. Bioinformatics 30: i19–i25.

Bulmer, M. G., 1971 The effect of selection on genetic variability.Am. Nat. 105: 201–211.

Casale, F. P., B. Rakitsch, C. Lippert, and O. Stegle, 2015 Efficientset tests for the genetic analysis of correlated traits. Nat. Meth-ods 12: 755–758.

Corradin, O., A. Saiakhova, B. Akhtar-Zaidi, L. Myeroff, J. Williset al., 2014 Combinatorial effects of multiple enhancer variantsin linkage disequilibrium dictate levels of gene expression to confersusceptibility to common traits. Genome Res. 24: 1–13.

Eicher, J. D., C. Landowski, B. Stackhouse, A. Sloan, W. Chen et al.,2015 Grasp v2.0: an update on the genome-wide repository ofassociations between SNPs and phenotypes. Nucleic Acids Res.43: D799–D804.

Eichler, E. E., J. Flint, G. Gibson, A. Kong, S. M. Leal et al.,2010 Missing heritability and strategies for finding the under-lying causes of complex disease. Nat. Rev. Genet. 11: 446–450.

Fellay, J., A. J. Thompson, D. Ge, C. E. Gumbs, T. J. Urban et al.,2010 ITPA gene variants protect against anaemia in patientstreated for chronic hepatitis C. Nature 464: 405–408.

Gusev, A., G. Bhatia, N. Zaitlen, B. J. Vilhjalmsson, D. Diogo et al.,2013 Quantifying missing heritability at known GWAS loci.PLoS Genet. 9: e1003993.

Haig, D., 2011 Does heritability hide in epistasis between linkedSNPs? Eur. J. Hum. Genet. 19: 123.

Han, B., H. M. Kang, and E. Eskin, 2009 Rapid and accuratemultiple testing correction and power estimation for millionsof correlated markers. PLoS Genet. 5: e1000456.

Hemani, G., S. Knott, and C. Haley, 2013 An evolutionary per-spective on epistasis and the missing heritability. PLoS Genet.9: e1003295.

Howey, R., and H. J. Cordell, 2014 Imputation without doingimputation: a new method for the detection of non-genotypedcausal variants. Genet. Epidemiol. 38: 173–190.

Ionita-Laza, I., S. Lee, V. Makarov, J. D. Buxbaum, and X. Lin,2013 Sequence kernel association tests for the combined effectof rare and common variants. Am. J. Hum. Genet. 92: 841–853.

Lappalainen, T., S. B. Montgomery, A. C. Nica, and E. T. Dermitzakis,2011 Epistatic selection between coding and regulatory var-iation in human evolution and disease. Am. J. Hum. Genet. 89:459–463.

Lee, S. H., D. R. Nyholt, S. Macgregor, A. K. Henders, K. T. Zondervanet al., 2010 A simple and fast two-locus quality control test todetect false positives due to batch effects in genome-wideassociation studies. Genet. Epidemiol. 34: 854–862.

Lin, D. Y., 2005 An efficient Monte Carlo approach to assessingstatistical significance in genomic studies. Bioinformatics 21:781–787.

Listgarten, J., C. Lippert, E. Y. Kang, J. Xiang, C. M. Kadie et al.,2013 A powerful and efficient set test for genetic markers thathandles confounders. Bioinformatics 29: 1526–1533.

Liu, J. Z., M. A. Almarri, D. J. Gaffney, G. F. Mells, L. Jostins et al.,2012 Dense fine-mapping study identifies new susceptibilityloci for primary biliary cirrhosis. Nat. Genet. 44: 1137–1141.

Patsopoulos, N. A., L. F. Barcellos, R. Q. Hintzen, C. Schaefer, C. M.van Duijn et al., 2013 Fine-mapping the genetic association of



the major histocompatibility complex in multiple sclerosis: HLAand non-HLA effects. PLoS Genet. 9: e1003926.

Pickrell, J. K., 2014 Joint analysis of functional genomic data andgenome-wide association studies of 18 human traits. Am. J.Hum. Genet. 94: 559–573.

Prabhu, S., and I. Pe’er, 2012 Ultrafast genome-wide scan forSNP–SNP interactions in common complex disease. GenomeRes. 22: 2230–2240.

Seaman, S. R., and B. Muller-Myhsok, 2005 Rapid simulation ofP values for product methods and multiple-testing adjustment inassociation studies. Am. J. Hum. Genet. 76: 399–408.

Slavin, T. P., T. Feng, A. Schnell, X. Zhu, and R. C. Elston,2011 Two-marker association tests yield new disease associa-tions for coronary artery disease and hypertension. Hum. Genet.130: 725–733.

Stranger, B. E., S. B. Montgomery, A. S. Dimas, L. Parts, O. Stegleet al., 2012 Patterns of cis regulatory variation in diverse hu-man populations. PLoS Genet. 8: e1002639.

Trynka, G., K. A. Hunt, N. A. Bockett, J. Romanos, V. Mistry et al.,2011 Dense genotyping identifies and localizes multiple com-mon and rare variant association signals in celiac disease. Nat.Genet. 43: 1193–1201.

Udler, M. S., K. B. Meyer, K. A. Pooley, E. Karlins, J. P. Struewinget al., 2009 FGFR2 variants and breast cancer risk: fine-scalemapping using African American studies and analysis of chro-matin conformation. Hum. Mol. Genet. 18: 1692–1703.

Visscher, P. M., M. A. Brown, M. I. McCarthy, and J. Yang,2012 Five years of GWAS discovery. Am. J. Hum. Genet. 90:7–24.

Wang, Z., J. H. Sul, S. Snir, J. A. Lozano, and E. Eskin,2015 Gene–gene interactions detection using a two-stagemodel. J. Comput. Biol. 22: 563–576.

Wellcome Trust Case Control Consortium, 2007 Genome-wideassociation study of 14,000 cases of seven common diseasesand 3,000 shared controls. Nature 447: 661–678.

Welter, D., J. MacArthur, J. Morales, T. Burdett, P. Hall et al.,2014 The NHGRI GWAS catalog, a curated resource of SNP-trait associations. Nucleic Acids Res. 42: D1001–D1006.

Wood, A. R., D. G. Hernandez, M. A. Nalls, H. Yaghootkar, J. R.Gibbs et al., 2011 Allelic heterogeneity and more detailedanalyses of known loci explain additional phenotypic variationand reveal complex patterns of association. Hum. Mol. Genet.20: 4082–4092.

Yang, J., T. Ferreira, A. P. Morris, S. E. Medland, P. A. F. Maddenet al., 2012 Conditional and joint multiple-SNP analysis ofGWAS summary statistics identifies additional variants influenc-ing complex traits. Nat. Genet. 44: 369–375.

Zaitlen, N., H. Min Kang, and E. Eskin, 2009 Linkage effects and anal-ysis of finite sample errors in the hapmap. Hum. Hered. 68: 73–86.

Zaitlen, N., S. Lindström, B. Pasaniuc, M. Cornelis, G. Genoveseet al., 2012a Informed conditioning on clinical covariates in-creases power in case-control association studies. PLoS Genet. 8:e1003032.

Zaitlen, N., B. Pasxaniuc, N. Patterson, S. Pollack, B. Voight et al.,2012b Analysis of case–control association studies with knownrisk variants. Bioinformatics 28: 1729–1737.

Communicating editor: E. Eskin


Appendix

Algorithms

Algorithm 1Method for sampling from the null distribution to determine significance threshold.

Input: significance level a, number of samples n, window size Wz; a set of joint tests T.Output: Significance threshold.Sample marginal test statistics using a conditional normal approximation.Compute the P-values associated to the marginal testsfor Jt 2 T doCompute S ¼ x2

Jt using (1)Compute the P-value associated to SendSort the P-values from all tests performedreturn ð12aÞ3 nth smallest P-value.

Algorithm 2Jester’s GWAS pipeline.

Input: A matrix of genotypes G and a vector of phenotypes Y for N individuals.Output: A set of pairs of variants meeting genome-wide significance.Perform standard QC on G and YEstimate the joint test significance threshold aLJT

for SNP Gi 2 G doTest Gi for association with YJointly test Gi with any of the preceding Wj markers correlated with Gi at level r2min or greaterendreturn SNP pairs with P-value , aLJT :

Proof of Observation 1

Consider the linear models

N:Y � 1J: Y � 1þ Gi þ Gj:

The likelihood-ratio test 2ðLJ 2LNÞ is asymptotically x22 under the null hypothesis of no association. In fact, it is possible to

compute the value of this test statistic directly, without fitting the model against a null phenotype.Observation 1. Let Zi; Zj be the Z-values of test statistics for the SNPs ði; jÞ against a phenotype Y. Let the correlation between Gi

and Gj be ri;j: Then the likelihood-ratio test statistic for the model J against the null N is

x2J ¼ 112 r2i; j

�Z2i þ Z2j 2 2rijZiZj

�

and is asymptotically x22 distributed.

Proof. The equality follows from setting up the normal equations and solving them. Let X be the N3 3 matrix of regressorsX ¼ ð 1!jGijGjÞ: Assume that in the linear model Y ¼ Xbþ e; the distribution of the error terms is e � Nð0;s2Þ: Then thenormal equations for the b-coefficients are

b ¼ ðX⊤XÞ21X⊤Y :

Solving this and simplifying yields

0@

b1bibj

1A ¼

0

N3

D

�rY ;i 2 rijrY ;j

�

N3

D

�rY ; j2 rijrY ;i

�

0BBBBB@

1CCCCCA;


where

D ¼ N3�12 r2ij�

is the determinant of X⊤X:The log-likelihood for a linear model is L ¼ 2 ð1=2s2ÞPN

i¼1ðYi 2b⊤XiÞ: Using the above calculation of b, we can find themodel log-likelihoods and compute the likelihood ratio

LN ¼ 2N2s2

LJ ¼ 2N2s2

�12 2rY ;ibi 2 2rY ; jbj þ b2

i þ b2j þ ri; jbibj

�

x2J ¼ 2ðLJ 2LNÞ:

Simplifying the above yields

x2J ¼ Ns2

112 ri; j

�r2Y ;1 þ r2Y ;2 2 2ri; jrY ;1rY ;2

�

¼ 1�12 ri; j

��Z2Y ;1 þ Z2Y ;22 2ri; jZY ;1ZY ;2

�:

Thus, given the marginal test statistics and the sample correlation of the genotype pair, we can compute the joint test statisticunder the null without computationally fitting themodel (similar results derived in other contexts can be found in Seaman andMuller-Myhsok 2005 and Yang et al. 2012). This, when combined with MVN sampling of the marginal test statistics, allows asubstantial speedup over a permutation test.

While the above is derived in the context of a continuous disease phenotype, it is straightforward to conclude that theframework is extensible to case–control (binary) phenotypes. While we assumed for simplicity the phenotype was standard-ized, the result is independent of the scale of Y and thus holds for the diseases on the underlying liability scale. Since the least-squares model does not rely on the assumption that the error terms are normally distributed (only that they are spherical), theresult extends to logistically distributed residuals (logistic regression). In this case the b’s are log-odds ratios.


GENETICSSupporting Information

www.genetics.org/lookup/suppl/doi:10.1534/genetics.116.188292/-/DC1

Local Joint Testing Improves Power and IdentifiesHidden Heritability in Association Studies

Brielin C. Brown, Alkes L. Price, Nikolaos A. Patsopoulos, and Noah Zaitlen

Copyright © 2016 by the Genetics Society of AmericaDOI: 10.1534/genetics.116.188292

0.0

0.5

1.0

1.5

2.0

2.5

-0.5 0.0 0.5

Density

-0.5 0.0 0.5Correlation

Association typeall

new

Wellcome Trust gEUVADIS

Figure S1: (left) Density of the correlation between SNPs in pairs that are genome-wide significant atFWER 5% in the Wellcome Trust dataset, with all pairs of significant SNPs in light blue and just thoseSNPs discovered using jester in dark blue. (right) Density of the correlation between SNPs in the mostsignificant pair for each gene containing an eQTL pair at FDR 5% in the gEUVADIS dataset, with all pairsfrom genes with significant eQTLs in light blue and just those eQTL’s discovered using jester in dark blue.

A ) B ) C )

D ) E ) F )

G ) H ) I )

Figure S2: Q-Q plots of the results of FaST-LMM on the WTCCC dataset. (A) Control-control analysis,15.6% of sets have a p-value of less than 0.10. (B) Bipolar disorder, 18.4% of sets have a p-value of lessthan 0.10. (C) Coronary artery disease, 13.4% of sets have a p-value of less than 0.10. (D) Crohn’s disease,16.5% of sets have a p-value of less than 0.10. (E) Hypertension, 13.4% of sets have a p-value of less than0.10. (F) Rheumatoid arthritis, 14.2% of sets have a p-value of less than 0.10. (G) Type-1 diabetes, 13.7%of sets have a p-value of less than 0.10. (H) Type-2 diabetes, 14.7% of sets have a p-value of less than 0.10.(I) Bipolar disorder with leave-one-chromosome-out GRM background kernel, 15.4% of sets have a p-valueof less than 0.10. In all cases we used 100-SNP sets. In (A) through (H), we used a likelihood ratio testwith 10 permutations per set and no background kernel. In (I), we used the sc davies score test to improvespeed with the background kernel present. In some cases, λGC is 0 because permutation tests result in morethan half of the sets having a p-value of 1.0.

Table S1: Loci containing a marginally significant SNP at the 0.05 level after correction for genome-wide multiple testing (p < 2.18e-7). (.xlsx, 9 KB)

Available for download as a .xlsx file at:


Table S2: Loci significant in the WTCCC consortium at level 0.05 after correction for multiple testing of all SNPs with their 100 closest neighbors. (.xlsx, 14 KB)



Table S3: Loci significant in the WTCCC consortium at level 0.05 after correction for multiple testing of all SNPs with their 50 closest neighbors and a correlation threshold of r^2<0.04. (.xlsx, 13 KB)



Table S4: Results of running SnipSnip on the WT disease cohort using the default parameters. (.xlsx, 10 KB)



Table S5: Replicated loci found in a GWAS on WTCCC variants imputed to 1000 genomes. (.xlsx, 10 KB)



Table S6: Loci reported as significant in Slavin et al Hum Gen 2011. (.xlsx, 9 KB)



Table S7: A sample of loci which appeared to be false positives in our dataset. (.xlsx, 10 KB)



Table S8: The number of SNPs and samples in our WTCCC analysis after QC. (.xlsx, 8 KB)



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Local Joint Testing Improves Power and Identifies Hidden ... · *Department of Computer Science, University of California, Berkeley, California 94720, †Harvard T. H. Chan School