Background. Genome-wide association studies have succeeded in detecting novel common variants which associate with complex diseases. As a result of the fast changes in next generation sequencing technology, a large number of sequencing data are generated, which offers great opportunities to identify rare variants that could explain a larger proportion of missing heritability. Many effective and powerful methods are proposed, although they are usually limited to continuous, dichotomous or ordinal traits. Notice that traits having nominal categorical features are commonly observed in complex diseases, especially in mental disorders, which motivates the incorporation of the characteristics of the categorical trait into association studies with rare and common variants.Methods. We construct two simple and intuitive nonparametric tests, MIT and aMIT, based on mutual information for detecting association between genetic variants in a gene or region and a categorical trait. MIT and aMIT can gauge the difference among the distributions of rare and common variants across a region given every categorical trait value. If there is little association between variants and a categorical trait, MIT or aMIT approximately equals zero. The larger the difference in distributions, the greater values MIT and aMIT have. Therefore, MIT and aMIT have the potential for detecting functional variants.Results.We checked the validity of proposed statistics and compared them to the existing ones through extensive simulation studies with varied combinations of the numbers of variants of rare causal, rare non-causal, common causal, and common non-causal, deleterious and protective, various minor allele frequencies and different levels of linkage disequilibrium. The results show our methods have higher statistical power than conventional ones, including the likelihood based score test, in most cases: (1) there are multiple genetic variants in a gene or region; (2) both protective and deleterious variants are present; (3) there exist rare and common variants; and (4) more than half of the variants are neutral. The proposed tests are applied to the data from Collaborative Studies on Genetics of Alcoholism, and a competent performance is exhibited therein.Discussion. As a complementary to the existing methods mainly focusing on quantitative traits, this study provides the nonparametric tests MIT and aMIT for detecting variants associated with categorical trait. Furthermore, we plan to investigate the association between rare variants and multiple categorical traits. The recent outcome of genome-wide association studies (GWASs) has been successful in detecting many common single nucleotide polymorphisms (SNPs) that associate with diseases. However, just a small part of heritability can be explained by these common variants (CVs) for most diseases. This spurs more people to find rare variants (RVs) associated with complex diseases. Some studies have already shown that RVs are very important for explaining missing heritability , 2014. Rγ), which summarize the sum test and the sum of squared score test. As the power of a SPU(γ) test depends on the selection of γ while the best choice of γ depends on the unexplored true relationship for RVs. Multiple SPU tests are combined by adaptive SPU (aSPU) test. Functional linear models or generalized functional linear models (GFLM) combine genetic variant positions and transform discrete genetic data to genetic variant function to detect gene respectively associated with binary or quantitative traits  , 2007 coe traits , 2014. Ke traits , 2015 deThe above mentioned existing methods are usually applicable to the dichotomous  or continuous trait. In practice, there exist categorical traits for complex diseases, especially in mental disease studies. It is apparent that this kind of data cannot be treated as dichotomous or continuous. In this regard, the conventional likelihood based methods can be employed to detect the association between genetic variants and a categorical trait. For example, the baseline-category logit model , 2012 cam genetic variants, there are 3m probable realizations of genotype patterns. Therefore, utilizing genotype patterns is not very appropriate, especially when common variants are presented in this gene or region or the number of genetic variants is great.It is usually not easy to know if the baseline-category logit model could fit the observed data well. In this situation, we want to develop a nonparametric test which is free of models while having the decent power results. Mutual information, a commonly used measure in information theory, is probably a right tool to gauge the dependence between two random variables. In GWASs, some methods based on mutual information have been proposed for feature selection utilizing the genotype patterns of one or multiple variants , 2010. FWe propose the mutual information based test (MIT) and adjust one (aMIT) to detect the association between multiple genetic variants and a categorical trait, which are intuitive and easily implemented. More importantly, the relative distribution of genetic variants is across all sites, not based on genotype patterns of each site. Through a range of simulation studies with varied combinations of the numbers of variants of rare causal (RC), rare non-causal, common causal (CC), and common non-causal, deleterious and protective, various minor allele frequencies (MAF) and different levels of linkage disequilibrium (LD), we demonstrate that our methods have higher power than the existing ones in terms of detecting functional variants. The robustness of the proposed test statistics to the proportions of alleles of rare to common, causal to non-causal, deleterious to protective, and linkage disequilibrium amount from weak to strong, is also shown in the simulation results. To further manifest the benefit of the proposed tests, we apply them to the data from the Collaborative Study on the Genetics of Alcoholism (COGA) which focuses on detecting ethanol-associated genes. The outputs show that MIT and aMIT are effective and powerful for dealing with the categorical trait.n independent individuals and a candidate gene or region of interest harboring m > 1 genetic variant sites. Let ith individual, where Xij being 0, 1, or 2 is the copy number of the minor allele at the jth site . Meanwhile, assume that there are a total of K categories for a categorical trait and let Yi ∈ {1, 2, …, K} denote the trait value of the ith individual. So the observed are Let us first introduce the notations used in this paper. Consider it model , 2012 caYi being k given genotype i = 1, …, n. The counts of each of the K categories of Yi can be regarded as a multinomial distribution with probabilities K − 1 logits, where m variants on the kth logit. The null hypothesis of no association between the genotypes and the categorical trait is m and K. Further, we realize through simulation study that the calculation of maximum likelihood estimates of the effect sizes is hard for the full model when there are a big proportion of rare variants. Therefore, we focus on the Score test in the remainder of this paper. See the Let line one , 2012 anχ2 distribution with m(K − 1) degrees of freedom, which implies that the power would be becoming low for big m and K. On the other hand, the Score test depends on the model itself and in practice it is not easy for us to judge if the baseline-category logit model could fit the data properly. Therefore, the nonparametric method is appealed and expected to be effective in detecting genetic variants associated with the categorical trait. Notice that the coexistence of alleles of causal with non-causal, common with rare, deleterious with protective, is a norm in practice and should be adequately addressed in constructing such test statistic, and various levels of linkage disequilibrium should also be incorporated into study.The asymptotic distribution of the Score test statistic under the null hypothesis is a B, aSPUB, GFLMB and KLTB, respectively. For GFLM test, we use B-spline to approximate genetic variant function and utilize Rao’s score test which performs well as shown in B-spline of order 4.As SKAT-O , 2012, aY = Y1, …, Yn and the multi-site genotypes {Xij, 1 ≤ i ≤ n, 1 ≤ j ≤ m} of the n individuals, j, j = 1, …, m, and m sites being considered. Let us introduce a discrete random variable S to describe the distribution of “frequencies” across the region of interest as follows: P(S = j) > 0 for every j. Similarly, for the individuals having categorical trait value of k , j and the overall m sites, which leads to the following conditional distribution I(⋅) is the indicator function.Next we begin to construct the nonparametric test statistic for association study between multiple genetic variant sites and a categorical trait. For the observed categorical trait m genetic variant sites, then the difference among the K + 1 distributions as defined in S and the conditional distribution of S|Y = k, i.e., KL, k = 1, …, K, and then summarize these differences by the following weighted sum S, Y). In fact, MI is the mutual information, a commonly used measure in information theory to capture the amount of information in a set of variables and gauges the dependencies among them. Let MIT be the nonparametric test based on statistic MI, which is the expected divergence between the conditional distribution of S|Y and unconditional distribution of S with respect to Y.Generally, if there is no association between the trait and the S and Y are independent, then MI = 0. If S depends on Y weakly, then the conditional distribution of S|Y is close to the unconditional distribution of S, which leads to a relatively small value of KL and so the MI. Alternatively, a relatively large mutual information MI could imply some dependencies between S and Y. Therefore, it is reasonable to use MIT as a test to detect the association between the categorical trait Y and m genetic variant sites.It can be concluded that if As Kullback–Leibler divergence is not symmetric, we propose the following adjusted test statistic: S, Y) based nonparametric test is denoted by aMIT. One feature of aMI observed from its expression is that every summand is positive whether P(S = j|Y = k) > P(S = j) or P(S = j|Y = k) < P(S = j).and the aMI statistic is p-values reported in the next section are calculated in this fashion. In the simulation study, we generate the data from a baseline-category logit model and then repeat the above procedure to obtain a p-value pr) or 1  depending on the corresponding MAF of the variant, where MAF is selected from a uniform distribution as shown in i = 1, …, n. Note To evaluate the proposed methods and compare their performances with Score, SKAT-O is zero , 2015. With subject with genotype K = 3, and α1 = − log(4) and α2 = − log(3) in the simulation study. To evaluate the type I error rates, we set α = 0.05. For power, we assign various The categorical trait value of the it model , 2012 as 1–4 see , the vecIn scenarios 6 and 8–10, the vectors n = 1,000 individuals is randomly chosen from this pool in each of the R = 1,000 independent replications. We fix B = 1,000 in the permutation procedure for the calculation of p-value.Based on these parameter settings, we simulate a pool of 2,000,000 individuals with known multi-site genotypes and categorical trait. A sample of K of categories to 5 and 8 to make comparison of the test statistics. When K = 5, we assign α1 = − log(2.2), α2 = − log(2.1), α3 = − log(1.5) and α4 = − log(1.2). To evaluate the type I error rates, we set α = 0.05. In scenarios 1–4 , α2 = − log(2.1), α3 = − log(1.5), α4 = − log(1.6), α5 = − log(2), α6 = − log(1.8) and α7 = − log(2.1). To evaluate the type I error rates, we set α = 0.05. In scenarios 1–4  and K = 8). These tables demonstrate that the estimated type I error rates of all tests are not significantly different from the predetermined nominal level for different LD amounts. As expected, SKAT-OB, aSPUB, GFLMB and KLTB were a little bit less conservative, as can be seen in K = 5) and K = 8).To check the validity of our proposed tests MIT and aMIT, in addition to Score, SKAT-OB, aSPUB, GFLMB and KLTB in different scenarios. Note that SKAT-O, aSPU and GFLM are implemented by using R packages. The power comparison of these seven tests in Simulation 1 is summarized in ρ increases from 0.5 to 0.9, the power results of MIT and aMIT decrease obviously in scenarios 1–4. This illustrates that the discrepancies between distributions of genetic variants given each categorical trait value decrease when the variants are in strong LD structure. In addition, power results of MIT and aMIT are relatively low in scenarios 6, 8, 9 and 10 with only RC variants. According to ρ in almost all scenarios. In strong LD structure, the advantage of aMIT becomes more obvious in scenarios 1–4. We could conclude that aMIT is more appropriate when both common and rare causal variants are present in the region of study.The following results are for the evaluation of the power of the proposed tests MIT and aMIT as well as Score, SKAT-OB, aSPUB, GFLMB and KLTB, they are not the winners for all 10 scenarios and 3 LD structures as expected. In scenarios 6 and 8, the performance of SKAT-OB is better than aSPUB or GFLMB. aSPUB or GFLMB has attracting performance in scenarios 1–5 and 7. The results of power comparison of SKATB and GFLMB are consistent with those in B is always the winner among the four conservative tests. It is not surprising to see that Score test has higher power than KLTB in some scenarios as both the data and Score test statistic are from the same baseline-category logit model, but it has lower power than KLTB in the other scenarios. With the exception of scenario 7 with ρ = 0.5, either MIT or aMIT is the winner among those seven tests. On average, aMIT is superior to MIT in Simulation 1.For the four conservative tests SKAT-OK = 5) and K = 8), and MIT and aMIT tests were almost always the winners. Because the degrees of freedom of the Score test statistic are respectively 4m and 7m (m = 24 or 32), the gap between Score and the winner increases when the number of categories increases. Among the four conservative tests, KLTB performs best when ρ = 0 except scenario 9, but does not have high power in scenarios 4 and 9 with ρ = 0.5 and in most scenarios with ρ = 0.9. SKAT-OB performs better than aSPUB and GFLMB in scenarios 6, 8 and 10. In ρ = 0.9. When ρ = 0 and 0.5, KLTB is the winner among the four conservative tests except scenario 2. aSPUB and GFLMB perform better than SKAT-OB in scenarios 5 and 7.The results of Simulation 2 are shown in ρ = 0.5 and 0.9 in both 75% and 100% cases, but Score is the winner in situation of linkage equilibrium. MIT or aMIT is recommended for the situations in which multiple sites in a region are in, weak or strong, LD.The results of Simulation 3 are shown in It is demonstrated for the most situations in This study was designed to locate the specific genes influencing a person’s likelihood of developing alcoholism. There are a total of 1,945 subjects in the COGA data which contain 1,594 ones in Health Research group and 351 ones in Alcoholism and Related Conditions group. All subjects were tested through the Semi-Structured Assessment for the Genetics in Alcoholism , 1994.Genotyping was sequenced by the Illumina Human 1M DNA Analysis at the Center for Inherited Disease Research. The sequence data contain 1,072,820 SNPs in 18,946 genes on all chromosomes. There are 32 subjects for which phenotypes are released, but no genotype data is available, so they are removed in the subsequent analyses. After removing variants that have no sequence variation , there are 17,868 genes on autosomes with 1,913 subjects.http://www.ncbi.nlm.nih.gov/projects/gap/cgi-bin/study.cgi?study_id=phs000125.v1.p1through dbGaP accession number phs000125.v1.p1. A number of researchers involve in this study and they analyze SNP one by one or one whole chromosome or utilize other related traits  = 8 in Using Bonferroni correction of multiple testings, a genome-wide significance of 0.05 requires the http://www.genome.jp/dbget-bin/www_bget?map05034). N-methyl-D-aspartate (NMDA) receptor which is a glutamate receptor and ion channel protein can be dephosphorylated by PP1. DARPP32 (dopamine- and cAMP-regulated phosphoprotein of 32 kDa) is a protein expressed mainly in neurons and restrains PP1. DARPP32 augments NMDA receptor phosphorylation, which adds channel function and offsets acute prohibition about ethanol  and is mainly reflected in the heart, skeletal muscle and the brain , 2012. T ethanol , 2009. P ethanol , 2009.http://www.genecards.org/cgi-bin/carddisp.pl?gene=HIST1H2AIkeywords=HIST1H2AI). The histone octamer contains two molecules of each of the histones H2A, H2B, H3 and H4, around which the DNA wraps .The brain could be affected by alcoholism which results in tolerance and dependence. Moreover alcoholism will have a serious harmful effects in other organs. PPIAL4A is a protein-coding gene and associates with liver cancer . Both alcohol abuse and HIV infection are believed to compromise immune function and the nervous system , 2014. Ihttp://www.ncbi.nlm.nih.gov/). From them, we select 202 functional genes which are for human sapiens and are present in COGA data. Top 10 genes detected by aMIT are shown in p-values less than 0.05 for five tests. The counts shown where all ellipses overlap indicate the number of (concordant) genes which are detected by all tests, while the counts that are in only one ellipse denote the number of (discordant) genes that are detected by the corresponding test. The counts of each ellipse for aMIT, Score, SKAT-OB, aSPUB, GFLMB and KLTB tests are respectively 90, 21, 46, 52, 34 and 68. As the Score test only detects 21 functional genes and is excluded in Venn diagram. There are six genes detected by all five tests in For comparison of all tests, we focus on functional genes as shown in literatures. There are a total of 304 genes associated with alcohol dependence based on National Center for Biotechnology Information  ρ = 0.5; (C) ρ = 0.9.Power results of seven tests with 1,000 individuals for trait with five categories. (A) Click here for additional data file.10.7717/peerj.2139/supp-4Figure S2ρ = 0; (B) ρ = 0.5; (C) ρ = 0.9.Power results of seven tests with 1,000 individuals for trait with eight categories. (A) Click here for additional data file.10.7717/peerj.2139/supp-5Figure S3The alcoholism pathway for human from KEGG.Click here for additional data file.10.7717/peerj.2139/supp-6Supplemental Information 1Click here for additional data file.10.7717/peerj.2139/supp-7Supplemental Information 2Click here for additional data file.10.7717/peerj.2139/supp-8Supplemental Information 3Click here for additional data file.10.7717/peerj.2139/supp-9Supplemental Information 4Click here for additional data file.


P‐value threshold. However, P‐values do not account for differences in power, whereas Bayes’ factors (BFs) do, and may be approximated using summary statistics. We use simulation studies to compare the power of frequentist and Bayesian approaches with overlap analyses, and to decide on appropriate thresholds for comparison between the two methods. It is empirically illustrated that BFs have the advantage over P‐values of a decreasing type I error rate as study size increases for single‐disease associations. Consequently, the overlap analysis of traits from different‐sized studies encounters issues in fair P‐value threshold selection, whereas BFs are adjusted automatically. Extensive simulations show that Bayesian overlap analyses tend to have higher power than those that assess association strength with P‐values, particularly in low‐power scenarios. Calibration tables between BFs and P‐values are provided for a range of sample sizes, as well as an approximation approach for sample sizes that are not in the calibration table. Although P‐values are sometimes thought more intuitive, these tables assist in removing the opaqueness of Bayesian thresholds and may also be used in the selection of a BF threshold to meet a certain type I error rate. An application of our methods is used to identify variants associated with both obesity and osteoarthritis.Diseases often cooccur in individuals more often than expected by chance, and may be explained by shared underlying genetic etiology. A common approach to genetic overlap analyses is to use summary genome‐wide association study data to identify single‐nucleotide polymorphisms (SNPs) that are associated with multiple traits at a selected  BMI) > 28 kg/m2) [Wilkin and Voss, FTO [Elliott et al., Multiple health disorders may afflict an individual at any given time, and several such disorders frequently cooccur more often than expected by chance. In contrast, certain pairs of disorders are rarely observed in the same individual, such that the presence of one disease appears to reduce the risk of developing the other. The cooccurrence of complex disorders with a genetic component significantly more, or significantly less, frequently than expected by chance suggests that there might be shared genetic variants that predispose to multiple disorders, or that protect against some disorders while predisposing to others. For instance, there is an increased osteoarthritis (OA) risk of 1.4–1.9 in the obesity class  of Crohn's disease, associated single‐nucleotide polymorphisms (SNPs) were identified in the same intron of CDKAL1 that harbors SNPs associated with type 2 diabetes, and it was shown that the associated alleles for the two diseases are not correlated [Barrett et al., Often summary statistics, rather than raw data, are available when data are shared from multiple studies, and association is often assessed by P‐value significance threshold selected for both studies. In order to test whether the number of significant variants for both traits is more than expected by chance, approximate independence among the SNPs is required so that contingency table methods may be applied. A set of SNPs with low linkage disequilibrium (LD) can be formed by LD pruning. However, when deciding between one of two SNPs in LD to remove, it is usually preferred to retain the SNP with stronger evidence of association with a trait. As there are two traits, this is complicated by the restriction that the same set of pruned SNPs is required for both traits. That is, only one measure of association strength may be considered when deciding the removal of one of two SNPs in LD.Alternatively, the results from the marginal GWAS of each trait may be analyzed in parallel to identify overlapping associated variants based on a BMI and height, SNPs were pruned based on the association metrics of the trait with the larger sample size [Elliott et al., In an overlap analysis of osteoarthritis with P‐values for the two traits at a given SNP.Overlapping loci between schizophrenia and bipolar disorder, between prostate cancer and cardiovascular disease risk factors , as well as between systolic blood pressure and each of several associated phenotypes, were identified by testing individual SNPs using GWAS summary statistics and a genetic pleiotropy‐informed conditional false discovery rate (FDR) method and conjunction FDR [Andreassen et al., A subset‐based approach was proposed for the meta‐analysis of related but distinct traits and has been applied to identify shared risk loci among different cancer types [Bhattacharjee et al., P‐values are used to assess variants for association with two traits (each coming from a different study), any power differences between the two studies are not accounted for. In particular, P‐values are influenced by the same factors that affect power—namely, sample size and minor allele frequency (MAF). Although for a fixed P‐value threshold power to detect a disease‐associated variant increases with sample size, the type I error rate remains the same as the P‐value threshold, irrespective of sample size.When P‐values, a Bayesian approach may be employed, which takes into account the power of the study through the incorporation of the variance of the effect estimate V in the calculation of the approximate Bayes’ factor  [Wakefield, P‐value, the ABF depends on both the usual Wald statistic (z2=β^2/V) and V, whereas the P‐value depends only on the Wald statistic. Therefore, because power is affected by sample size, the ABFs from different study sizes are comparable, whereas P‐values do not account for the differing powers of the tests. Bayesian approaches to analysis are sometimes considered less appealing than P‐values due to their higher level of complexity, but the advantage of ABFs being directly comparable across studies may be crucial when studies of different powers are to be jointly analyzed.Rather than focusing on P‐values and ABFs. This calibration table was necessary in our comparisons of the frequentist and Bayesian approaches for detecting variants associated in two traits, and may also be of more general use when comparing frequentist and Bayesian versions of a method. In addition, the calibration table removes some of the opaqueness of Bayesian thresholds by providing the false‐positive rate for a given Bayesian threshold or may assist in deciding on an ABF threshold to satisfy a certain type I error.To assist in performing comparisons between the frequentist and Bayesian approaches, we have generated a reference table of equivalent thresholds between the two approaches for a range of sample sizes and parameter settings, which acts as a point of reference between ABF approach. We propose a method of overlap analysis when only summary statistic data are available for both traits and, in an extensive simulation study, compare the frequentist and Bayesian approaches to testing for association at a single SNP. In addition to identifying SNPs that have evidence of association in both traits, we test for an excess of overlapping associated SNPs beyond that expected by chance. The proposed methods are applied to the overlap analysis of obesity (Genetic Investigation of ANthropometric Traits (GIANT) Consortium; Berndt et al. [Our primary interest is in the overlap analysis of traits from two different GWAS, of differing sample size and power, as such scenarios are most likely to benefit from an t et al. ) and knet et al. ).In the identification of overlapping SNPs, no assumptions of independence are needed at the SNP or sample level but more restrictive assumptions may be needed when testing for an excess of overlapping signals. In testing for more overlap than expected by chance, we assume that the traits have not been measured on the same individuals, which is likely to hold, because two different studies are of interest. Although we assume independence between the individuals, such that there is not any overlap between the control sets, we found little difference in the results when there was a shared cohort within the controls of our data application.xj, according to a genetic model. For example, in a strict additive model xj = 0,1,2 minor alleles are possessed by the individual at the SNP. Letting β denote the effect estimate at a particular SNP, such that the odds ratio OR = exp(β), the null hypothesis of no effect (H0: β = 0) is compared with the alternative H1: β≠0. The BF compares how likely the observed data are under the two models and is defined byBF values indicate more evidence in favor of H1 over H0; if the data are equally probable under both hypotheses then BF = 1 [Stephens and Balding, In the case‐control setting, each SNP is often tested for association with the trait by fitting a logistic regression to model the probability of disease for an individual as a function of the coded genotype H1) requires specification of a prior distribution for β under H1; this prior distribution reflects the plausibility of the various effect values before observance of the data. The probability under H1 may then be calculated by integrating over all possible values of β, weighted according to the prior distribution. A Normal distribution with mean 0 and variance W is often chosen as the prior distribution for the effect β [Stephens and Balding, BFs with ease.Calculation of Pr, and V= Var (β^)), for each trait an ABF may be calculated at each variant:Z=β^/V,β^∼N,β∼N and 2)N is the prior odds of no association, π0 is the prior probability that there is no association at the SNP, and R = type II error cost/type I error cost. The roles of π0 and R differ, as π0 influences the number of significant associations, whereas R determines the expected number of false discoveries and missed signals [Wakefield, R = 1 and 1 – π0 (the prior probability of an association existing) set to 10−4 – 10−6, so that a genome‐wide threshold for log10BF is between 4 and 6 [The Wellcome Trust Case Control Consortium, The null hypothesis of no association at an SNP is rejected if R greater than 1 indicate that one is in “discovery mode,” and the cost of failing to identify an associated variant is higher than the cost of falsely detecting a null associated variant. For instance, under R = 4, the cost of missing a true signal is four times the cost of misidentifying a null variant as associated. Therefore, when the objective is to obtain a list of candidates for followup, rather than a definitive list of signals, larger values of R are favored.Values of BMI and height, various P‐value thresholds were examined, with a focus on α = 10−3 [Elliott et al., π0 values of 0.99 and 0.999 to reflect that we are not searching for SNPs that are genome‐wide significant in both traits and values of R > 1 such that we are in “discovery mode”; genome‐wide significance would require setting π0 between 0.9999 and 0.999999 [The Wellcome Trust Case Control Consortium, In overlap analyses, a less‐stringent threshold may be considered, rather than requiring genome‐wide significance to be attained at a single variant for both traits. This favors a discovery setting for detecting associations in both traits, which can subsequently be validated in further replication studies. In particular, the focus is on identifying new putative signals for downstream validation, such that more false positives are preferred over more false negatives. For example, in the overlap analysis of osteoarthritis with ABF is calculated with respect to each trait and then tested for association upon selection of π0 and R. Approximate independence is needed among the SNPs in order to rely on contingency table methods for analysis of the distribution of SNPs with high/low ABF (ABF above or below PO/R) over the two traits.Although the proposed analysis may be extended to more than two traits, for ease of exposition we focus on two traits. For each SNP at which there are summary statistic data available for both traits, the ABF* and P* that reflect the strength of evidence for association in both traits. At a given SNP, let ABF1 and ABF2 be the respective ABFs for traits 1 and 2, and let M be the maximum ABF observed at any SNP, for either trait. A Bayesian association metric for pruning may then be defined byI(E) is the indicator function, taking on value 1 when event E = {ABF1 > PO/R and ABF2 > PO/R} holds and 0, otherwise. When selecting between one of two SNPs in LD to remove, the form of ABF* increases the chance of retaining an SNP that has evidence of association with both traits, rather than an SNP that has high evidence strength for one trait, but little evidence for the other trait.In the pruning of the SNPs according to both traits 1 and 2, we create new association statistics P‐values takes a slightly different form as follows:1P and P2 are the respective P‐values for traits 1 and 2, at a given SNP. Although P* is not a proper probability, it serves the purpose of maximizing the retention of SNPs that have sufficiently small P‐values for both traits.The analogous form for ABF* (or increasing P*) for the selected trait and any SNP within 500 kb of the first SNP and in LD (r2 > 0.1) with it is pruned out. Remaining SNPs are pruned out in a similar manner by continuing through the list of ordered SNPs. This is carried out using the clumping algorithm in PLINK version 1.07 [Purcell, SNPs are then ordered by decreasing Purcell, .ABF* and P* are only used for pruning the data so that the SNPs are approximately independent, while simultaneously retaining SNPs that meet the significance threshold for both traits. Examination of association concordance between the traits is based on the individual ABFs (ABF1 and ABF2) and P‐values (P1 and P2) of the studies. In addition, as overlap SNPs are identified based on meeting the ABF  threshold for both traits, the direction of effect does not influence the overlap detection and may be the same or different among the traits.The k if kABF > PO/R (referred to as high ABF) and low evidence otherwise (low ABF). This amounts to testing for SNP conditional independence between high (low) ABF of trait 1 and high (low) ABF of trait 2, where the association within each pair is conditional on the SNP. This is equivalent to testing for equal marginal frequencies between high (low) ABF of trait 1 and high (low) ABF of trait 2, as done by McNemar's mid‐P test [Fagerland et al., P test has been selected rather than McNemar's exact test because it has been shown that the mid‐P test has excellent power and only minor violations of significance level [Fagerland et al., We propose to test for more overlap than expected by chance between the genetic contributions to the two traits by examining the concordance between the levels of association evidence (high or low) at each SNP for the two traits. An SNP is considered to have high association evidence with trait P‐value is calculated by constructing a matched‐pair contingency table . For example, n11 is the number of SNPs that have ABF > PO/R for each of the traits 1 and 2, whereas n10 and n01 correspond to the counts of SNPs that are discordant with respect to the traits and high/low ABF. A similar table may be constructed for P‐values based on significance criteria α. The mid‐P‐value is given byP‐value and n = n01 + n10, the total number of discordant SNPs. This differs from the χ2 contingency table analysis of Elliott et al. [P‐values (columns) and did not account for concordance/discordance at SNPs. A flow chart of the analysis steps proposed here is provided in Figure The mid‐le Table , based ot et al. , in whicP‐values and ABFs and a calibration between the two sets of thresholds is required in order to compare the performance of the approaches.Overlap analyses may be completed using either Bayesian or frequentist approaches to measuring association significance. However, there does not exist a correspondence between PFP) changes with sample size, there is no simple correspondence between thresholds from the two approaches. Thresholds for the Bayesian and frequentist approaches may be calibrated by matching the PFP resulting from each approach. PLINK version 1.07 [Purcell, MAF >0.05.Because the Bayesian proportion of false positives  and a lower α, αL,   set as the PFP for the number of cases in the larger study . The lower α is applied to each study for overlap analysis, and likewise for the upper α. Conceptually, there is simplicity in applying the single ABF threshold to both studies, with an automatic adjustment of type I error rate according to study size. In contrast, the P‐value threshold dictates the type I error rate as identical, irrespective of sample size.For a single GWAS with R, ranging from 1 to 20. Ten different settings for equal‐sized case‐control samples of size 2,000 each up to 100,000 each are considered in the simulations  against a quadratic function of log10(N), where N is the number of cases in the study. QQ plots of the standardized residuals suggest approximate normality, whereas plots comparing the fitted –log10(PFP) values and –log10(PFP) estimates against log10(N) suggest that the regression models appropriately fit the data. Examples of these plots are given in supplementary Figure S1 for R = 2, 15, and 20.As the N each of cases and controls was found to coincide well for case‐control ratios of 1:1.5 or 1:2 and N cases . Therefore, the calibrations provided are likely to be good approximations for case‐control studies where there may be up to twice as many controls.Although the calibration between approaches is based on a 1:1 case‐control ratio, we found that there was little difference in the results for case‐control ratios of 1:1.5 and 1:2, as in the arcOGEN and GIANT studies, respectively. In particular, the calibration based on MAF and effect sizes of the SNP in different studies for various sample size combinations.Power is compared between the frequentist and Bayesian approaches to detect a single SNP that is associated with two traits. The objective is to examine detection of overlap at a single SNP by each approach, and how the powers change with the k has kN each of cases and controls, and the sizes considered are 5,000; 10,000; 15,000; 20,000; and 30,000. For notational convenience we assume 1 < N2N. At a shared causal variant, the MAF is either 0.1 or 0.2 and the OR for each trait is set to each possible combination of OR pairs involving 1.1 and/or 1.2. As the direction of effect does not affect the level of association evidence, we only consider the positive effect direction for both traits.As in the threshold calibration simulations, power approximations are based on 5 million independent SNPs. Various combinations of study sizes for overlap analysis are considered, where study π0 = 0.99 or 0.999 and eight values of R ranging from 1 to 20; an SNP is identified as associated with both traits if ABF > PO/R for both traits and the proportion of such SNPs estimates the power of overlap detection based on ABFs. P‐value levels of significance are selected for a given Bayesian decision rule according to Table 2 and supplementary Table S1, based on R, π0, and N1 (for upper α) or N2 (for lower α); the power for upper α is approximated by the number of SNPs having P‐value <αU for both traits, while power for αL is defined in a similar manner.Bayesian thresholds are determined based on BMI ≥30 kg/m2, while controls have BMI <25 kg/m2. The arcOGEN data had been imputed using the 1000 Genomes CEU haplotypes from the 2010 interim release in NCBI build 37 (hg19) coordinates [The 1000 Genomes Project Consortium, http://genome.sph.umich.edu/wiki/LiftOver) in order to bring the GIANT data to build 37.In the GIANT Extremes obesity meta‐analysis, obesity class I cases were defined as individuals who have MAF >0.05 in the 1000 Genomes CEU population. After LD pruning based on the association metric described in Materials and Methods, the number of SNPs included in the overlap analysis ranged from 88,980 to 91,122, depending on the threshold settings.The GIANT study excluding the 1958 Birth Cohort consists of 32,142 cases and 64,461 controls, whereas arcOGEN has 7,410 cases, and 11,009 controls. There were 2,087,589 SNPs present in both datasets that had BFs have the advantage over P‐values of a decreasing PFP as study size increases, whereas for P‐values the PFP fluctuates near the P‐value threshold α regardless of study size (as expected). The PFP at various R values under π0 = 0.99 is compared in Figure π0 = 0.99 and π0 = 0.999, respectively. There is a general trend of a 0.7‐fold increase in the exponent of the type I error estimates between samples having cases and controls each of size 2,000 and those having 100,000 for each.Here, we empirically illustrate in single‐disease associations that π0 = 0.99, R = 4, the type I error estimates for 8,000 each of cases and controls and for an arcOGEN‐sized study are 1.07 × 10–3 ‐sized study are 5.54 × 10–4  studies, as described in Materials and Methods. For example, when –3 Table  and 1.01–4 Table  and 4.62P‐value threshold for a given Bayesian threshold. The general regression for each parameter setting of R and π0 takes the form −log10(PFP)=β0+β1 lo g10N+β2( lo g10N)2, where N is the number of cases in the study, and occasionally the linear term is removed from the final fitted model, as it is not statistically significant at level 0.05. The coefficient estimates and their standard errors from each of the fitted models are provided in supplementary Table S2, for π0 = 0.99, 0.999 and a range of R values. An estimate of –log10(PFP) for specific values of π0 and R may then be found for a certain number of cases N by referring to the appropriate fitted model and using the coefficient estimates from supplementary Table S2. This is illustrated for case‐control samples of 15,000 each, and PFP estimates at π0 = 0.99 and π0 = 0.999, for a range of cost ratios R, which are provided in Table 2 and supplementary Table S1.When the number of cases is different than the settings considered in the simulations, we use a regression model to determine the analogous R = 20 and π0 = 0.99 in supplementary Table S5. The Bayesian approach consistently attains a higher power than the frequentist method based on the lower P‐value threshold (from larger study), which is too stringent for the smaller‐sized study , upper α,  being slightly lenient for the larger study, the Bayesian approach tends to attain at least the same power  display a higher power gain (up to 4%) for the ABF implementation over the upper P‐value threshold , the P‐value approach with threshold αU either has a lower power than the ABF approach or is greater by a negligible amount  in which the effect size is larger in the smaller sample ; see supplementary Table S5. However, this gain in using the upper α approach is only observed when the smaller study is at most 5,000 each and the larger study has 10,000 each, and the gain dissipates with sample sizes beyond 15,000 (supplementary Table S5).Among the scenarios considered, the one setting that displays a slight power gain (∼2%) for the frequentist over the Bayesian is in a high‐power setting  we compare the proportion of signals detected by ABFs that are not identified by P‐values and vice versa. These conditional proportions indicate that despite similar power differences between ABF and P‐value approaches, the higher‐powered method does not catch a similarly larger proportion of variants than the other; when the ABF approach is higher powered, conditional proportions for ABF‐only detections are larger than conditional proportions for P‐value‐only detections when P‐values have higher power than ABFs.As a single overlap SNP is assumed in each of the 5 million replications, among these true association signals detected by MAF 0.1 and OR 1.1, ABFs identify approximately 99% of the variants detected by either method, based on π0 = 0.99 or 0.999, whereas P‐values identify 92–93% of the variants when π0 = 0.99 and as little as 89.4% when R = 2, π0 = 0.999 . For example, at R = 2, π0 = 0.99 the power advantage with ABFs is a 1.9% increase (supplementary Table S3), but 8.4%  of the detected signals are found only by ABFs, whereas the reverse proportion is 0.26% for signals detected only by P‐values (supplementary Table S6).For two studies consisting of equal‐sized case‐control samples of sizes 10,000 each and 20,000 each, with a shared causal variant having MAF 0.2 in studies consisting of 5,000 each of cases and controls (OR 1.2) and 10,000 each (OR 1.1), the P‐value approach has a general power gain of 2% over ABFs (supplementary Table S5), and the conditional proportions indicate that P‐values only detect 2–4% more variants than ABFs (supplementary Table S6). For instance, at R = 2, π0 = 0.99, the P‐value approach is higher powered by 1.9% (supplementary Table S5), yet 3%  of the identified signals are found only by P‐values, and the complementary proportion for ABF‐only‐detected signals is 0.17% (supplementary Table S6). Similar behavior is observed for the overlap analysis of studies consisting of 5,000 each and 15,000 each, with the proportion of variants detected only by P‐values ranging from 1% to 3% (supplementary Table S6).In contrast, when the causal variant has The proposed methods were applied to the overlap analysis of obesity  are 0.991 and 0.988, respectively, whereas the respective measures are 0.996 and 0.995 when the concordance is measured for the set of common SNPs with a P‐value <0.01 in the full GIANT meta‐analysis.Concordance between the full GIANT study and that with the exclusion of the 1958 Birth Cohort is near 0.99, indicating that the reduction in sample size has little impact on this large meta‐analysis. Specifically, in comparing all SNPs with π0 = 0.99. As in the examination of type I error to detect an association at a single variant in a single study, the marginal type I error estimate for the Bayesian approach is smaller for the larger of the two studies.Based on the sample sizes of the GIANT study excluding the 1958 Birth Cohort and of the arcOGEN study, type I error estimates for the overlap analysis were obtained via a simulation study of 5 million independent SNPs and are compared in Figure ABFs and P‐values, within the merged list of 80 overlap SNPs identified by ABFs  and/or P‐values (0.0065), there were 15 pairs of SNPs in the same LD clump (r2 >0.1 and within 500 kb). The level of LD was then determined for each pair of such SNPs via the software SNAP  are labeled with a double asterisk in Table P‐value < 9 × 10–5) have a single asterisk.The top 20 independent signals that have been identified by each method are provided in Table ABFs and P‐values, the strongest evidence of an overlap association with both obesity and osteoarthritis is a variant in FTO, which is unequivocally associated with adiposity [Fawcett and Barroso, FTO that had been identified by Elliott et al. [r2 = 0.838 with rs12149832) and Panoutsopoulou et al. [r2 = 0.605 with rs8044769), suggesting that they are part of the same signal. Furthermore, two additional independent FTO variants are identified as associated with both obesity and OA, and both variants are ranked higher by ABFs rather than P‐values .For the Bayesian and frequentist approaches, there is 80% agreement in the variants identified within the top five signals, as well as within the top 10 and 20 signals. Among the top 20 P‐values in Table 4 (π0 = 0.99) and supplementary Table S3 (π0 = 0.999). When π0 = 0.99, there is a clear trend of more significant P‐values for the ABF analysis route, whereas the frequentist route counts are not considered to be different from chance at significance level 0.05 at R = 1 for both P‐value thresholds, as well as at R = 2 and 4 for the lower α threshold.We also tested if the number of detected overlap SNPs at various thresholds is more than expected by chance, and display these counts together with their McNemar mid‐αL, log10θ, αU), where θ = PO/R, there is a tendency for an ordering of the counts of identified overlap variants with the number based on ABF strength being between those based on each of the two P‐value thresholds  for a fixed ABF threshold; for a fixed P‐value threshold, tests based on P‐values have identical type I error rates regardless of sample size (and power of the test). In the overlap analysis of two studies with different powers, this ABF approach simplifies the selection of a threshold for use in both studies, rather than choosing a P‐value threshold that is either too lenient for the larger study or too strict for the smaller study.The use of BFs, rather than P‐values. These evaluations focus on identifying shared associations at the SNP level irrespective of any direction of effect. In an overlap analysis of studies consisting of different sample sizes, the Bayesian approach had a consistent power advantage over the more stringent P‐value threshold , and a tendency to attain at least the power of the more lenient P‐value threshold .For the detection of variants associated with two traits, we made extensive comparisons between association strength assessed by BFs and by ABFs and P‐values for a range of sample sizes, as well as a simple means of estimating a P‐value threshold coinciding with a particular Bayesian threshold rule 0, R) in the gene SLC39A8/ZIP8, which has been strongly implicated in OA pathogenesis [Kim et al., FTO whether or not there is a true association with both obesity and OA, there was difficulty in comparing the ABF and P‐value approaches. This was overcome by considering conditional probabilities in our simulation studies.In our overlap analysis of obesity and osteoarthritis, a variant in ABF approach identified a signal, given that this signal was identified by at least one of the methods. Likewise, the analogous probability was examined for P‐values. We found that in scenarios of similar power differences between the approaches, the ABF approach was able to capture a higher proportion of overlapping associated variants than P‐values.In simulation studies under the alternative hypothesis, we considered the probability that the ABF route lends simplicity in threshold selection for studies of different sizes, as the ABF is directly comparable between two studies irrespective of the study size. In contrast, a relatively small P‐value does not have the same meaning in studies of very different sizes.Although Bayesian approaches are sometimes considered less appealing than frequentist, there is a clear advantage when a single threshold is to be used for multiple studies. In particular, the type I error rate is appropriately adjusted for a given Bayesian threshold, such that the type I error is smaller for the larger, more powerful study. The Figure S1: Standardised residual QQ‐plots to assess normality are provided in the left panel for the regression models with R=2 (a), R=15 (c) and R=20 (e). The right panel displays corresponding plots of the estimated values (from simulations) of –log10(PFP) against log10(N) with the fitted –log10(PFP) regression line for R=2 (b), R=15 (d) and R=20 (f).Table S1: Type I error estimates using a Bayesian threshold log10θ, determined from π0 = 0.999 and varying R. Estimates are based on 5 million independent SNPs from equal‐sized case‐control samples, each of size N. Estimates at N=15,000 are the result of a regression at each R value of the PFP estimates against a quadratic of log10N.Table S2: Regression coefficient estimates from model log10(PFP)=β0+β1log10N+β2(log10N)2 together with their standard errors σi. All coefficient estimates have p‐value < 0.01.Table S3: Overlap power results coinciding with Figure 3, where Ni denotes the sample size for each of the cases and controls in study i, ORi denotes the OR of the causal variant in study i, which has the specified MAFTable S4: Overlap power results based on R=20 and π0=0.99 for the ABF threshold and coinciding p‐value threshold (from Table 2) , where Ni denotes the sample size for each of the cases and controls in study i, ORi denotes the OR of the causal variant in study i, which has MAF 0.1.Table S5: Overlap power results for the scenario where the causal variant has MAF 0.2 and a larger effect in the smaller sample: OR1 = 1.2 and OR2 = 1.1. The sample size of each of the cases and controls in study i, is denoted by Ni.Table S6: Probabilities conditional on overlap SNPs detected by ABF or upper α, αU for various values of R and π0=0.99 where probabilities conditional on this set of SNPs are denoted CP.Table S7: Number of overlap variants identified by the ABF (log10θ threshold), according to various R values with π0=0.999 and the corresponding lower and upper p‐value thresholds, based on 30,000 and 8,000 cases, respectively. The McNemar p‐value follows the counts of detected overlap variants.Click here for additional data file.


Genome-wide association studies (GWAS) employing large sample sizes and sophisticated statistical methods have recently yielded detailed information on the set of genes affected in various psychiatric disorders. This is especially important for polygenic, highly heritable disorders such as schizophrenia (SCZ) . The suc+, K+, and Ca2+. In addition, some of the SCZ-linked genes are involved in regulation of the Ca2+ concentration in the intracellular medium, which is another great contributor to neuron excitability. All above aspects of electrophysiology are included in a recent multi-compartmental model of L5PC [2+ spike. In this work, we rely on data from functional genomics studies that describe the effects of variants of certain ion channel or calcium transporter-encoding genes on the channel activation/inactivation properties or intracellular Ca2+ dynamics. We carry out our study by linking these effects to a change in the corresponding neuron model parameters, and observing the implication that these variants have on the information integration in an L5PC.A total of 108 genetic loci were recently confirmed to be associated with the risk of SCZ . These l of L5PC , which ain vitro studies of more extreme genetic variations, including loss of function mutations. A central assumption of this approach is that the effects of SNP variants can be represented as scaled-down versions of those of the more extreme variants, and that the emergence of the full psychiatric disease phenotype results from the combined effect of a large number of subtle SNP effects.It should be noted that information does not generally exist for the effect of single nucleotide polymorphism (SNP) variants identified through GWASs on the biophysical parameters required for the computational models. We instead use information obtained from Our results show a multitude of alterations of the firing behavior and integration of apical stimuli in neurons equipped with the considered gene variants. An especially interesting observation is that the variants affect the suppression of a second apical stimulus, which might have a connection with the deficit in prepulse inhibition, a condition often observed in SCZ patients. Although the analyses presented here are specific to L5PCs and SCZ-related genes, our "biophysical psychiatry" framework may be directly applicable to other cell types and other polygenic diseases, such as bipolar disorder and autism, given an identification of risk genes related to neuronal excitability. Furthermore, our approach could be directly applied to biophysically detailed models of neuronal networks and extended to consider synaptic ion channel-encoding genes that are relevant in SCZ [


Mitochondria play a critical role in the cell and have DNA independent of the nuclear genome. There is much evidence that mitochondrial DNA (mtDNA) variation plays a role in human health and disease, however, this area of investigation has lagged behind research into the role of nuclear genetic variation on complex traits and phenotypic outcomes. Phenome-wide association studies (PheWAS) investigate the association between a wide range of traits and genetic variation. To date, this approach has not been used to investigate the relationship between mtDNA variants and phenotypic variation. Herein, we describe the development of a PheWAS framework for mtDNA variants (mt-PheWAS). Using the Metabochip custom genotyping array, nuclear and mitochondrial DNA variants were genotyped in 11,519 African Americans from the Vanderbilt University biorepository, BioVU. We employed both polygenic modeling and association testing with mitochondrial single nucleotide polymorphisms (mtSNPs) to explore the relationship between mtDNA variants and a group of eight cardiovascular-related traits obtained from de-identified electronic medical records within BioVU.Using polygenic modeling we found evidence for an effect of mtDNA variation on total cholesterol and type 2 diabetes (T2D). After performing comprehensive mitochondrial single SNP associations, we identified an increased number of single mtSNP associations with total cholesterol and T2D compared to the other phenotypes examined, which did not have more significantly associated SNPs than would be expected by chance. Among the mtSNPs significantly associated with T2D we identified variant mt16189, an association previously reported only in Asian and European-descent populations.Our replication of previous findings and identification of novel associations from this initial study suggest that our mt-PheWAS approach is robust for investigating the relationship between mitochondrial genetic variation and a range of phenotypes, providing a framework for future mt-PheWAS. While energy production is the function most often associated with mitochondria, the organelle plays a vital role in other cellular processes including cholesterol synthesis, fatty acid oxidation, ammonia detoxification, calcium homeostasis, and apoptosis, suggesting that mitochondrial dysfunction could have far-reaching effects. Indeed, mitochondrial dysfunction has been observed in a variety of diseases, including amyotrophic lateral sclerosis (ALS)f cancer.Mitochondria maintain their own DNA separate from the nuclear genome. The human mitochondrial genome consists of a double-stranded, circular chromosome spanning 16,569 base pairs. This maternally inherited, compact genome contains 37 genes encoding 2 ribosomal RNAs, 22 transfer RNAs, and 13 protein-encoding genes that are essential components of the oxidative phosphorylation complexes. Rare mutations in mitochondrial DNA (mtDNA) give rise to a spectrum of diseases, including Leber’s Hereditary Optic Neuropathy (LHON), Myoclonic Epilepsy with Ragged Red Fibers (MERRF), Maternally Inherited Diabetes and Deafness (MIDD), and prostate cancer, multiplPhenome-Wide Association Studies (PheWAS) have been used to explore the association between nuclear single nucleotide polymorphisms (SNPs) and a wide array of phenotypes. To date, PheWAS have successfully used electronic-medical record (EMR) data and large population-based survey data-15 to reWhile there has been some research focused on identifying the impact of mtDNA variants on a number of complex traits, this relationship has been primarily explored through association testing with single traits or outcomes. Further work is needed to better characterize the relationship between mitochondrial genetic variation and a wide range of outcomes; this can be done by applying the PheWAS approach. Thus, the goal of this work was to develop a framework for implementing a mitochondrial PheWAS (mt-PheWAS). A method yet to be explored for characterizing the relationship between mitochondrial variation and phenotypes, in a PheWAS context, is the use of polygenic modeling, which cTo test our mt-PheWAS framework, we explored the relationship between mtDNA variation and eight cardiovascular-related phenotypes using Metabochip genotype data from African Americans in the Vanderbilt University biorepository, BioVU. We began with a polygenic approach, employing mixed linear modeling to investigate the overall contribution of mitochondrial genetic variation on trait variance. Single mtSNP association analysis was then performed with all eight traits to identify specific genotype-phenotype associations. Using the polygenic approach we identified two traits with evidence for association with mitochondrial genetic variation. Our single mtSNP association analysis confirmed the correlation between the number of significant mtSNPs observed for each trait and the overall proportion of trait variance explained by mitochondrial genetic variation, suggesting that our proposed mt-PheWAS framework, which includes a phenotype filtering step via polygenic modeling, is a valid approach for investigating the effect of mtDNA variation for a range of phenotypes.The Vanderbilt University Medical Center (VUMC) biorepository, BioVU, contains more than 170,000 individual de-identified DNA samples linked to a de-identified version of the EMR, known as the synthetic derivative. As partIn this pilot PheWAS, we accessed the African American samples in EAGLE BioVU and selected eight cardiovascular-related traits for analysis, including: body mass index (BMI), total cholesterol, high-density lipoprotein cholesterol (HDL-C), low-density lipoprotein cholesterol (LDL-C), triglycerides, mean corpuscular hemoglobin (MCH), T2D, and hypertension. BMI was defined by manually excluding extreme outliers that were likely a result of conversion measure inconsistencies within the EMR. Total cholesterol, HDL-C, LDL-C, and triglycerides were reported in milligrams per deciliter (mg/dL). Mean corpuscular hemoglobin was reported in picograms per cell (pg/cell). To obtain values for each quantitative trait, the median value for each year was determined and then the median of all years was stored as a single value per individual. For all continuous traits, only a single observation within the synthetic derivative was required for an individual to be included in the analysis. Cases and controls for T2D, were defined as previously described, except We performed polygenic analysis using mixed-modeling to determine the overall contribution of mitochondrial genetic variation captured by the Metabochip to the variance of the eight selected traits. By first using polygenic modeling, phenotypes can be prioritized or filtered based on putative contribution of mtDNA variation, assuming that a lack of evidence for influence of mtDNA variation implies a reduced chance of identifying specific single mtSNP associations. Genome-wide Complex Trait Analysis (GCTA), which eFor each trait, GCTA was used to fit a mixed linear model and estimate the proportion of variance explained (PVE) by nuclear and mitochondrial genetic variation. Mixed models consist of fixed and random effects. Here, the fixed effects included age, sex, and the first two nuclear principal components (PCs) as covariates. Eigenstrat was used to generate nuclear PCs from the 192,139 autosomal SNPs that passed QC. The random effect is empirical genetic relatedness, which was estimated using GRMs, created via GCTA, for the nuclear and mitochondrial genomes, using 192,139 and 130 SNPs, respectively.Expectation-maximization (EM), the iterative method for finding the maximum likelihood estimate, was used for restricted maximum likelihood (REML) analysis using GCTA. REML provides estimates of the proportion of trait variance explained by genetic variation in the nuclear and/or mitochondrial genome. A likelihood ratio test (LRT) was performed comparing full and reduced models to determine the significance of mitochondrial genetic variation on the overall mixed linear model for each trait. The likelihood ratio test measures the significance of a specific model component. The full model contained both a nuclear and mitochondrial GRM, while the reduced model contained only a nuclear GRM. Here, we used the likelihood ratio test to evaluate the contribution of mitochondrial genetic variation captured by the Metabochip to the phenotypic variation or risk observed in the selected cardiovascular-related traits.We performed single mtSNP analysis for all traits to determine if filtering based on results from our polygenic analysis was beneficial. We excluded 44 mtSNPs with a minor allele frequency less than 1%, leaving 86 mtSNPs available for the single mtSNP association analysis. PLINK was usedAll eight traits in our analysis had relatively low PVE by nuclear and mitochondrial variation. Nuclear PVE ranged from 0.33% for MCH to 2.95% for triglycerides. Mitochondrial PVE ranged from 0.02% for MCH to 0.33% for total cholesterol Figure . The likThrough polygenic modeling we identified total cholesterol and T2D as key traits and proceeded with an mt-PheWAS to determine if the use of polygenic modeling for phenotype prioritization is robust. Linear and logistic regressions adjusted for age, sex, and the first two nuclear PCs were performed for continuous and binary traits, respectively, to investigate the relationship between single mtDNA variants and all phenotypes in this study  were significantly associated with both total cholesterol and T2D  associated with T2D in our population are common to the African mitochondrial haplogroup L1c. This haThree mtSNPs  significantly associated with increased risk of T2D in our population are found on the L3e1 African mitochondrial haplogroup which has previously been associated with hypertriglyceridemia in black South Africans on anti-retroviral therapy. Given tWhile we were successful in establishing a mt-PheWAS framework for future EAGLE and PAGE I studies, our framework is not without limitations. First, the PheWAS approach, even when applied to large datasets such as EAGLE BioVU, can be limited in sample size and thus potentially power depending on the outcomes included in the study. This mt-PheWAS is no exception as the sample sizes available for analysis varied from 1,338 cases of T2D to 9,559 subjects for MCH. Additional limitations of the PheWAS approach include the high-throughput manner in which phenotypes are defined, and that regression models are only minimally adjusted for standard covariates. Because the mt-PheWAS analyses presented herein were exploratory in nature we did not correct for multiple testing. Further work will be necessary for external replication and validation of these results. Finally, as previously mentioned, this present study is limited to genotypic data from the Illumina Metabochip, a custom array designed for fine-mapping specific GWAS-identified regions previously associated with specific phenotypes identified from mostly European-descent populations. The mitochondrial variants included on the Metabochip are also limited, impacting our ability to determine haplogroups for the samples in this study.We outlined and tested a framework for performing mt-PheWAS to investigate the relationship between mitochondrial genetic variation and a range of phenotypes. We characterized the utility of polygenic modeling as a method for prioritizing phenotypes for PheWAS by performing both polygenic modeling and comprehensive single mtSNP association testing for a group of eight metabolic traits. Further, we identified multiple single mtSNP associations for total cholesterol and T2D. Our data indicate that, despite relatively limited mtSNP coverage, the Illumina Metabochip is useful in identifying mitochondrial genotype-phenotype associations. Our results also demonstrate that the EAGLE mt-PheWAS framework is capable of identifying known genetic associations and has the potential to uncover novel associations contributing to the complex relationship between human health and mitochondrial genetic variation.BMI: Body mass index; DNA: Deoxyribonucleic acid; EAGLE: Epidemiologic architecture for genes linked to environment; GCTA: Genome-wide complex trait analysis; GRM: Genetic relationship matrix; GWAS: Genome-wide association study; HDL-C: High-density lipoprotein cholesterol; LDL-C: Low-density lipoprotein cholesterol; LRT: Likelihood ratio test; MCH: Mean corpuscular hemoglobin; mtDNA: Mitochondrial deoxyribonucleic acid; mt-PheWAS: Mitochondrial phenome-wide association study; mtSNP: Mitochondrial single nucleotide polymorphism; PAGE: Population architecture using genomics and epidemiology; PCs: Principal components; PheWAS: Phenome-wide association study; PVE: Proportion of variance explained; SD: Standard deviation; SNP: Single nucleotide polymorphism; T2D: Type 2 diabetes.The authors have no competing interests to declare.SLM was involved in study conception, design, and coordination, as well as drafting and revising the manuscript. JBH conducted the polygenic analyses and was involved in drafting and revising the manuscript. RJG extracted phenotype data from the synthetic derivative and ran single SNP association analyses. JB and EFE extracted phenotype data from the synthetic derivative. SAP was involved in study design and manuscript revision. WSB assisted in extracting phenotype data from the synthetic derivative and manuscript revision. DC was involved in study conception and design, and manuscript revision. All authors read and approved the final manuscript.Mitochondrial and nuclear PVE and LRT p-values. This table shows data from GCTA, including PVE and SE, for all eight metabolic traits.Click here for fileSNP ID, SNP Location, Regression p-values, and number of significant SNPs. This table shows p-values from regression analysis using PLINK.Click here for file


Although genome-wide association studies have identified over 100 risk loci that explain ∼33% of familial risk for prostate cancer (PrCa), their functional effects on risk remain largely unknown. Here we use genotype data from 59,089 men of European and African American ancestries combined with cell-type-specific epigenetic data to build a genomic atlas of single-nucleotide polymorphism (SNP) heritability in PrCa. We find significant differences in heritability between variants in prostate-relevant epigenetic marks defined in normal versus tumour tissue as well as between tissue and cell lines. The majority of SNP heritability lies in regions marked by H3k27 acetylation in prostate adenoc7arcinoma cell line (LNCaP) or by DNaseI hypersensitive sites in cancer cell lines. We find a high degree of similarity between European and African American ancestries suggesting a similar genetic architecture from common variation underlying PrCa risk. Our findings showcase the power of integrating functional annotation with genetic data to understand the genetic basis of PrCa. Over one hundred loci have been identified to be associated with the familial risk of prostate cancer but the functional effects are poorly understood. Here the authors use single-nucleotide variant and epigentic data to show an underlying genetic architecture marked by histone modification. Family history is a well-established risk factor for prostate cancer (PrCa), which has an estimated heritability of 58%—one of the highest across common cancers234567Recent work form the ENCODE/ROADMAP consortia102Here, we use targeted and genome-wide SNP array data from 59,089 male PrCa cases and controls of European  as implemented in the GCTA softwarei is then estimated as We analysed multiple functional annotations and quantified the fraction of variance in trait explained by SNPs that are localized within each functional class. Our approach models the phenotype (PrCa) of a set of individuals as being drawn from a multivariate normal distribution with variance components estimated based on genetic data  plus an environmental term (see Methods)13The variance component model has previously been shown to yield robust estimates under the assumption that causal variants are typed and uniformly sampled from a given component1320Our primary functional analyses focus on the densely genotyped iCOGS sample , whose large sample size allowed for highly accurate estimates of component-specific P=2.6 × 10−16 by Z-test), whereas the variants near normal-specific ARBS explained 0.0% of the P=0.11 by Z-test) (P=4.4 × 10−7 for difference by Z-test)  directly in primary human tissue  Z-test) . The dif Z-test) . This diNext, we looked for marks that contribute to the heritability of PrCa across a broad spectrum of functional annotations without prior assumptions on relevance to disease. We investigated 544 epigenetic annotations spanning six major classes , which localized 22% of the total P=2 × 10−18 by Z-test; 16.7% of P=0.01 by Z-test); and both LNCaP and PrEC to be significantly higher than RWPE1   . More brAs H3k27ac typically marks active enhancers, we further evaluated variants with respect to their enhancer or ‘super'-enhancer status ; DHS marks in other cancer cell types (P=3.9 × 10−5 by Z-test); and repressed segmentations (P=2.1 × 10−20 by Z-test). To further refine our model, we restricted to the significant annotations (and the background components accounting for LD to coding regions) and re-evaluated them jointly, referred to as the ‘selected' model. This selected model localized 51.0% of the Although the results above showcase the power of the variance component approach in finding epigenetic marks relevant for PrCa, such marks often overlap making the causal mark difficult to identify . To acco of SNPs . The loc of SNPs . Estimat of SNPs  but may P=3.0 × 10−16 by Z-test, P=0.29 by Z-test, Having inferred the selected model, we re-analysed each of the 82 marginally significant categories jointly with the selected model (see Methods). Only three marks remained significant: two H3k27ac annotations in the colon crypt and one H3k27ac annotation in pancreas . This imρ=0.90 between AAPC and BPC3 across eight components), suggesting a similar pattern of aggregate contribution to risk coming from common variants marked by epigenetic classes across European and African American ancestries .We evaluated replication of our model using two separate genome-wide SNP data sets of PrCa, one of European ancestry  and one of African ancestry  for PrCa (see Methods). To account for the smaller sample size, we focused on the eight-component selected model, only retaining significant components and three coding-proximal classes and AAPC . Howeverand AAPC . AlthougP=2.2 × 10−4 for difference by Z-test). Interestingly, although ARBS were significantly enriched in all 11 traits, the enrichment was no longer significant after excluding autoimmune traits. Overall, these differences indicate that the LNCaP H3k27ac mark is uniquely informative for PrCa, whereas variants near the ARBS and DHS cancer elements  . When we constructed the GRS from SNPs recently discovered in a much larger PrCa GWAS  and 0.098 (joint P=1.3 × 10−23 from multiple regression), respectively  a genetic risk score (GRS) from the genome-wide significant SNPs; (ii) the single best linear unbiased predictor (BLUP) using a single variance component from all SNPs; and (iii) the weighted sum of individual BLUPs from each epigenetic category in the selected model . Evaluated by cross-validation, the GRS yielded an R2=0.071 . In a joectively . The conUsing large-scale genotype data from over 59,089 men of European and African American ancestries jointly with epigenetic annotations, we identified highly significant differences in SNP heritability in silico and without strictly relying on individually significant SNPs. However, as with any analysis of array-based data, the With most GWAS associations falling outside coding regions, our analyses offer an important resource for prioritizing potential loci and focusing future studies on the most heritable genomic regionset al.; and Hazelett et al.) are available at https://data.broadinstitute.org/alkesgroup/ANNOTATIONS/PRCA/. The full list of individual annotations with web-links to the corresponding boundary definitions is provided in the Sample collection and processing for functional annotations was made publically available by the ENCODE/ROADMAP consortia207The ARBS assay was performed as described in REF ref.  and summThe 13 tumours used in this study were androgen dependent and not exposed to androgen deprivation therapies. All of the tumours were specimens obtained from radical prostatectomies, derived from men with early stage disease. These samples were not selected based on any specific features; therefore, we would expect that the distribution of risk variants would be similar to a random sampling of PrCa cases. Large-scale genetic surveys have shown that somatically acquired alterations in primary localized prostate tumours  are infrequent. Based on these previous results, we believe that somatically acquired genetic events in regions related to androgen biology are not common and, therefore, do not influence our results.Informed consent was obtained from all subjects and all studies were approved by local Research Ethics Committees and/or Institutional Review Boards.P value<0.01; case–control missingness P value<0.05; imputation INFO score>0.30. In addition, close relatives were pruned such that no pair of individuals had genetic relatedness (GRM) coefficients>0.05. The top 10 principal components and a coded study label were always included as fixed-effects. All analysed samples, cases and controls, were males.Quality control is crucial for accurate heritability estimation, where many small artifacts can add up to large biases. All data sets went through a stringent QC process with the following exclusion criteria: minor allele frequency (MAF)<1%; fraction of missing/uncalled SNPs>5%; Hardy–Weinberg equilibrium The iCOGS consortium genotyped balanced cases and controls on a custom targeted arrayvariants .The National Cancer Institute Breast & Prostate Cancer Cohort Consortium (BPC3) consortium genotyped individuals on the Illumina HumanHap610 quad arrayThe AAPC consortium genotyped individuals of African ancestry on the Illumina Human1M array233The Wellcome Trust Case Control Consortium Genotyping genotyped cases for 11 traits as well as shared controls on multiple Illumina and Affymetrix arrays3536http://www.uk10k.org) was used only for simulation, and so stringent quality control was not applied. After relatedness filtering, 3,047 samples and 15,691,225 non-singleton variants were retained.The UK10K whole-genome sequence data from ALSPAC and TWINSUK . Total We estimated the SNP heritability REF ref. . BrieflyREF ref.  statistiFor specific models of interest, we extended the individual annotation model described above to test intersecting and non-intersecting components. This allowed us to evaluate precisely which sub-annotations of overlapping components were likely to be causal. For the tumour/normal model, we expanded each tumour/normal mark by 5 kb in both directions from the center to capture nearby genes and other regulatory regions so that tumour  covered 3.3% (1.4%) of the SNPs, respectively. We estimated REF ref. , testingREF ref.  are listThe variance component model has previously been shown to yield robust estimates under the assumption that causal variants are typed and uniformly sampled from a given functional category1320We confirmed that estimates of re typed . Under tre typed . None ofectively . Althougectively . We note51.13% 0.% and 46.Lastly, we performed the real data partitioned analysis in subsets of individuals to evaluate biasedness and power to detect significant enrichment. We confirmed that no significant differences were observed between estimates from the entire study compared with those averaged across subsets of the study . As such39We used the sequenced UK10K common variants to evaluate how well the iCOGS genotyped and imputed SNPs captured underlying heritability by simulating phenotypes using causal variants from sequencing and estimating heritability from the iCOGS SNPs  was shown to be highly conservative both in the null and in the enriched scenario and unlikely to be biased due to tagging of untyped markers. We note that previous work has shown estimates from imputed SNPs (but not genotyped SNPs) may be contaminated by markers very close to an enriched annotationFST bins. This framework evaluated the potential bias resulting from markers that had drifted to different frequencies in the two populations. The FST was estimated out-of-sample in the HapMap CEU European and YRI Yoruba populations. We tested the null six-component model  and observed no significant deviations from the null under any class of differentiated SNPs (FST (FST>=0.35).To assess potential biases in estimating ted SNPs . Howeverusal FST , indicatR2), as it has a natural relationship to SNP heritability122 was then computed from a regression of phenotype on the predictor score with 10 PCs included as covariates to account for ancestry, subsequently subtracting the R2=0.021 from a model with PCs only. P values were estimated for each of the coefficients in the multiple regression of phenotype ∼ GRS+single-BLUP+multi-BLUP+PCs. To ensure that prediction across data sets was independent, we carefully removed all iCOGS individuals with a GRM value of >0.05 to any individual in the BPC3 when computing BLUP coefficients. We separately analysed the predictor in 26,000 iCOGS samples that had age at diagnosis, but did not observe significant differences before/after including age as a covariate.We sought to validate the utility of our functional atlas by applying it to genetic prediction. The aim of genetic prediction is to use training individuals with genetics  and diagnosed phenotype to accurately predict the phenotype into individuals with only genetic data available41How to cite this article: Gusev, A. et al. Atlas of prostate cancer heritability in European and African-American men pinpoints tissue-specific regulation. Nat. Commun. 7:10979 doi: 10.1038/ncomms10979 (2016).Supplementary Figures 1-3, Supplementary Tables 1-16 and Supplementary Note 1Estimates of partitioned heritability from all analyzed annotations, with corresponding web resource


M. officinalis were evaluated for genotypic variation and phenotypic and genotypic correlation for the traits: LS (leaf to stem ratio), SV (spring vigor), LA (leaf area), PH (plant height), DW (herbage dry weight), SD (stem diameter), SN (stem number), Cou (coumarin content), SY (seed yield), across two locations, Yuzhong and Linze, in Western China. There was significant (P < 0.05) genotypic variation among the HS families for all traits. There was also significant (P < 0.05) genotype-by-environment interaction for the traits DW, PH, SD, SN, and SV. The estimates of HS family mean repeatability across two locations ranged from 0.32 for SN to 0.89 for LA. Pattern analysis generated four HS family groups where group 3 consisted of families with above average expression for DW and below average expression for Cou. The breeding population developed by polycrossing the selected HS families within group 3 will provide a significant breeding pool for M. officinalis cultivar development in China.Yellow sweet clover is a widely spread legume species that has potential to be used as a forage crop in Western China. However, limited information is available on the genetic variation for herbage yield, key morphological traits, and coumarin content. In this study, 40 half sib (HS) families of  Melilotus officinalis is one of the most common species in the Melilotus genus. This species has adaptation to environmental constraints such as drought and cold . Genetic variation for key traits have been reported for some of the important forage grasses and legumes: ryegrass  estimate genotypic variation for key traits, and (b) identify families with a combination of superior agronomic performance and low coumarin expression in comparison to two commercial controls.The objective of our study was to conduct a preliminary assessment of the performance of half sib (HS) families of PI 552553 and PI 552554, PI 595394, PI 634019, Ames 22891, and Ames 25658) were selected from a set of 51 accessions that were evaluated for biomass production, agronomy and low coumarin, in Yuzhong, Gansu Province, during 2012–2013 (results not presented). Elite genotypes representing each of the germplasm accessions were polycrossed in isolation, using honey bees, to generate a breeding population to be used for cultivar development. A total of 40 HS families were generated by harvesting each of the genotypes individually. All harvested seeds from the individual genotypes were kept separately as individual HS families.Six germplasm accessions  and Linze  in Gansu Province, China. There are different climate conditions between Yuzhong and linze. Yuzhong in Loess Plateau region is a medium temperate semi-arid climate, whereas Linze in the Hexi Corridor is typical desert climate and characterized by an arid climate . Within each plot, the seed was planted at a spacing of 30 cm within-rows and 60 cm between-rows. The plots were fertilized with 150 kg (NH4)2HPO4 ha−1 after sowing.At each location, the experimental plots were arranged in a randomized complete block design containing three replicates. Each replicate consisted of the 40 HS families the six parental germplasm accessions and two commercial checks. The origins of these entries are provided in Table 2); PH, plant height (cm); DW, herbage dry weight (g/plant); SD, stem diameter (cm); SN, stem number; Cou, coumarin (% of dry matter); SY, seed yield (g/plant). All the traits were measured in the second year (2015).The traits measured were: LS, leaf to stem ratio; SV, spring vigor; LA, leaf area . The morphological traits  were measured at the flowering stage (50% of the plants had open flowers), resulting in a minimum of three individuals per replicate. LA was measured from three middle leaflets per plant by using a flatbed scanner (EPSON GT-15000) and a WinSEEDLE 2011 image analysis system (Regent Instruments Inc.). Individual plant was harvested for DW measurement at the flowering stage after measuring morphological traits. At harvest, three randomly sampled plants from each replicate were cut off at 3 cm above the soil, placed in paper bags and dried at room temperature (about 20–25°C) with good ventilation until no change in weight was recorded. After measuring DW, the dried samples were hand separated into leaf blade and stem (including the inflorescence and leaf sheath) components and weighted to determine the LS ratio. Three sub samples from each field replicate at Yuzhong were combined and ground in a mill to pass through a 1 mm screen for Cou determination. SY was determined from two randomly sampled individuals taken from each replicate when 90% of the pods turned blackish brown at the Linze field. Cou was quantified using HPLC  with a mobile phase of methanol-water (65:35) through an Agilent-XDB C18 column  on only the 40 HS families to estimate genotypic variation, and (b) using all entries in the trial that consisted of the 40 HS families, the six parental germplasm accessions and two check cultivars, which enabled comparison of progeny, parents, and the commercial material. The analysis was conducted using the variance component analysis procedure, Residual Maximum Likelihood (REML) option, in GenStat 7.1 (2003). A mixed linear model was used for the analyses across the two locations using the REML algorithm.Yijk is the value of an attribute measured from HS family i in replicate k in location j, and I = 1,…,ng, j = 1,…,nl, k = 1,…,nr; M is the overall mean; gi is the random genotypic effect of HS family i, N; lj is the fixed effect of location j, N; rjk is the random effect of replicate k within location j, N; (gl)ij is the effect between HS family i and environment j, N; εijk is the residual effect for HS family i in replicate k in location j, N.The linear model used in the analysis was,The mixed model analysis generated HS family means based on Best Linear Unbiased Predictors (BLUP)   Fehr, .HS family mean repeatability at a single site:rp) analysis was carried out using GenStat 7.1 (2003). The multivariate MANOVA procedure, within GenStat 7.1 (2003), enabled estimation sums of cross-products, using the multisite trait data from the 40 HS families. Mean cross products were then calculated and resolved to estimate genotypic covariance components. The genotypic covariance components were used together with the σ2g estimates, from REML analysis, to determine genotypic correlation coefficients (rg) according to Falconer  investigate any changes in type (positive or negative) and magnitude of the association among the seven traits across Yuzhong and Linze. Pattern analysis consisted of a combination of cluster and principal component analysis (PCA)  provide a graphical summary of the performance of the 40 HS families, six parental germplasm accessions and the two check cultivars of Gabriel, . To idenGabriel, .P < 0.05) variation among the 40 M. officinalis HS families  was high for the traits DW, SD and SV, which ranged from 0.89 to 0.96  genotypic variation among the 40 HS families. There was also significant (P < 0.05) genotype-by-location interaction, depending on the traits (Table P > 0.05) genotype-by-location interaction for the traits LS and LA. Line mean repeatability (R2) across the two locations varied from: relatively high for the traits DW and LA; intermediate for PH, LS, SD, and SV; and low for SN.Analysis of variance for mean trait expression across the two sites Yuzhong and Linze indicated significant . At Linze, DW was positively correlated with SD and PH similar to that showed in Yuzhong. However, SN and LA showed a weak positive associated with DW Figures .Clustering of the 40 HS families, together with the 6 parental germplasm accessions and 2 check cultivars, was truncated at the four group level. Group 4, the largest group contained 17 members, followed by group 1, group 3 and group 2, which contained 14, 11, and 6 members, respectively  genotypic variation and high to moderate line mean repeatability reported from our study, indicates the potential for genetic improvement of the nine traits examined. There are no reported studies in M. officinalis similar to ours that estimate the magnitude of genotypic variation for key traits such as DW, Cou, PH, and SY.Previous studies on genotypic variation within M. officinalis ecotypes ranging from 112 to 145 cm. Second year mean plant height (PH) measured in our study ranged from 144 to 188 cm. Martino et al.  for offering the The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.