Implicit in the definition of average effect is a linear model relating genotype to phenotype. The fraction of the phenotypic variance ascribable to polymorphic sites with nonzero average effects in this linear model is called the heritability, and we describe methods for estimating this quantity from GWAS data. Finally, we show that the theory of compressed sensing can be used to provide a sharp estimate of the sample size required to identify essentially all sites contributing to the heritability of a given phenotype.The aim of a genome-wide association study (GWAS) is to identify loci in the human genome affecting a phenotype of interest. This review summarizes some recent work on conceptual and methodological aspects of GWAS. The  Modern genotyping technology has enabled genome-wide association studies (GWAS), which have led to a “golden age” of discovery in quantitative genetics Much of our discussion can be extended to binary phenotypes (such as disease diagnosis) through the device of treating liability as a quantitative trait affected by multiple genetic and environmental causes.2Y. A direct means to determine this quantity is to measure the phenotypic effect of experimentally changing the allelic state of the gene borne by a gamete. Confounding such an experiment, however, is dependence of the phenotypic effect on the allelic states of other genes in the zygote's genome. This nonlinear interaction is called dominance if it occurs between genes at the same site but inherited from different parents and epistasis if it occurs among genes at different sites.  Fixing the allelic states everywhere else in the genome, we can write the effect of substituting We are interested in determining the quantitative influence of a polymorphic site on a given phenotype. Consider a biallelic site with alleles It is not possible to estimate (1) for all backgrounds. There are roughly 10 million single-nucleotide polymorphisms (SNPs) in the human genome where the frequencies of both base pairs  exceed 0.01. Considering just these polymorphic sites alone, we have a number of multi-SNP genotypes equaling three to the power ten million. The developmental process maps each of these genotypes to an expected phenotypic value, but the astronomically large number of possible genotypes rules out any attempt to estimate this causal mapping in its totality. Even if a given genotype has a relatively high probability, in the sense of containing a common allele at each site, it is quite possible that no individuals in the population actually bear that genotype. Thus, even if it were possible to perform any conceivable mutagenic experiment k) of alleles at the other genomic locations. The symbol α to represent the average effect of gene substitution was first used by Fisher We are thus forced to seek some more tractable object that preserves biological meaning. A natural thought is that we should concentrate on some weighted average of the possible gene substitutions at any given polymorphic site,G be the vector whose ith entry is the expected phenotype obtained by all organisms with a fixed multi-site genotype (arbitrarily labeled as the ith) developing within the current range of environmental conditions, X the matrix whose ijth entry is the number of genes  of the jth allelic type present in the ith genotype, α the vector of average effects, and R the vector of residuals , which essentially implies that the individual's breeding value does not contain all possible information about its phenotypic value that can be obtained from a linear combination of its single-site genotypes; some is abandoned in the residual. Thus, the choice of weights in Eq. ℓ2 norm in Eq. All other choices will lead to the appearance of the covariance term 2 Cov—with all other causal sites and is itself in Hardy–Weinberg equilibrium. Let p1 and p2 denote the respective frequencies of p1 its partner gamete will also carry p2 its partner gamete will carry the alternative p1, p2) are precisely those leading to Fisher's average effect of gene substitution In general, the weights in Eq. 3Y is the vector of phenotypes, X is the genotype matrix, R is the vector of genetic residuals and E is the vector of non-genetic  residuals.The concept of average effect is encapsulated in the linear modelX. Such confounding must be absent or remediable if we are to use empirical regression analysis to estimate the elements of α, as defined causally above. The inability to address analogous forms of confounding has been a bane to many fields of science limited to observational data We have tacitly assumed the absence of any correlation between the non-genetic residuals and any column of A potential objection to the linear model of quantitative genetics, which features coefficients that are averages over a large number of contexts, is that it sacrifices too much of biological interest for dubious gain. Holders of such a position tend to emphasize the importance of the full genetic architecture as represented by Eq. An important preliminary point is that scans for linear average effects (more or less standard GWAS practice) will not necessarily preclude the detection of causal sites that interact nonlinearly with each other. In order for a site involved in an epistatic interaction to exhibit an average effect equaling zero, the various terms in Eq. The detection of sites with nonzero average effects thus serves as an excellent starting point even if the investigator's ultimate goal is the characterization of epistasis. There is an important respect, however, in which epistasis (defined in this quantitative–genetic sense) is less biologically significant than average effects. It turns out that nonlinear interactions do not make substantial contributions to familial resemblance.δij is the dominance deviation of the genotype with alleles pi and pj. Eq. p and 1 − p to denote the respective frequencies of p)2, parent and offspring have the same dominance deviation δ11. Similarly, with probability 2p(1 − p) they have different deviations (δ11 and δ12), and with probability p2 they share the heterozygous deviation (δ12). Observe thatLet us say that It follows that the correlations between the phenotypes of ancestors and descendants are exactly the same regardless of whether the conditional phenotypic means of the possible genotypes actually lie on the line determined by the average effect or deviate nonlinearly.do resemble each other. This simple fact points to the importance and size of h2, the proportion of the phenotypic variance due to variance in additive genetic value.This absence of nonlinear contributions to ancestor–descendant correlations does not generalize to all other forms of residual (non-additive) genetic variance. In particular, when there are interactions among genes at different loci, these can alter the correlations between relatives. However, these epistatic variance components have coefficients in the expression for a given correlation that decrease geometrically with the order of the interaction, and thus the great bulk of the contribution to the resemblance between relatives (other than monozygotic twins) continues to be made by the additive genetic variance. And this brings us to a commonsensical observation: if individual differences were caused primarily by non-additive genetic differences, then relatives would not strongly resemble each other, but it is unquestionably true that in our world relatives p between zero and one before absorption at one of these two boundaries should be roughly proportional to 1/pGiven the undoubted importance of physical interactions between gene products in biological pathways, why do we not observe a more prominent role of epistasis in the genetic architectures of quantitative traits? One answer is that the typical allele frequencies at polymorphic sites may suppress the effects of the interactions that do occur. Once a new allele appears by mutation, the amount of time that it spends at each possible frequency A). A fair conclusion to draw from this trend is that variation at a typical causal site perturbs the relevant biological system by a small amount. The smallness of individual effects implies even smaller nonlinear deviations from strict additivity Another answer is suggested by the striking concordance of GWAS findings across distinct populations. For instance, genetic effects from studies of East Asians are strongly correlated with estimates from studies of Europeans 4p will typically exceed the number of individuals in the dataset n. In so-called p > n problems of this kind, the partial regression coefficients are not identifiable with ordinary least squares. In the next section, we show how the statistical theory of compressed sensing can be applied to directly estimate the individual average effects in the p > n regime. Here, we show how an important aggregate quantity—h2, the proportion of the phenotypic variance due to all genomic sites with nonzero average effects—can be estimated without knowledge of the individual sites contributing to this aggregate.Having established that the average effect is the biologically relevant quantity to estimate, we now address how such quantities are estimated. The most straightforward approach is to estimate the average effects in Eq. h2 by determining the extent to which the correlations between relatives increases with the degree of biological relatedness. Under some simplifying assumptions the correlation between relatives is given byClassical methods of quantitative genetics estimate h2 from empirical correlations between relatives is often thought to be problematic because of the possibility that relatives resemble each other not only for genetic reasons but environmental ones h2 so as to minimize the possibility that the so-called missing heritability is attributable to biases of pedigree studies.The use of Eq. genomic-relatedness-matrix restricted maximum likelihood (GREML) —is perhaps the most important innovation in quantitative genetics to have been introduced in the last dozen years, and it has provided nearly definitive evidence for the view that undiscovered sites with common alleles account for a substantial portion of missing heritability.Classical methods based on the correlations between relatives have been substantially augmented by a novel technique that makes use of GWAS data from nominally unrelated individuals σA2, to mean the variance that would be removed from the total phenotypic variance by multiple regression on all markers genotyped, sequenced, or imputed in a given study, as sample size goes to infinity. Because causal sites with a rare allele may not be present or represented by LD proxy in a given study, this additive genetic variance is less than the true additive genetic variance contributed by all polymorphic sites in the genome that we defined previously. Likewise, a site with a nonzero partial coefficient in the multiple regression now under consideration may not be a true causal site with a nonzero average effect but only an LD proxy for such a site. For convenience, however, we continue to use the terms “additive genetic variance,” “heritability,” “average effect” and their corresponding symbols in what follows.For the moment we redefine the additive genetic variance, e = R + E and the expectation is over random e. As before, the heritability is h2 = σA2/(σA2 + σE2). If we assume that LE holds approximately, then X′X ≈ nIp and the additive genetic variance is approximately α′α. We can see that Eq. n)E(u′Z′Zu) is the variance of chip-based breeding values and hence equal to σA2.We see from Eq. σA2 given X and Y. GREML treats Eq. σA,GREML2 and σE,GREML2, where, in the notation of A = (1/p)XX′ is the matrix of realized relatedness coefficients.The goal is to estimate i and i′ is replaced by the chance genetic similarity (which is either slightly greater or slightly less than a mean of zero) between essentially unrelated individuals Eq. h2 and hGREML2 are not necessarily equal even under the same conditions that render Eq. h2αα′ can be replaced by a diagonal matrix with all elements equal to the inner product α′α. As shown in h2 and hGREML2 is that all sites are in LE. In practice, the two quantities will be very close if the causal sites are distributed randomly across the genome with respect to LD hGREML2 < h2. A number of methods have been proposed to bring these two quantities into close agreement regardless of minor allele frequency and LD (13)Despite the surface similarity between Eqs. genetic correlation is simply the correlation between the breeding values with respect to two phenotypes. The GREML method and variants have been used to estimate the heritabilities of several human traits and also the genetic correlations between them. The One advantage of GREML-type methods for heritability estimation over classical pedigree-based methods is that the former can partition heritability among different regions of the genome. Partitioning by chromosome has shown that the heritability contributed by each chromosome is often strongly correlated with its length LD Score regression has been introduced, and it can be put to some of the same uses as GREML h2 to be obtainable from LD Score regression.  For instance, if high-LD genomic regions tend to be devoid of causal SNPs, then the slope of LD Score regression will be biased downward (and the intercept biased upward).Very recently, a new method called In fact, the first use of LD Score regression suggested by its developers is not the estimation of heritability but rather the control of confounding. This use follows from the interpretation of the intercept as the expected chi-square statistic of a SNP with an LD Score of zero. The lowest possible LD Score of a SNP is in fact one, which is obtained when a SNP is in perfect LE with all other SNPs. This essentially means that a hypothetical SNP with an LD Score of zero fails to tag the average effect of any SNP in the genome, including whatever average effect the SNP itself may have. Therefore, if the intercept of LD Score regression departs upward from unity , the departure must be due to confounding, poor quality control, sample overlap, or other artifacts. This simple and ingenious method of estimating the distribution of truly null SNPs should in most cases lead to a much better global inflation of the association statistics than the overly conservative genomic control Z-statistics of two traits, and here it also offers many advantages over GREML: computational speed, input consisting of summary statistics rather than individual-level data, and absorption of confounding into the intercept. So far LD Score regression has produced estimates of genetic correlations very similar to those yielded by GREML We close this section with some practical recommendations. In as-yet unpublished work, we have found that LD Score regression can return different heritability estimates than GREML even when applied to the same data. Thus, when the purpose is to estimate the heritability of a phenotype, GREML is the tool of choice since it is unbiased or can be made to be nearly so. In contrast, when the purpose is functional partitioning of heritability, we strongly recommend LD Score regression over GREML because the former method scales much better computationally with the number of categories to which the heritability is allocated. LD Score regression can also estimate a genetic correlation from the association 5For the vast majority of phenotypes studied so far, the majority of the sites with nonzero average effects contributing to the heritability have not yet been identified. We now discuss a particular means by which progress toward this goal might be advanced.p). The number of subjects (n) is increasing dramatically, but p > n will probably continue to hold for some time. As we stated earlier, the partial regression coefficients are not identifiable in this regime. Partly for this reason, GWAS investigators usually perform separate univariate regressions of their phenotype on each SNP and take forward the marginal coefficients obtained in this way. This approach is inherently unsatisfying, however, because the concepts of average effect and heritability rest on the partial coefficients. Therefore there is value in introducing some constraint (assumption) to deal with the ill-posed p > n problem in the GWAS setting.A typical GWAS evaluates millions of polymorphic sites (genomic selection (GS) depends on a prior distribution quantifying the assumption that most of the SNPs in a given panel have no average effect. A major drawback of this approach is the heavy computational cost of sampling methods for estimating the parameters of a Bayesian model. Reference compressed sensing (CS) Ŷ is the estimated breeding value given by λ depends on the heritability contributed by the SNPs assayed in the study, which can be estimated with GREML. The minimum of Eq. O(np). LD increases the number of computations by either a constant or an amount that increases slowly with p (consistent with log p). A memory-efficient implementation of lasso employing PCO is available in the latest version of PLINK The Bayesian approach known as α is equal to s. CS theory shows that under fairly general conditions, if n is sufficiently large compared to s—but, crucially, not necessarily larger than p and perhaps much smaller—then the lasso or other ℓ1-penalized schemes can select all polymorphic sites with nonzero coefficients in a multiple regression problem with high probability.  More specifically, if the sample size n′ < n is treated as a free parameter, then successive applications of the lasso to increasingly larger subsets of the data will result in a sharp transition from very poor selection to excellent selection. This transition can be observed in the behavior of the P-values returned by the standard univariate regressions of the phenotype on each of the SNPs selected by the lasso.Suppose that the number of nonzero elements in the true s-dimensional subspace. That is, if the true α in fact has s ≪ p nonzero elements, then these will be recovered by the lasso with high probability. There is evidence that, at least among sites where both alleles are common, s ≪ p for a wide range of traits n is expected to exceed s by a large factor even while falling well short of p, the prospects of recovering more heritability are quite promising, especially in light of the current push to generate large and widely available datasets. Note that although there is a relationship between ℓ1-constrained solvers and the double Laplace prior that is debated in GS, CS theory is not based on this and holds for many different coefficient distributions and design matrices The CS approach makes no assumption about the distribution of the average effects. Instead it implicitly attempts to confine the estimate Finally, a given SNP is often strongly correlated—in tight LD—with several neighboring SNPs in the genome. This raises an obvious problem for the standard GWAS approach, since a causal SNP will lead many neighboring SNPs to exhibit nonzero univariate regression coefficients. The lasso does not in fact solve this problem. Although the lasso is statistically consistent under fairly general conditions, it may require a prohibitively large sample size to select only the causal sites in an LD block while setting the coefficients of all other sites to zero. Thus, in the presence of LD, “good recovery” means the selection of many sites that are false positives strictly speaking but nevertheless are in strong LD with one or more sites where the average effect is truly nonzero 6ℓ1-penalization and large but reasonably realistic sample sizes.In this review we have argued that the average effect of gene substitution—a weighted average of the phenotypic changes that would result from idealized mutagenic experiments—is the pivotal quantity to be estimated in GWAS. Although this averaging may conceal important nonlinear effects of genetic variation on the focal phenotype, the identification of sites with nonzero average effects is at least an important starting point. In any event new methods of heritability estimation based on DNA-level data confirm classical findings from the correlations between relatives that much phenotypic variation is attributable to the average effects of gene substitution across all causal sites. Pinning down all of this additive genetic variance to individual locations in the genome with high confidence continues to be a challenge, since the average effects are typically very small, but the theory of CS provides reason to believe that a transition to good recovery is attainable with a combination of Lurking not so far in the background behind all of these issues are the complications introduced by LD. Even if an oracle reveals to us the identity of a true causal site, that site's univariate regression coefficient may fail to equal its average effect of gene substitution as a result of LD. Perhaps a far more important concern is that LD prevents easy identification of causal sites responsible for GWAS signals in the first place. Furthermore, LD raises problems for GREML-type methods of heritability estimation that can probably stand further scrutiny. Notwithstanding these issues, however, the remarkable progress in quantitative genetics over the last decade leaves little doubt about the bountifulness of this research frontier.URLshttp://cnsgenomics.org/software/gcta;GCTA-GREML, http://www.github.com/bulik/ldsc;LD Score regression, https://www.cog-genomics.org/plink2.PLINK,


Motivation: To increase the signal resolution for large-scale meta-analyses of genome-wide association studies, genotypes at unmeasured single nucleotide polymorphisms (SNPs) are commonly imputed using large multi-ethnic reference panels. However, the ever increasing size and ethnic diversity of both reference panels and cohorts makes genotype imputation computationally challenging for moderately sized computer clusters. Moreover, genotype imputation requires subject-level genetic data, which unlike summary statistics provided by virtually all studies, is not publicly available. While there are much less demanding methods which avoid the genotype imputation step by directly imputing SNP statistics, e.g. Directly Imputing summary STatistics (DIST) proposed by our group, their implicit assumptions make them applicable only to ethnically homogeneous cohorts.Results: To decrease computational and access requirements for the analysis of cosmopolitan cohorts, we propose DISTMIX, which extends DIST capabilities to the analysis of mixed ethnicity cohorts. The method uses a relevant reference panel to directly impute unmeasured SNP statistics based only on statistics at measured SNPs and estimated/user-specified ethnic proportions. Simulations show that the proposed method adequately controls the Type I error rates. The 1000 Genomes panel imputation of summary statistics from the ethnically diverse Psychiatric Genetic Consortium Schizophrenia Phase 2 suggests that, when compared to genotype imputation methods, DISTMIX offers comparable imputation accuracy for only a fraction of computational resources.Availability and implementation: DISTMIX software, its reference population data, and usage examples are publicly available at http://code.google.com/p/distmix.Contact:dlee4@vcu.eduSupplementary information:Supplementary Data are available at Bioinformatics online. Genotype imputation methods  are commZ-scores) for unmeasured SNPs from genome-wide association studies (GWASs) consisting of both family and independent cohorts. The methods were shown to (i) substantially reduce the computational burden and (ii) be practically as accurate as commonly used genotype imputation methods. These methods were successfully applied in gene-level joint testing of functional variants using only summary data . However, it is possible to determine whether an individual subject is a study member by using only the subject's genotypes and in-cohort study AFs  that theDirectly Imputing summary STatistics for unmeasured SNPs from MIXed ethnicity cohorts (DISTMIX). DISTMIX inherits the main advantages of DIST, i.e. speed, not requiring genetic data access and applicability to pedigree data, while gaining the capability to accurately impute association summary statistics from multi-ethnic studies.In this article, we extend DIST imputation method/software to This is achieved by (i) predicting a study’s proportions (weights) of ethnicities from a multi-ethnic reference panel based only on (common) Single Nucleotide Polymorphisms (SNPs) AFs from the studied cohort or taking, as the weights, user-specified ethnic proportions drawn from one's prior information on ethnic composition of the study samples, (ii) computing ethnicity-weighted correlation matrix based on the estimated/user-specified weights and genotypes of ethnicities from the reference panel and then (iii) using the weighted correlation matrix in a DIST procedure.N ethnic groups and that the vector G for individual genotypes in the study cohort is a mixture of random genotypes from (not admixed from) the N ethnic groups with weight vector G then follows a mixture distribution ith ethnic group, assumed to have genotype mean G can be derived asAssume that the reference panel consists of S be the vector of the ‘estimated study population’ SNP reference allele frequencies (RAFs), e.g. the weighted mean of case and control frequencies using the studied condition prevalence and its complement as weights, respectively. Let ith ethnicity of the reference panel. By dividing Let Due to the strong LD among SNPs, the calculation of the correlation using all SNPs in a genome might lead to a poor estimation. To avoid this, we sequentially split GWAS SNPs into 1000 non-overlapping SNP sets, e.g. first set consists of the 1st, 1001st, 2001st, etc. map ordered SNPs in the study. The large distances between SNPs in the same set, makes them quasi-independent which, thus, improves the accuracy of the estimated correlation. Typically, the study AF information is not publicly accessible. Thus, to make DISTMIX applicable even to summary data sets lacking AF information, we added an option for users to pre-specify the weights based on their prior knowledge on ethnic composition of the study cohort of interest. This option should be most useful when (i) fairly accurate proportion information about ethnicities involved in the cohort is available and (ii) all ethnicities in the cohort have reasonably close proxies in the reference panels.ith ethnic group respectively and Based on estimated/pre-specified weights Z-scores, DISTMIX uses the square root of the imputation information to normalize (to a variance of one) the conditional expectations , five sets of 100 summary data sets of Ilumina 1 M autosomal SNPs from five different ethnicity combinations in 1KG: (i) 40% ASW + 60% GBR (Cohort 1), (ii) 60% CHB + 40% MXL (Cohort 2), (iii) 20% ASW + 30% CHB + 30% GBR + 20% MXL (Cohort 3), (iv) 30% CEU + 25% CHS + 5% PUR + 40% YRI (Cohort 4) and (v) 10% ASW + 15% CEU + 15% CHB + 12.5% CHS + 15% GBR + 10% MXL + 2.5% PUR + 20% YRI (Cohort 5) (See Supplementary Table S1 for abbreviations for ethnicities in 1KG and Section 1 in Supplementary Data for null summary data set simulations).To assess the Type I error rate and the accuracy of ethnicity weight estimation for the proposed method, we simulated, under the null hypothesis of no association (HSupplementary Table S2) and 1KG (phase 1 release version 3 with 1092 subjects and minor AF (MAF) ≥ 0.5%), we imputed each null GWAS summary data from Cohorts 1-4. For summary data from Cohort 5, we only estimated ethnicity proportions. To assess the robustness of DISTMIX when the reference panel does not incorporate best-matching ethnicities, we also imputed simulated data sets from Cohort 3 using a subset of 1KG reference panel which excluded the relevant ethnicities (GBR and MXL). Based the DISTMIX H0 results, we estimated empirical Type I error rates across different nominal levels.Using DISTMIX at its default settings . The analysis of 7 425 593 markers imputed by DISTMIX shows that DISTMIX prediction is fairly comparable to IMPUTE2 , Supplementary Fig. S2): P-value < 5 × 10−8)/suggestive  signals for IMPUTE2 but not for DISTMIX . While IMPUTE2 applied to PGC SCZ2 discovery phase identified 88 (83.8%) statistically significant regions out of these 105 regions, DISTMIX successfully detected 81 (77.1%) as significant, including two regions not identified by IMPUTE2. However, the regions not detected by just one of the two methods yielded, for the smaller signal, p-values just below the significance threshold . The running time and peak memory usage were slightly under 12 hours and 1 GB, respectively. Remarkably, the running time translates to a single core computation time of less than one week.DIST and ImpG assume that the genotypes and association statistics have identical correlation structures. However, while the assumption is reasonable for homogeneous cohorts, it might not be met when there are relevant covariates which confound genotypes, e.g. ancestry principal components in ethnically mixed studies. To adequately analyze such cohorts, we propose DISTMIX, a very fast and novel method/software for directly imputing summary statistics of untyped makers from cosmopolitan cohorts without using subject-level genotype data. The proposed method (i) uses mixture proportions for each ethnicity in a reference panel (e.g. 1KG) either (a) provided by the user or (b) estimated based on the in-cohort estimated AFs of common variants, (ii) uses these proportions to determine the cohort LD as a mixture of the LDs of the ethnicities from the reference panel and (iii) uses the mixture LD in DIST procedure to impute statistics at untyped variants.As shown by our simulation and empirical studies, for cosmopolitan cohorts, DISTMIX (i) accurately estimates in-study weights of ethnicities from a reference panel (when they are not provided by the user), (ii) maintains the Type I error rate at or below the nominal level, (iii) delivers comparable imputation accuracy to commonly used genotype imputation methods while (iv) dramatically reducing computational needs. Moreover, given that the relatedness between subjects in a cohort does not affect the estimated mixture LD, DISTMIX can be used ‘as-is’ for meta-analyses containing family data.Compared to summary statistics based imputation methods like DISTMIX, genotype imputation methods offer more flexibility to researchers; once haplotype phasing and genotype imputation are done for a sample cohort, researchers can conduct different GWASs using different phenotypes and covariates without re-imputation. While the current DISTMIX version imputes only one set of summary values, given that the most computer intensive part is the estimation of the correlation matrix, we believe that a future version simultaneously imputing Z-score for multiple traits is attainable with minimal effort.http://www.haplotype-reference-consortium.org), imputation procedures will be required to both impute new studies and re-impute previously published GWASs. This process will require a sudden increase in processing capabilities due to these larger panel sizes. For example, even after an impressive ∼20× speed improvement, the genotype imputation using the HRC panel, will still be around 2 times slower than the same imputation using present methods with the 1KG panel (Due to the emergence of very large reference populations such as the Haplotype Reference Consortium (HRC) including more than 30 000 subjects at over 50 million SNPs (When compared to genotype imputation methods e.g. IMPUTE2 and MACH (ur paper . (Its coR25DA026119 (D.L.), MH100560 (S.A.B. and B.P.R.), AA022717  and 1P50AA022537 (S.A.B. and B.P.R.).This work was supported by Conflict of Interest: none declared.


Time-varying phenotypes have been studied less frequently in the context of genome-wide analyses across ethnicities, particularly for mood disorders. This study uses genome-wide association studies of depressive symptoms in a longitudinal framework and across multiple ethnicities to find common variants for depressive symptoms. Ethnicity-specific GWAS for depressive symptoms were conducted using three approaches: a baseline measure, longitudinal measures averaged over time, and a repeated measures analysis. We then used meta-analysis to jointly analyze the results across ethnicities within the Multi-ethnic Study of Atherosclerosis , and then within ethnicity, across MESA and a sample from the Health and Retirement Study African- and European-Americans .This study uses genome-wide association studies of depressive symptoms in a longitudinal framework and across multiple ethnicities to find common variants for depressive symptoms. Ethnicity-specific GWAS for depressive symptoms were conducted using three approaches: a baseline measure, longitudinal measures averaged over time, and a repeated measures analysis. We then used meta-analysis to jointly analyze the results across ethnicities within the Multi-ethnic Study of Atherosclerosis , and then within ethnicity, across MESA and a sample from the Health and Retirement Study African- and European-Americans .−8 < p-value ≤ 5×10−6) in each ethnicity for each approach to analyzing depressive symptoms. The repeated measures analyses resulted in typically smaller p-values and an increase in the number of single-nucleotide polymorphisms (SNP) reaching genome-wide suggestive level.Several novel variants were identified at the genome-wide suggestive level  contains supplementary material, which is available to authorized users. With advances in the ability of statistical software to handle data with repeated measures, longitudinal data analysis is becoming more feasible in genetic association studies. While these analyses are more complicated and computationally intensive than analyses using only baseline measures, longitudinal data has been used to identify variants that influence complex traits above and beyond that of cross-sectional measurements . BecauseThere are a number of circumstances where longitudinal data analysis may be more informative or powerful than cross-sectional analyses based on single or time averaged measures. If there is substantial variability over time in the outcome or interaction of other covariates or SNPs with time, a longitudinal analysis will clearly be more informative . For a gDepressive symptoms exist on a spectrum, varying in both severity and duration, and are often measured in population-based studies using the 20-item Center for Epidemiological Studies Depression scale (CES-D). Given the benefits of longitudinal analysis, the ability to detect genetic predictors of depression may be enhanced by analyzing depressive symptoms both over time and quantitatively , rather p = 9.19×10−3). This SNP reached genome-wide significance (p = 4.78×10−8) in overall meta-analysis of the combined discovery and replication samples  In the present study, we use longitudinal data on a continuous measure of depressive symptoms collected over a 9 year period from three exams in MESA to conduct GWAS on depressive symptoms in four race/ethnicities. We also contrast different approaches of incorporating the repeated measures into the GWAS: (1) analyzing a single time-point measure (baseline), (2) averaging measures over time, and (3) conducting a repeated measures outcome analyses. Finally, we jointly analyze repeated measures GWAS results from MESA and up to ten exams from the Health and Retirement Study. The MESA study includes a total of 650, 507, and 5,178 participants with one, two, and three measures, respectively, while the HRS sample consists of 34, 147, and 9,982 individuals with one, two, and three-plus measures, respectively) in an overall meta-analysis for European Americans and African Americans to increase power. To our knowledge, there have been no GWAS of repeated measures of depressive symptoms measured over time in individuals of multiple race/ethnicities.Descriptive statistics for MESA and HRS are presented in Table exam = 0.25, p < 0.0001), AA , and HA  sub-groups, but this increase in trend was only significant in EA. The CA sub-group showed a non-significant decrease in depressive symptom score over time . The intraclass correlation (within-person correlation) across all exams for which an individual had a valid CES-D score (up to three time-points) ranged from 0.44 in AA to 0.60 in EA.In MESA, the mean baseline depressive symptom score ranged from 6.3 (standard deviation (SD): 6.6) in the CA subsample to 9.9 (SD: 9.2) in the HA subsample out of a possible score of 60. CES-D scores increased over time in the EA  and decreased significantly in AA participants over time . The intraclass correlation for the HRS participants across exams was 0.48 for EA participants and 0.51 for AA participants.The HRS analysis sample contains 10,163 respondents , with 8,652 EA (85 %) and 1,511 AA (15 %). Mean age at baseline was 58 years. The CES-D8 depressive symptom score in HRS EA increased significantly over study waves . This gene has previously been associated with cancer pathogenesis . There were no other genome-wide significant SNPs in any of the ethnicities for any of the baseline, average, and repeated-measures modeling approaches though there were many suggestive p < 10−6 findings.Table is (e.g. ) but hasp < 5×10−4) from each pair of SNPs for the baseline CES-D score compared to the averaged CES-D score phenotype  genome-wide suggestive SNPs from baseline to repeated measures for each ethnicity , with some (at least two SNPs appearing in multiple approaches as genome-wide suggestive within each ethnicity) consistency in the SNPs across approach  SNP with p < 1×10−6. The meta-analysis only included SNPs with ethnicity-specific minor allele frequency (MAF) > 5 % calculated within ethnicity using only MESA participants. These meta-analyses showed no genome-wide significant results. Thirteen SNPs reached a genome-wide suggestive threshold in these meta-analyses. The smallest p-value was in the repeated measures meta-analysis on chromosome 2, . This SNP was only present (with MAF > 5 %) in the CA and HA subsamples. This SNP is in the intronic region of the STAT1 gene, IFN-γ transcription factor signal transducer and activator of transcription 1, previously implicated as a tumor suppressor . In AA the smallest observed p-value  was located downstream of the RBM38 oncogene. RBM38 encodes an RNA binding protein found to regulate MDM2 (12q14.3-q15) gene expression through mRNA stability [http://omim.org/).Results from the joint-analyses (MESA + HRS) for EA and AA, separately, are presented in Table tability , 20, buttability   is located on chromosome 2 (in the STAT1 gene). The SNP rs41379347 was found previously in the MESA meta-analysis across ethnicity. This SNP was only present (with MAF > 5 %) in the MESA CA and HA samples, and thus, no new information was gained in the joint analysis across MESA and HRS.For the meta-analysis across all ethnicities in both HRS and MESA, we found no SNPs reaching genome-wide significance, though we found seven SNPs reaching genome-wide suggestive thresholds Table . The mosp = 4.78×10−8). In our EA subsample, p-values for this SNP in our baseline and repeated measures analysis were 0.116 and 0.055, respectively, with consistent effect directions (+) as the Hek, et al. [There has been one published GWAS conducted on depressive symptom scores , for whi2 < 0.8) genome-wide suggestive SNPs from baseline to repeated measures for each ethnicity  and meta-analyzed them across ethnicity and across study. Though our joint meta-analysis of all ethnicities in both studies comprises 16,498 individuals, and the power to detect genetic variants of depression has been shown to increase when assessing depression quantitatively — as opposed to using a dichotomous definition or cutoff point  — we did et al.,  and preset al. [p = 0.055) less than half that of the baseline measures model (p = 0.116). If we consider this SNP a true signal , we indeed demonstrate that the p-value has decreased from the baseline to the repeated measures analysis.Hek, et al.  identifiA repeated measures analysis makes use of the full information content in the outcome and exposure/covariates for longitudinal data. For example, in an analysis with repeated measures data, if there is drop-out in the study and we use subject level averages, the homoscedasticity assumption of linear models is violated as different averages will be based on different number of observations and the ones with more observation will have higher precision. Averaging the exposure data may also lead to substantial loss in power. If there is a time trend or interaction of covariates (or SNPs) with time, a longitudinal model is expected to have larger power than a cross-sectional or averaged model. Longitudinal modeling is a better general framework as it allows incorporation of time-varying covariates (instead of averaging them) and allows exploration of G × E interaction in follow-up analysis with cumulative exposure trajectory. Although we saw an increase in the number of unique genome-wide suggestive SNPs for repeated measures compared to baseline, we note that since most of the SNPs are non-significant, this may be simply a comparison of false positives. However, in view of the existing literature one can argue that a longitudinal analysis is generally more efficient than using a summary quantity in the presence of repeated measures data.For repeated measures, there are multiple modeling approaches. GEE produces unbiased and consistent estimates of the fixed effect parameters, even under misspecification of the correlation structure. Also, if the correlation structure is correctly specified, there is gain in terms of efficiency. GEE can be argued as a better framework than a linear regression model in terms of its robust estimates of the standard error and behavior of QQ plots as it protects under model misspecification . That isThough GWAS have been used for over a decade, most variants identified for diseases have had very modest effect sizes, often explaining less than 1 % of the variance of quantitative traits . BecauseSIRT1 gene (p = 2.53×10−10) and the other in an intron of the LHPP gene (p = 6.45×10−12) [TPH2, HTR2A, MAOA, COMT) have rarely been identified/replicated as predictors of MDD in GWAS [The depressive symptom GWAS literature to date includes one GWAS, with only one genome-wide significant result . The lit5×10−12) . Meta-an in GWAS , 38–40. One potentially important reason that SNPs detected through GWAS and biological candidate genes rarely replicate is because despite the CES-D correlating strongly with depression and having been used in hundreds of studies, the CES-D is not a diagnostic tool. The CES-D only measures depressive symptoms over the past week. The MESA study exams were spaced approximately 12 – 24 months apart (the HRS surveys 24 months apart). It is possible that failure to capture changes in depressive symptoms between the assessments introduced measurement error in the phenotype. Additionally, in the baseline and repeated measures analyses, though log-transformed to improve normality, the distribution of CES-D still deviated from the normal distribution. This is a consistent limitation of CES-D scores in the literature, and it should be noted that the p-values from our baseline and repeated measures models may reflect the non-normal distribution of the phenotype.We included only common variants (those with ethnicity-specific MAF > 5 %) in our analysis. One reason we may not have found any significant genetic variants of depressive symptoms is that we did not look at rare variants or copy number variants. New methods for analyzing rare variants or SNP sets, such as Sequence Kernel Association Testing (SKAT), are being developed and applied and may help to further elucidate genetic predictors of depressive symptoms at a gene-level and across ethnicities . AdditioSince combining genetic information across ethnicities can result in false-positive findings from population stratification within genetically distinct populations, we conducted GWASs separately by ethnicity adjusting for ethnicity-specific principal components and filtered initial GWAS results by ethnicity-specific minor alleles to remove low frequency variants for more robust findings. The meta-analysis software accounts for both magnitude and direction of effect when combining information across studies (in this case different ethnicities) which is especially appropriate when studies contain differences in ethnicity, phenotype distribution, gender or constraints in sharing of individual level data .Identifying genes that are associated with depression has tremendous potential to transform our understanding and treatment of depression. Utilizing longitudinal measures in GWA studies for depressive symptoms allows researchers to get a better picture of depression over the life-course. Though this study did not find any gene variants that reached genome-wide significance in the repeated measures approach, it provides a first step in examining depressive symptoms in different longitudinal settings and also across multiple ethnicities.http://www.ncbi.nlm.nih.gov/projects/gap/cgi-bin/study.cgi?study_id=phs000209.v12.p3. Written informed consent was obtained from participants after the procedure had been fully explained and institutional review boards at each site approved study protocol , Johns Hopkins Office of Human Subjects Research IRB, University of California Los Angeles Office for the Protection of Research Subjects IRB, Northwestern University Office for the Protection of Research Subjects IRB, Wake Forest University Office of Research IRB, Columbia University IRB).MESA is a longitudinal study supported by NHLBI with the overall goal of identifying risk factors for subclinical atherosclerosis . The MESDepressive symptom score was assessed using the 20-item CES-D Scale , which wApproximately one million SNPs were genotyped using the Affymetrix Genome-Wide Human SNP Array 6.0. Imputation was performed using the IMPUTE 2.1.0 program in conjunction with HapMap Phase I and II reference panels . Imputation SNPs were filtered at an INFO score of 0.80. We accounted for population substructure by including the top four ethnicity-specific principal components (estimated from genome-wide data) as adjustment covariates in all analyses, as proposed previously by MESA investigators and elsewhere , 48.The Health and Retirement Study (HRS) was used as a joint sample to be combined with MESA GWAS results in a meta-analysis . These tOver 12,000 HRS participants were genotyped for about 2.5 million SNPs using the Illumina Human Omni-2.5 Quad beadchip. Genotypes were imputed for EA and AA using MACH software . Imputation SNPs were filtered at an INFO score of 0.80. We accounted for population substructure by including the top four ethnicity-specific principal components (estimated from genome-wide data) as adjustment covariates in all analyses. There were 10,163 HRS participants after removing those with missing outcome, covariate or genetic information. A total of 34 (0.3 %) had only one measure of CES-D8, 147 (1.4 %) had two measures, and 9,982 (98.2 %) had three or more CES-D8 measures, for a total of 72,273 observations.We contrasted GWAS results using different approaches to incorporate the time-varying phenotypic data: using a single (baseline) measure, taking the average across exams, or conducting a repeated measures analysis that accounts for correlation of responses within individuals.Baseline and averaged GWA studies were analyzed using a one-step linear regression approach, adjusting for age, sex, site (in MESA) and the first four genome-wide principal components, stratified by race in PLINK v.1.07 , 51. EacFor the repeated measures, we used generalized estimating equations (GEE) to account for within-individual correlations between repeated CES-D measures . Within To examine whether p-values from GWAS in MESA were consistent in rank across the three analysis approaches , we calculated Spearman’s correlations between the ranks of p-values for SNP-phenotype associations within ethnic group.To increase statistical power to detect SNP association, we performed a fixed-effects meta-analysis combining results across all four ethnicities within the MESA study for each of the three phenotype definitions , weighting by sample size. In order to further investigate consistency of associations across different studies we also conducted a meta-analysis for EA and AA (separately) across the MESA and HRS studies for the repeated measures phenotype. We use only the AA and EA samples due to the availability of a large enough sample size for these two ethnicities in HRS. Finally, we performed a meta-analysis across all ethnicities and all studies to further elucidate any genetic variants across ethnicity. For the analysis that includes both MESA and HRS, the repeated measures phenotype was selected to allow for maximum power. All meta-analyses were performed using METAL .http://www.ncbi.nlm.nih.gov/projects/gap/cgi-bin/study.cgi?study_id=phs000209.v12.p3.Data supporting the results of this article are available in the dbGap repository, phs000209.v12.p3,


P-value in a linear regression of the risk factor for each variant is less than Genome-wide association studies, which typically report regression coefficients summarizing the associations of many genetic variants with various traits, are potentially a powerful source of data for Mendelian randomization investigations. We demonstrate how such coefficients from multiple variants can be combined in a Mendelian randomization analysis to estimate the causal effect of a risk factor on an outcome. The bias and efficiency of estimates based on summarized data are compared to those based on individual-level data in simulation studies. We investigate the impact of gene–gene interactions, linkage disequilibrium, and ‘weak instruments’ on these estimates. Both an inverse-variance weighted average of variant-specific associations and a likelihood-based approach for summarized data give similar estimates and precision to the two-stage least squares method for individual-level data, even when there are gene–gene interactions. However, these summarized data methods overstate precision when variants are in linkage disequilibrium. If the  Mendelian randomization is a technique for using genetic variants to estimate the causal effect of a modifiable risk factor from observational data [Davey Smith and Ebrahim, P-value threshold, and recently the release of association estimates in published GWA studies for all measured variants has been advocated [Editorial, One potential source of such data is genome-wide association (GWA) studies, which examine the associations of many genetic variants with a trait. Many large GWA study consortia have been assembled, with sample sizes in some cases running into hundreds of thousands [Ehret et al., For the causal effect to be consistently estimated, each variant used in a Mendelian randomization analysis must satisfy three assumptions [Didelez and Sheehan, it is associated with the risk factor,it is not associated with any confounder of the risk factor–outcome association,it is conditionally independent of the outcome given the risk factor and confounders.A variant satisfying these assumptions is known as an instrumental variable (IV) [Greenland, X and the outcome Y. Genetic variant k, We assume that summarized data are available for multiple genetic variants that are single nucleotide polymorphisms (SNPs) and satisfy the IV assumptions for the risk factor of interest X on Y using genetic variant k is The ratio estimate of the causal effect of X on Y, β, which is assumed to be the same for all genetic variants k, can be estimated by direct maximization of the likelihood or by Bayesian methods [Thompson et al., Alternatively, a model can be constructed by assuming a linear relationship between the risk factor and outcome and a bivariate normal distribution for the genetic association estimates:By combining the estimates of association from multiple variants into a single estimate of the causal effect, an assumption is made that the variants provide independent information. There are several reasons why this may not be the case. First, the causal estimates are derived from the same data, and so will not be entirely independent. However, correlation between the estimates should be low unless the sample size is particularly small. Secondly, there may be statistical interactions between variants in their associations with the risk factor (gene–gene interactions). Thirdly, the distribution of genetic variants may be correlated (linkage disequilibrium).We perform simulation studies to assess the impact of the assumption that multiple genetic variants provide independent information on the causal estimate, in particular in the presence of gene–gene interactions and linkage disequilibrium. We compare the causal effect estimate (and its precision) obtained from summarized data to that obtained if individual-level data on the variants, risk factor and outcome were available on the whole study population.i, according to the following model:.. parameters represent gene–gene interactions. The causal effect of X on Y is U represents negative (unmeasured) confounding between X and Y. The IVs We initially assume that the genetic variants used as IVs are independently distributed. Individual data were generated for 5,000 participants, indexed by K-dimensional multivariate normal distribution for each individual i. For each draw, if the kth component was positive, a variant allele was recorded for the kth variant. The draws represent the two haplotypes for each individual [Lunn et al., . is an indicator function. We took five values of the correlation parameter r2) of 0 (no linkage disequilibrium), 0.06, 0.13, 0.26 and 0.41.We repeated the simulation in the absence of gene–gene interactions, but using correlated genetic variants. In order to simulate data on the variants, two random draws A weak instrument is a variable that satisfies the IV assumptions, but does not explain a large proportion of variation in the risk factor, so that the statistical association between the risk factor and the IV in the dataset is ‘weak’ [Burgess et al., http://www.r-project.org) using the optim command to directly maximize the likelihood.Estimates of the causal effect using all the genetic variants are calculated using individual-level data with the two-stage least squares 2SLS) method [Baum et al., SLS methoAn estimate of the correlation between the genetic associations with risk factor and outcome of In each scenario, results from 10,000 simulated datasets for the comparison of the individual-level and summarized data methods are given. We present the mean and median estimates across simulations, the standard deviation (SD) of estimates, the mean standard error (SE), the coverage of the 95% confidence interval for the causal effect  by the likelihood-based method throughout. Coverage for the IVW method was consistently underestimated at around 93%, indicating that the method gave estimates that were slightly too precise (the mean SE was less than the SD of the estimates). Estimates from the likelihood-based and 2SLS methods had similar efficiency, with the 2SLS analyses giving slightly less variable estimates (lower SD), but the likelihood-based analyses giving slightly more precise estimates (lower mean standard error). The IVW method had the greatest empirical power, although this was offset by the coverage levels not achieving nominal levels. Power from the likelihood-based method was marginally lower, and from the 2SLS lower still.Overall, despite gene–gene interactions leading to misspecification of the genetic model in the 2SLS method and effect modification in the genetic associations in the summarized data methods, the assumption of independence of the information provided by uncorrelated variants did not seem to give misleading results.Results from the scenarios with variants in linkage disequilibrium are given in TableWe repeated the simulation in the absence of gene–gene interactions and linkage disequilibrium, but using 20 genetic variants with smaller effects on the risk factor to investigate the performance of the methods with weak instruments. Our simulations (see Supporting Information) suggest that the IVW and likelihood-based methods have similar behavior with weak instruments to the 2SLS method. In particular, this means that when the expected value of the F statistic is greater than 10, the bias of the causal estimate is less than 10% of the bias of the confounded observational estimate from an OLS regression analysis [Staiger and Stock, PCSK9 and SORT1 gene regions), chromosome 2 (APOB), chromosome 5 (HMGCR), and chromosome 19 (LDLR); details of the variants are given in the Supporting Information. The variants are not in linkage disequilibrium. A P-value of Low-density lipoprotein cholesterol (LDL-C) is a known causal risk factor for coronary artery disease (CAD). Genetic variants associated with LDL-C have been found in many different regions of the human genome. We take a published study reporting genetic associations of variants with LDL-C, high-density lipoprotein cholesterol (HDL-C), and triglycerides (TG), and with CAD risk from a meta-analysis of GWA studies [Waterworth et al., We see that the estimates from both summarized data methods are similar, and that changing the correlation parameter in the likelihood-based method has little impact. The graph indicates that variants with a greater magnitude of association with LDL-C also have a greater association with CAD risk. The overall estimate of causal association passes close to the estimate from each of the variants, giving plausibility to the instrumental variable assumptions, and suggesting that changes in LDL-C from different biological mechanisms may have similar effects on CAD risk [Burgess et al., In this paper, we have considered methods for Mendelian randomization using summarized data on multiple genetic variants. The target for estimation is a non-genetic parameter, the causal effect of the risk factor on the outcome. Each variant provides additional information on this parameter, and so the most precise estimate can be obtained using all available variants that are valid instrumental variables [Burgess et al., The IVW and likelihood-based methods make different assumptions about the distribution of variables. The IVW method uses an asymptotic estimate of the standard error of the causal (ratio) estimate from each variant; this is known to underestimate the true variation in the estimate, especially when the IV is weak [Burgess and Thompson, P-value of around 0.001; an F statistic of 20 to a P-value of around P-value of around P-value of below P-values well below R2) for each variant of around 0.1%. When sample sizes and the strength of genetic variants are limited, it may be necessary to restrict the number of variants used in a Mendelian randomization analysis in order to mitigate against bias from weak instruments.With weak instruments, estimates using both of the summarized data methods demonstrated bias similar to that of the 2SLS method. If the distributions of genetic variants are uncorrelated, then each variant explains independent variation in the risk factor. For variants of equal strength, the expected F statistic in the univariate linear regression of the risk factor on one of the variants is approximately the same as the expected F statistic in the multiple regression on all of the variants. An F statistic of 10 corresponds to a Close to unbiased estimates with weak instruments can be obtained from individual-level data using the limited information maximum likelihood (LIML) method [Angrist and Pischke, A limitation of the use of Mendelian randomization is that the instrumental variable assumptions cannot be assessed without supplementary data. Although the IV assumptions can never be fully tested empirically, they can be assessed to some extent, for example by testing the association of the genetic variants with measured covariates to assess potential pleiotropy. This can be undertaken using individual-level data. It is also possible with summarized data, as with HDL-C and TG in the example, although genetic associations with a full range of covariates would not necessarily be measured or routinely reported by a GWA study. These associations could be checked in the literature; however, the assumption is necessary that the literature-based estimates are valid for the population under investigation. Other assessments, such as addressing population stratification by the evaluation of genetic principal components, or testing for the attenuation of genetic associations with the outcome on adjustment for the risk factor [Glymour et al., In addition, many of the parametric assumptions required by IV methods for effect estimation, such as linearity of genetic associations or of the risk factor–outcome association [Didelez and Sheehan, Not all GWA studies measure data on a large number of phenotypic variables, and so genetic associations with the risk factor and the outcome may not be available in the same sample. Estimates of the association of the genetic variants with the risk factor and the outcome may be obtained from independent sources. This is known as a two-sample IV analysis [Pierce and Burgess, Correlation between genetic associations with the risk factor and outcome arising from estimation of the coefficients in the same source is ignored by the inverse-variance weighted method, but can be acknowledged in the likelihood-based method. If the sources for the estimates are neither identical nor disjoint, but instead overlap, then a meta-analysis approach would be recommended to correctly account for the structure in the data. In the absence of study-specific estimates, we advocate the likelihood-based method with a sensitivity analysis for the correlation parameter.If two genetic variants are in complete linkage disequilibrium, then inclusion of both variants in an individual-level analysis model would not lead to additional information. However, if variants are in partial linkage equilibrium, although the information provided by each variant is not independent, each variant does provide additional information on the causal effect. Summarized data methods using variants in linkage disequilibrium overstate precision.Typically, GWA studies report the association of a single lead variant in a genetic region. If this variant is not the causal variant, or if there are multiple causal variants in the region, then additional information may be obtained by considering multiple variants per region. Information on such variants could be included correctly in a summarized analysis by considering conditional effects of variants on the risk factor and outcome by adjustment for the lead variant in a regression model [Yang et al., k in study X on Y is 2. If a particular study does not provide an estimate The likelihood-based model introduced in this paper can be naturally extended into a hierarchical (multilevel) model in order to combine summarized associations from multiple studies. We assume that genetic variant The winner's curse is the phenomenon that the association estimate of the variant with the strongest association from a GWA study tends to be overestimated [Göring et al., Sample code for estimating causal effects from summarized data for multiple variants associated with a risk factor in a single study and in multiple studies for R and WinBUGS is provided in the Supporting Information.If individual-level data are available, these should be used directly to perform a Mendelian randomization analysis. However, if individual-level data are not available, then valid statistical inference can still be obtained from summarized data on the associations of genetic variants with the risk factor and the outcome. On the basis of the simulations in this paper and the theoretical explanations for the differences in results, we recommend the likelihood-based model for applied analysis of summarized data. However, analyses should be restricted to uncorrelated genetic variants (no linkage disequilibrium), and care should be taken when including large numbers of variants to assess potential weak instrument bias by examining the F statistic in the regression of the risk factor on the variants.


PPI-LRT). When some parental genotypes are missing, one can use the expectation-maximization algorithm to fit the combined model. We also develop a second composite test (PPI-CT) based on a linear combination of the parent-phenotype-based test statistic and that from the traditional log-linear, transmission-based test. We evaluate the proposed methods through non-centrality parameter calculations and simulation studies and compare them to the previously proposed approaches, parenTDT and combTDT. We show that incorporation of parental phenotype data often improves statistical power. As illustration, we apply our method to a study of young-onset breast cancer and find that it improved precision for SNPs in FGFR2 and that estimated relative risks based on triads are closely replicated using the parental data.In studies of case-parent triads, information is often collected about history of the condition in the parents, but typically parental phenotypes are ignored. Including that information in analyses may increase power to detect genetic association for autosomal variants. Our proposed approach uses parental phenotypes to assess association independently of the usual case-parent-based association test, enabling cross-generational internal replication for findings based on offspring and their parents. Our model for parental phenotypes also resists bias due to population stratification. We combine the information from the two generations into a single coherent model that can exploit approximate equality of parental and offspring relative risks to improve power and can also test that equality. We call the resulting procedure the Parent-phenotype Informed Likelihood Ratio Test ( In the case-parents design, a design commonly used in genetic studies, investigators collect genotype (and exposure) data from affected individuals and their biological parents. They then carry out analyses designed to detect the distortions in transmission to affected offspring that are seen for SNPs associated with susceptibility. Such analyses typically neglect information on parental phenotype. That information may, however, be able to contribute additional power, especially for diseases that are not rare in a lifetime.parenTDT, is implemented in PLINK , a family-based study of breast cancer diagnosed before age 50. DNA samples from the cases, their parents, when available, and unaffected control sisters (when parents were missing) were genotyped using the Illumina HumanOmniExpressExome-8v1 array. About 20% of the mothers had themselves been diagnosed with breast cancer. This study motivated us to develop our method and will serve to illustrate its application.Family-based studies typically collect parental phenotype data because investigators want to ascertain first-degree family history. An example is the Two Sister Study  can be maximized. The model for risk can be parameterized to impose equality of parental and offspring relative risks or to test that equality. The maximization can make use of the expectation-maximization (EM) algorithm when some parental genotypes are missing, provided that missingness is noninformative, that is, unrelated to the unmeasured genotype, conditional on the observed data  can be modified to accommodate a log-additive (as used in our simulations), dominant or recessive mode of inheritance.Here the μWe model the phenotype of the mother of an affected daughter using a log-binomial model as follows:M,F) are parents who differ in their genotypes. Thus, robustness comes at a price. Also, we are assuming that the relative risks do not depend on epistasis with other causative variants that are enriched in parents of cases. That is, we assume that the conditioning on CD can be ignored in the modeling. . The risk parameterization in (3) also can be modified to accommodate log-additive, dominant or recessive models. Model (3) can be fitted using procedures for generalized linear models that are readily available in statistical packages.In model (3), risk in mothers of cases depends on paternal genotype through the αS1 or S2 for developing the disease compared to a fetus born to a mother with no copies. Model (2) above can be modified to accommodate maternally-mediated effects by introducing two maternal genetic-effect risk parameters, ρ1 and ρ2, as in Wilcox et al.  is called a maternally-mediated genetic effect. Suppose a fetus born to a mother with one or two copies of a risk allele has a relative risk of x et al. :(4)ln. For homogenous populations, we assumed Hardy-Weinberg equilibrium (HWE); for structured populations, we admixed two homogenous populations with different allele frequencies and baseline risks. We then calculated the frequencies of triads with an affected mother by multiplying each triad frequency by the baseline risk in mothers of affected offspring , modified as needed according to the mother's genotype and the scenario's maternal relative risk parameters . We obtained the frequency distribution of triads with unaffected mothers by subtracting the mother-affected triad frequencies from the overall triad frequencies. In scenarios where both parents can be affected, we first calculated the triad genotype frequencies stratified on the mother's phenotype. We then considered the father's phenotype in a similar way to further stratify the frequencies. The expected counts were eventually obtained by multiplying the calculated frequencies by 300, the total number of triads in the study.To calculate expected counts, we first ignored mother's phenotype and calculated case-parent triad frequencies based on the specified allele frequency, population structure, and risk parameters [child inherited genetic effects . We also considered several scenarios in which we assumed a stratified population with two equal-sized subpopulations where the ratio of baseline disease risks (risk in noncarriers) was either 1 or 3. The baseline disease risks in mothers of affected offspring in the two subpopulations were either the same  or different (0.1 and 0.2 for the two subpopulations). The allele frequencies in the two subpopulations were either the same  or different (0.1 and 0.3).We used simulations to explore the Type I error rates under the null, with 5000 replicates of each simulated scenario. We considered null scenarios in a homogenous population with or without maternally-mediated genetic effects ; (2) the likelihood ratio test using the combined likelihood of formula (1) with log-additive mode of inheritance (PPI-LRT). Under log-additive risk scenarios these two tests perform very similarly (data not shown). That similarity might be expected: the PPI-CT is based on separate maximization of the transmission and parental-phenotype models, each with its own risk parameter, whereas the PPI-LRT maximizes a likelihood that is the product of the same two likelihoods but with the relative risks for mothers and for offspring constrained to be the same. Whether fit separately or together under the constraint, if the models are correctly-specified, the two tests should be similar for large samples. In the following comparisons, we used PPI-CT for scenarios with no missing data and PPI-LRT when some genotypes are missing.The information from the two generations can be combined in two ways: (1) the composite test based on Offspring), the log-binomial model with log-additive mode of inheritance for testing association with parental phenotypes (Parent), the composite test based on CZ (PPI-CT), TDT, parenTDT, and the combined TDT (combTDT). In the absence of maternally-mediated genetic effects and when the sample size was 300, Parent showed slightly inflated Type I error rates of 0.06 and 0.066 for scenarios 3 and 4. This inflation was due to the relatively small number of families that were both genetically informative and had an affected mother, which reduced the faithfulness of the asymptotic approximation. When the sample size was increased to 600 or 1200, all methods maintained nominal Type I error rates and Offspring and Parent provided correct R1 and Rm1 estimates, respectively : in that event one would expect the msR to be between 1 and the maternally-mediated relative risk. For example, in row 5 the apparent relative risks for mother's genotype on her own phenotype  are between R1 = R2 = 1 and S1 = 1.4, S2 = 1.96, because her genotype is confounded by the causative genotype of her own mother in that one maternally-mediated effects scenario. The Parent, PPI-CT, parenTDT, and combTDT tests indeed show inflated Type I error rates when there are maternally-mediated effects.For Type I error rates, we evaluated the following tests: the log-linear model with log-additive mode of inheritance for testing transmission distortion  and fit a single intercept version to data from selected stratified scenarios. Type I error rates increased from 0.057 to 0.211 and from 0.051 to 0.183 in the two scenarios that we examined, documenting the need for mating-type-based intercept parameters.Parent test always performed better than parenTDT; so did our proposed PPI-CT vs. combTDT  scenarios, across different allele frequencies our proposed T Figure . NCP calh Figure .PPI-LRT was able to retrieve through use of the EM algorithm most of the lost power due to missing data. The TDT-based approach, however, suffered due to its need to discard families with missing genotypes .When genotypes were missing from 20% of the fathers, s Figure . The PPId Figure . HoweverWe observed similar patterns when the disease under consideration could affect both males and females Figure . The powZ statistics from the transmission-based and parent-phenotype-based tests under scenarios for Figure Another use of the parent-phenotype test when no genotypes are missing is as a replication for findings from the transmission-based test. We explored this role by examining the agreements in relative risk estimates and the corresponding FGFR2), a cell surface receptor with tyrosine-protein kinase activity, plays an essential role in the regulation of cell proliferation, differentiation, migration, and apoptosis. This gene has been consistently identified as a risk locus for breast cancer, and 7 SNPs in FGFR2 have had a reported GWAS p-value less than 10−5  as a comparison in this paper. Yu et al.  effect from an inherited gene effect. Consequently, the estimated relative risks can be biased if a maternally-mediated effect is involved. These problems also apply to other approaches, such as a case-control association study, but they are rarely acknowledged. Finally, while incorporating information related to parental phenotypes should always add power, that power gain will be modest if the disease is rare in parents of affected offspring. Breast cancer was a likely candidate, because its lifetime risk is so high , epistasis can potentially produce bias (away from the null) in estimation based on that parental phenotype model if genetic background acts synergistically with the variant under analysis. However, there was little evidence of that phenomenon in our breast cancer example.Some assumptions beyond the usual Mendelian inheritance assumption are needed for strict validity of the estimation of relative risks. Because Family-based studies often collect parent phenotype data and consequently improved methods for using that data to enhance genetic risk assessment will be widely applicable. Our proposed strategy for combining parent-phenotype information with genotype data from case-parents designs resists bias due to population structure, delivers improved power, provides relative risk estimates and can handle missing genotypes, thereby offering advantages over existing approaches.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.


In the past decade, rapid advances in genomic technologies have dramatically changed the genetic studies of complex diseases. Genome-wide association studies (GWAS) have been widely used in dissecting genetic structure of complex diseases. As of December 18th, 2014, A Catalog of Published Genome-Wide Association Studies (GWAS) had reported significant association of 15,177 SNPs with more than 700 traits in 2,087 publications T[P, respectively. A breeding equation is given byH is a heritability matrix and denoted byWhere Suppose that the phenotype can) be decomposed as a summation of additive effect, dominant effect and environment effect:kP byA, D and E represent the genetic additive, dominant and environmental effect, respectively. Denote the covariance matrix between the breeding value and phenotype values byIt is known thatIt follows from thi trait iih is a function of the genetic covariance between the thi trait and other traits. In other words, the heritability of each trait is influenced by its correlation with other multiple traits. This clearly demonstrates that the trait by trait genetic study will overlook the influence of other traits. The missing heritability may be due to trait by trait genetic analysis. The joint genetic analysis of multiple traits may increase the heritability.There has been increasingly consensus that individual genetic and epigenetic variants, individual genes, individual linear pathway and individual trait analysis cannot capture the intrinsic genetic and epigenetic complexity of multiple phenotypes.To completely capture the heritability, the right research direction is to jointly investigate genetic, expression, miRNA, epigenetic, metabolic variants, physiological traits, medical imaging measurements and environments in multiple traits which are often interactively organized networks. Integrative analysis of genetic, epigenetic, imaging and environmental variation in multiple phenotypes will fully uncover the heritability and facilitate the understanding the mechanism of the complex diseases. The popular methods for integrative analysis are mainly based on correlation and association analysis. These methods cannot efficiently detect, distinguish and characterize the true biological, mediated and spurious pleiotropic effects. Therefore, these approaches may not provide clear biologically or clinical relevant information that allows the mechanisms of genetic effects to be discovered and understood. To overcome these limitations, developing a new framework and novel statistical methods for inferring causal networks of genotype-phenotypes with NGS data and detecting, distinguishing and characterizing the true biological pleiotropic, mediated pleiotropic and spurious pleiotropic effects of genetic variants are urgently needed.An essential issue for using causal graphs to study genetics of multiple phenotypes is how to accurately and efficiently estimate the structure of causal graph from observational data. Structure learning of casual graphs has been shown to be NP-hard. Early methods for structure learning mainly focused on approximation algorithms, but such methods are unable to ensure the generation of the true causal graph. To obtain the causal graph from observation data as close to the biological causal graph as possible, “score and search”-based methods for exact learning causal graphs of genotype-phenotype to find the best-scoring structures for a given dataset are being developed. The accurate and robust estimation of the genotype-phenotype causal networks by the “score and search” methods will shift the paradigm of genetic studies of correlated multiple phenotypes from association analysis to causal inference, and dramatically facilitate discovery of the mechanism underlying multiple traits.Although their application to genome-wide genotype-phenotype network construction is difficult due to computational limitations, the “score and search” based causal inference methods are suitable to the phenome-wide association studies where starting phenomics, defined as the unbiased study of a large number of phenotypes in a population. We study the complex networks between multiple expressed phenotypes and genetic variants. Since the number of genetic variants in the phenome-wide association is quite limited and hence the size of the genotype-phenotype network is limited, the required computational time of construction of genotype-phenotype networks using causal inference is in the range the current computer system can reach. Advances in biosensors and sequencing technologies generate large amounts of phenotype and genetic data. Causal genetic and epigenetic network analysis may emerge as a new paradigm of genetic studies of complex traits. The main purpose of this editorial is to stimulate discussion about what are the optimal strategies to facilitate the development of a new generation of genetic analysis. I hope that more and more real data analysis in the future will greatly increase the confidence in causal inference for genotype-phenotype studies.


To determine the reasons for large standard deviation of bronchodilator response (BDR) and establish whether there is a potential heritable component in healthy subjects.1 after inhaling 400 µg salbutamol). Univariate quantitative genetic modeling was performed.67 monozygotic and 42 dizygotic adult twin pairs were assessed for bronchodilator response (%change in FEVP < 0.05), while no association was found with smoking habits, body mass index, or age. Within pair correlation in monozygotic twins was modest (0.332), but higher than in dizygotic twins (0.258). Age-, sex-, and baseline FEV1-adjusted genetic effect accounted for 14.9%  of the variance of BDR, shared environmental effect for 18.4% (95% CI 0%-46.8%), and unshared environmental effect for 66.8% (95% CI 46.8%-88.7%).Multiple regression modeling showed a significant association between BDR and sex and baseline FEV1 (Our twin study showed that individual differences in BDR can be mostly explained by unshared environmental effects. In addition, it is the first study to show low, insignificant hereditary influences, independently from sex, age, and baseline FEV1. Although no consensus exists, the latest American Thoracic Society (ATS)/European Respiratory Society (ERS) guideline recommends that, during a single testing session, an increase in FEV1 or FVC>12% and ≥200 mL from baseline is considered a significant BDR  were recruited from the Hungarian Twin Registry  as part Participants were recruited from general population via email, telephone, mail, or during twin festivals. Exclusion criteria included pregnancy, acute respiratory infection within three weeks of measurement, chronic obstructive airway diseases including asthma and chronic obstructive pulmonary disease (COPD), or foreseeable lack of compliance with test procedures. Participants were tested in two large hospitals in Budapest, Hungary by the same trained personnel . Prior to testing, they were asked to refrain from smoking for at least 3 hours, drinking alcohol or coffee for 10 hours, and eating for 1 hour.1 measurements were performed in accordance with guidelines of the American Thoracic Society/European Respiratory Society Task Force . The spirometer was calibrated daily using a 1-L syringe. FEVsk Force .1 after inhaling 400 µg salbutamol). Salbutamol was inhaled from a metered dose inhaler without a spacer device and post- bronchodilator spirometry was recorded after 15 minutes. Bronchial reversibility was considered if the increase in FEV1 was at least 12% and 200 mL  were computed for MZ and DZ twins separately. MZ and DZ subsamples were compared by Twin resemblance within MZ and DZ pairs was evaluated using Pearson correlation coefficients obtained with a saturated model in the Mx software ; the sat1 values (using the % change in FEV1 as a continuous variable)   ,26. Thesmption”) .P < 0.05.Using these models, it is possible to decompose the phenotypic variance of BDR into additive genetic (A), shared environmental (C), and unshared environmental (E) components (ACE model). Shared environment includes those factors that are not related to individual lifestyle, such as familiar socialization, air pollution, shared womb, while unique environment includes smoking or nutrition. All twin analyses were adjusted by age, sex, and baseline FEV1. The analyses were carried out with Stata  and Mx softwares  . The lev1 change compared to MZ twins, although the difference was not significant . 11 participants had a positive BDR test. Although BDR (FEV1 change) showed no correlation with baseline FVC (L) (P > 0.05), a significant but weak inverse correlation was noted with FEV1/FVC . Participants with FEV1/FVC<0.70 (n = 13) showed a greater BDR response than participants with FEV1/FVC > 0.70 .61.5% of twins were MZ and 38.5% were DZ (72% women) . No sign1 change in the regression model   .1 was modest but higher in MZ twins  than in DZ twins , suggesting a weak genetic effect in the expression of BDR. ACE analysis indicated that genetic and shared environmental effects were modest and that they together explained about one-third of total variance in FEV1 change , while unshared environmental influence explained the largest part of variance (E: 67%) .Intraclass correlation of percent change in FEV(E: 67%) . In the Although the assessment of bronchodilator response has become routine in clinical practice, background of the large variation of BDR in asymptomatic persons has remained unclear. BDR response is a common, but not a specific measure of bronchial asthma, which has considerable prevalence among non-asthmatic persons . We founGenetic influences have been investigated in diseases related to pathologic BDR. For example, heritability of asthma has been widely demonstrated -34. AlthSmoking status is an important environmental factor to be examined. Although smoking increases the risk of airway responsiveness , Lund etThe main strength of the present study is that all BDR tests were performed by the same trained researchers and the same validated device at all sites. Furthermore, the results can be generalized to the non-twin adult population, assuming that the enrolled twins did not differ from non-twin individuals with regard to the considered traits.1 in a healthy twin population. Unshared environmental effects explained most of the BDR variance, underscoring the importance of environmental factors  in determining individual differences in BDR in healthy adult individuals. This finding might explain the frequently experienced large standard deviation of BDR assessments in asymptomatic persons without airways disease, emphasizing the importance of lifestyle factors that influence BDR test results.In conclusion, the present study revealed a low heritability of BDR independently of sex, age, and baseline FEV


However, elucidating the causal genes underlying GWAS hits remains challenging. We applied the summary data-based Mendelian randomization (SMR) method to 28 GWAS summary datasets to identify genes whose expression levels were associated with traits and diseases due to pleiotropy or causality . We identified 71 genes, of which 17 are novel associations (no GWAS hit within 1 Mb distance of the genes). We integrated all the results in an online database (The online version of this article (doi:10.1186/s13073-016-0338-4) contains supplementary material, which is available to authorized users. Genome-wide association studies (GWAS) have identified thousands of genetic loci associated with various complex traits, disorders, and diseases , 2. The bXY) can be expressed as bXY = bZY/bZX, where bZY is the effect size of Z on Y and bZX is the effect size of Z on X [bXY using summary data from independent studies [bZY) from GWAS summary data and the estimate of SNP effect on gene expression (bZX) from summary data of an independent eQTL study. In this case, trait is the outcome (Y), gene expression is the exposure (X), and the top cis-eQTL that is strongly associated with gene expression is used as the instrument (Z) (we used cis-eQTL with PeQTL <5e-8 in this study). Here we use “association” rather than “causal association” because previous results [1 - > X, Z2 - > Y, and Z1 and Z2 are in LD). We provide details below of a test to distinguish pleiotropy  from linkage that is of less biological interest. The purpose of this study is to identify genes whose expression levels are associated with complex traits due to a shared causal variant. We therefore do not further distinguish between causality and pleiotropy .Details of the SMR method can be found in the Zhu et al. paper . In brief Z on X . This apf Z on X  is a twof Z on X , 18. It  studies . For the results  suggest bXY estimated at any of the cis-SNPs that are associated with gene expression  is expected to be equal to that estimated at the top associated cis-eQTL . Note that the HEIDI test takes into account non-independence of cis-eQTLs due to LD . Probes that show evidence of heterogeneity (e.g. PHEIDI <0.05) are rejected.As mentioned above, significant SMR results could also reflect linkage , which may be of less interest, at least in the first round of gene prioritization. To exclude SMR results that may reflect linkage, Zhu et al.  proposedu et al.  for morehttp://www.cnsgenomics.com/shiny/SMRdb/) [The previous SMR study analyzed three traits (body mass index (BMI), height, and waist-to-hip ratio adjusted by BMI) and two diseases (rheumatoid arthritis and schizophrenia) and identified 21 novel genes (genes that passed the SMR and HEIDI tests and that are located >1 Mb from the nearest GWAS hit) . In this/SMRdb/) , which iPeQTL <5 × 10–8. For each probe, the top associated cis-eQTL was used as the instrument for the SMR test. The SMR test was performed for each of the 5967 probes on 28 traits and disorders/diseases , this was reduced to 71 gene-trait associations (77 probes)  steps , associaare tool , 12. We There were 15 genes associated with more than one trait or disease (Additional file p value from the SMR method and the HEIDI test. In addition, Manhattan plots are given based on the p value from the SMR analysis and regional association plots are provided for those probe-trait associations that pass both the SMR and HEIDI tests.The results from this analysis can be queried and viewed in the online application . ResultsSMR, as indicated by the results, provides a means of using summary statistics from GWAS and eQTL data to prioritize likely functionally relevant genes within previously identified regions of association and in some cases identify novel gene associations.CD, Crohn’s disease; eQTL, Expression quantitative trait loci; GWAS, Genome-wide association study; HDL, High-density lipoprotein; HEIDI, Heterogeneity in dependent instruments; IBD, Inflammatory bowel disease; LD, Linkage disequilibrium; LDL, Low-density lipoprotein; MR, Mendelian randomization; QC, Quality control; SMR, Summary data-based Mendelian randomization; TC, Total cholesterol; UC, Ulcerative colitis