Fusarium culmorum isolates collected from natural field environments to assess their variation for two quantitative traits, aggressiveness and deoxynivalenol (DON) production on wheat plants grown in four different field environments (location-year combinations). Seventeen Fusarium graminearum pathogenicity candidate genes were assessed for their effect on the aggressiveness and DON production of F. culmorum under field conditions.Quantitative traits are common in nature, but quantitative pathogenicity has received only little attention in phytopathology. In this study, we used 100 HOG1 was found to be significantly associated with aggressiveness and deoxynivalenol (DON) production, explaining 10.29 and 6.05% of the genotypic variance, respectively.For both traits, genotypic variance among isolates was high and significant while the isolate-by-environment interaction was also significant, amounting to approximately half of the genotypic variance. Among the studied candidate genes, the mitogen-activated protein kinase (MAPK) To the best of our knowledge, this is the first report of a protein kinase regulator explaining differences in field aggressiveness and mycotoxin production among individuals from natural populations of a plant pathogen.The online version of this article (doi:10.1186/s12863-017-0511-9) contains supplementary material, which is available to authorized users. Quantitative traits are a key feature in nature . They arFusarium culmorum is a hemibiotroph, with a wide host range encompassing most of the cereals [While qualitative plant-pathogen molecular interactions, especially gene-for-gene interactions, have been widely studied, quantitative realtionships have received far less attention , 5. It i cereals , which mTriticum aestivum L.) and other small-grain cereals worldwide [Fusarium species have been reported as causal agents of FHB, among them the haploid ascomycetes Fusarium graminearum and Fusarium culmorum are two of the most important. F. culmorum has been traditionally related with FHB epidemics in the Mediterranean region [F. graminearum, which has been extensively studied and whose full genome sequence has been published [F. culmorum genome was just recently released [Fusarium head blight (FHB) is a devastating disease of bread wheat  determine the phenotypic variance for aggressiveness and DON production in replicated field experiments across two locations and 2 years with a moderately susceptible bread wheat cultivar as host, (ii) study sequences of the 17 candidate genes to identify nucleotide diversity within selected gene regions, (iii) test these quantitative trait nucleotides (QTNs) for their association with aggressiveness and DON production and estimate the proportion of genotypic variance explained by them.To enhance our understanding of quantitative pathogenicity, we performed a candidate gene association mapping based on pathogenicity-related candidate genes that firstly, have been reported or predicted as related with quantitative variations in pathogenicity, but do not affect the survival of the fungus and secondly, play a role in the pathogenicity signaling cascade. Based on the sequenced F. culmorum isolates from a previous diversity study [x Triticosecale) to minimize plot-by-plot interference. Fungal material consisted of four field populations (one from Russia and three from Germany), one transect population from Syria and one international collection  with a FHB rating of 6 on the 1–9 scale, where 1 = without disease and 9 = fully infected.Field experiments with these isolates were conducted during 2014 and 2015, and across two locations: Hohenheim  and Oberer Lindenhof  in Southwestern Germany. The experiments followed an incomplete block design (α design) with two replications. Experimental units were three-row plots , which were machine sown with 220 kernels per m5 conidiospores ml−1 was sprayed onto wheat heads during full flowering. Inoculum for each isolate was sprayed on its corresponding plot, according to the randomization of the experiment design, using a hand atomizer with constant air pressure of 3 bar from a tractor to ensure full coverage of all heads of the plot with the same dosage. All plots flowered simultaneously, because only one homogeneous wheat cultivar was used. This allowed inoculation and ratings for all plots at the same dates per location. Contamination with natural inoculum was negligible as verified by the border plots which had always a FHB rating < 5%.Inoculum production was done in shaking cultures according to an existing procedure . For inoTo assess aggressiveness of isolates, FHB symptoms were visually rated in each plot at least three times starting with the onset of symptom development, about 14 days after inoculation and was continued at 3- to 5-day intervals until the beginning of the yellow ripening stage. Rating was performed as percentage of infected spikelets per plot (0–100%). This reflects both the percentage of infected spikes per plot and the percentage of infected spikelets per spike in a single rating. The arithmetic mean of at least three ratings (i.e. the mean FHB ratings was used as aggressiveness trait).To measure DON production, wheat plots were harvested by hand at full ripening, carefully threshed in a single-head thresher  and cleaned with reduced wind speed. The remaining fragments of glumes and rachis were manually picked out to retain highly shrunken kernels in the sample. Cleaned wheat grain was ground in a commercial laboratory mill with a sieve size of 1 mm. Later, the coarse meal was analyzed to quantify the amount of DON by a commercially available immunotest .Phenotypic data of aggressiveness and DON production were obtained from one experiment performed during 2 years and across two locations, yielding four test environments. Aggressiveness data and DON production were arcsin transformed to meet the required normal distribution and subjected to outlier detection with the method BH-MADR  suggested by Bernal-Vasquez et al. . For theh2) was estimated as heritability on an entry-mean basis following the approach suggested by Piepho and Möhring [where E, R, I, and B denote environment, replication, isolate, and block or their interaction, respectively. Variance components were determined by the restricted maximum likelihood (REML) method. Significance of variance components was tested by model comparisons with likelihood ratio tests . Heritab Möhring . All sta Möhring  and R [4 Möhring  combinedFusarium spp., aggressiveness and/or trichothecene biosynthesis were used in our study  using the program MEGA6 [Seventeen candidate genes with a confirmed or predicted role in pathogenesis of dy Table . Based ody Table  for amplRes v4.0 , availabam MEGA6  to identPlabsoft [p values obtained from the one-degree-of-freedom score test were corrected for possible inflation [G) explained by each SNP was derived from the sums of squares of the SNP in a linear model using aggressiveness or DON production as dependent variables. As we found high multi-colinearity among SNPs within the candidate genes, only one SNP out of a group of highly linked SNPs (HOG1–380) was used in the linear model to assess the proportion of explained genotypic variance [r2) was used to estimate linkage disequilibrium (LD) between each pair of marker loci [Modified Rogers genetic distances  based oPlabsoft . PrincipPlabsoft  among inPlabsoft . A mixedPlabsoft . The p vnflation . The provariance . All calvariance  includinvariance  and APE variance . The squker loci  using TAker loci .F. culmorum isolates successfully produced symptoms on the inoculated wheat spikes and differences among isolates were observed at all environments. The overall mean of aggressiveness was 15.97%, varying from a minimum of 4.2% for isolate FC60 and a maximum of 19.8% for the isolate S109. The overall mean for DON production was 12.98 mg kg−1 ranging from 0.7 mg kg−1 to 22.95 mg kg−1 for FC50 and 9D22, respectively. Nivalenol (NIV) chemotypes displayed always the lowest DON production values as well as lowest aggressiveness values. Significant correlation between aggressiveness and DON production was observed  different from zero for both traits. Isolate-by-environment interaction was also significantly different from zero and about half that of the genotypic isolate variance . High LD was detected among SNPs within individual genes . Additionally, some SNPs in genes on different chromosomes showed high LD, for instance, the genes TRI6/MSB2, TRI6/CUT, MSB2/CUT. HOG1 displayed the lowest level of LD with any of the other studied genes.Analysis of the sequences of 17 genes for 100 HOG1 were found to be significantly associated (p < 0.05) with aggressiveness and DON production. Given high collinearity, all three SNPs were analyzed as only one haplotype, which explains 10.29 and 6.05% of the genotypic variance of aggressiveness and DON production, respectively. Any haplotype was restricted to a single population, so no bias by population structure can be expected. Additionally, we used principal coordinate and kinship matrix analysis to correct for population structure. Associated polymorphisms are located within the gene at positions 380, 382 (intron 3) and 724 (intron 5) relative to the start codon  with DON production and one insertion in CUT  with aggressiveness . This result and previous information concerning the function of those genes, suggested that they might be involved in the pleiotropic control of several basic physiological functions, among them pathogenicity [The fact that the majority of SNPs were found in genes encoding secreted or membrane proteins, could be explained by their role in the molecular communication with the host and signal perception from the environment, which might be subject to positive selection pressure as widely reported –85. By cgenicity –93.TRI6 and CUT  HOG1 is a core component of the high osmolarity glycerol (HOG) pathway and has been well characterized in S. cerevisiae [S. cerevisiae Fus3/Kss1, Slt2, and Hog1 MAPKs, and function in separate signaling cascades to regulate infection-related morphogenesis, cell wall remodeling, and high osmolarity stress response, respectively [Fusarium graminearum as a model and generated deletion mutants for 96 protein kinase genes, out of them 42 kinase mutants were significantly reduced in virulence or non-pathogenic [FgHOG1 is a core component of the HOG pathway in F. graminearum, which has been involved in the response to various environmental stresses [HOG1 regulation confer advantages in the response of F. culmorum to multiple stresses, especially to the osmotic and oxidative stresses resulting from the plant defense mechanisms. Our study further supports the observation of Talas et al. [revisiae . MAPK parevisiae . Most fuectively –99. The thogenic . The FgHstresses . Based os et al. , suggestHOG1 was 10.29 and 6.05% for aggressiveness and DON respectively. Similar results have been reported for F. graminearum, where genome-wide association reveled quantitative trait nucleotides explaining from 9% up to a maximum of 24% of genotypic variance [Quantitative traits are controlled by complex interactions of genes, and therefore single or few genes explaining a large percentage of genetic variation are not expected . Consistvariance . The posHOG1 haplotype expressed on average the highest values for aggressiveness and DON production, which could be an effect of selection favoring these most aggressive genotypes. This fact highlights the importance of integrated plant disease management strategies to prevent undesired selection of the most aggressive genotypes of F. culmorum. Consistently, plant breeding must then steadily increase the level of resistance in cultivars, e.g. by pyramiding effective quantitative disease resistance loci.Isolates having the most frequent HOG1 are located in introns three and five. The fact that SNPs located within a noncoding region of HOG1 are associated with the variation in aggressiveness and DON production could be explained by two hypotheses. Firstly, the detected SNPs are in linkage disequilibrium (LD) with causal polymorphisms in nearby genes or regulatory sequences that are responsible for the trait variance. Secondly, the nucleotide change within the intron is involved in post-transcriptional regulation, like alternative splicing, associated with the response to multiple stresses. Alternative splicing has been reported in fungi, including F. verticillioides [F. graminearum [F. graminearum, grown under just one stress condition, 231 genes undergoing alternative splicing were found, but more genes are expected to follow post-transcriptional regulation if tested under different stresses [Arabidopsis thaliana [F. graminearum the alternative splicing events took place at different vegetative growth stages and suggested they might be important in adaptation of F. graminearum to changing environmental conditions. Furthermore, active functionality of intronic polymorphisms has been found in other organisms e.g. humans [The three SNPs found in llioides  and F. gminearum –103. In thaliana . Zhao et. humans  and pigs. humans .HOG1 located both in exons  and introns . On the other hand, some other genes had polymorphic SNPs with MAF > 5% but showed no association or had p values just slightly higher than the significance threshold Number of isolates, sampling scheme, origin, and host characterizing the Additional file 2:Primer sequences, PCR conditions, and the full amplified sequences for the candidate genes used in this study. (XLS 53 kb)Additional file 3:Best linear unbiased estimates (BLUEs) for mean aggressiveness and DON production calculated across four environments (location × year combinations) for 100 F. culmorum isolates. (XLSX 15 kb)Additional file 4:Genotyping information of 100 isolates of F. culmorum. (XLSX 21 kb)Additional file 5:F. culmorum isolates. (PDF 10 kb)Histograms for mean aggressiveness and DON production. Histograms of best linear unbiased estimates (BLUEs) for mean aggressiveness (top) and DON production (bottom) calculated across four environments (location × year combinations) for 100 Additional file 6:F. culmorum isolates. Population structure and familial relatedness based on 10 SSR markers. Principal coordinate analysis for 100 F. culmorum isolates, based on modified Rogers’ distance. Number in parentheses refer to the proportion of variance explained by the principal coordinate. (PDF 17 kb)Principal coordinate analysis for 100 Additional file 7:p values for association tests against mean aggressiveness and DON production. (LOG 402 bytes) (XLS 34 kb)Characteristics of identified single nucleotide polymorphisms (SNPs) in the candidate genes and


The relationship between genetic variability and individual phenotypes is usually investigated by testing for association relying on called genotypes. Allele counts obtained from next-generation sequence data could be used for this purpose too. Genetic association can be examined by treating alternative allele counts (AACs) as the response variable in negative binomial regression. AACs from sequence data often contain an excess of zeros, thus motivating the use of Hurdle and zero-inflated models. Here we examine rough type I error rates and the ability to pick out variants with small probability values for 7 different testing approaches that incorporate AACs as an explanatory or as a response variable. Model comparisons relied on chromosome 3 DNA sequence data from 407 Hispanic participants in the Type 2 Diabetes Genetic Exploration by Next-generation sequencing in Ethnic Samples (T2D-GENES) project 1 with complete information on diastolic blood pressure and related medication. Our results suggest that in the investigation of the relationship between AAC as response variable and individual phenotypes as explanatory variable, Hurdle-negative binomial regression has some advantages. This model showed a good ability to discriminate strongly associated variants and controlled overall type I error rates. However, probability values from Hurdle-negative binomial regression were not obtained for approximately 25 % of the investigated variants because of convergence problems, and the mass of the probability value distribution was concentrated around 1. Diastolic blood pressure (DBP) measures the pressure during heart relaxation. High DBP increases the risk of heart attacks, stroke, and kidney failure. DBP is dependent on the age, gender, and medication of an individual . A genetThe relationship between genetic variability and DBP is commonly investigated by testing for association between called genotypes and phenotypes. In sequence data, genotypes are called relying on sequence reads. Alternatively, association tests without calling genotypes have been suggested .Depth in DNA sequence data refers to the number of reads at a position. In next-generation sequence data there are 2 counts of allelic depth, the number of reference alleles, and the number of alternative alleles. Here we use the number of alternative allele counts (AACs) and the total read depth. AACs are genotype measurements that are more informative than called genotypes in the sense that the 2 counts—“zero reference alleles out of 100” and “1 reference allele out of 100”—would translate into the same called genotype. In other words, after applying user-defined data quality filters, the uncertainty in genotype calling is rarely taken into account in statistical analyses.Several statistical procedures can be used for testing association between allele counts and a phenotype of interest. When AAC is regarded as the response variable and the total read depth as an offset, standard models for count data can be used. The response variable can also be defined as the ratio of the AAC to the total read depth. In this case, linear regression can be used to investigate the genotype–phenotype relationship. It is also possible to model the phenotype as a response variable, and the ratio “AAC/total read depth” as an explanatory variable.We used data from the Genetic Analysis Workshop (GAW) 19, which are provided for 1943 Hispanic samples that have been whole-exome sequenced as part of the Type 2 Diabetes Genetic Exploration by Next-generation sequencing in Ethnic Samples (T2D-GENES) Project 1 to compare different regression techniques.Phenotype data were provided for 1943 Hispanics who participated in the T2D-GENES Project 1, and included 4 variables: DBP, age, gender, and medication . We exclRegarding genotype measurements, exonic regions were isolated using Agilent TruSeq capture reagents, and individually barcoded samples sequenced in Illumina HiSeq 2000 instruments. Across the coding sequence of 18,281 genes, an average read depth of approximately 82-fold was reached. We used VCFtools (version 0.1.4a) to extract the data needed: counts of reference and alternative alleles , genotype (GT field in the FORMAT tag), and average genotype quality (GQ field in the FORMAT tag). Total read depth was calculated as the sum of the counts for the reference and the alternative alleles. We also used VCFtools to calculate the minor allele frequency (MAF). Our analysis focused on biallelic variants in chromosome 3. Variants with a MAF of less than 0.003 were excluded, leaving a total of 8957 variants for analysis.We compared different regression models and treated AAC both as response and as explanatory variable. The relationship between AAC as response variable , and adjusted-DBP as explanatory variable was first investigated by negative binomial regression. Zero-inflated negative binomial (ZI-NB) and Hurdle-negative binomial (Hu-NB) models are more flexible than negative binomial regression in the presence of zero inflation , 7. CompWe also investigated the genotype–phenotype relationship based on the ratio “AAC/total read depth” and adjusted-DBP, as response and explanatory variables in standard linear and robust linear regression .p values) from different regression models. These analyses do not amount to a systematic model comparison relying on extensive simulations, but they could be suggestive of the most promising modeling approaches.Type I error rates were roughly estimated assuming that the large majority of the 8957 investigated variants were under the null hypothesis of no genetic association. Quantile–quantile (Q-Q) plots were used to explore possible disparities between small probability values . Note that treating the ratio “AAC/total read depth” as a response or explanatory variable in standard linear regression resulted in identical p values. In robust linear regression, treating the ratio “AAC/total read depth” as a response variable resulted in a high proportion of missing p values (83 %). The reason was a perfect model fit after downweighting outliers  by robust regression. Figure Among the 7 investigated models, standard linear regression generated the lowest proportion of missing p values of less than 0.05 from ZI-NB and Hu-NB regression models was lower for variants with a median AAC of less than 60 than for variants with higher median AACs. By contrast, this proportion did not depend on the median AAC for standard and robust linear regression.Motivated by this result, the rest of the manuscript focuses on the 4 regression models with the best calibrated overall rough type I error rates: ZI-NB and Hu-NB, standard linear regression, and robust linear regression with the ratio “AAC/total read depth” as a response variable. Table p values from ZI-NB and Hu-NB regression were particularly relevant for variants with a MAF greater than 0.05. The relationship between rough type I error rates and the MAF showed no clear pattern. For example, the proportion of p values less than 0.05 from Hu-NB regression decreased with increasing the MAF, and showed a U-pattern for standard linear regression. As expected, p values from robust linear regression were practically not available for variants with a MAF of less than 0.05.Interestingly, convergence problems and missing P values from robust linear regression were practically not available for variants with an average genotype quality of less than 60,000.Variants were also grouped into 3 balanced categories according to their average genotype qualities . Rough type I error rates slightly decreased with increasing average genotype quality for ZI-NB and Hu-NB regression models. By contrast, approximate type I error rates increased with increasing average genotype quality for standard and for robust linear regression. p values for the 4 most promising regression models. To interpret results, the proportion of missing p values and the properties of each model discussed above should be kept in mind. Although 4 % of p values were smaller than 0.05 for Hu-NB and 6 % for ZI-NB regression, the mass of the p value distributions was concentrated around 1 . Hu-NB regression picked out variants with small p values more clearly than the ZI-NB version (A) with similar proportions of missing p values, and similar dependence patterns of the rough type I error rates on the median AACs and on the average genotype quality. However, test statistics from ZI-NB regression were likely not properly calibrated for variants with MAFs in the interval .Figure p values, but p values were within 95 % confidence bands. It should be kept in mind that robust linear regression only generated p values for variants with a MAF greater than 0.05, and for variants with an average genotype quality greater than 60,000. Note the differential scales of the y-axis in Fig. Figure The direct inspection of raw counts is an established approach to investigate differential expression based on RNA sequence data , but the analysis of DNA sequence data almost always focuses on called genotypes. Satten et al  proposedThe possibility of using AAC instead of called genotypes motivated the present research. The underlying distribution of AAC reflects the reliability of called genotypes, and a direct analysis of AAC would permit integration of this uncertainty into association results. However, next-generation sequence data is noisy and the quality of the called genotypes depends on the chromosomal position. Lots of variants are artifactual and rely on small counts.The exclusive use of real data without additional simulations is a limitation of the present study. Nonparametric and quintile regression could be potential alternatives to robust linear regression in the presence of outlying AACs. We investigated the dependency of results on AAC, but data was not available for variants with low-quality genotype calls. It would be interesting to examine the behavior of Hu-NB regression for these variants.We took advantage of real data to compare different models that investigate the relationship between sequence allele counts and the adjusted-DBP. The methods with the best control of rough type I error rates were ZI-NB and Hu-NB regression for the relationship between AAC and adjusted-DBP, and standard and robust linear regression for the relationship between the ratio “AAC/total read depth” as a response variable and adjusted-DBP as an explanatory variable.p values, occurrence of convergence problems, and robustness of p values against departing DBP observations indicated that Hu-NB regression constitutes a promising approach to assess the association between AAC and individual phenotypes.The simultaneous consideration of discriminative ability of variants with small


Z-scores or (ii) inverse-variance weighting of allelic effect sizes after conversion onto the log-odds scale. Our conclusions thus provide essential recommendations for the development of robust protocols for meta-analysis of binary phenotypes with linear models.Linear mixed models are increasingly used for the analysis of genome-wide association studies (GWAS) of binary phenotypes because they can efficiently and robustly account for population stratification and relatedness through inclusion of random effects for a genetic relationship matrix. However, the utility of linear (mixed) models in the context of meta-analysis of GWAS of binary phenotypes has not been previously explored. In this investigation, we present simulations to compare the performance of linear and logistic regression models under alternative weighting schemes in a fixed-effects meta-analysis framework, considering designs that incorporate variable case–control imbalance, confounding factors and population stratification. Our results demonstrate that linear models can be used for meta-analysis of GWAS of binary phenotypes, without loss of power, even in the presence of extreme case–control imbalance, provided that one of the following schemes is used: (i) effective sample size weighting of  A random-effects model is then used to evaluate the evidence of association for an SNP by accounting for the contribution of the GRM to the overall variance of the trait. This flexible modelling framework can incorporate fixed effects to account for covariates, and can be used to estimate components of heritability that are explained by (subsets of) genotyped SNPs.9Linear mixed models (LMMs) have received increasing prominence in the analysis of genome-wide association studies (GWAS) of complex human traits because they account for genetic structure, across participants, which arises from population stratification, cryptic relatedness or close familial relationships.10 Recent studies have also demonstrated that LMMs have less power than traditional logistic regression modelling techniques in GWAS of case–control phenotypes unless ascertainment is adequately accounted for.12Linear models assume that the outcome of interest is a quantitative trait with a Gaussian distribution. However, it has become increasingly common to use LMM approaches in population- and family-based GWAS of binary phenotypes because of their flexibility in accounting for structure, and their computational tractability in comparison with logistic mixed models. Linear models have the disadvantage that allelic effect estimates cannot be interpreted, directly, in terms of the odds ratio (OR), although approximations on the log-odds scale can be obtained.at the cohort level have been explored previously,10 their utility in the context of meta-analysis has not been investigated. In this study, therefore, we present simulations to compare the type I error rates and power of generalised linear (mixed) models under alternative weighting schemes in a fixed-effects meta-analysis framework. We consider a range of study designs that incorporate variable case–control imbalance across GWAS to reflect the increasing use of large-scale, population-based biobanks, and investigate the impact of confounders and population stratification on the properties of the analytical strategies. We conclude by making recommendations for the development of robust protocols for meta-analysis of GWAS of binary phenotypes with linear (mixed) models, which will be highly relevant in the era of large-scale consortium efforts to unravel the genetic basis of complex human diseases.While the properties of linear (mixed) models in the analysis of GWAS of binary phenotypes n participants, with binary phenotypes, genome-wide genotypes and additional covariates denoted by y, G and x, respectively. We denote the phenotype of the ith participant by yi∈{0, 1}, and their genotype at the jth SNP by Gij∈, coded under a dosage model in the number of minor alleles. In a generalised linear mixed modelling framework,Consider a GWAS of g(.) is the link function, β is the allelic effect of the jth SNP on the phenotype and γ is a vector of covariate regression parameters. In this expression, u is a vector of random effects, defined by u~MVN, for the variance component λ and GRM K, derived from genome-wide SNP data  to account for population structure. A likelihood ratio test with one degree of freedom is then formed by comparing the maximised log likelihood of the unconstrained model (1) with that obtained under the null hypothesis of no association, β=0. Note that model (1) reduces to a generalised linear model (no random effects) for λ=0, which is appropriate in the absence of structure because of population stratification and/or familial relationships.where jth SNP. However, under a linear regression model, for the identity link function, the maximum-likelihood estimate of the allelic effect, 10 given byUnder a logistic regression model, for the logit link function, the maximum-likelihood estimate of the allelic effect, andβLIN=0, because the effect of any SNP on the phenotype is expected to be small. Here, we estimate 10where N GWAS, for which we have tested for association of the phenotype with the jth SNP under a generalised linear model (1). We denote the effective sample size of the kth GWAS by nk, given byConsider nk0 and nk1 denote the number of controls and cases, respectively. In the kth GWAS, we also denote the P-value obtained from the regression model by pk, and the estimated allelic effect from the regression model by where Z-score for association of the jth SNP across GWAS byUnder an effective sample size weighting scheme, we obtain a combined φ−1 is the inverse normal distribution function. Alternatively, under an inverse-variance weighting scheme, we obtain an estimate of the allelic effect of the jth SNP on the phenotype, and the corresponding variance, across GWAS bywhere whereZ-score for association of the jth SNP across GWAS byWe then obtain a combined We have performed a series of detailed simulations to investigate the type I error rates and power of alternative approaches to study-level association testing of a binary phenotype (linear and logistic regression modelling) in the context of fixed-effects meta-analysis (with effective sample size or inverse-variance weighting schemes), summarised in q; and (ii) the allelic OR for the risk allele, denoted ψ.Our first study design consisted of 10 cohorts of a binary phenotype, ascertained from the same population, each comprising of 2000 participants. We considered three scenarios for case–control imbalance, described in For each model, we generated 10 000 replicates of genotype data for the causal SNP in the study participants. For each replicate, genotypes were simulated in the required numbers of cases and controls in each cohort, according to the causal SNP RAF and allelic OR, and assuming Hardy–Weinberg equilibrium. Specifically, genotypes in cases and controls were simulated from a multinomial distribution, with probabilities given byR denotes the risk allele and where To assess the impact of confounders on the alternative analysis strategies, we also simulated a binary covariate for each individual from a Bernoulli distribution, taking the value 1 in cases with probability θ and (1−θ), respectively, and were otherwise ascertained from sub-population B. The RAFs in sub-populations A and B were assumed to be 0.4 and 0.6, respectively, and used to generate genotypes at the causal SNP under Hardy–Weinberg equilibrium, from a multinomial distribution, as defined above. For each individual, we then simulated genotype data for 1000 additional uncorrelated SNPs, assuming Hardy–Weinberg equilibrium, and independent of case–control status, from a multinomial distribution. For each SNP, we assumed minor allele frequencies of 0.2 and 0.8, respectively, in sub-populations A and B. Genotypes at the 1000 SNPs were then used to construct the GRM within each cohort.We also investigated the impact of population stratification on the alternative analysis strategies. Within each cohort, cases and controls were ascertained from sub-population A with probabilities Our second study design consisted of two cohorts of a binary phenotype, ascertained from the same population. The first cohort consisted of 1000 cases and 1000 controls. The second cohort represented a large biobank of 100 000 individuals, within which we investigated the impact of the extent of case–control imbalance on the meta-analysis. For each scenario, we assumed a causal SNP RAF of 0.5 and an allelic OR of 1.25, and generated 10 000 replicates of genotype data for the causal SNP in the study participants. For each replicate, genotypes were simulated in the required number of cases and controls in the two cohorts, assuming Hardy–Weinberg equilibrium, from a multinomial distribution, as described above.P-values under a linear regression model (no random effects) within each cohort for each replicate. To obtain parameter estimates under a logistic regression model (no random effects) within each cohort, we used a Firth bias-corrected likelihood ratio test, also implemented in EPACTS, which has been demonstrated to be more robust to case–control imbalance than Wald or score statistics for binary outcomes.13 To obtain parameter estimates under a LMM (random effects for GRM) within each cohort, we used EMMAX,1 also implemented in EPACTS. We combined summary statistics through fixed-effects meta-analysis with effective sample size and inverse-variance weighting using METAL14 and GWAMA,15 respectively.For both study designs, we used a linear Wald test, implemented in EPACTS, to obtain parameter estimates and association P<0.05 and P<0.01, and at the traditional genome-wide standard of P<5 × 10−8. For estimated allelic effect sizes on the log-odds scale (from the logistic regression model and after conversion from the linear regression model), we also evaluated bias and mean square error (MSE).Across all scenarios, each test of association, after meta-analysis, was evaluated at nominal significance thresholds of without random effects for the GRM and for simulations generated in the absence of structure or confounders. P<0.05, irrespective of the analytical approach and the extent of case–control imbalance.We first considered the properties of fixed-effects meta-analysis of association summary statistics obtained from linear and logistic regression models without random effects for the GRM and for simulations generated in the absence of structure, but where the binary phenotype was also correlated with a confounding variable. We assumed a causal SNP with RAF 50% and an allelic OR of 1.15 for the binary phenotype. We next considered the properties of fixed-effects meta-analysis of association summary statistics obtained from linear and logistic regression models θ, that a case is ascertained from sub-population A. Irrespective of the extent of population stratification, the type I error rate was consistent with the nominal significance threshold of P<0.05 for any fixed-effects meta-analysis strategy using the linear model with random effects for the GRM. However, as expected, type I error rates became increasingly inflated as the extent of population stratification was elevated for all fixed-effects meta-analysis strategies using the linear model without a random effect for the GRM.We then considered the properties of fixed-effects meta-analysis of association summary statistics obtained from linear regression models, with and without random effects for the GRM and for simulations generated in the presence of population stratification (cases and controls ascertained from sub-populations A and B). Finally, we considered the properties of fixed-effects meta-analysis of association summary statistics obtained from linear and logistic regression models without random effects for the GRM, for simulations generated in the absence of structure. In these simulations, association summary statistics were aggregated from a population biobank of 100 000 participants with extreme case–control imbalance and a balanced case–control study of 2000 participants. 16 for the meta-analysis of association summary statistics from LMMs implements inverse-variance weighting of allelic effect estimates without conversion to the log-odds scale.We have presented simulations to evaluate the utility of linear models in the context of meta-analysis of GWAS of binary phenotypes. Our results highlight that the extent of case–control imbalance across studies can have a major impact on the performance of a linear regression model. We have demonstrated that, for extreme imbalance, meta-analysis under inverse-variance weighting of allelic effect estimates from a linear regression model results in a substantial reduction in power, unless they are first converted onto the log-odds scale. This is of particular importance because existing, widely used softwareFor a binary phenotype, under a linear regression model, the standard error of an allelic effect estimate is dependent on multiple factors, including allele frequency, total sample size, OR and variance of the trait. For a fixed total sample size, the variance of the trait  decreases as the case–control imbalance becomes more extreme. However, the power to detect association with the binary phenotype is less in imbalanced studies, and they should, in fact, be given less weight in any meta-analysis. Correction of allelic effect estimates from the linear regression model onto the log-odds scale circumvents this issue by inflating the corresponding standard error by a factor that is inversely proportional to the case–control imbalance.20 The utility of linear models in these extremely imbalanced case–control designs has not been previously studied in the context of meta-analysis. Crucially, our investigation highlights that linear models can be used for meta-analysis of GWAS of binary phenotypes, without loss of power, even in the presence of extreme case–control imbalance, provided that one of the following schemes is used: (i) effective sample size weighting of Z-scores or (ii) inverse-variance weighting of allelic effect sizes after conversion onto the log-odds scale.Case–control imbalance is becoming increasingly widespread in GWAS of binary phenotypes, particularly with the availability of large-scale, extensively studied, population-based biobanks, often with linkage to electronic medical records.22 Heteroscedasticity can occur in the presence of population stratification, for example, when strata have variable case–control imbalance or heterogeneous disease risk. Under these circumstances, LMMs are valid only for variants that have similar RAFs across strata, such that there is only weak confounding due to structure. Otherwise, computationally efficient software will be required to implement logistic mixed models on the scale of the whole genome.Our simulations demonstrate that meta-analysis of association summary statistics for binary phenotypes from LMMs is robust to population stratification, even in the presence of extreme case–control imbalance. However, it is important to note that this conclusion is valid only when population stratification does not lead to violation of the LMM assumption of homoscedasticity, for which residual variances are constant, irrespective of covariates.


The evaluation of less frequent genetic variants and their effect on complex disease pose new challenges for genomic research. To investigate whether epigenetic data can be used to inform aggregate rare-variant association methods (RVAM), we assessed whether variants more significantly associated with colorectal cancer (CRC) were preferentially located in non-coding regulatory regions, and whether enrichment was specific to colorectal tissues.Active regulatory elements (ARE) were mapped using data from 127 tissues and cell-types from NIH Roadmap Epigenomics and Encyclopedia of DNA Elements (ENCODE) projects. We investigated whether CRC association p-values were more significant for common variants inside versus outside AREs, or 2) inside colorectal (CR) AREs versus AREs of other tissues and cell-types. We employed an integrative epigenomic RVAM for variants with allele frequency <1%. Gene sets were defined as ARE variants within 200 kilobases of a transcription start site (TSS) using either CR ARE or ARE from non-digestive tissues. CRC-set association p-values were used to evaluate enrichment of less frequent variant associations in CR ARE versus non-digestive ARE.−4). Additionally, we found enrichment of stronger CRC association p-values for rare variant sets of CR ARE compared to non-digestive ARE .ARE from 126/127 tissues and cell-types were significantly enriched for stronger CRC-variant associations. Strongest enrichment was observed for digestive tissues and immune cell types. CR-specific ARE were also enriched for stronger CRC-variant associations compared to ARE combined across non-digestive tissues (p-value = 9.6 × 10Integrative epigenomic RVAM may enable discovery of less frequent variants associated with CRC, and ARE of digestive and immune tissues are most informative. Although distance-based aggregation of less frequent variants in CR ARE surrounding TSS showed modest enrichment, future association studies would likely benefit from joint analysis of transcriptomes and epigenomes to better link regulatory variation with target genes. Colorectal Cancer (CRC) is a leading cause of cancer-related morbidity and mortality worldwide . An undeAlthough GWAS enable the discovery of common variant associations, array-based GWAS are not well-suited to evaluate the role of less frequent (0.1% < MAF < 1%) variants on CRC risk. Whole-genome sequencing (WGS) studies offer an alternative approach to array-based GWAS for investigating rare variants. Specifically, WGS can be performed on a reference set that is used to impute sequenced variants into samples with existing genome-wide genotype array data ,7. Recengenome-wide search for rare and less frequent variant associations, an important challenge is to identify units of analysis outside of coding regions that are biologically meaningful and enriched for associations with CRC.The power of rare-variant association methods (RVAM) can be improved in a variety of ways. By utilizing functional genomic data, tests of single variant trait associations can be restricted to regions of putative functional significance (or weighted accordingly). Power can also be improved by using aggregate testing for rare-variants. In aggregate RVAM, variants are aggregated within a set  and tested for association with a phenotype. To date, most RVAM have focused on the 1–2% of the genome that encodes for proteins ,11 whereTo define non-coding regulatory regions that modulate gene expression, we used functional genomic data from the NIH Roadmap Epigenome project and ENCODE in 127 different tissues and cell-types, including 3 colorectal epigenomes . We then2 = 0.93). The KS test enrichment p-value, however, was not correlated with the number of ARE variants in a tissue or cell-type (Pearson correlation r2 = 0.02). For the 127 tissue and cell-type specific ARE, all but neuron cultured cells showed statistically significant (α = 0.05/127 comparisons = 3.9×10−4) enrichment of CRC associations from the one-sided Kolmogorov-Smirnov (KS) test  CRC associations  when compared to non-ARE regions of the genome. On average there were 692,408  variants positioned in ARE of the 127 tissues and cell-types examined in this analysis. For comparison, there was an average of 7,585,498  common variants outside of the ARE regions. The number of ARE variants in a tissue was highly correlated with the number of ARE in a tissue (Pearson correlation rKS) test . We founKS) test . Embryon−4; −4 to 0.001). These epigenomes are derived from tissues and cell-types that are anatomically distant from CR tissues and with more divergent epigenomes .Next, we investigated whether colorectal (CR) tissue-specific ARE were enriched for low p-values of CRC-variant association in comparison to the ARE of non-CR tissues and cell-types. To do so, we pooled ARE in the three reference CR tissues into a single set and made comparisons to ARE in each of the remaining 124 tissues and cell-types. We then generated an empirical p-value using adaptive resampling with up to 10,000 iterations. After adjustment for 124 multiple comparisons, CR ARE were only enriched for low p-values of CRC-variant association in comparison to ARE in iPSC cells  was maintained for enrichment analysis. After LD pruning we still found significant enrichment of stronger CRC-variant associations in CR ARE in comparison to ARE combined across non-digestive tissues and cell-types at LD thresholds of r2 = 0.9, 0.8, and 0.5  near ARE, we employed a priority pruning scheme, where the variant with the lowest CRC association p-value in an LD block  . AccordiConsistent with the results from previous studies , we founIn addition, for aggregate testing of rare-variant associations, we found that sets based on CR-specific ARE were enriched compared to sets based on ARE from non-digestive cell-types. We acknowledge that physical proximity of enhancers to genes has limited predictive accuracy for identifying the gene targets . However2 ≥ 0.5 threshold, we considered all variants that tag one of the 48 known, common-variant loci for CRC risk . Finally, we were able to leverage high-quality epigenetic data that have been uniformly processed by the Roadmap and ENCODE epigenome consortia. By utilizing DHS available across a subset of the 127 Roadmap epigenomes, the resolution of predicted functional elements was greatly improved and thus aided in reducing background variation less likely to be related to CRC.Although these data aided in honing in on likely functional regions, the ARE we investigated only cover a small portion of the genome. On average, each cell-type specific ARE covered 3% of the autosome, leaving 97% of the genome untested in this analysis. In addition, the rare variants in this analysis were mainly imputed from a panel of 919 samples with 6x coverage WGS as opposed to more expensive sequencing at higher depths. While this internal sequencing panel has the advantage of being potentially enriched for risk variants given the higher proportion of CRC cases, lower coverage sequencing has decreased ability to confidently call rarer variants. Consequentially, we were unable to impute and test the CRC association for many of the true rare variants present in our study population. Based on the QC assessment we are confident in the calling of the variants from the WGS panel that were included in this study, and in the subsequent imputation. However, it should be noted that assessing the imputation quality of rarer variants remains an active area of study. Balancing sample size with sequencing coverage is an important consideration for rare variant studies. In light of the decreasing cost of WGS, we would recommend future studies to use higher coverage sequencing in order to better assess the burden of rarer regulatory variation. Another important consideration is the role of other types of functional elements both within the coding region (such as frameshift or splice variants) and in the non-coding regions . Furthermore, we had access to the epigenomes from only 3 non-diseased colorectal tissues. With more epigenetic data from relevant tissues and cell-types, the predicted ARE from CR and other digestive tissues would be more comprehensive and precise.ARE defined by the Roadmap and ENCODE epigenetic data represent empirical estimates of the genomic location of enhancers and promoters. These elements regulate multiple genes and operate as nodes in gene expression networks. As is, we are treating the ARE as independent, distinct units. A logical next step is to define gene-enhancer links, where the entire regulatory-coding module can be treated as a unit of analysis . As new gene expression and epigenetic data become available, we will be able to define gene-enhancer links ,23 and cAll participants gave written informed consent and this study has been approved by the Fred Hutchinson Cancer Research Center (FHCRC) Institutional Review Board.Study-specific eligibility criteria, details about genotyping, and quality control (QC) analyses can be found in Peters et al . Briefly2<0.3) were removed from subsequent analysis. Distributions of sequencing depth, mapping quality, beagle allelic R2, minor allele frequency and minor allele count were examined for QC purposes.610 CRC cases and 309 controls from the WHI study were sequenced with low-pass coverage and served as the internal WGS imputation panel for this study . Detailshttp://www.broadinstitute.org/~meuleman/reg2map/HoneyBadger2_release/). Chromatin accessible regions were defined using the union of DNaseI-hypersensitivity sequencing (DNase-seq) peaks across 53 tissues and cell types. Enhancer and promoter states were previously annotated for the epigenomes of 127 tissues and cell-types (Roadmap + ENCODE) using a 5-mark 15-state Hidden Markov Model (ChromHMM) [Annotations for active regulatory elements (AREs) ARE were downloaded from Wouter Meuleman Reg2Map (hromHMM) . Active We defined CR AREs using 2 rectal mucosa tissues  and one colon mucosa tissue (E075). We defined non-digestive AREs by excluding AREs from 12 digestive tissues , due to similarity with CR epigenomes . Pairwishttp://genome.ucsc.edu/cgi-bin/hgTables). For each set, we pooled variants within 200kb upstream and downstream of the TSS (We anchored variant sets on transcription start sites (TSS), as defined by dbXref MySQL from UCSC Genome Browser  with a missense coding variant. Two of the five loci contained missense mutations  predicted by PolyPhen2 [We defined the known colorectal cancer loci as 48 index variants likely to have independent effects on CRC risk and variants in LD with index variants , center (when appropriate), batch effects (ASTERISK only), and the first three PCs from EIGENSTRAT to account for population substructure within each individual study. To conduct functional set-based association analysis of rare variants, MAF < 0.01 and cumulative variance in set ≥ 0.095, we tested for association with CRC risk using MiST [For variants with MAF ≥ 0.01 and imputation Ring MiST , adjustiing MiST .obs. For each resampling, a random set of size X was drawn from the total X+Y AREs and assigned to group 1. The remaining AREs were assigned to group 2. The p-value from KS test was obtained, and denoted by Psim. The number of resamples varied from 10, 100, 1000, and up to 10,000 until 20% of the total number of p-values (Psim) were less than or equal to Pobs. The empirical p-value was calculated as the ratio of the number of Psim ≤ Pobs and the total number of resamples.Due to LD among variants, the asymptotic distribution for the KS test is not valid. We therefore used the resampling technique to estimate the p-value. Specifically, suppose there are X AREs in group 1 and Y AREs in group 2. A KS test was performed and the p-value was denoted as PA p-value ≤ 0.05 was considered statistically significant. For 124 tissue comparisons the significance threshold was set to 0.05/124 and suggestive threshold was set to 0.05/19 given that several of the tissues examined were either biological duplicates  or have highly similar epigenomes and cellular attributes .For the comparison of CR versus non-digestive tissues the significance threshold was considered to be 0.05. For the 124 tissue comparisons the significance threshold was set to 0.05/124 and suggestive threshold was set to 0.05/19 given that many of the epigenomes were highly correlated.S1 Fighttp://www.broadinstitute.org/~meuleman/reg2map/HoneyBadger2_release/DNase/p2/regions_all.bed, downloaded 2/9/2016) overlapping enhancer and promoter states marked by the H3K4me1 histone modification. Clustering was performed using the average H3K4me1 signal confidence scores, -log10, in the ARE of consolidated epigenomes for 127 tissues and cell-types . The tissues and cell types were hierarchically clustered using Pearson correlation as the distance measure and complete linkage followed by optimal ordering of leaves. The leaves are colored by the broad categorization of each epigenome. Digestive tissues are colored in light purple. Immune cell-types are colored in green.AREs were defined as accessible chromatin regions ((PDF)Click here for additional data file.S2 FigThe negative logarithm of the Colorectal ARE (y axis) and the combined Non-digestive ARE (x axis) CRC association P-value is plotted for each variant (dot). The red line indicates the null hypothesis that the two distributions of p-values are the same.(TIF)Click here for additional data file.S3 FigCDH1 locus. The first track shows the RefSeq gene annotations. The following 5 tracks are Roadmap ChIPseq histone modifications for colon mucosa. The following track ‘ChromHMM’ demarks the enhancer regions derived from the 15-state hidden markov modeling of these histone modifications. Next, the DHS marks across 52 Roadmap and ENCODE cell lines used to further refine likely transcription factors. The intersect of enhancer/promoter ChromHMM segments and DHS marks were used to define the Active Regulatory Elements (ARE) of colon mucosa. Variant sets were anchored on TSS as defined by protein coding gene transcripts with validated RefSeq records. If a gene had multiple TSS, the 5'-most and 3'-most TSS were used as anchors. Accordingly, variants overlapping ARE within 200Kb of a TSS were pooled into a test set, as shown in the highlighted blue region. Only sets with a cumulative variance of greater than 0.095 were analyzed.UCSC genome browser image of an example variant set in the known (PDF)Click here for additional data file.S1 TableResults for the kolmogorov-smirnov (KS) test for p-values of common variants in ARE vs those not in ARE are presented for 127 cell-types and tissues.(XLS)Click here for additional data file.S2 TableResults for the kolmogorov-smirnov (KS) test for p-values of common variants in ARE of 3 CR tissues in comparison to ARE of another cell-type or tissues presented for 124 cell-types and tissues.(XLS)Click here for additional data file.S3 Table2≥0.5 in all European 1000 Genomes Project populations (CEU+FIN+GBR+IBS+TSI).Functional annotation of 48 known loci defined as the Index variants and variants tagged by index with r(XLS)Click here for additional data file.S4 TableResults for the kolmogorov-smirnov (KS) test for p-values of common variants in CR ARE vs non-digestive tissue ARE across 124 cell-types and tissues.(XLS)Click here for additional data file.S5 Table(XLS)Click here for additional data file.S6 Table(XLS)Click here for additional data file.S1 Text(DOCX)Click here for additional data file.


CDKAL1 locus; and (ii) 99% credible sets with six or fewer variants for five distinct association signals.Trans-ethnic meta-analysis of genome-wide association studies (GWAS) across diverse populations can increase power to detect complex trait loci when the underlying causal variants are shared between ancestry groups. However, heterogeneity in allelic effects between GWAS at these loci can occur that is correlated with ancestry. Here, a novel approach is presented to detect SNP association and quantify the extent of heterogeneity in allelic effects that is correlated with ancestry. We employ trans-ethnic meta-regression to model allelic effects as a function of axes of genetic variation, derived from a matrix of mean pairwise allele frequency differences between GWAS, and implemented in the MR-MEGA software. Through detailed simulations, we demonstrate increased power to detect association for MR-MEGA over fixed- and random-effects meta-analysis across a range of scenarios of heterogeneity in allelic effects between ethnic groups. We also demonstrate improved fine-mapping resolution, in loci containing a single causal variant, compared to these meta-analysis approaches and PAINTOR, and equivalent performance to MANTRA at reduced computational cost. Application of MR-MEGA to trans-ethnic GWAS of kidney function in 71,461 individuals indicates stronger signals of association than fixed-effects meta-analysis when heterogeneity in allelic effects is correlated with ancestry. Application of MR-MEGA to fine-mapping four type 2 diabetes susceptibility loci in 22,086 cases and 42,539 controls highlights: (i) strong evidence for heterogeneity in allelic effects that is correlated with ancestry only at the index SNP for the association signal at the  There is increasing evidence from genome-wide association studies (GWAS) that common SNPs driving complex human trait associations are shared across diverse populations ,2, and fOne approach to allow for heterogeneity in allelic effects between GWAS is to utilise meta-analysis under a random-effects model. The RE2 meta-analysis increases power over the traditional random-effects model by taking account of the expected homogeneity of allelic effects between GWAS under the null hypothesis of no association for which all allelic effects are zero . HoweverTo address the shortcomings of existing methodologies for aggregating GWAS from diverse populations, we have developed a novel approach to detect and fine-map complex trait association signals via trans-ethnic meta-regression. This approach uses genome-wide metrics of diversity between populations to derive axes of genetic variation via multi-dimensional scaling. Allelic effects of a variant across GWAS, weighted by their corresponding standard errors, can then be modelled in a linear regression framework, including the axes of genetic variation as covariates. The flexibility of this model enables partitioning of the heterogeneity into components that are correlated with ancestry and residual variation, which would be expected to improve fine-mapping resolution. Here, we present the results of a detailed simulation study to investigate the properties of trans-ethnic meta-regression for the detection and fine-mapping of loci containing a single causal variant contributing to a binary phenotype over a range of scenarios for heterogeneity in allelic effects between diverse populations. We compare the performance of the meta-regression with fixed- and random-effects (RE2) meta-analysis, implemented in METASOFT , and withttp://www.geenivaramu.ee/en/tools/mr-mega).We have developed a novel approach to aggregate association summary statistics across GWAS from diverse populations to account for heterogeneity in allelic effects that is correlated with ancestry . Briefly, we employ trans-ethnic meta-regression to model allelic effects as a function of axes of genetic variation, derived from a matrix of mean pairwise allele frequency differences between GWAS. The meta-regression model partitions heterogeneity in allelic effects between GWAS into two components: (i) heterogeneity that is correlated with ancestry; and (ii) residual heterogeneity. Bayes’ factors in favour of association can be derived from the meta-regression model for each variant, enabling fine-mapping and construction of credible sets. The meta-regression methodology has been implemented in the MR-MEGA (Meta-Regression of Multi-Ethnic Genetic Association) software  in each population . Association summary statistics for the causal variant were aggregated across populations using the meta-regression model, implemented in MR-MEGA, including three axes of genetic variation as covariates to separate ancestry groups. For comparison, we also aggregated association summary statistics via fixed-effects (inverse-variance weighted log-odds ratios) and random-effects (RE2) meta-analysis implemented in METASOFT . We haveP < 0.05), across all heterogeneity scenarios considered, for fixed- and random-effects meta-analysis, and for meta-regression including three axes of genetic variation to account for heterogeneity in allelic effects between ancestry groups , greatest power to detect association was attained for the meta-regression including three axes of genetic variation as covariates . The gaianalysis .P < 0.05) for this scenario , power was low for all methods, but greatest for random-effects meta-analysis . As expescenario . Power tP < 0.05), as expected . For each replicate, we considered two settings: (i) ‘perfect’ data, where all variants in the region were captured, with no missing genotypes or errors, for benchmarking purposes; and (ii) ‘imperfect’ data, where only 100 randomly selected variants in the 2 Mb region were retained, to represent a typical GWAS array, and the resulting scaffold of genotypes was imputed up to haplotypes from the 1000 Genomes Project Phase 3 reference panel  Materia; (ii) MAψ = 1.10; African-specific, ψ = 1.25; Eurasian, ψ = 1.10; Native American, ψ = 1.30; and non-ancestral, ψ = 1.35.We considered three metrics of fine-mapping performance across simulations: (i) the number of variants in the 99% credible set; (ii) the mean posterior probability ascribed to the causal variant; and (iii) the coverage of the causal variant by the 99% credible set. Smaller credible sets correspond to fine-mapping at higher resolution, whilst the mean posterior probability for the causal variant measures accuracy. For each heterogeneity scenario, we considered population-specific odds-ratios with approximately 80% power to detect association with the meta-regression model : homogenWe first considered the ‘perfect’ data setting, where all variants in the region were captured, with no missing genotypes or errors , Table 1We then considered the more realistic ‘imperfect’ data setting, in which a subset of genetic variation across a locus was assayed directly with a GWAS array, with subsequent imputation up to haplotypes from the 1000 Genomes Project Phase 3 reference panel . CoveragWe also compared, across simulations, the computational burden of each of the trans-ethnic meta-analysis approaches to assess association with variants within the locus . Using aWe considered nine GWAS of kidney function, assessed by the estimated glomerular filtration rate (eGFR), in 71,461 individuals of African American, East Asian, European and Hispanic/Latino ancestry . AnalyseP-values for eGFR from the trans-ethnic meta-regression and the fixed-effects meta-analysis (P < 5×10−8) of association with eGFR from the trans-ethnic meta-regression , SHROOM3 , UNCX  and PDILT-UMOD . Signals of association at these loci were stronger from the fixed-effects meta-analysis than the meta-regression when the lead SNP demonstrated little evidence of heterogeneity in allelic effects between GWAS. The strongest evidence of heterogeneity in allelic effects in the fixed effects meta-analysis, as assessed by Cochran’s Q statistic, was observed for the lead SNP at WDR72 . In the meta-regression analysis, the heterogeneity was partially correlated with ancestry (P = 0.00053), where allelic effects of the lead SNP on eGFR are specific to populations of European and East Asian descent  for index SNPs for each distinct signal across the four susceptibility loci from meta-regression accounting for ancestry with three axes of genetic variation as covariates . The heterogeneity was primarily accounted for by the third axis of genetic variation (P = 0.0046), which separates GWAS of South Asian ancestry from those of African American, East Asian, European and Mexican American descent  and rs231353 (4 variants mapping to 38.5 kb of KCNQ1-OT1). At the CDKN2A-B locus, the 99% credible sets for both association signals incorporate a total of 12 non-overlapping variants that map to the same <5 kb interval. Annotation of the 99% credible sets revealed inclusion of no coding variants, consistent with previous reports that T2D association signals at these four loci are most likely to be mediated through gene regulation   , on multST)  used in ST) . ConsequThe meta-regression model assumes a linear trend in allelic effects with each axis of genetic variation included as a covariate. Whilst it is unlikely that this linear trend will hold exactly, we have demonstrated that axes of genetic variation are sufficient to cluster GWAS of similar ancestry, but also distinguish populations within the same ethnic group . ConsequThe meta-regression model enables partitioning of heterogeneity in allelic effects between GWAS that is correlated with ancestry from residual variation due to other sources (such as variable phenotype definition). Heterogeneity in allelic effects due to ancestry is of particular relevance to fine-mapping, since it can occur as a result of differences in patterns of LD between diverse populations, which we model in the meta-regression framework by including axes of genetic variation as covariates. Consequently, the meta-regression model offers substantial gains in fine-mapping resolution over fixed- and random-effects meta-analysis, even for heterogeneity scenarios in which allelic effects do not follow a linear trend in the axes of genetic variation . We alsoThere has been recent development of novel methods for fine-mapping that utilise meta-analysis summary statistics and a reference panel of LD between variants across a locus, including CAVIAR , PAINTORAn alternative approach to allow for multiple causal variants is to first dissect ‘distinct’ association signals at a GWAS locus through (approximate) conditional analysis . ConditiUnfortunately, the results of our simulation study highlight that there is no single optimal approach to the aggregation of GWAS from diverse populations across the range of scenarios for heterogeneity in allelic effects we have considered. For example, under a scenario in which allelic effects are homogeneous across ethnic groups, there is a small loss in power for the meta-regression model compared to fixed- and random-effects meta-analysis that is due to the inclusion of axes of genetic variation as covariates that are not predictive of heterogeneity. Our analyses have focussed on three axes that distinguish populations of African, East Asian, European, Native American and South Asian ancestry. Reducing the number of axes of genetic variation included as covariates in the meta-regression model would decrease the loss in power, compared to fixed- or random-effects meta-analysis, under a scenario of homogenous allelic effects across populations. However, the power of the meta-regression model to detect SNP association would then be decreased when heterogeneity in allelic effects between GWAS is driven by ancestry. One solution to this dilemma is to use both fixed-effects meta-analysis and meta-regression for aggregation of GWAS from diverse populations, although thresholds of significance should be adjusted to account for multiple testing at each SNP.CDKAL1 locus, which was accounted for by one axis of genetic variation. Allelic effect sizes increased along this axis, separating those of South Asian ancestry from other ethnic groups, consistent with previous reports that this locus has greater impact on populations of European and East Asian descent.One of the advantages of the meta-regression approach is that we can assess the contribution of each axis of genetic variation to heterogeneity in allelic effects between GWAS. For example, we observed strong evidence for heterogeneity in allelic effects on T2D susceptibility due to ancestry at the A second advantage of the meta-regression approach is that additional covariates can be included to investigate other sources of potential heterogeneity in allelic effects between studies. For example, where sex-specific association summary statistics are available, inclusion of sex as covariate provides an assessment in allelic effects between males and females, after accounting for ancestry. Inclusion of imputation quality metrics as a covariate enables confirmation that apparent heterogeneity in allelic effects between studies is not a reflection of variable imputation success, which may vary according to ancestry because of the availability of closely matched population haplotypes in the reference panel, for example.In conclusion, trans-ethnic meta-regression, as implemented in the MR-MEGA software, offers a powerful approach for the discovery and fine-mapping of complex trait loci across GWAS from diverse populations. With the increasing availability of multi-ancestry GWAS of complex human traits, powerful statistical methodology for trans-ethnic meta-analysis, such as that implemented in MR-MEGA, shows great promise for future improvements in our understanding of the genetic basis of common diseases.K GWAS of a complex trait. At each variant, we assume that all GWAS are aligned to the same reference allele. We denote the reference allele frequency of the jth SNP in the kth GWAS by kjp. We construct a matrix of pairwise Euclidean distances between GWAS across autosomal variants, denoted D = [kkd’], whereConsider a series of jI is a binary indicator variable of the inclusion of the jth variant in the distance calculation. We recommend dividing the genome into 1 Mb bins, and utilising one variant with MAF of at least 5% in all GWAS from each bin to minimise the impact of LD. We then implement multi-dimensional scaling of the distance matrix, D, to derive T axes of genetic variation, denoted xk for the kth GWAS. Note that the choice of the number of axes of genetic variation will depend on the population diversity of GWAS, but is restricted to T ≤ K-2.In this expression, jth variant, we denote the estimated effect of the reference allele in the kth GWAS, and the corresponding variance, by kjb and kjv, respectively. We then model the reference allele effect across GWAS in a linear regression model, given byjα is the intercept and tjβ is the effect of the tth axis of genetic variation for the jth variant. The contribution of the kth GWAS is weighted by the estimated inverse variance of the reference allele effect at the jth variant, denoted jα, as the expected allelic effect of the jth variant for a population of ancestry represented by zero on each of the T axes of genetic variation.For the jth variant across GWAS by comparing the deviance of model (1) with jα = β1j = … = Tjβ = 0 to that for which the parameters are unconstrained, with the resulting test statistic denoted jX having an approximate chi-squared distribution with T + 1 degrees of freedom. We can also test for the presence of heterogeneity in allelic effects between GWAS that is correlated with ancestry by comparing the deviance of model (1) with β1j = … = Tjβ = 0 to that for which the parameters are unconstrained, with the resulting test statistic having an approximate chi-squared distribution with T degrees of freedom. Finally, the deviance of model (1), with all parameters unconstrained, provides a test of residual heterogeneity in allelic effects between GWAS after accounting for ancestry, having an approximate chi-squared distribution with K-T-1 degrees of freedom.We test the null hypothesis of no association of the tth axis of genetic variation to heterogeneity in allelic effects by comparing the deviance of model (1) with tjβ = 0 to that for which the parameters are unconstrained, with the resulting test statistic having an approximate chi-squared distribution with one degree of freedom.We can also assess the contribution of the jth variant in the locus, we approximate the Bayes’ factor in favour of association  including ranked variants until their cumulative posterior probability of driving the association attains or exceeds 0.99.Consider a locus encompassing a pre-specified interval from an index variant. For the ociation  byΛj=exible set  for the http://www.geenivaramu.ee/en/tools/mr-mega). For each study, a flat file of association summary statistics is required, including one row per variant, and columns for the variant name and position in the genome, effect and other alleles, effect allele frequency, allelic effect and standard error, and sample size. For each variant, MR-MEGA aligns studies to the same effect allele, and flips the allele frequency and allelic effect if required. MR-MEGA then performs multi-dimensional scaling of mean genome-wide allele frequency differences between each pair of GWAS. Meta-regression is undertaken in a linear regression framework, as described above, including axes of genetic variation as covariates in the model. MR-MEGA can perform genomic control at the study level, and/or after meta-regression. For each variant, MR-MEGA provides: (i) P-value and Bayes’ factor in favour of association, accounting for heterogeneity that is correlated with ancestry; (ii) P-value for heterogeneity that is correlated with ancestry; and (iii) P-value for residual heterogeneity.We have implemented the methodology in the MR-MEGA (Meta-Regression of Multi-Ethnic Genetic Association) software , whilst power was evaluated at genome-wide significance (P < 5×10−8). Next, we tested for heterogeneity, at nominal significance (P < 0.05), in allelic effects between populations that is correlated with ancestry using the meta-regression model implemented in MR-MEGA. Finally, we tested for residual heterogeneity, at nominal significance (P < 0.05), in allelic effects between populations: (i) from the meta-regression model implemented in MR-MEGA after accounting for ancestry; and (ii) using Cochran’s Q statistic from the fixed-effects meta-analysis implemented in METASOFT  and random-effects (RE2) meta-analysis implemented in METASOFT . False pMETASOFT .For each replicate, the 2 Mb region was centred on a single causal variant, selected at random from those reported in the reference panel from Phase 3 of the 1000 Genomes Project  with MAFWe first considered the ‘perfect’ data setting, where all variants in the region are captured, with no missing genotypes or errors, for benchmarking purposes. For each replicate of data, we considered the 1 Mb region centred on the causal variant. Within each population, we tested all variants in this region for association with case-control status in a logistic regression framework under an additive model in the log-odds ratio in PLINK , and obtWe then considered the more realistic ‘imperfect’ data setting. For each replicate of data, genotypes at only 100 randomly selected variants in the 2 Mb region were retained, to represent a typical GWAS array. Within each population, separately, this scaffold of genotypes was imputed up to haplotypes from the 1000 Genomes Project Phase 3 reference panel  using IM2) for log-odds ratios; and (ii) the Bayes’ factor from MANTRA  approximate Bayes’ factors  on the bm MANTRA  using thm MANTRA , assuminm MANTRA . Under tr2≥0.3 (Each GWAS was pre-phased and imputed up to the 1000 Genomes Project Phase 1 reference panel  using IMr2≥0.3 . Kidney r2≥0.3 . Within r2≥0.3 . Within r2≥0.3  (Supplemr2≥0.3 .λGC=1.029). Heterogeneity in allelic effects between studies at each variant was assessed by means of Cochran’s Q-statistic from the fixed-effects meta-analysis implemented in METASOFT (λGC=1.017).Association summary statistics for each variant passing quality control in at least 50% of the total sample size were aggregated across studies via fixed-effects meta-analysis, with inverse-variance weighting, implemented in METASOFT . AssociaMETASOFT . We implMETASOFT . We thenMETASOFT  (λGC=1.0r2 ≥ 0.3 (10 Bayes’ factor >6).We made use of summary statistics derived by the T2D-GENES Consortium  for sever2 ≥ 0.3 . These vr2 ≥ 0.3  using thWe implemented multi-dimensional scaling of the Euclidean distance matrix to derive three axes of genetic variation to separate GWAS between ancestry groups . For eacHMG online.Conflict of Interest statement. None declared. Supplementary Figures and TablesClick here for additional data file.