RHBDD1) and rs17759796 (MAPK1), rs1121980 (FTO) and rs6567160 (MC4R), obtained from a consensus of nine different epistatic approaches. Gene interaction maps and tissue expression profiles constructed for these interacting loci highlights co-expression, co-localisation, physical interaction, genetic interaction, and shared pathways emphasising the neuronal influence in obesity and implicating concerted expression of associated genes in liver, pancreas, and adipose tissues insinuating to metabolic abnormalities characterized by obesity. Detecting epistasis could thus be a promising approach to understand the effect of simultaneously interacting multiple genetic loci in disease aetiology, beyond single locus effects.Genome wide association studies (GWAS) have focused on elucidating the genetic architecture of complex traits by assessing single variant effects in additive genetic models, albeit explaining a fraction of the trait heritability. Epistasis has recently emerged as one of the intrinsic mechanisms that could explain part of this missing heritability. We conducted epistasis analysis for genome-wide body mass index (BMI) associated SNPs in Alzheimer’s Disease Neuroimaging Initiative (ADNI) and followed up top significant interacting SNPs for replication in the UK Biobank imputed genotype dataset. We report two pairwise epistatic interactions, between rs2177596 ( Nevertheless, complete understanding of the pathophysiology of complex diseases remains elusive through GWAS, and the genetic variations identified through GWAS explains only a fraction of the heritability of the disease3. GWAS carried out for adult human height, detected associations with common variants that could explain about 60% of population variation4. Near-independent genome-wide significant SNPs explain about ∼6.0% of the variance of BMI (by 785 SNPs) in ~ 700,000 European ancestry individuals5. However, by carrying out GWAS on a relatively small cohort size of 96 cases and 50 controls, a variant causing an amino-acid replacement in the complement factor H gene (CFH) was found to increase the risk of age-related macular degeneration (AMD) by sevenfold when occurring in homozygous state6. Also, just 52 genome wide associated variants explain more than half of the genomic heritability for AMD7. Thus, GWAS has been a huge or moderate success depending on the disease trait or phenotype of interest. It has also been proposed that undetermined heritability is due to incomplete linkage disequilibrium (LD) between low frequency or rare causal variants and genotyped SNPs, and thus not detected by stringent significance tests8. Another proposition is that rare variants contribute to the missing heritability and optimally designed rare variant association studies would highlight important biological pathways for understanding disease aetiology9. Furthermore, evaluating each SNP individually and enforcing stringent correction for multiple testing can result in crucial variants to be overlooked. This is a severe problem given that these variants arise from components of pathways and genes that work in tandem to impact the concerned phenotype10.Susceptibility to complex human diseases, example, type 2 diabetes and Alzheimer’s disease, among others are conferred by more than one gene as well as environmental influences. Technological advances in genomics have equipped researchers to make substantial progress in the field of genome wide association studies (GWAS) which is a robust hypothesis-free approach to scan entire genomes of individuals for identifying genetic loci that define susceptibility to complex diseases. GWAS have identified thousands of loci implicated in complex diseases unequivocally11. Bateson’s theory was corroborated by Sewall Wright12, where he acknowledged the relevance of gene–gene interaction by stating that selection pressure acts on the effects of the genetic background instead of individual genes. Shortly after, Sir Ronald Fisher described epistasis as the divergence from added effects on quantitative traits due to alleles at different loci13. Epistasis denotes the event in which the status of a trait arising from a genetic background deviates from the sum of its single locus effects, and can be interpreted as the effect of one locus being dependent on the allelic state of another or several other loci14. This idea has further been expounded when epistatic or gene–gene interactions among multiple loci in the genome have been observed for model organisms15. Even for human complex traits, it has been proposed that genetic interactions could explain some of the “missing heritability” undetected by GWAS17, and can thus act as a governing factor underlying the biology of non-Mendelian phenotypes18. Epistasis from a biological perspective represents the synergy of gene products that are part of interconnected pathways associated with the concerned phenotype19. Significant epistasis analysis in recent years have furthered our understanding of complex traits, such as, atrial fibrillation20, lung cancer21 and multiple sclerosis22, among others. In the pre-GWAS era, increased evidence for linkage at one locus had been observed when the interaction with another locus was considered for type 123 and type 2 diabetes24 and inflammatory bowel disease26 showed that genetic variance for complex traits is predominantly additive and a large sample size of millions of unrelated individuals are needed for precise estimation of epistatic variance. Recently, successful epistasis in humans have been detected through genome screening projects28, and by statistical methods of epistasis analysis31. Campbell et al. has argued that studies about genotypic combinations in model organisms could facilitate our understanding for detection of epistasis in natural populations32.In this communication, we use the terms epistasis and genetic interactions interchangeably.Additionally, Bateson proposed that a variant or allele at one locus could prevent a variant at another locus from manifesting its effect33. We employed nine different epistasis detection tools representing exhaustive, heuristics, and stochastic algorithms and identified 20 significant epistatic interactions for human BMI. We then take these top SNPs comprising the interactions for follow-up in the UKB imputed genotype dataset, constituting more than 188,000 individuals to carry out replication analysis. Our analysis shows that variants at genomic loci in or near FTO and MC4R; RHBDD1 and MAPK1, exhibit reproducible pairwise interactions associated with human BMI.In this study, we have used population data from 785 individuals belonging to the Alzheimer’s Disease Neuroimaging (ADNI) cohort in order to detect second order genetic interactions for SNPs known to be associated with body mass index (BMI). A recent exhaustive review meticulously details the journey of identifying single locus effects associated with human BMI, and how multidisciplinary analytical approaches could enhance our understanding of the biology of obesity and identify newer treatmentsWe identified twenty significant pairwise interactions among BMI-associated loci (Supplementary Table RHBDD1) and rs17759796 (MAPK1), rs1121980 (FTO) and rs6567160 (MC4R), from a consensus of nine different epistatic approaches. The detailed characterization of these interactions is given in the following sections.We finally obtain two pairs of significant interactions in more than 188,000 individuals between rs2177596  (Table p = 5.61E−06), freq = 46% (ADNI), 42% (UKB) and A , freq = 14% (ADNI), 15% (UKB) respectively. Additionally, one interaction, as a consensus of GMDR and MDR, between rs1121980(G/A) and rs6567160 (C/T) (padj = 0.001) was replicated independently in the UKB genotype matrix, with corresponding BMI increasing alleles: A , freq = 44% (ADNI), 42% (UKB) and C , freq = 23% (ADNI), 23% (UKB) (Table MON1A/RBM5) and rs8050136 (C/A) (FTO/RPGRIPL1), identified as interacting in ADNI, failed to meet the criteria for permutation testing in MDR  in the UKB.One of the significant interacting SNP pairs in ADNI replicated in the UKB dataset, as a consensus obtained from SNPRuler and AntEpiSeeker- rs2177596 (A/T) and rs17759796 (C/A), (B) Table . MoreoveP < 0.0001)  or homozygous carriers (P = 0.0185) of BMI decreasing allele for rs6567160, are more likely to exhibit higher BMI for this SNP pair  Table . SimilarThis analysis shows the importance of deciphering the simultaneous effects from multiple SNPs acting in conjunction to influence the phenotypes of our interest in large-scale population datasets.34. Similarly, we examine the interaction effects versus main effects for rs2177596 and rs17759796  and rs6567160 (chr18:57829135) is annotated to FTO and MC4R is unequivocally associated with BMI in the UKB cohort of 188,620 individuals . Our in-depth analysis reveals that FTO co-expresses with MGRN138 which in turn shares a physical interaction with MC4R, and it has been shown that MGRN1 inhibits MC4R signalling by displacement of Galpha(s), accounting for coat colour and obesity, features of the mahoganoid phenotype in mouse, and plays a key role in insulin sensitivity42. These results could further our understanding of the mechanism of energy intake and expenditure balance, with respect to satiety and weight loss or gain.Our results show for the first time that a pairwise interaction among SNPs mapping to RHBDD1 and COL4A4, the former is a functional component of endoplasmic reticulum-associated degradation for misfolded membrane proteins, and required for the degradation process of some specific misfolded endoplasmic reticulum (ER) luminal proteins, and apoptosis43, and is found to genetically interact with MAPK144, a gene annotated to rs17759796. It is also known that many pathways in adipose tissue, liver, and pancreas can be disrupted during ER stress, and ER stress is one of the primary characteristics of obesity45. We thus report here the tissue specific expression results in liver and pancreas from GTEx for these two interacting loci.The gene network map for interacting pair rs2177596 (chr2:227890283) and rs17759796 (chr22:22190163) is shown in Fig. FTO (rs1121980) and MC4R (rs6567160) associated with human BMI in more than 188,000 individuals. Individually, both FTO and MC4R have emerged as strong signals for human obesity46. In mice, studies have shown that FTO can regulate fasting and feeding, and therefore variation in FTO can result in changes of feeding behaviour and obesity47. Recently, it has been shown that engineered deletion in the rs1421085 (r2 > 0.9 with rs1121980 in Europeans) conserved cis-regulatory module can affect organismal phenotypes relevant to obesity in mouse48. MC4R deficiency is known to be the most common cause of monogenic obesity49, and gain-of-function variants in MC4R is associated with lower risk of obesity, type 2 diabetes, and coronary artery disease50. We delve deeper into the individual-wise distribution of the FTO and MC4R alleles as explained in the previous section, and observe that carriers with rs6567160-TT  are predisposed to lower BMI in conjunction with rs1121980-AG, GG . This is even more intriguing when we see that the entire UKB dataset has 61,969 individuals in the lower BMI category . Thus, we posit that it might be possible that the BMI decreasing allele of rs6567160 near MC4R, contributing to its expression levels, has a significant mitigating effect on obesity in conjunction with the homozygous decreasing allele or heterozygous stature of the FTO SNP. FTO and MC4R are expressed in high levels in the hypothalamus and cortex in the brain as seen in GTEx tissue expression profiles  for MC4R significantly increases the expression  of MC4R in cortex, while the lead SNP rs10521305  for FTO significantly decreases the expression  of FTO in cortex. Similarly, significant increase and decrease of MC4R and FTO expression levels are observed in the hypothalamus for the corresponding lead SNPs rs8083758  and rs10521305  respectively  and not yet known to be associated with BMI, as well as not in LD (1000G European dataset) with the BMI-associated SNPs  for which significant epistasis has been identified in this study. rs6567160 and rs1121980 had been found to be associated with BMI from array-based genotypes and HapMap imputed studies. This makes us postulate that there could be another SNP in or near MC4R  that is most likely to be causally associated with BMI, and in moderate LD with rs6567160 (BMI-associated), rs11873305 and rs8083758. Similarly, another SNP in or near FTO  could possibly be the causal variant for BMI, and in moderate LD with eQTL lead SNPs rs10521305 and rs1121980 (BMI-associated). It would be motivating to uncover such SNPs f1 and m1 and investigate epistatic interaction between them, thus elucidating the network biology of obesity further , which further provides evidence for the possible mechanisms we propose in Fig. Our results show a significant pairwise interaction between les Fig. A. The eQMAPK1 and RHBDD1. Our allelic combination analysis above do not reveal any statistically significant trend for belonging to higher or lower BMI for any of the nine possible genotype combinations for these two SNPs. We investigate the tissue-specific expression data for these two genes in GTEx. The two genes are expressed highly together in liver, pancreas, adipose-subcutaneous, and adipose-visceral tissues. In addition, MAPK1 is widely expressed in several other tissues  and rs8050136 (FTO/RPGRIPL1), identified as interacting in the discovery dataset, failed to meet the criteria for permutation testing in MDR . Thus, future studies in FTO might shed more light for understanding the biology of obesity, and lead to our precise understanding of how FTO plays a role in energy intake and expenditure.We have detected and replicated two significant pairwise interactions for human BMI between genome-wide associated loci in more than 188,000 individuals. Interestingly, we uncover for the first-time interactions among SNPs near P < 1E−04. This suggests that there are loci waiting to be discovered for governing the biology of obesity, and probing upto a threshold of comparable significance for SNPs already achieved in GWAS to uncover such latent interactions is useful.Our input list consisted of SNPs in established genome wide significant thresholds as well as sub genome wide significance levels, yet significant epistasis interactions have been uncovered for SNPs that were associated with BMI for single locus effects within 51 that biological interpretation of epistasis is usually easiest when the penetrance values all equal either 0 or 1, leading to a clear relationship between genotype and phenotype. However, this explanation is not straightforward for human complex genetic diseases due to their polygenic and multifactorial nature. In humans, due to the complexity of genomic architecture and multitudes of factors influencing complex traits like BMI, our results are probably the tip of the iceberg and many more indiscernible genetic interactions among human BMI associated loci are waiting to be uncovered.This epistasis study on BMI implicated loci helped us identify mechanisms potentially implicated in the biology of BMI that cannot be captured by single locus effects analysis. Some of the networks we uncovered, especially the connections to energy homeostasis, endoplasmic reticulum stress, concerted expression profiles of interacting genes in liver, pancreas, adipose tissue, and hypothalamus have direct implications in obesity biology. In statistical epistasis, interactions are defined by genetic variations and not by physical interaction of biomolecules in real systems, the latter is also hard to establish experimentally. Even though statistical models can implicate genetic variants that do not occur in transcribed regions, for which the functionality in biological mechanisms becomes hard to experimentally prove, they are still our most desired approach, especially in humans, to provide insights into unknown biological mechanisms occurring through interactions among loci across the genome. Additionally, statistical models can define instances where multiple genetic factors have a non-additive effect on a phenotype. It has already been acknowledged52 reported that one more strongly associated variant uncovered from whole genome sequencing was moderately correlated with both of the interacting SNPs (showing very low levels of LD between them) identified by Hemani et al.58, and the inclusion of this third variant as a covariate removed any evidence for interaction. This means that the apparent epistasis reported by Hemani et al. for SNPs on the same chromosome can actually be attributed to a single causal allele having moderate levels of LD with each of the two SNPs, and has recently been dubbed as phantom epistasis53 between unlinked markers.Despite their widely accepted potential role in capturing the phenotypic variance in traits owing to genetic effects, epistatic interaction in human genetic analysis has been debated in recent times. This is largely because of imperfect linkage disequilibrium between causal variants with large additive effect size and nearby tagging loci resulting in inflated test statistics for interaction terms. Wood et alThis is not the scenario in our results since we have detected inter-chromosomal interactions. On the contrary, our expression profile analysis reveals plausible mechanisms Fig. C involviGenetic variations making us susceptible to disease traits or determining the phenotypic variation in quantitative traits is a result of intricate selective forces at play striving to achieve the optimal balance in human systems. Epistasis is one of the intrinsic mechanisms on which such stabilising control ought to exist. Therefore, detecting statistical epistasis and deciphering biological implications for the same is of utmost importance in understanding disease mechanisms. Yet, we are cognizant that epistasis detection is limited by a number of factors. Statistical tests of interaction are limited to testing specific hypothesis in relation to genotypic measures in study subjects, and we will have insufficient statistical power to investigate all possible allelic combinations when dealing with rare variants. Additionally, when the causal variant or putative functional variant is in LD with another common variant, it is highly likely that the latter will show evidence for interaction in statistical tests due to linkage disequilibrium. In addition to these, inadequate controlling for overall genetic background, incidence of false positives, uncorrected environmental effects can constrain the identification of true epistatic effects present in human complex traits from statistical analysis.Our results in discovery and replication dataset of more than 188,000 individuals highlight the importance of studying the interaction of SNPs for understanding the genetic architecture of complex traits. This is again more prominent in our in-depth analysis of the allelic combinations observed in individuals with high versus low BMI. We reiterate that our results are suggestively informing about plausible mechanisms to uncover putative interacting variants associated with obesity. We hope that our results will encourage large scale future studies to uncover epistasis in humans that will expound further the biology and genetic underpinnings of complex traits.We considered BMI as our phenotype of interest in this work and set out to identify second order epistatic interactions among genetic loci associated with BMI at a genome wide level. The entire workflow is given in Fig. Data used in the preparation of this article were obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). The ADNI was launched in 2003 as a public–private partnership, led by Principal Investigator Michael W. Weiner, MD. The primary goal of ADNI has been to test whether serial magnetic resonance imaging (MRI), positron emission tomography (PET), other biological markers, and clinical and neuropsychological assessment can be combined to measure the progression of mild cognitive impairment (MCI) and early Alzheimer’s disease (AD).The Alzheimer’s Disease Neuroimaging Initiative (ADNI) along with UK BioBank (UKB) data repositories were used in this analysis, and we retrieved age, gender, height (in cm), and weight (in kg) for each participant. Among the 808 samples genotyped in the ADNI study, 785 had all the aforementioned fields. While 485,281 out of 487,405 samples with imputed genotypes in the UKB study had the required phenotype fields. UKB samples that self-identified as 'White British' and belonged to a similar genetic ancestry based on a principal components analysis of the genotypes  were retained. From this set, 188,620 samples did not possess any missing genotypes, and were used for further analysis.2. Sample characteristics i.e., age and gender were parsed as covariates and BMI measure was selected as the phenotype. We have provided a threshold of BMI 25 kg/m2 in order to suffice the condition of certain programs used in our study that requires the user to specify a class variable for the phenotype, although the approach is linear regression to identify interaction scores, based on the guidelines laid down by the World Health Organisation with respect to the European population .BMI for these individuals was calculated by formula (weight in kilograms)/(height in metres)padj < 0.01) in BMI between CN and MCI, CN and Dementia, MCI and Dementia or MCI + CN versus Dementia in Mann–Whitney–Wilcoxon test  and Control Normal (CN). We did not find any significant difference  reported in these publications and retaining the most significant SNPs among those present within 500 kb of each other.We selected 466 genetic loci Table  to be anTOMM40 region (rs2075650) with significantly different frequencies (padj < 0.01) was removed.In order to rule out allelic bias due to any probable differential cognitive status among high and low BMI individuals, we checked for significant differences in allele frequencies of the 359 BMI-associated loci in a pairwise comparison of the CN, MCI, Dementia groups . One SNP in the p-value > 10−6 were retained. Out of the 466 loci  were further selected.For the ADNI genotype matrix, only bi-allelic variants without missing genotype values and Hardy–Weinberg equilibrium exact test ci Table , 343 varci Table  were selp-value <= 10−4), 318 were present in the UKB imputed genotype set  were not present in the UKB imputed genotype set, and the rest were investigated for interaction.56, COE57, TEAM58, MDR59, GMDR60, PLINK61; MCMC: BEAM62 and Heuristic: AntEpiSeeker63, SNPRuler64; have been developed and are generally used to statistically define gene–gene interactions or multi-order epistasis from large scale population data.Multiple tools based on different classes of algorithms, for example, Exhaustive: FastANOVA56 relies on the application of ANOVA test for the detection of 2 locus interactions in a semi-exhaustive manner. It employs an upper bound which is the sum of one term derived from single-SNP ANOVA test, and the other derived from SNPs and independent of any phenotype permutation, to ensure effective SNP pair pruning.FastANOVA57 employs a similar approach like FastANOVA, where the single locus test and the genotype of the loci pairs are required to compute the upper bound and reduces the number of computations pertaining to permutation testing by grouping the SNP pairs according to their genotypes. The approach carried out by COE also makes for a tighter upper bound which results in an efficient SNP pruning mechanism and can be applied on all statistical tests that are convex by nature.COE58 uses the construction of minimum spanning trees to define a contingency table that features the observed frequency of genotype permutations of each SNP pair related to its phenotype state. The table is then updated for every permutation of phenotype state across the population. Given that this method only considers those individuals with differing genotypes between SNP pairs, the computational burden to associate a SNP pair to the state of the phenotype is greatly reduced.TEAM59 is a nonparametric method that uses machine learning to reduce a 3 × 3 dimensional genotype matrix into a binary classification of case and control. MDR trains its models on 9/10th of the input genotype matrix and carries out the testing phase on the final (10th) partition. Finally, the MDR model with the least prediction error and the most cross validation consistency is selected.MDR60, based on the same principles as the MDR approach, can additionally handle quantitative phenotypes by taking into account a score statistic, generated by carrying out a generalized linear regression (GLM) with appropriate link function and suitable covariates, which is then used to map n-dimensional genotype combination into a 1-dimensional space. Final results are obtained after permutation testing.GMDRPlink 1.961.Calculates the odds ratio between loci A and B along with standard error. This procedure is performed for both cases and controls, and the epistasis test is defined as:Can input quantitative phenotype values and uses linear regression to fit the modelPLINK does not support including covariates or carrying out permutation testing for epistasis tests.62 is a Bayesian implementation that defines both single locus and multi-locus disease association from case–control datasets. It classifies a pair of loci as interacting if their combined distribution better generalises the phenotype data compared to considering the loci independently. It uses Markov Chain Monte Carlo on a case–control SNP matrix to iteratively build the posterior probabilities of phenotype association for each marker.BEAM63 utilises Ant Colony Optimization (ACO) algorithm to identify statistical epistatic SNP pairs. Here, the SNPs being assessed form the probability distribution function that is updated through weights (pheromones). As the probability density function is fitted for the input genotype matrix, the epistatic interactions (paths) with higher corresponding scores get sampled by probes with increased frequency, resulting in these interactions being tagged with higher weight scores.AntEpiSeeker64 employs predictive rule learning to identify and assess SNP interactions. With the premise that n loci interactions and phenotype class are governed by rules which can be found and evaluated qualitatively more efficiently than the interactions themselves. SNPRuler builds an enumeration tree with SNPs as nodes and phenotypes representing the leaves, it then prunes the search space using an upper bound on χ2 statistic.SNPRulerP value threshold (P < 1E−4) to obtain robust epistasis results.All the tools described above and employed in this communication use permutation testing or multiple correction or in-built stringent We executed all the nine programs on a x86_64 architecture-based machine with an Intel(R) Xeon(R) Silver 4214 with 32 GB of memory (RAM) and CPU processing at a maximum clock speed of 3.2 GHz. The OS on the system was RHEL distribution CentOS 7.P < 0.05. PLINK—fast-epistasis and—epistasis completed runs in 0.151 and 0.04 s respectively.We directed COE, TEAM, FastANOVA, MDR and GMDR to carry out 1000 permutations. They clocked run times of 1 min 54 s, 16 s, 11 min 37 s, 16 min 8 s and 9 min 19 s respectively. BEAM, SNPRuler and AntEpiSeeker took 1 min 15 s, 1.14 s and 10 s respectively to output interactions at Bonferroni corrected For executing the pairwise interaction analysis between 343 markers in 785 individuals, MDR had the highest memory consumption at 3200 MB. GMDR follows next with a consumption of 573.552 MB, followed by TEAM at 180 MB and SNPRuler at 180.06 MB. FastANOVA consumed 9.53 MB. BEAM, AntEpiSeeker had similar memory signatures with values of 2.84 MB, 2.18 MB respectively. COE consumed the least memory of 1.61 MB.65, from European sub-populations of 1000 Genomes Project (phase3). Only variants with R2 ≥ 0.9 were selected for further analysis.We obtained the variants in high LD with the SNPs that emerged significant in our epistatic models, using the LDproxy tool66, SNPNexus67, Hypergeometric Optimization of Motif EnRichment (HOMER)68 and gene enhancer regions69.We used each interacting SNP along with its corresponding LD variants as input for gene annotation in Combined Annotation Dependent Depletion (CADD)70, for the following subcategories- co-expression, co-localization, physical interaction, genetic interaction and shared pathways (Fig. The gene annotations were then parsed to generate a gene interaction network for the detected epistatic models. The gene interaction networks were generated using GeneMANIAays Fig. .For each of the detected SNP interactions, we extracted the number of samples for each genotype combination, thus resulting in nine combinations depending on the homozygous state for effect or other allele and heterozygous state of the two alleles for each pair of SNPs. We then compared the sample proportions in the high and low BMI groups for significant differences of these combinations using a two-sample z test for proportions Table .Supplementary Information 1.Supplementary Information 2.Supplementary Information 3.Supplementary Information 4.Supplementary Information 5.Supplementary Information 6.Supplementary Information 7.Supplementary Information 8.


Publicly available genome-wide association studies (GWAS) summary statistics exhibit uneven quality, which can impact the validity of follow-up analyses. First, we present an overview of possible misspecifications that come with GWAS summary statistics. Then, in both simulations and real-data analyses, we show that additional information such as imputation INFO scores, allele frequencies, and per-variant sample sizes in GWAS summary statistics can be used to detect possible issues and correct for misspecifications in the GWAS summary statistics. One important motivation for us is to improve the predictive performance of polygenic scores built from these summary statistics. Unfortunately, owing to the lack of reporting standards for GWAS summary statistics, this additional information is not systematically reported. We also show that using well-matched linkage disequilibrium (LD) references can improve model fit and translate into more accurate prediction. Finally, we discuss how to make polygenic score methods such as lassosum and LDpred2 more robust to these misspecifications to improve their predictive power. This work studies the impact of misspecifications in summary statistics from genome-wide association studies. It provides an overview of such misspecifications, how they can arise, and what negative consequences they can have on follow-up analyses. It also investigates possible corrections, with the main goal of improving polygenic scores. We approach this from three different angles. First, based on additional summary information such as the imputation INFO scores and allele frequencies from the GWAS summary statistics, we refine our previously proposed QC.We use the UK Biobank imputed (BGEN) data.Among genetic variants on chromosome 22 and with a minor allele frequency larger than 0.01 and an imputation INFO score larger than 0.4 (as reported by the UK Biobank), we sample 40,000 of them according to the inverse of the INFO score density so that they have varying levels of imputation accuracy . We readWe also use the UK Biobank data for validation/testing in real-data analyses, and use the same individuals of Northwestern European ancestry as described in the previous section. We sample 10,000 individuals to form a validation set and use the remaining 352,307 individuals as a test set. We restrict to the 1,054,315 HapMap3 variants used in the LD reference provided in Privé et al.,To define phenotypes in the UK Biobank, we first map ICD10 and ICD9 codes  to phecodes using R package PheWAS.To derive polygenic scores, we use published GWAS summary statistics listed in ,In this paper, we extensively use the following formula:It is assumed that the marginal (GWAS) effects followWe can impute In practice, we also bound these estimates to be between section “”. In EquInstead of using a regularized version of the correlation matrix ,Following the notations from Privé et al.,In this new implementation of the lassosum model, which we call lassosum2, the input parameters are the correlation matrix Here we introduce the small changes made to LDpred2 (-grid and -auto) in order to make them more robust. First, LDpred2-low-h2 simply consists in running LDpred2-grid while testing For LDpred2-auto, we introduce two new parameters. The first one, shrink_corr, allows for shrinking off-diagonal elements of the correlation matrix. This is similar to parameter “s” in lassosum section “”, and acWe form nearly independent LD blocks using the optimal algorithm developed in Privé.e blocks . Twelve We have also developed a new “compact” format for the SFBMs (sparse matrices on disk). Instead of using something similar to the standard “compressed sparse column” format which stores all ,To be used with GWAS summary statistics from FinnGen, we investigate three different LD reference panels. To define homogeneous ancestry groups in the UK Biobank, we include all individuals within a specific distance to a population center in the PC analysis space.To be used with GWAS summary statistics from Biobank Japan, we also investigate three different LD reference panels. We use either the 504 East Asian (including 104 Japanese) individuals from the 1000G, 400 Japanese-like UK Biobank plus the 104 Japanese 1000G individuals , or 2,041 East Asian UK Biobank individuals . For the small LD references , we restrict to variants with a minor allele frequency (MAF) >0.02. For the one based on 2,041 individuals, we restrict to MAF >0.01. We also construct versions of these LD references with independent LD blocks, as described in the previous section. 2,527, 1,769, and 2,196 independent LD blocks are identified for these three LD references, respectively.,,,,We design GWAS simulations where variants have different sample sizes, which is often the case when meta-analyzing GWAS summary statistics from multiple cohorts with different sets of variants.We conduct further investigations to explain the results of section “”. The fi LDpred2  and S5. e is 0.2 . Indeed,ple size . Finallyple size ”. This cple size  and furtple size .As secondary analysis, we rerun these simulations with a smaller heritability of 4% instead. While predictive performance are overall much lower, relative performance are less attenuated when using the maximum sample size, otherwise results are highly consistent as before . We alsoMarchini and Howiemp/INFOj . As a dimp⋅INFOj  and S10.ˆ/se(γˆ) . This isole data  and S13.To compare these three corrections, we conduct a simulation using the same 40,000 variants from chromosome 22 as before, whereby we simulate quantitative phenotypes assuming a heritability of 20% and 2,000 causal variants using the “true” dataset (cf. section “When performing similar simulations with a heritability of 4% (instead of 20%), correction “sqrt_info” still provides slightly higher predictive performance for all methods (compared with no correction), yet the other two corrections sometimes provide lower predictive performance . In the Here we design simulations to understand the impact of using a mismatched LD reference panel, e.g., that comes from a different population compared with the one used to compute the GWAS summary statistics. We use the same simulation setup as before see , i.e., u,,In this section, we transition to using real data. Breast cancer GWAS summary statistics are interesting because they include results from two mega-analyses,mosome 8 , which amosome 8 , confirmTherefore, providing an accurate imputation INFO score is useful for two reasons. First, it allows for correcting for a reduced standard deviation when using imputed data in the QC step we propose to better uncover possible problems with the GWAS summary statistics. Second, using one of the proposed corrections based on INFO scores may lead to an improved prediction when deriving polygenic scores. We apply these corrections to the two breast cancer summary statistics. In the comparison, we first use the QC proposed in Privé et al.atistics . All oth,We use other external GWAS summary statistics for which INFO scores are reported see ; they alWe also investigate results for vitamin D GWAS summary statistics, which do not report INFO scores or allele frequencies, as opposed to previous ones. The QC procedure is thus less precise and uses allele frequencies from the LD reference . HoweverFor all phenotypes, PRS-CS-auto is very robust, whatever the QC procedure used  inferred from GWAS summary statistics with the ones computed from a reference panel.Note that, in this study, we mostly use GWAS summary statistics that include extended information , yet most GWAS summary statistics do not provide such exhaustive information.We have assessed the impact of these misspecifications in GWAS summary statistics on the predictive performance of some PGS methods. Using both the Bayesian LDpred2 models,In conclusion, we recommend adopting these changes, i.e., performing the (refined) QC proposed here, forming independent LD blocks in the LD matrix, and using more regularization when needed. We also recommend using well-matched LD reference panels. More regularization can be achieved by testing additional smaller values for the heritability parameter in LDpred2-grid, and using the two new parameters introduced here in LDpred2-auto section “”. Note t


Manihot esculenta Crantz) is a staple crop for ~800 million people in sub-Saharan Africa. Its production and productivity are being heavily affected by the two viral diseases: cassava brown streak disease (CBSD) and cassava mosaic disease (CMD), impacting greatly on edible root yield. CBSD is currently endemic to central, eastern and southern Africa, if not contained could spread to West Africa the largest cassava producer and consumer in the continent. Genomic selection (GS) has been implemented in Ugandan cassava breeding for accelerated development of virus resistant and high yielding clones. This study leveraged available GS training data in Uganda for pre-emptive CBSD breeding in W. Africa alongside CMD and fresh root yield (FRW). First, we tracked genetic gain through the current three cycles of GS in Uganda. The mean genomic estimated breeding values (GEBVs), indicated general progress from initial cycle zero (C0) to cycle one (C1) and cycle two (C2) for CBSD traits and yield except for CMD. Secondly, we used foliar data of both CBSD and CMD, as well as harvest root necrosis and yield data to perform cross-validation predictions. Cross-validation prediction accuracies of five GS models were tested for each of the three GS cycles and West African (WA) germplasm as a test set. In all cases, cross-validation prediction accuracies were low to moderate, ranging from -0.16 to 0.68 for CBSD traits, -0.27 to 0.57 for CMD and -0.22 to 0.41 for fresh root weight (FRW). Overall, the highest prediction accuracies were recorded in C0 for all traits tested across models and the best performing model in cross-validation was G-BLUP. Lastly, we tested the predictive ability of the Ugandan training sets to predict CBSD in W. African clones. In general, the Ugandan training sets had low prediction accuracies for all traits across models in West African germplasm, varying from -0.18 to 0.1. Based on the findings of this study, the cassava breeding program in Uganda has made progress through application of GS for most target traits, but the utility of the training population for pre-emptive breeding in WA is limiting. In this case, efforts should be devoted to sharing Ugandan germplasm that possess resistance with the W. African breeding programs for hybridization to fully enable deployment of genomic selection as a pre-emptive CBSD breeding strategy in W. Africa.Cassava ( The raising energy demand globally in face of climate change is popularizing cassava as an alternative source of renewable fuel with full potential to replace fossil fuel in the developed countries . BesidesDespite the importance of cassava as food security, especially in sub-Saharan Africa, average yields still remain low (12 t/ha) compared with yield average of 20 t/ha recorded in Asia countries like Thailand . A numbeFortunately, cassava that lagged previously in terms of genomic resources relative to cereal crops like maize, rice and wheat and legumes such as common beans, ground nuts and soya beans, has received significant funding to develop complete reference genome assembly . With thGenomic selection has been reported to offer some advantages over phenotypic selection breeding scheme: (i) genomic selection allows for more cycles of recombination per unit time than phenotypic selection, (ii) selection is solely based on estimates of marker effects without prior knowledge of the QTL and also captures variation due to loci with small effects . AnotherThrough the Next Generation Cassava Breeding project, Uganda embraced genomic selection tool for cassava improvement in early 2010s. The breeding program has so far developed three recurrent genomic selection cycles, and some of the elite material has been channeled to the variety development pipeline. Our primary traits of focus include: CMD resistance, fresh root weight, end-user root quality attributes  and CBSDhttps://www.nextgencassava.org/) to predict CBSD in West Africa using 35 clones shared from IITA, Ibadan , cycle one (C1) and cycle two (C2). Briefly, C0 population was derived from forty-nine diverse progenitors that were assembled from International Institute of Tropical Agriculture (IITA), International Center for Tropical Agriculture (CIAT) and NaCRRI. Germplasm from CIAT (Columbia) targeted improvement of quality and yield traits, while germplasm from the IITA (Tanzania), and NaCRRI (Uganda) breeding programs targeted improvement of CBSD resistance. Botanical seeds from crosses  of forty-nine progenitors were planted in a seedling nursery at Namulonge, and the sprouted seedlings were evaluated in an unreplicated seedling trial at Namulonge in 2012. A total of 466 C0 seedlings were selected visually as a training population for implementation of GS based on their CMD and CBSD resistance, and evaluated for two years (2013 and 2014) at Namulonge , Kasese (mid-western Uganda) and Ngetta (northern Uganda), using an alpha lattice design with two replications. Namulonge, Kasese and Ngetta were specifically chosen because of high viral disease pressure (cassava brown streak disease and cassava mosaic disease) and whitefly (vector) populations . The C1 All clones in the training set  were evaluated for CBSD and CMD severity, fresh root weight and harvest index. CBSD foliar severity was assessed at three (CBSD3S) and six CBSD6S) months after planting using a standard scale of 1-5; where 1 = no apparent symptoms, 2 = slight foliar chlorosis, but with no stem lesions, 3 = pronounced foliar chlorosis and mild stem lesions with no die back, 4 = severe foliar chlorosis and severe stem lesions with no die back, and 5 = defoliation, severe stem lesions and die back . Cassava−1) using a hanging weighing scale of 200 kg capacity. On the other hand, CBSDRS was recorded on all harvested roots per plot using a scale of 1-5; where 1 = no observable necrosis, 2 = ≤ 5% of root necrotic, 3 = 6 to 25% of root necrotic, 4 = 26 to 50% of root necrotic with mild root constriction, and 5 = > 50% of root necrosis with severe root constriction  and cassava brown streak root necrosis severity (CBSDRS). All the ten plants were harvested and partitioned into roots and above-ground biomass (leaves and stems). Fresh root weight (FRW) and above-ground biomass were separately weighed , Nigeria. A total of 5,000 botanical seeds were generated from bi-parental crosses involving forty-eight elite progenitors. The progenitors were selected per se based on their yielding ability and resistance to cassava mosaic disease (CMD). Accordingly, these seeds were shipped and planted in a seedling nursery at Namulonge. Out of the 5000 botanical seeds, 1980 successfully emerged, giving rise to 106 families. The 1980 seedlings were thus established in an unreplicated seedling trial during the second rains of 2018 (September/October). A total of 569 clones were selected from the seedling trial for further evaluation at the clonal stage during the 2019-2020 season, which was laid out using an augmented randomized block design at Namulonge. At the end of clonal evaluation, only 297 clones remained, as half of the clones were directly culled by CBSD. These 297 clones constituted the validation set for genomic prediction, and were assessed for CMD and CBSD severity fresh root yield as the 3rd trait evaluated, following the same procedure previously described for the training population.Leaf samples were obtained from the clonal evaluation stage of the training  and the validation (germplasm from Nigeria) populations and shipped to Intertek, Australia, for DNA extraction and genotyping. Both C0 and C1 clones were originally genotyped using genotyping by sequencing (GBS) platform with 46K single nucleotide polymorphism (SNP) chip at Genomic Diversity facility of Cornell University . Howeverprcomp function in R. The first two principal components (PC) were used to visualize population structure.We used the 21,938 SNPs to assess the population structure of the training population from Uganda  and validation population from West Africa. The SNP genotypes were coded as -1, 0, or +1. Principal component analysis (PCA) was done on scaled SNP markers using the To estimate heritability for each trait per cycle of GS population  and the WA clones, we fitted linear mixed models based on experimental design for each trial, followed by extraction of variance components using restricted maximum likelihood procedure . The varlme4 package in R, accounting for the environmental differences as well as trial evaluation year as below:For genomic prediction, we fitted a two-stage prediction model. At the first stage the raw phenotypes were merged across trials  into a single data set and fitted the linear mixed model using y represents raw phenotypic value; β represents fixed effect of the grand population mean, , study year, and location, with X being the corresponding incidence matrix linking observations to those effects. c and r represent random effects of clones with Zclone and Zrep(loc/study year) being corresponding incidence matrices for clones and replications nested in location-study year respectively. The residuals ϵ were distributed as: ranef function available in lme4 package  that were used for assessment of gains from genomic selection using the three evaluated Uganda’s GS cycles . A one-way analysis of variance was performed to test for significant differences among the means of the GEBVs for the three cycles for each trait using R  and WA clones. To do the cross-validation, the BLUPs that were extracted from the first stage analyses per trait were used as the response variable to fit a second stage prediction model for five genomic prediction models with different statistical assumptions. These models were: genomic best linear unbiased prediction (G-BLUP) , BayesiaY = 1β +Xg + ϵ , with g ~ N  and ϵ ~ , where Y represents the vector of BLUPs, β represents an overall population mean, X represents the design matrix linking observations to genomic values, g being vector of genomic estimated breeding values for each clone, and ϵ represents the vector of residuals. We assumed, g has a known covariance structure defined by the realized genomic relationship matrix K, while I representing identity matrix.To implement G-BLUP, we fitted a model: Y = 1β +Zg + ϵ , with g~N  and ϵ ~ (0 I2σg), where Y represents the vector of BLUPs, β represents an overall population mean, X represents the design matrix linking observations to genomic values, g being vector of genomic estimated breeding values for each clone, and ϵ represents the vector of residuals. We assumed, g also has a known covariance structure defined by the realized genomic relationship matrix K and I representing identity matrix. Specifically, BRR assigns a Gaussian prior with common variance to each marker effect, and applies homogeneous shrinkage to all marker effects. BL employs a double-exponential prior distribution for marker effects, which places strong shrinkage to markers with little to no effect on the trait. Bayes A applies a scaled-t prior distribution to marker effects, and places slightly less shrinkage on markers with zero effect, thereby allowing more flexibility for marker effects. Lastly, Bayes B assumes that most of the markers have zero effect on the trait, and assumes that the markers with an effect on the trait will follow a scaled-t prior distribution as in the case of Bayes A, making it relatively more stringent when compared to Bayes A. All the four Bayesian models used in this study were fitted using the BGLR function available in the R package BGLR , the clones were randomly split into five subsets (5-fold), where 4/5 of the subsets were used to train the model, while 1/5 was reserved for model validation and this was replicated 5 times. The accuracy of genomic prediction for each fold was then computed as Pearson correlation coefficient between the genomic estimated breeding values and BLUPs for each trait as a response variable.0, C1 and C2 to predict disease severity and fresh root weight in the validation population (West African population) that comprised 297 clones. Similarly, the prediction accuracy for each model was assessed using Pearson’s correlation between the GEBVs and the BLUP values per trait.Lastly, we carried out independent validation for the WA clones, the five evaluated genomic prediction models  were trained using C2 > 0.65).Plot-based heritabilities were low to intermediate Table 1.Using a boxplot, we summarized variations for genomic estimated breeding values across GS cycles for the six traits assessed, with overall genetic progress recorded for most traits except for CMD Figure 1Principal component analysis revealed a slight genetic differentiation between the Ugandan and West African cassava populations Figure 2Cross-validation prediction accuracies were performed using five models  to assess prediction accuracy of genomic selection for CBSD resistance, CMD resistance and fresh root weight within the training and validation populations. We observed modest prediction accuracies for all evaluated traits and populations Figure 3Analyses were performed using C0, C1, and C2 to assess prediction accuracy of genomic selection for CBSD resistance, CMD resistance and FRW in the West African population (297 clones) that was part of the pre-breeding populations evaluated in Uganda for CBSD resistance. We observed extremely low prediction accuracies for all traits Table 3.The challenges of rapid human population growth and climate change invariably affect agricultural productivity, and thus the need for increased genetic gains . Current2< 0.2) to high (H2 > 0.6), and were well in range with heritability estimates in literature  and validation set (West African cassava population), with a slight population structure and genetic differentiation between the two populations Figure 2Several genomic prediction models have been developed to predict trait performance under different genetic architecture and the five GP models  chosen for this study also differed in assumptions about the genetic architecture of the evaluated traits. Results revealed that models performed similarly for the most part, but there also occasions where G-BLUP was slightly superior to Bayesian models used in this study. These results were in good agreement with earlier findings from Average cross validation prediction accuracies across the three populations for CBSD and CMD resistance fresh root weight ranged between 0.26 to 0.48, and were comparable to findings by Wolfe et al. (2017); On the other hand, independent validation prediction accuracies of genomic selection were generally low, and they were lower than cross-validation prediction accuracies for CMD, CBSD traits and fresh root weight. Given that the training and validation populations were fairly genetically similar, the low prediction accuracies for independent validations could be attributed to genotype by environment interaction i.e. the training and validation populations were evaluated during different seasons. These low predictions could also be attributed to the fact that west African cassava populations were deficient in CBSD resistance alleles . No consThe C0 training set yielded the lowest prediction accuracies, with negative average accuracies for all traits across all models. The disparity between the predictive ability of the C1, C2 and the C0 training sets might be because the C1 training set was able to capture more genetic signals for CBSD foliar and root symptom expression in the West African clones than C0 training set. This phenomenon was noted by Based on the findings of this study, the breeding program in Uganda has made genetic progress through GS accelerated breeding cycles for most target traits, especially for CBSD root necrosis which is one of the must to have traits in a variety, demonstrating the worthwhile of GS for rapid population improvement and variety development. In general, low prediction accuracies were recorded from using Ugandan training set to predict traits in African clones, suggesting inadequacy of utilizing Ugandan training set, especially for CBSD pre-emptive breeding in WA. In this case, efforts should be devoted to sharing Uganda’s germplasm that possess resistance with the W. African breeding programs for hybridization to fully enable deployment of genomic selection as a pre-emptive CBSD breeding strategy in W.Ahttps://www.nextgencassava.org.Publicly available datasets were analyzed in this study. This data can be found here: OA Conceptualized the study, collected and analyzed data, and wrote the original manuscript. WE collected data and reviewed the manuscript. AU collected data and reviewed the manuscript. FM collected and analyzed the data, and reviewed the manuscript. PI collected data and reviewed the manuscript. MK collected data and reviewed the manuscript. CE acquisition of the funding and reviewed the manuscript. RK collected data and reviewed the manuscript. All authors contributed to the article and approved the submitted version.This work was supported by Next Generation Cassava Breeding Project funded by Bill and Melinda Gates Foundation, funding granted through Cornell University (grant number OPP1048542).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.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Modern GWAS studies use an enormous sample size and ultra-high density SNP genotypes. These conditions reduce the mapping resolution of marginal association tests–the method most often used in GWAS. Multi-locus Bayesian Variable Selection (BVS) offers a one-stop solution for powerful and precise mapping of risk variants and polygenic risk score (PRS) prediction. We show (with an extensive simulation) that multi-locus BVS methods can achieve high power with a low false discovery rate and a much better mapping resolution than marginal association tests. We demonstrate the performance of BVS for mapping and PRS prediction using data from blood biomarkers from the UK-Biobank . The article is accompanied by open-source R-software that implement the methods used in the study and scales to biobank-sized data. These advances in data availability have not been fully matched with adequate changes in the analyses-methods used.Genome-Wide Association Studies (GWAS) have reported large numbers of variants associated with many important traits and diseases; however, for complex traits many small-effect risk-loci remain unmapped. In the last decade, several public  remains the method most frequently used for mapping in GWAS. SMR tests for the marginal association between a phenotype (or a disease indicator) and individual SNPs and does not account for linkage disequilibrium (LD) between variants. Therefore, it can lead to significant associations of phenotypes with SNPs that are physically distant from causal variants–we refer to this phenomenon as poor mapping resolution. Importantly, the mapping resolution of SMR deteriorates with sample size because a large sample size increases the power to detect weak marginal associations between SNPs and phenotypes  models [) models , 7 offerWe implemented an efficient algorithm to generate samples from the posterior distribution of BVS models for problems involving hundreds of thousands of samples–the software is part of the BGLR R-package . In thisn = 315,874). From the imputed genotype SNPs, after filtering  and LD-pruning (R-squared <0.9), we retained 5,593,953 SNPs (see Supplementary Methods more details).We used data from the UK-Biobank  comprisiFor the evaluation of power and FDR, we simulated complex traits with 500 (randomly chosen) casual variants and a trait heritability of 0.5 . We conducted 10 whole-genome simulations, each involving 500 causal loci and 5,593,453 SNPs without effects. We also considered a second simulation scenario with the same heritability and a smaller number of causal variants (50); thus, with larger SNP-effect sizes.We evaluated six regression methods: marginal association testing (via SMR) and five variable selection methods . The SMR was a simple linear regression fitted via ordinary least squares using the phenotype as the response and one SNP as the predictor.Variable Selection methods were multiple regression models of the formThe To apply variable selection methods on a whole-genome scale, we leveraged the fact that LD decays within relatively short distances; therefore, following Funkhouser et al. , we applLASSO [λ). We formed a grid with 1000 values that was evenly spaced in the log-scale. The same grid of values of λ was used across each of the segments to which LASSO regression was applied . For each λ in the sequence we obtained a discovery set and a rejection set consisting of the SNPs with non-zero and zero effect in λ at which the SNP becomes active in the model; these ranks were used to evaluate power and FDR over the regularization path.The LASSO  regressiLASSO  R-packagForward regression also produces a sequence of solutions The Bayesian Variable Selection regression, we first used a model from the Spike-Slab family known as BayesC [iid Normal Xβ and (co)variance matrix For the s BayesC . Brieflys BayesC  are iid πIn a Bayesian models, priors that assign non-zero probabilities to null effects also specifies probabilities over possible models; this plays a very important role in error control . Therefon BayesC  with a Gπ, The hyper-parameters  for the-package .Forward regressions were implemented using the FWD function available in the BGData R-package, and LASSO regressions were fitted using the glmnet [SNP filtering was done using PLINK , genomice glmnet  R-package glmnet .λ at which the SNP entered in the model for the LASSO regressions , and (iv) the reduction in the RSS produced when the SNP entered in the model in the FWD regression . We then produced discovery and rejection sets for each method by selecting the top-k SNPs of each of the ranks . For each discovery set we estimated the proportion of the 500 causal loci recovered in the discovery set and the proportion of SNPs in the discovery set that were not causal loci .To estimate power-FDR curves, for each of the simulation scenarios and method we ranked SNPs based on the evidence for association produced by each method: (i) the p-values for the SMR , (ii) single-SNP posterior probabilities of inclusion for the BVS method  the value of To evaluate the ability of each method to fine-map causal variants we estimated the power-FDR performance at different mapping resolutions. Specifically, for an x-kbp mapping resolution , a discovery was considered true  if the distance with the closest causal variant was smaller (larger) than x-kbp.The simulation study demonstrated that the FWD and the BVS methods BayesC and SuSiE had the best performance. Furthermore, the performance of BayesC and SuSiE were very similar and better than that of FINEMAP; therefore, for analysis of the real data we used BayesC and SMR, which is the method most used in GWAS.The biomarkers that we analyzed , serum creatinine, low- and high-density lipoprotein cholesterols , and triglycerides) are often monitored in medical checkups and are related to metabolic syndrome . Therefore, after identifying individual SNPs that cleared the BFDR thresholds mentioned above, we also identified short segments that had elevated inclusion probability but did not clear the BFDR-threshold. For these segments we estimated the posterior probability of the segment  and included that segment in the discovery set if the segment BFDR was smaller than 0.05 or 0.1. Therefore, the discovery sets for the BVS method consisted of individual SNPs and short segments that cleared one of the two BFDR thresholds.Analyses were performed using the same genotypes used in the simulation (~5.6 million SNPs). All the traits were adjusted by the effects of sex, age, center, and with the top-10 SNP-derived eigenvectors. For rejection we used p value < 5e-8) with SNP effects estimated from SMR. These estimates do not account for LD; therefore, we considered a second PRS in which SNPs where selected based on SMR p-values and then SNP effects were estimated using BayesC. For these PRSs, we used p-value thresholds for SNP selection ranging from 1e-12 to 1e-4. Finally, we considered a whole-genome PRS derived using the estimates of effects from the local Bayesian regressions implemented using model BayesC (the same approach used for mapping). These local Bayesian regressions covered all the available SNPs (~5.6 million); however, to simplify the computation of the PRS we only used the SNPs with posterior inclusion probability greater than 1/1000.To evaluate the prediction accuracy of polygenic risk scores (PRS) we set aside data from 10,000 individuals for testing. As a baseline PRS we used one based on GWAS-significant SNPs  error control. We conclude from these results that, for data from unrelated white Europeans, using a BFDR < 0.05 as a decision rule leads to an FDR ≤ 0.1 for a mapping resolution of ~125 kbp.We used the results from the most challenging simulation scenario  to evaluate the empirical FDR of standard decision rules including SMR Table BayesC identified a much smaller number of variants than the SMR; however, the number of independent segments identified by BayesC were typically higher than those identified by SMR except for Glucose. Most often BayesC selected one or a few variants within each of the segments Fig. . The segp-value < 5e-8) and with SNP effects estimated from SMRs achieved prediction correlations ranging from 0.09  to 0.302 –the results from these PRSs are represented in blue in Fig. p-values from SMR and then estimating the effects of the SNPs using BayesC . In principle, the large sample size and the high-marker density should improve our ability to map risk variants. However, these conditions deteriorate the mapping resolution of SMR–the most frequently used methodology used in GWAS. We illustrated this problem with extensive simulations and with the analysis of six blood biomarkers. With a sample size of ~300,000 and high marker density, SMR can lead to significant associations for variants that are up to 300–1000 kbp apart from the causal variant depending on the effect size, and the extent of LD in the region Figs. , S2. ThiTo address the poor mapping resolution of SMR several methods have been proposed. One approach is to ‘weight’ the evidence of association of SNPs within a region to estimate an approximate posterior probability of association , 23. HowTo address limitations of two-steps procedures, here we considered four variable selection methods  that account for multi-locus LD. These methods are not new; however, the adoption of these methods in human GWAS has been limited in part because achieving high power with variable selection methods often requires a very large sample size. The advent of Big Data in genomic research has opened new opportunities for the use of these methods in GWAS.n ≥ 100,000) these two methods can achieve high power with low FDR and very fine mapping resolution, even for very-small-effect variants.Among the four variable selection methods considered, the FWD regression and the BVS methods (both SuSiE and BayesC) were the ones that achieved the best power-FDR performances. With a large sample size  power-FDR performance. This is not surprising considering the links that exist between these two methods and subset selection. The FWD regression is an approach developed to approximate subset selection constraining the search to a path that adds one predictor at a time . Furthern = 300,000). The information in the appendix also provides the computing times required for up to 100 iterations of SuSiE and SuSiE-sufficient statistics. It took on average 17 min for BLRXy to generate 10,000 posterior samples for a model involving 10,000 SNPs and a sample size of 300,000. The computing times of BLRXy were similar to those of SuSiE-sufficient statistics and considerably lower than those of SuSiE when sample size was large. These results show that it is doable to apply Bayesian regressions using the local-overlapping segments approach used in Funkhouser et al. [Collecting samples from the posterior distribution of high dimensional Bayesian models is computationally demanding. However, advances in hardware and in algorithms has made the application of BVS to biobank-size data feasible. As a reference we provide in Supplementary Fig. r et al.  and adopIn this study we focused on a specific BVS model that uses a prior with point of mass at zero and a Gaussian slab. Our simulation results suggest that the power-FDR performance of different BVS methods  is very similar see Fig.  providedOne concern that is often raised about Bayesian models is the need of specifying prior hyper-parameters and the influences that these may have on inferences. In the case of BayesC there are two hyper-parameters: the prior proportion of non-zero effects and the variance of the slab. To avoid specifying these hyper-parameters a-priori, we treated them as unknown and assigned priors to each of them. For the variance, we choose a scaled-inverse chi-square with small DF which results in limited influence of the prior on inferences when sample size is large. For the proportion of non-zero effects, we used a Beta prior with a prior mean of 1/100 . One could use a uniform prior ; however, adequate FDR control and stringent variable selection can be better achieved by using priors that are informative; this can be particularly important for studies involving a much smaller sample size than the one presented here.In regions of high LD collinearity may lead to many SNPs with elevated inclusion probability without any of them reaching stringent FDR thresholds ; thus, reducing power. In our analysis of blood biomarkers, we illustrated how this problem can be addressed using methods which identify sets of variants that are jointly associated with a phenotype.Finally, we evaluated various strategies to build PRSs; our results suggest that the prediction accuracy that can be achieved using a whole-genome BVS procedure implemented using local regressions is similar to the highest prediction accuracy that can be achieved fitting a BVS to SNPs filtered based on marginal association tests. Therefore, we conclude that BVS applied using local Bayesian regressions can be used for both fine mapping and accurate PRS prediction.Supplementary MethodsSupplementary Data


Spatial variation and genotype by environment (GxE) interaction are common in varietal selection field trials and pose a significant challenge for plant breeders when comparing the genetic potential of different varieties. Efficient statistical methods must be employed for the evaluation of finger millet breeding trials to accurately select superior varieties that contribute to agricultural productivity. The objective of this study was to improve selection strategies in finger millet breeding in Ethiopia through modeling of spatial field trends and the GxE interaction. A dataset of seven multi-environment trials (MET) conducted in randomized complete block design (RCBD) with two replications laid out in rectangle (row x column) arrays of plots was used in this study. The results revealed that, under the linear mixed model, the spatial and factor analytic (FA) models were efficient methods of data analysis for this study, and this was demonstrated with evidence of heritability measure. We found two clusters of correlated environments that helped to select superior and stable varieties through ranking average Best Linear Unbiased Predictors (BLUPs) within clusters. The first cluster was chosen because it contained a greater number of environments with high heritability. Based on this cluster, Bako-09, 203439, 203325, and 203347 were the top four varieties with relatively high yield performance and stability across correlated environments. Hence, scaling up the use of this efficient analysis method will improve the selection of superior finger millet varieties. Eleusine coracana (L.) Gaertn.) is the fourth most important after sorghum, pearl millet, and foxtail millet , assumed to be full rank. A random effect including a vector of genotype by environment effects, up are formed from the extraneous trend effects in each environment  with associated design matrix Zp, and Gg is variance matrix for genotype by environment effects, Gp is the variance matrix of extraneous trend effect and R is the variance matrix of the residual errors. In the model, the variance parametric in these variance matrices are directly estimated using REML estimation method. The model can be fitted to unbalanced (an incomplete genotype by environment table) due to the assumption that ug is random, which means that interaction effects can be predicted in the absence of data.A general model for the analysis of GxE data can be built by stacking the data vectors for each trial, R, are considered. In the mixed model MET formulation, the vector for residual effects, e, can be partitioned into residual effects within individual trials, jth) variances of genetic effects at each environment and covariances of genetic effects between environments, and Gv holds the  variances of environment effects for each genotype and the covariances of environment effects between genotypes.The random effects for genotypes, are combined across trials to form the random genotype by environment effects, as Gv = Im, then var (ug) = Ge ⊗ Im. A simplistic model for Ge sometimes used in practice is to consider the results of each trial analysis individually. This is equivalent to a model that allows for heterogeneous genetic variances across environments, but assumes independence between environments.An assumption traditionally made in MET analyses of plant breeding trials is that effects between genotypes are independent, so A more plausible model for the variance matrix of genetic effects is one which includes co- variance to model similarity in genetic performance between environments. In practice, it has been found that most MET data have heterogeneous covariance between environments as well as heterogeneous genetic variances , 27.Ge. This model captures the nature of heterogeneous variances and covariances found to occur in most MET data.Based on a factor analytic model, Smith et al.  proposedΛt×k) and heterogeneity of genetic covariance, or correlation, between pairs of environments (due to Λ).The form of the variance matrix of genetic effects, 2j) value for the jth trial was determined using an extended technique that takes unbalanced data into account, as suggested by Cullis et al, [th environment, and σ2gj is the genetic variance at environment j.The heritability  . The iniThe presence of global and extraneous variation associated with the row and column direction can be checked with the help of a model diagnosis tool, in particular the sample variogram , which wThe FA models were considered for genotype by environment (GxE) analysis while keeping the spatial models provided in the individual trial analysis. The adequacy of the FA models of several k orders was formally assessed as it was fitted within a mixed model framework based on the percentage of GxE variance explained by the factor components. The other important result from factor analysis was a cluster analysis using a dendogram, shown in In addition to the dendrogram, other typical summaries from the factor analysis included a heatmap of the genetic correlations between all trials. This is presented in The genetic variance, error variance, and heritability for each trial from the final fitted Spatial+FA models are presented in The heritability of yield at each trial is shown in A standard method for estimating random effects in a mixed model is best linear unbiased prediction (BLUP), which has the property of minimum mean square error of prediction, and they can form a more accurate estimation of the underlying effects. Genotype effects are mostly fitted as random terms in a plant breeding context where accuracy of genotype ranking is important for selection of superior genotypes. This is more required in the early stages of genotype trials conducted with a large number of entries. The performance of genotypes can be ranked based on the values of BLUPs averaged across correlated environments of the 1st cluster (C1), excluding Bako2021 and Assosa2019 since they showed low genetic correlation with the other trials and low genetic variance. Following advances in statistical science and knowledge, methods of data analysis for crop variety evaluation programs have improved over recent years , 33, 34.Control by blocking, which is based on observable factors like soil type and topography, is commonly used in on-station trials, but several possible inputs are unknown or unmeasured, which stresses the importance of incorporating spatial information into the analysis of experiments to improve the precision of genotypes evaluation trials. This is especially important for field trials in Ethiopia, where the problem varies from plot to plot, as some findings justify . The spaThe ANOVA-based approach always assumes constant variance across environments and no correlation between environments. We conducted MET analysis by fitting heterogeneous variance for residuals and a factor analytic model to the GxE effects, which results in the Restricted Maximum Likelihood (REML) estimates for genetic correlation between environments, and hence cluster analysis using a dendrogram and bi-plot. The results of MET data analysis showed that modeling GE interactions with FA models in combination with models for spatial variations resulted in a significant improvement in the estimates of genetic parameters, and this was demonstrated with evidence of heritability. Results from a related study on sorghum , durum wWe found two clusters of correlated environments using the dendrogram and the bi-plot, which aided selection of superior finger millet varieties within each cluster. Only one cluster was chosen for the entire variety selection because it formed with relatively high heritability and encompassed more environments. The second cluster, on the other hand, was found to have low heritability and fewer environments.Combining MET with spatial and FA models allowed for a better understanding of the genetic effect and enhanced the precision and accuracy of genotype evolution by allowing the breeder to also take the GxE interaction effect into consideration. This makes it possible to isolate the genetic effect or further explore the GxE interaction effect, depending on the goal. The genotypes with the highest potential for a further verification study that might be used as a released variety could be found using the fitted information.S1 Table(TXT)Click here for additional data file.


P < 5 × 10−8) with GDM, mapping to/near MTNR1B (P = 4.3 × 10−54), TCF7L2 (P = 4.0 × 10−16), CDKAL1 (P = 1.6 × 10−14), CDKN2A-CDKN2B (P = 4.1 × 10−9) and HKDC1 (P = 2.9 × 10−8). Multiple lines of evidence pointed to the shared pathophysiology of GDM and T2D: (i) four of the five GDM loci (not HKDC1) have been previously reported at genome-wide significance for T2D; (ii) significant enrichment for associations with GDM at previously reported T2D loci; (iii) strong genetic correlation between GDM and T2D and (iv) enrichment of GDM associations mapping to genomic annotations in diabetes-relevant tissues and transcription factor binding sites. Mendelian randomization analyses demonstrated significant causal association  of higher body mass index on increased GDM risk. Our results provide support for the hypothesis that GDM and T2D are part of the same underlying pathology but that, as exemplified by the HKDC1 locus, there are genetic determinants of GDM that are specific to glucose regulation in pregnancy.Gestational diabetes mellitus (GDM) is associated with increased risk of pregnancy complications and adverse perinatal outcomes. GDM often reoccurs and is associated with increased risk of subsequent diagnosis of type 2 diabetes (T2D). To improve our understanding of the aetiological factors and molecular processes driving the occurrence of GDM, including the extent to which these overlap with T2D pathophysiology, the GENetics of Diabetes In Pregnancy Consortium assembled genome-wide association studies of diverse ancestry in a total of 5485 women with GDM and 347 856 without GDM. Through multi-ancestry meta-analysis, we identified five loci with genome-wide significant association ( Gestational diabetes mellitus (GDM), defined as hyperglycaemia with onset or first recognition during pregnancy, is associated with increased risk of pregnancy complications and adverse perinatal outcomes, including pre-eclampsia, stillbirth, large for gestational age, neonatal hypoglycaemia, preterm birth, low Apgar scores and admission to neonatal intensive care . Whilst GDM and T2D share both genetic and non-genetic risk factors, including obesity, poor diet and sedentary lifestyle ,10. FamiP < 5 × 10−8), mapping near MTNR1B and CDKAL1, both of which have also been previously implicated in T2D risk.There have been considerable advances in our understanding of the genetic contribution to T2D through large-scale genome-wide association studies (GWAS) across diverse populations . In contTo gain novel insight into the genetic architecture of GDM, the GENetics of Diabetes In Pregnancy (GenDIP) Consortium assembled GWAS of diverse ancestry in a total of 5485 women with GDM and 347 856 women without GDM. With these resources, we aimed to improve our understanding of the aetiological factors and molecular processes driving the occurrence of GDM, including the extent to which these overlap with T2D pathophysiology, and investigate the effects of potential causal metabolic risk factors on the disease through Mendelian randomization (MR).We began by aggregating GDM association summary statistics across GWAS through multi-ancestry meta-analysis: the effective sample size was 72.2% European, 13.4% East Asian, 9.9% South Asian, 2.8% Hispanic/Latino and 1.7% African  and S2. MTNR1B  and CDKAL1 . The remaining three loci for GDM mapped to/near TCF7L2 , CDKN2A-CDKN2B  and HKDC1 . Through approximate conditional analyses, conducted using ancestry-matched linkage disequilibrium (LD) reference panels for each GWAS, we observed no evidence for multiple distinct association signals at genome-wide significance at any of the five GDM loci , where the lead SNV demonstrated stronger effects on GDM in GWAS of East Asian ancestry than in other populations, despite the risk allele being common in all ancestry groups , where there were marked differences in the effects on GDM of the lead SNV between GWAS undertaken in different ancestry groups  at the CDKN2A-CDKN2B locus . There was also a highly significant enrichment of GDM associations at T2D loci , indicating that they would be discovered at genome-wide significance with larger effective sample sizes. Indeed, after excluding the four overlapping GDM-T2D loci, a weighted genetic risk score of lead T2D SNVs was significantly associated with GDM . Extending our analyses, genome-wide, using LD-score regression, we observed strong genetic correlation between GDM and T2D: rG (95% CI) 0.744 . Weaker genetic correlations between GDM and other glycaemic traits, BMI and birth weight were also observed . To fur Project . We obseobserved . These rMTNR1B locus  Investigators  for GDM associations mapping to protein coding exons, binding sites for FOXA2, NFE2 and TFAP2, and chromatin states in adipose tissue and skeletal muscle that mark enhancers and transcribed regions  genic regions ; (ii) ch regions . FOXA2 i regions . Skeleta regions . These e regions , althougHKDC1 locus (rs9663238) demonstrates only weak statistical evidence of T2D association in previously reported trans-ancestry GWAS meta-analyses from the DIAMANTE Consortium . GDM risk alleles at the lead SNV, and/or at variants in strong LD (European ancestry r2 > 0.9) with it, have been previously associated, at genome-wide significance, with higher 2-h plasma glucose (2HPG) in pregnant women in the HAPO Study and two replication studies of European ancestry (G (95% CI) 0.149 . In addition to demonstrating the association of the maternal SNVs at this locus with GDM in the current study, we observed that 99% credible set variants are lead SNVs for HKDC1 expression quantitative trait loci in a range of tissues in the GTEx Project (HKDC1 (Hexokinase Domain Containing 1) catalyses the phosphorylation of hexose to hexose 6-phosphate and is involved in glucose homeostasis and hepatic lipid accumulation. Haplotypes of variants associated with 2HPG in pregnancy disrupt regulatory element activity and reduce HKDC1 expression across diverse tissues , which has been demonstrated to reduce hexokinase activity in multiple cellular models   , includiase.org) . We did ase.org) . Of the ase.org) . The estase.org) . The cauase.org) .MTNR1B, TCF7L2, CDKAL1, CDKN2A-CDKN2B and HKDC1. Our results demonstrated strong correlation in the effects of previously reported associations for T2D and those observed for GDM, and highlighted overlapping molecular mechanisms and tissues that mediate associations for both diseases. In contrast, variation at the HKDC1 locus is not strongly associated with T2D, but instead plays a more important role in glucose metabolism during pregnancy than outside of pregnancy. The genetic diversity of GWAS contributing to our meta-analysis enabled identification of ancestry-correlated heterogeneity in allelic effects on GDM at two loci. Such heterogeneity could reflect variable impact of different pathophysiology driving glycaemic dysregulation in pregnancy between ancestries and emphasizes the need for increased sample sizes in under-represented population groups. In contrast, results were consistent between GWAS in which all women had a universal blood-based test and those that did not, suggesting little impact from misclassification due to selective use of diagnostic tests only in those deemed to be at high-risk. Finally, MR analyses revealed a significant causal effect of higher BMI on GDM risk, consistent with the causal association observed with T2D. Taken together, these results provide further support for the hypothesis that T2D and GDM are part of the same underlying pathology. However, they also highlight there are pathways to GDM that impact on glucose regulation only in pregnancy, and that additional GDM-specific associations will be revealed through GWAS in larger sample sizes.We have conducted the largest and most ancestrally diverse GWAS meta-analysis for GDM, where we identified associations mapping to All human research was approved by the relevant institutional review boards and conducted according to the Declaration of Helsinki. All participants provided written informed consent.r2 < 0.3 or info < 0.4) and/or minor allele count < 5 were excluded from downstream association analyses  were corrected for residual structure by means of genomic control   that areP-values for inflation due to residual structure between GWAS using genomic control adjustment. We considered only those SNVs reported ≥50% of the total effective sample size in downstream analyses.Our primary multi-ancestry analysis utilized meta-regression, implemented in the MR-MEGA software, which allows for allelic effect heterogeneity between GWAS that is correlated with ancestry . We firsFor each SNV, we also conducted fixed-effects meta-analysis across GWAS under an inverse-variance weighting of allelic log-ORs using GWAMA . We corrP < 5 × 10−8) in the multi-ancestry meta-regression that were separated by at least 500 kb. Loci were defined by the genomic interval mapping 500 kb up- and downstream of each lead SNV.We identified lead SNVs attaining genome-wide significant evidence of association  evidence of residual GDM association in the meta-regression, we concluded that there was a single association signal at the locus.Each GWAS was first assigned to one of the ancestry groups  represenP-values and standard errors of allelic effects from each ancestry group for residual inflation due to structure between GWAS by genomic control adjustment if the inflation factor was > 1. We estimated the mean effect allele frequency across GWAS from each ancestry group, weighted by the effective sample size of the study.We aggregated association summary statistics across GWAS from the same ancestry group via fixed-effects meta-analysis based on inverse-variance weighting of allelic log-OR to obtain effect size estimates using GWAMA . We corrWe extended the meta-regression model implemented in the MR-MEGA software to investigate the impact of ancestry and the use of a universal blood-based test to define GDM status on heterogeneity in allelic effects on GDM at lead SNVs. We modelled allelic log-ORs across GWAS in a linear regression framework, weighted by the inverse of the variance of the effect estimates, incorporating a covariate indicating whether GDM status was defined by a universal blood-based test  in additP-value) for GDM and those reported for T2D. We excluded lead SNVs for T2D that also attained genome-wide significance for GDM. For the remaining SNVs, we regressed the log-ORs for GDM (weighted by their corresponding variances) on the log-OR for T2D, as implemented in grs. summary function . We then used an iterative approach to identify a joint model of enriched annotations from this set. At each iteration, we dropped the annotation from the joint model that minimized the reduction in the penalized likelihood. We continued until no additional annotations worsened the fit of the joint model at nominal significance (P < 0.05). We next used the cross-validation likelihood because the significance of parameter estimates from the penalized likelihood cannot be assessed using standard statistical approaches. For the selected joint model, we identified the penalty that maximized the cross-validation likelihood. Finally, we dropped any annotations from the joint model that resulted in a decrease in the cross-validation likelihood.We tested for genome-wide enrichment of GDM associations that map to genomic annotations using fGWAS . To do tgression . We firsHKDC1 locus, we calculated the posterior probability of driving the GDM association for each SNV under an annotation-informed prior model derived from the globally enriched functional and regulatory annotations identified by fGWAS. Specifically, for the At the ible set  for the HKDC1 locus for significant (q < 0.05) cis-expression quantitative trait loci (eQTLs) across tissues in the GTEx Project (We conducted a look-up of 99% credible set variants at the  Project . We repohttps://www.mrbase.org) for metabolic measures. We selected all subcategories of metabolites, which included ‘amino acid’, ‘carbohydrate’, ‘cofactors and vitamins’, ‘energy’, ‘fatty acid’, ‘keto acid’, ‘lipid’, ‘metabolite salt’, ‘metabolites ratio’, ‘NA’, ‘nucleotide’, ‘peptide’, ‘protein’, ‘unknown metabolite’ and ‘xenobiotics’. We also selected the following subcategories of risk factors: ‘anthropometric’, ‘hormone’, ‘immune system’, ‘kidney’ and ‘metal’. We identified European ancestry GWAS in MR-Base for each selected metabolic trait. Where more than one GWAS was available for a trait, we gave preference to women-specific studies with the largest sample sizes and numbers of SNVs. Any GWAS undertaken only in men were excluded.We systematically searched the MR-Base GWAS catalogue ; (ii) ‘directional filtration’ that removed instruments from ‘top hits’ that are likely to be related to the outcome through reverse causation using Steiger filtering (Q statistic (P < 0.05); and (iv) combined ‘directional filtration’ and ‘heterogeneity filtering’. The 14 MR models were: seven mean-based methods , three median-based methods  and four mode-based methods . The best combination of instrument selection-MR method was identified using a variable predicted by MoE, scaled between 0 and 1, where 1 indicates best performance.For each metabolic trait with more than five genetic instruments, we conducted MR analyses using a ‘mixture of experts’ (MoE) machine learning approach . This apiltering ; (iii) ‘For metabolic traits with five or fewer genetic instruments, the MoE approach could not be applied because many of the MR models require larger numbers of SNVs. For these metabolic traits, we used either the Wald ratio estimate (one SNV) or the inverse-variance weighted estimate (between two and five SNVs).https://github.com/mattlee821/EpiCircos).All analyses were conducted in R version 3.6 using the packages ‘TwoSampleMR’ (version 0.5.4) and ‘MRInstruments’ for the MR analyses and ‘EpiCircos’ (https://tools.gi.ut.ee/tools/GENDIP_PervjakovaEtAl2022.txt.gz.Meta-analysis summary statistics can be downloaded from: Supplementary_Figures_ddac050Click here for additional data file.Supplementary_Tables_ddac050Click here for additional data file.