Large-scale longitudinal biobank data can be leveraged to identify genetic variation contributing to human diseases progression and traits trajectories. While methods for genome-wide association studies (GWAS) of multiple correlated traits have been proposed, an efficient multiple-trait approach to model longitudinal phenotypes is not currently available. We developed GAMUT, a genome-wide association approach for multiple longitudinal traits. GAMUT employs a mixed-effects model to fit longitudinal outcomes where a fast algorithm for inversion by recursive partitioning of the random effects submatrix is introduced. To evaluate performance of the algorithms introduced and assess their statistical power and type I error, stochastic simulation was conducted. Consistent with our expectation, power was greater for cross-sectional (CS) than longitudinal (LT) effects, particularly with a diminishing LT/CS ratio. With a minimum minor allele count of 3 within genotype by time categories, observed type I error was roughly equal to theoretical genome-wide significance. Additionally, 28 blood-based biomarkers measured at 2 time points on participants of the UK Biobank were used to compare GAMUT against single-trait standard and longitudinal GWAS (including rate of change). Across all biomarkers, we observed 539 (CS) and 248 (LT) significant independent variants for the GAMUT method, and 513 (CS) and 30 (LT) for single-trait longitudinal GWAS, respectively. Only 37 variants were identified by modeling rates of change using standard GWAS. Genome wide association studies have traditionally been carried out using cross-sectional data and one outcome at a time. With the advent of global biobanks and direct-to-consumer genomic testing, longitudinal health data recorded on diverse clinical aspects of each individual have opened the door for more statistically rigorous genome-wide association modeling. The availability of such data makes it possible to discover novel genetic variants associated with trajectories of trait changes or disease progression within individuals, as well as pleiotropic variants impacting multiple phenotypes.2. Mixed models are a commonly used approach for handling relatedness in conventional GWAS, e.g. as implemented with EMMA3, GEMMA4, and SAIGE5. While mixed models may also be used to model multiple-traits or longitudinal phenotypes, computational efficiency may be difficult to achieve for analysis of large-scale cohorts. This is due to the fact that mixed model approaches require the complex task of estimating variance components before setting up and solving a large system of equations, which requires the inversion of large matrices associated with the random components in the mixed model. Sikorska et al.6 introduced computationally efficient approaches to utilize mixed models in longitudinal GWAS. Their approximate approaches were shown to be precise in estimating cross-sectional and longitudinal effects of each SNP, where cross-sectional effects are those comparable to conventional GWAS and longitudinal effects define how each SNP may impact the change in a trait over time. In an effort to simplify computations for longitudinal GWAS, researchers have often collapsed the multiple measurements into one rate of change between the earliest and the latest measurement of each individual. The rates of change were then fed into conventional GWAS workflows where associations with each phenotype were investigated independently. The collapsing approach was historically discussed and found to be theoretically problematic due to loss of information8.Mixed models are the approach of choice for the analysis of longitudinal data because they account for variability between measurements across multiple time points on one phenotype as well as variability among measurements on multiple phenotypes10. In addition, the availability of repeated measurements of the same phenotype on each individual affords an opportunity to assess genetic effects on changes in disease traits or biomarkers over time. Despite the advantages longitudinal and multiple-trait approaches each provides for identifying genetic determinants of disease and disease progression, implementation of such methods is also known to be computationally burdensome.When individuals are assessed for multiple correlated phenotypes, a multivariate approach to jointly evaluate those phenotypes was shown to be more statistically rigorous1, for longitudinal phenotypes to a multiple-trait setting. The approach efficiently models multiple correlated phenotypes as well as multiple measurements recorded through time. To evaluate the computational efficiency of the approach as well as its ability to identify variant associations what would otherwise be missed with a conventional GWAS framework, 28 quantitative traits with repeated measures in up to 16,622 UK Biobank participants were assessed. Methods to obtain the inverse of large matrices are also introduced in an effort to maximize the computational efficiency of multiple-trait longitudinal GWAS.In the current study, we extend the mixed model approach, GALLOPIn standard GWAS, we test the association of each variant with the risk to a disease or to an extreme value of a quantitative trait, such as high cholesterol. In longitudinal GWAS, we test the association of the genetic variant with the progression of the disease or with the change in a quantitative biomarker for the disease over time. Single-trait longitudinal GWAS fits genetic variants one-by-one in the mixed model  which inFollowing from a standard GWAS of a single longitudinal phenotype, multiple-trait longitudinal GWAS have been explored and shown to improve statistical power for discovery. In this type of analysis, multiple correlated traits are jointly modeled and missing records are implicitly inferred based on the covariance between traits. Multiple-trait longitudinal GWAS is typically performed in 3 steps: estimating variance components, then constructing the components of the mixed-model equations, and performing the association analysis. First, genetic and environmental variances and covariances are estimated once using a null model without genotypes, and then these are utilized in a transformed version of Henderson’s mixed model equations that are used with minor modifications for the hypothesis testing of each variant separately.10, both the single- and multiple-trait mixed models can be written as in  was utilized in estimating variance components, in which a single covariance between effects of every 2 traits but Computationally efficient average information restricted maximum likelihood , where A and D are square submatrices, the inverse is obtained using the identity,To simplify computations for the single-trait case, Sikorska et al.ystem in  so that ystem in  by \docuD in the next round. As shown in Fig. A, B, C, and D at round 0 and used that as the inverse of the larger D submatrix at round 1, i.e. D submatrix of the next round; note that the D matrix itself was not needed in the next round.For more than 4 blocks, the same identity in  were appFor the current multiple-trait model, the inverse was obtained using our proposed recursive partitioning in less computing time and resources than with other direct sparse inverse techniques see “” for the1. In principle, the linear system in 10) inclujth time point of individual For individual Three correlated traits were considered in the current simulation with 3 CS and 3 LT effects for each SNP. We use the vector In our simulation strategy, we chose to reduce the covariance between cross-sectional and longitudinal effects. We tested multiple ratios for the cross-sectional to longitudinal effects by setting the value of The UK Biobank is a prospective cohort study with rich genetic and health data from half a million participants. The UK Biobank study was carried out in accordance with relevant guidelines and regulations as approved by the NHS National Research Ethics Service . Participants in the study gave full informed signed consent.First and second measurements of 28 blood biomarker traits of UK Biobank participants of European ancestry were evaluated for cross-sectional and longitudinal associations with imputed array genotypes. Phenotypes assessed were from UK Biobank field IDs  and heart disease who may need more than statin.To compare GALLOP and GAMUT with an approach that evaluates SNPs for their associations with rates of change, a single value per individual was derived as the difference between the two measurements divided by the time interval between measurements. The GWAS model for rates of change did not include time but included the baseline measurement as a scaled covariate. All other covariates were the same across the methods studied. Models for rates of change included those without both baseline and time, as well as an addition of both baseline and time.To test the impact of comorbidity and the number of repeated measures on the longitudinal GWAS outcomes, triglycerides (TG) were extracted from the primary care data, referred to as general practice or GP data. TG measures on 8968 participants of European ancestry who were diagnosed with coronary artery disease (CAD) at any age using all available clinical history information were extracted from the UK Biobank GP data. The dataset included nearly 99,000 observations on 8968 individuals with 3 to 35 TG measures per participant over an average period of 6 years. A comparable group of 8587 individuals with 3–35 repeated measures per individual was randomly selected from the UK Biobank cohort for the purpose of comparison. The objective was to evaluate the reliability and benefit of controlling for diseases interfering with biomarker measures on the quality of longitudinal effects. With the onset of such diseases, trait trajectories might be perturbed in a way that impairs the detection of true genome-wide longitudinal signals. A single trait longitudinal GWAS was run on each dataset and the impact of comorbidity on the quality of estimates was reported. Mixed models for the two datasets were adjusted for cholesterol-lowering drugs as they might lower triglycerides as well.Four sample sizes of one, two, three and ten thousand individuals were simulated. In addition, 5 longitudinal to cross-sectional ratios of 1, 2, 5, 20, and 100% (LT ratio scenarios) were simulated and replicated 100 times. LT ratio scenarios were simulated with 3000 individuals each; and sample size scenarios were simulated with LT effects that were 20% of the CS effects (LT to CS ratio of 1:5). Data sets simulated were analyzed with GAMUT and GALLOP. As shown in Fig. Bonferroni-corrected significance threshold was calculated as 0.05 divided by the total number of variants scanned. Type I error realized in the simulation was taken as the proportion of non-causal variants with p-values below the Bonferroni-corrected significance threshold. Table To study statistical power for the multiple- versus single-trait approach, standard errors of all variants in two simulation runs were compared. In the first run, 15% of values were assigned to be randomly missing for one of the three phenotypes and in the second run, 50% randomly selected records were set to be missing for the same phenotype. Standard errors were consistently smaller with the multiple trait analyses, especially when a greater proportion of data was missing. In addition, Fig. Because standard errors were shown to be reduced for all variants, both causal and noncausal, power and type I errors associated with multiple- vs. single-trait approaches were studied in a scenario where 15 and 50% of individuals were missing for their baseline and second records. Figure 14. Variants detected by the 3 approaches are reported in the following sections. Benchmarking data included 28 blood biomarkers in the UK Biobank, where all individuals with 2 measurements for at least one biomarker were utilized in the analyses.Performance of GAMUT vs. other approaches in the context of real-world data is shown next. GAMUT results are compared with a single-trait longitudinal approach using GALLOP and a single-trait conventional GWAS on each phenotype rate of change using REGENIEZ’R–1Z + G–1 took 59 s vs. 21.6 min using direct sparse inversion. For 20 traits, inversion by recursive partitioning took 2.2 min vs. extrapolated 130 min consumed by direct sparse inversion /2 = 378 pair-wise variance component sets of estimates were obtained using AI-REML. Although the variance of each trait was estimated multiple times when paired with other traits, covariances estimated were unique. CS and LT variances of each biomarker trait in a genetic variance–covariance matrix of order 56 were averaged across all other traits. Pairwise covariances were unique. Residual variances and covariances between traits were similarly summarized, where variances were averaged while pairwise covariances were unique. Although variances were estimated multiple times, they were consistent, especially for the CS components, as the boxplots of Fig. *27/2 = 3The weakest variance components were estimated for Testosterone, measured in both sexes. Figure Similarly, genetic and residual correlations were positive and strong among LDL direct, Apolipoprotein B and Cholesterol of cluster-4 Fig. . Results2 of 0.4, a window of 500 kb, and a p-value threshold of 5e-8. Numbers of significant SNPs in the table were taken from the number of clumps found across the genome and summed for all biomarkers.Results of longitudinal genome-wide association scans performed on biomarker phenotypes as 4 multiple-trait longitudinal runs using GAMUT, 28 single-trait longitudinal runs using GALLOP, and 28 conventional runs using conventional GWAS on biomarker rates of change between first and second measurements were presented in Table Collectively, GAMUT resulted in a total of 539 significant cross-sectional and 248 longitudinal associations, whereas the single-trait longitudinal GWAS resulted in 513 cross-sectional and 30 longitudinal associations. The conventional GWAS on rates of change yielded 37 significant longitudinal associations across the 28 biomarker phenotypes. Agreement between GAMUT and GALLOP was consistent, i.e. 98 of cross-sectional and 90% of longitudinal variants identified by GALLOP were a subset of those identified by GAMUT. There was little overlap between conventional GWAS and the other two methods. All variants identified by rate of change GWAS were observed as cross-sectional associations in the other two approaches. For example, the 9 and 11 variants associated with rate of change in direct and total bilirubin were, in fact, identified as having cross-sectional, but not longitudinal associations with these traits using GALLOP and GAMUT. Additionally, variants identified by rate of change GWAS were generally the most significant cross-sectional associations uncovered by the other two approaches . Longitudinal or progression effects on the other hand were more difficult to validate but still provided multiple clinical insights. In particular, a variant on chromosome 15 (rs117268014), captured only by GAMUT as cross-sectionally and longitudinally associated with both direct and total bilirubin. The variant is in the vicinity of Gremlin1 gene (GREM1) and shown by QTLbase16 to be a blood expression QTL for Rho GTPase activating protein 11A (ARHGAP11A), a gene positioned near GREM1 and a methylation QTL for Eukaryotic Translation Initiation Factor 5A2 (EIF5A2), a gene whose overexpression correlates with multiple cancers including colorectal, gastric, and esophageal cancers. Overexpression of the gene was reported to correlate with cancer progression and poor survival17. Note also that the role of GREM1 itself is well established in the onset and prognosis of colorectal and gastric cancers. In particular its role in promoting colorectal cancer cell metastasis, motility, and invasion18.Cross-sectional effects were well powered and consistent with the biomarker GWAS literature (e.g. Ref.Unlike the single trait outcomes across the random UK Biobank sample with 2 and 0 cross-sectional and longitudinal genetic signals in Table In the current study, an efficient and powerful approach to identify genetic variants associated with cross-sectional and longitudinal effects was developed. The approach capitalizes on the availability of broad phenotyping, in which individuals are assessed for multiple clinical traits, as well as deep phenotyping, characterized by multiple measurements of these traits over time. GAMUT successfully modeled both the multiple-trait and the longitudinal aspects of the data while maximizing computational efficiency, outperforming single-trait longitudinal analysis when up to 16 traits were examined. It is imperative to emphasize that a multivariate analysis is inherently more computationally costly than the cumulative cost of the equivalent univariate analyses. The computational advantage of our multivariate approach up to 16 traits is explained by, first, the algorithmic differences between GAMUT and GALLOP in transforming the major random effects matrix of the mixed model equations into an identity, and second, having to build and transform the coefficient matrix only once for all traits. The approach is particularly useful for joint analysis of strongly correlated traits measured in real-world data collected over time. While handling missing values in longitudinal data can be cumbersome, GAMUT provides a framework in which missing records in one or more traits are implicitly estimated based on genetic and environmental covariances with the traits that have more complete data.Because longitudinal effects are likely to be much smaller than cross-sectional effects as seen in the UK Biobank blood biomarker data, sample sizes required to detect genetic variants associated with disease progression are expected to be manyfold greater than what is required for cross-sectional disease association, as was shown in our simulation. In order for the current approach to be useful, it is essential to have sufficient data at multiple time points per individual, e.g. primary care data or repeated measures in extended large-scale clinical trials. In addition, the UK Biobank continues to assess participants over two time points for thousands of traits such as the repeat MRI imaging study of brain, heart, and abdomen. Although our simulations suggest that multiple-trait approaches offer limited advantages over single-trait analysis in the presence of complete data with no missing observations, such a scenario is unlikely to exist in either observational real-world data collection or prospective clinical trials.In the current Biomarker analysis, longitudinal variant associations above genome-wide significance suffered from inflation for 3 possible reasons. First, longitudinal effects were orders of magnitude smaller than their cross-sectional counterparts; second, the number of individuals with repeated measurements was limited, and finally time points within individuals were ≤ 2 visits in the current UK Biobank phenotypic data. Inflation was shown to be controlled when a sample of participants, similar in their clinical history and with many more repeated measures, was extracted from the UK biobank primary care data and utilized in longitudinal GWAS.In this paper, we demonstrate that GAMUT is a computationally efficient framework that accounts for genetic and environmental co-variability in multiple longitudinally assessed quantitative traits. Although univariate modeling approaches have been successfully used to identify important disease associations, they also miss novel insights as they fail to leverage the correlation among pathophysiological processes that lead to disease onset or progression. We have shown this to be the case in an analysis of real-world data from the UK Biobank, where multiple cross-sectional and longitudinal insights would have remained undetected using other standard statistical methods and assert that our approach has broad applicability to large-scale collections of data available in global biobanks and prospective clinical studies today.Supplementary Tables.


Ordinal traits are important complex traits in crops, while genome-wide association study (GWAS) is a widely-used method in their gene mining. Presently, GWAS of continuous quantitative traits (C-GWAS) and single-locus association analysis method of ordinal traits are the main methods used for ordinal traits. However, the detection power of these two methods is low.To address this issue, we proposed a new method, named MTOTC, in which hierarchical data of ordinal traits are transformed into continuous phenotypic data (CPData).Then, FASTmrMLM, one C-GWAS method, was used to conduct GWAS for CPData. The results from the simulation studies showed that, MTOTC+FASTmrMLM for ordinal traits was better than the classical methods when there were four and fewer hierarchical levels. In addition, when MTOTC was combined with FASTmrEMMA, mrMLM, ISIS EM-BLASSO, pLARmEB, and pKWmEB, relatively high power and low false positive rate in QTN detection were observed as well. Subsequently, MTOTC was applied to analyze the hierarchical data of soybean salt-alkali tolerance. It was revealed that more significant QTNs were detected when MTOTC was combined with any of the above six C-GWAs.Accordingly, the new method increases the choices of the GWAS methods for ordinal traits and helps to mine the genes for ordinal traits in resource populations. This includes count data for quantitative traits and hierarchical data for resistance traits, such as the number of main stem nodes , the numOrdinal traits are discrete traits that are controlled by multiple genes. However, their phenotypic data is hierarchical and non-continuous and contains relatively limited information; accordingly, GWAS for ordinal traits is more complex than that for continuous quantitative traits. The threshold model represents a reasonable method for the genetic analysis of ordinal traits, and most association mapping methods are developed under this framework . GeneralAccordingly, in this study, we proposed a method for transforming ordinal phenotypes into continuous phenotypes (MTOTC). First, the hierarchical phenotypic data for ordinal traits (HData) was transformed into continuous phenotypic data (CPData). Subsequently, FASTmrMLM , one GWA2Here we proposed a method, named MTOTC, to transform the discrete hierarchical data (HData) of ordinal traits into continuous phenotypic data. Then, GWAS for continuous quantitative traits (C-GWAS) are used to analyze the transformed continuous phenotypic data. The new method was described as below.2.1Arabidopsis thaliana lines harboring 10,000 SNPs with a minimum allele frequency >0.1 . This is MTOTC. Then, the predicted CPData is analyzed by C-GWAS methods, such as FASTmrMLM Figure 12.2.1P-value ≤0.05). To further improve the quality of the significant correlated SNPs in the initial screening for reducing interference and improving detection accuracy, logistic regression was used as a secondary SNP screening method. Logistic regression was performed using function “glm”  and “polr”  with a P-value ≤0.05. The aim of this step was to further eliminate SNPs that were not associated with the traits for simplifying the iterations in the following multi-locus genetic model.The Chi-square test in R 4.0.5 (function “chisq.test”) was used to scan the SNPs in the whole genome using a single marker method , set The parameters were estimated using empirical Bayes, as follows, and the Newton–Raphson method.Among them,Then, the empirical Bayesian estimates of these SNPs effects were obtained in the multi-locus model (1) based on the selected significant SNP markers and ordinal phenotype, and estimates of these effect were used to predict the phenotype, obtaining the continuous phenotypic data (CPData) of ordinal trait.2.3When continuous phenotypic data was obtained by the above MTOTC method, a C-GWAS method could be used to detect significant loci. In this work, FASTmrMLM, one C-GWAS method, was used. So loci significantly associated with ordinal traits were detected by FASTmrMLM using the obtained continuous phenotypic data and the potential associated markers identified in the above-described initial screening. The GWAS method is henceforth referred to as MTOTC+FASTmrMLM. Moreover, the effects of five other C-GWAS  methods are also discussed based on the MTOTC method for ordinal trait, in order to verify the feasibility of MTOTC.2.4We conducted six simulation studies to evaluate the feasibility of the new method. For each study, the loci 278, 2143, 2054, 3698, 1716, 6178, and 8501, located on chromosomes 1, 2, 2, 2, 1, 4, and 5, respectively, were selected as the causal loci related to the simulated trait. There were three types of phenotypic data in the simulation experiment—original data (OData), which were continuous and generated by Monte Carlo simulation; HData, which were generated from the above OData according to specific distribution proportions ; and CPData, which were generated from the above HData by MTOTC. Then, FASTmrMLM, one multi-locus C-GWAS algorithm, was used to conduct GWAS for CPData.33.13.1.1P-value >0.98 and an unusually large absolute value of effect estimate in logistic regression) were not truly related to the phenotype and interfered greatly with subsequent association analysis. Therefore, to further improve the quality of the screened significantly related SNPs and detection accuracy, logistic regression was used as a secondary screening method for SNPs in MTOTC.To determine the most suitable threshold value for the Chi-square test and logistic regression in the initial screening, four probability thresholds  were set for the Chi-square test in the first simulation study, while three probability thresholds  were set for logistic regression. The Chi-square test can eliminate a large number of SNPs that are not significantly related to a given phenotype. However, the simulation study showed that some SNPs screened in the above Chi-square test   was the lowest when the P-value was 0.0001, followed by 0.01, 0.05, and 0.10  when the P-value was 0.0001, followed by 0.01 and 0.05  Table 1.3.1.3The third simulation study investigated the effect of the number of hierarchical levels on MTOTC. Based on symmetrical distribution, the number of hierarchical levels was set to 2, 3, 4, and 5, respectively, and the number of replicates was 10,000. Meanwhile, we compared the results of OData, HData and CPData using FASTmrMLM.CV) of the OData was between 29.5% and 55.5%. Among the 10,000 replicates, the number of replicates beyond the CV range of the OData  also increased with increasing hierarchical level. Thus, the CV range of CPData2 was the closest to that of the OData. Third, among the 10,000 replicates, the skewness range between the CPData and the OData was the closest at 2 hierarchical levels. Among them, the skewness range of the OData was between −1.00 and 0.46 and the range of CPData2 was between −1.28 and 0.35. As the number of hierarchical levels increased, the skewness of the CPData gradually deviated from that of the OData; the kurtosis showed the same tendency as the skewness.Compared with CPData from the other hierarchical levels, the distribution of CPData2  was closer to the original data (OData). First, the frequency distribution of the CPData was closer to that of the OData when the hierarchical level was low, especially when it was equal to 2 Figure 4MTOTC performed well for the estimates of QTN position under different numbers of hierarchical levels. The position estimates via MTOTC+FASTmrMLM  were unbiased at loci 278, 2143, and 3698 , CPData3 (1:3:1), and CPData5 (1:2:4:2:1), 10 replicates were set at equal intervals from 1,000 to 10,000. As a result, the results across various numbers of replicates at each locus and for each hierarchical levels  were insignificant Figure 53.1.5In the fifth simulation study, we investigated the effect of distribution proportion skewness on the new method under three hierarchical levels. Here the distribution proportion skewness were set as symmetrical distribution , uniform distribution (1:1:1), and skewed distribution (4:2:1). The indicators were the relative power, false-positive rate, the estimates of QTN effects and positions. The skewed distribution had the lowest relative power at loci 278, 2143, and 3698, followed by the uniform distribution, and the symmetrical distribution  compared with the other five GWAS methods, which may be related to its relatively higher false-positive rate. Additionally, the numbers of significant QTNs detected by pKWmEB, mrMLM, and FASTmrMLM in CPData  were second only to the number of QTNs detected with pLARmEB.Four QTNs  for salt tolerance were simultaneously detected in the index data and at least one CPData; however, none of them was detected in HData5. For instance, Chr13-64738 was simultaneously detected in CPData2 by five methods and in the salt tolerance index data by two methods. Chr13-65248 was detected in CPData5 by four methods and in both CPData5 and the index data by FASTmrMLM. Three QTNs  for alkali tolerance were simultaneously detected in the index data and in at least one CPData, two of them were also detected in HData5.The results of six GWAS methods for the CPData of salt-alkali tolerance showed that only a few significant QTNs were coincident between 2009 and 2010, which can be explained by the differences in environmental influences between the two years. For salt tolerance, no QTNs were found to overlap between 2009 and 2010 in the six methods. For alkali tolerance, only Chr1-5051 and Chr16-82333 were detected in both years. There was indeed an environmental (year) effect according to variance analysis of the phenotypic results for the two years .3.2.2Error! Hyperlink reference not valid.http://www.Soybase.org/) was also used to screen candidate genes. A total of 34 potentially candidate genes for salt tolerance and 25 potentially candidate genes for alkali tolerance were mined.Potential candidate genes were mined from 100 kb upstream to 100 kb downstream  of signiGlyma05g25331, Glyma05g25420, Glyma05g25450, and Glyma05g25460 were all detected by five GWAS methods in CPData5 in 2009. Only one gene, Glyma13g25266, was detected in both the index data and CPData2 detected by five GWAS methods in CPData2 and two methods in the index data in 2010. In addition, five candidate genes were detected only in CPData2 by five methods, and nine candidate genes were detected only in CPData5 by three or more methods. No overlapping genes were found between HData5 and the index data or the CPData , between haplotypes TCAT and AATT (P=0.0091) in 2010, and between haplotypes TCAT and TCTT (P=0.0471) in 2010. However, for haplotype blocks of other salt tolerance QTNs, it was showed that the significant phenotypic differences existed between haplotypes only in a single year, and the haplotype pairs with significant differences included haplotype AGTGC and TACCC (P=0.0348), AGTGC and TGTCA (P=0.0345) for Chr5-24153; haplotype GCG and ATA (P=0.0408) for Chr10-52140; haplotypes GTAGA and GTAGT (P=0.0397), GTAGT and AAGTT (P=0.0540) for Chr11-54042.In haplotype block with the significant QTNs Chr13-64738 for salt tolerance, t-test showed significant phenotypic differences between haplotypes ACAT and AATT , between haplotypes CTGACG and CCGGAG (P=0.0005 in 2009), between haplotypes CTGACG and CCGAAG (P=0.0231 in 2009), between haplotypes TCGAAG and CCGAAG , and between haplotypes CCAAAG and CCGGAG (P=0.0296 in 2010). For Chr3-14262, the haplotype pairs with significant differences were detected as follows: TTT and TCT , TTT and GCT (P=0.0102 in 2010), GCT and TCT (P=0.0171). The other haplotype blocks of alkali tolerance showed significant phenotypic differences between haplotypes only in a single year and they include: GTGT and TTAT (P<0.0001), TTGT and TTAC (P=0.0038), TTAT and TAGT (P=0.0132) for Chr13-67342; CAG and TGT (P=0.0183) for Chr1-5051; ATCG and GATC (P=0.0009) for Chr7-34669; TAGGCG and AATGCA (P=0.0157), and TAGGCG and TATGCG (P=0.0128) for Chr20-105040.There were two significant QTNs Chr16-82333 and Chr3-14262 for alkali tolerance with significant phenotypic differences across haplotypes in both years. The Chr16-82333 recorded significant differences between haplotypes CTGACG and CCGGAG  and six alkali stress-related candidate genes  were found in the haplotype block.Genes with significant phenotypic differences across haplotypes were considered as the candidate genes 3, inclu4In this study, we established a method for transforming ordinal phenotypes into continuous phenotypes (MTOTC) based on hierarchical data for ordinal trait phenotypes and molecular marker data in resource populations. Therefore, the process of association analysis for ordinal traits is as follows: first, MTOTC is used to transform HData into continuous phenotypic data (CPData), and then a C-GWAS method (i.e. GWAS method for continuous quantitative traits) is selected to analyze the CPData to identify the QTNs that are significantly associated with ordinal traits.In this study, simulation experiments and soybean saline-alkali tolerance analysis indicated that the new method, MTOTC, is suitable for ordinal traits when they are less than five hierarchical levels. Moreover, the combination of MTOTC with any one of the proposed C-GWAs methods exhibited high power, low false-positive rates, and low bias in estimating the positions and effects of the QTN. The purpose of MTOTC is to provide a different approach for undertaking GWAS for ordinal traits. The feasibility of the MTOTC method was verified in real data analysis of soybean salt-alkaline tolerance using 286 soybean accessions. Compared with HData5 , a greater number of significant QTNs was detected concurrently by at least two GWAS methods or in two years, and more candidate genes for salt and alkali stress were screened in the CPData for salt and alkali tolerance traits. A greater number of QTNs was detected simultaneously by multiple GWAS methods in the CPData than in the index data and HData for salt-alkaline tolerance. For the three types of data, the number of QTNs detected simultaneously was respectively 4, 1, and 1 in salt tolerance and respectively 5, 2, and 3 in alkali resistance.When the phenotype distribution of the CPData generated by the new method were closer to those from the index data of salt-alkali tolerance, the GWAS results were better, and a greater number of candidate genes could be mined. This may be beneficial for selecting the appropriate distribution proportion to obtain hierarchical data of ordinal trait, screening stable QTNs, and promoting the development of molecular breeding. We also applied symmetric distribution (1:2:4:2:1) to generate HData5 for the salt tolerance index data and used MTOTC to generate the corresponding CPData5. The phenotype distribution of CPData5 with symmetric 1:2:4:2:1 exhibited a large deviation from that of the index data, and the phenotype distribution of CPData5 with uniform 1:1:1:1:1 was closer to that of the index data. Under the six methods, there were no overlapping QTNs in CPData5 and the index data for salt tolerance, which was far inferior to the above uniform distribution observed with the distribution proportion 1:1:1:1:1, under which three coincident QTNs were detected in CPData5 and the index data. This result corresponded precisely to the results presented in simulation study 5.P ≤ 0.05 threshold, a large number of SNPs that were significantly unrelated to the trait could be eliminated. Meanwhile, the simulation experiment showed that the retention rates of related loci remained high. MTOTC serves to simplify the model and save a substantial amount of computing time for subsequent association studies.MTOTC performed well in the initial SNP screening. After preliminary screening under a MTOTC helps to improve association analyses of ordinal traits. Regarding coefficient of variation, skewness, kurtosis, and frequency distribution, compared with the HData, the results obtained for the CPData were closer to those of the OData. Meanwhile, the results using six GWAS methods showed that the statistical power, the false-positive rate, and the position estimates in CPData were better than those in HData. Moreover, MTOTC performed better when the frequency distribution of the CPData was close to that of the OData.The fewer hierarchical levels, the more suitable MTOTC is. Regarding the relative power in CPData under different hierarchical levels, a trend of increasing relative power with increasing number of hierarchical levels was found for all six methods when there were four or less hierarchical levels. When there were five hierarchical levels, the power of MTOTC+FASTmrMLM was close to that of FASTmrMLM in HData, but slightly lower than the power from logistic regression; only three GWAS methods had higher relative power in CPData than in HData. In addition, MTOTC had a tendency to increase variation, especially with increasing numbers of hierarchical levels. This indicates that MTOTC is more suitable for ordinal traits with fewer hierarchical levels, especially those with two or three levels. Among the six GWAS methods, FASTmrEMMA, FASTmrMLM, and mrMLM are significantly better when combined with MTOTC. This is partly attributed to that the distribution and parameter estimation principles set in MTOTC were relatively consistent with those in these three GWAS models.This study will contribute to further research in association analysis of ordinal traits. This is especially in improving the retention rate of small-effect loci in preliminary screening, reducing the impact on variability when transforming ordinal phenotypes into continuous phenotypes, and developing novel methods for association analyses of ordinal traits.The original contributions presented in the study are included in the article/MY, JF, and YW designed the methodologies. MY, JF, JZ, and JCZ drafted the manuscript, conducted simulation studies, and analyzed the data. TZ and JF revised the paper. All authors contributed to the article and approved the submitted version.


Here, we present an expanded utility of the R package qgg for genetic analyses of complex traits and diseases. One of the major updates of the package is, that it now includes Bayesian linear regression modeling procedures, which provide a unified framework for mapping of genetic variants, estimation of heritability and genomic prediction from either individual level data or from genome-wide association study summary data. With this release, the qgg package now provides a wealth of the commonly used methods in analysis of complex traits and diseases, without the need to switch between software and data formats.https://github.com/psoerensen/qgg). Notes on the implemented statistical genetic models, tutorials and example scripts are available at our GitHub page https://psoerensen.github.io/qgg/.The methodologies are implemented in the publicly available R software package, qgg, using fast and memory efficient algorithms in C++ and is available on CRAN or as a developer version at our GitHub page ( With the increasing availability of large genetic biobanks and a simultaneous increase in number of collected samples by biobanks, there is a demand for software tools that allow for robust and efficient genomic analyses. Tools such as PLINK , and direct fast and memory-efficient processing of genetic data without the need to re-format the binary PLINK files  constructing PGS with utilities in genomic medicine, (ii) fine mapping of GWAS results and (iii) accurate estimation of quantitative genetic parameters.btad656_Supplementary_DataClick here for additional data file.


Schizophrenia is a chronic psychiatric disorder with inconsistent behavioral and cognitive abnormalities with profound effects on the individual and the society. Individuals with schizophrenia have altered thyroid function, but results from observational studies are conflicting. To date, it remains unclear whether and in which direction there is a causal relationship between thyroid function and schizophrenia. To investigate causal paths, a bidirectional two-sample Mendelian randomization (MR) study was conducted using summary statistics from genome-wide association studies including up to 330,132 Europeans. Thyroid function was described by the normal-range thyroid-stimulating hormone (TSH) and free thyroxine levels as well as an increased and decreased TSH status. The iterative radial inverse-variance weighted approach with modified second order weights was used as the main method. Based on a discovery and replication sample for schizophrenia, pooled effect estimates were derived using a fixed-effect meta-analysis. Robustness of results was assessed using both a range of pleiotropy robust methods and a network analysis that clustered genetic instruments potentially responsible for horizontal pleiotropy. Genetic liability for hypothyroidism was inversely associated with schizophrenia (The online version contains supplementary material available at 10.1007/s10654-023-01034-z. Schizophrenia is a chronic psychiatric disorder with inconsistent behavioral and cognitive abnormalities . Based oThere is accumulating evidence that individuals with schizophrenia have altered thyroid function, but results from observational studies do not show a consistent picture , 15. In The MR design investigates the causal relationship between a modifiable risk factor and an outcome based on observational data, using the random genetic assignment at conception as a natural experiment. Our two-sample MR study based on summary data from genome-wide association studies (GWASs) from different cohorts of European ancestry. Detailed information about the MR-design can be found elsewhere .To obtain unbiased estimates, the MR design must satisfy three core assumptions, which we will address below. A genetic instrument has to be strongly associated with the exposure of interest (relevance assumption), must not be associated with a confounder of the exposure-outcome association (independence assumption), and must influence the outcome only through the exposure (exclusion restriction assumption).Regarding the thyroid hormone measurements, we used summary level data from a meta-analysis GWAS including 54,288 subjects from 22 and 49,269 subjects from 19 independent cohorts for TSH and FT4, respectively . IndividTwo datasets were available for schizophrenia. As the discovery sample we used data from the Psychiatric Genomics Consortium (PGC) (wave 3) including 39,910 cases and 60,558 controls of European ancestry. As the PGC specializes in psychiatric phenotypes, the data are expected to be of the highest quality. In replication analyses we used summary level data from the FinnGen study (8th release) with 6,280 cases and 330,132 controls .In order to fulfill the relevance assumption, SNPs (single nucleotide polymorphisms) associated with the respective exposure were selected considering an imputation score greater than 0.8 and below the genome-wide significance threshold of Regarding the models using TSH and FT4 levels as continuous exposures, we calculated the variance explained by genetic instruments and quantified the instrument strength by calculating the SNP-specific F-statistics, with a value of 10 or more indicating sufficient strength and thus absence of weak instrument bias. Statistical power was calculated for a sufficient range of unknown true effects .Since the independence and exclusion restriction assumptions cannot be tested, plausibility must be assessed. Thus, focusing on the evidence, our statistical analyses consisted of four steps. First, bidirectional MR analyses were performed iteratively on the discovery and replication samples. Second, a broad range of pleiotropy robust methods were applied to assess horizontal pleiotropy. Third, meta-analyses pooled estimates were derived combining the results from discovery and replication analyses. Fourth, a network analysis was performed to identify clusters of phenotypes that serve as a potential confounder factors for an exposure outcome association and removed the affected SNPs within further sensitivity analyses.The radial regression was used iteratively as the main framework . In eachDirectional pleiotropy in the final models was assessed by the radial MR-Egger intercept test and widespread horizontal pleiotropy by the MR-PRESSO global test . AdditioIn the fourth step, we applied a PhenoScanner search to identify all known phenotypes associated with the genetic instruments used in our analyses , 24. We Results are presented either on the identity or the log scale  and age and sex frequency-matched healthy controls . It was found that the proportion of schizophrenia was significantly higher in patients with hypothyroidism than in controls and multivariable logistic regression models confirmed an independently positive association between hypothyroidism and schizophrenia ) . A recenThyroid hormones influence neurodevelopmental processes such as proliferation, migration, differentiation, and synapse formation of neurons . In adulThe present study is the first two-sample MR on the causal association between thyroid function and schizophrenia. Our findings might be of clinical significance as they showed reliable results by employing various MR methods. In addition, the presented results seem not to be affected by pleiotropy, because the estimates obtained in the sensitivity analyses were consistent. Heterogeneity was minimized by a more conservative iterative implementation of the radial regression framework with modified second-order weights, which improved outlier detection and removal as well as heterogeneity assessment compared to the usual approach. Furthermore, consistency of point estimates could be confirmed before and after removal of outliers by this method. However, there are also several limitations. The findings of the study were based on data from individuals of European descent and replicated by using data from the FinnGen study. Notwithstanding the presence of population stratification, i.e. the presence of some genetic differences between individuals from northern European countries compared to individuals of other European origins, the results also appear to be generalizable to “other subpopulations”. Whether the results can be transferred to non-European ethnicities have to be investigated in further studies. A further shortcoming of the study is,that we were unable to differentiate between first episode and multiple-episode psychosis .In conclusion, the present investigation found an inverse relationship between hypothyroidism and schizophrenia. The results underscore the relevance of the thyroid function in the manifestation of schizophrenia. Research on the role of the hypothalamic-pituitary-thyroid axis in the development of schizophrenia should be subject of further research.Below is the link to the electronic supplementary material.Supplementary Material 1: Figure


N = 255,896). We then investigated genetic relationships leveraging genomic data in European ancestry for migraine , CKD , and two traits of kidney function . Observational analyses suggested no significant association of migraine with the risk of CKD . While we did not find any global genetic correlation in general, we identified four specific genomic regions showing significant for migraine with eGFR. Cross-trait meta-analysis identified one candidate causal variant (rs1047891) underlying migraine, CKD, and kidney function. Transcriptome-wide association study detected 28 shared expression–trait associations between migraine and kidney function. Mendelian randomization analysis suggested no causal effect of migraine on CKD . Despite a putative causal effect of migraine on an increased level of UACR , it attenuated to null when accounting for both correlated and uncorrelated pleiotropy. Our work does not find evidence supporting a causal association between migraine and CKD. However, our study highlights significant biological pleiotropy between migraine and kidney function. The value of a migraine prophylactic treatment for reducing future CKD in people with migraine is likely limited.Epidemiological studies demonstrate an association between migraine and chronic kidney disease (CKD), while the genetic basis underlying the phenotypic association has not been investigated. We aimed to help avoid unnecessary interventions in individuals with migraine through the investigation of phenotypic and genetic relationships underlying migraine, CKD, and kidney function. We first evaluated phenotypic associations using observational data from UK Biobank (The online version contains supplementary material available at 10.1007/s00439-023-02575-9. The vascular dysfunction basis of migraine, a common neurological disorder, is well established . We next conducted a genome-wide cross-trait analysis to characterize the shared genetic architecture and causality. In addition to the binary diagnostic outcome, we further incorporated two continuous measures on kidney function. The overarching goal of our study was to gain insight into mechanistic links underpinning migraine and CKD. The overall study design is shown in Fig. 2) at baseline or had a diagnosis of CKD before migraine during follow-up. In total, 255,896 participants were included.UKB is a large population-based prospective cohort study with over 500,000 individuals aged 40–69 years at baseline, recruited in 22 study assessment centers throughout UK between 2006 and 2010  independent SNPs and used these SNPs as IVs . We also applied and obtained GWAS summary statistics  for other analyses.The hitherto largest GWAS of migraine was conducted by the International Headache Genetics Consortium (IHGC), aggregating five study collections  totaling ~ 870,000 individuals of European ancestry   and 15 independent SNPs associated with migraine without aura (MO) were used as IVs   Consortium, aggregating 23 participating studies totaling ~ 480,000 individuals of European ancestry   for continuous variables, and as counts and percentages for categorical variables. Person-years at risk for the migraine-free category (unexposed) were accumulated from baseline until migraine diagnosis, CKD diagnosis, death, loss to follow-up, or end of follow-up, whichever came first. For the migraine category (exposed), person-years at risk were accumulated from baseline or migraine diagnosis during follow-up until CKD diagnosis, death, loss to follow-up, or end of follow-up, whichever came first. We constructed a Cox proportional hazards regression model with exposure to migraine modeled as a time-dependent variable. We used three sets of adjustments. Estimates in model 1 (basic model) were adjusted only for sex and age. Estimates in model 2 (antimigraine use model) were further adjusted for antimigraine medication usage , in addition to sex and age. Estimates in model 3 (full model) were further adjusted for assessment center, income, Townsend deprivation index, smoking, drinking, physical activity, sleep duration, BMI, type 2 diabetes mellitus, hypertension, and dyslipidemia on top of model 2. In the sensitivity analysis, we excluded participants with less than a year of follow-up or a diagnosis of CKD within a year after developing migraine. All statistical analyses were done using SAS version 9.4 . A two-sided rg) across the genome using software linkage-disequilibrium score regression (LDSC)  was used to define statistical significance.Genetic correlation represents an average sharing of genetic effect between two traits that is independent of environmental confounders. We first quantified the global genetic correlation  was used to define statistical significance.While global genetic correlation depicts an average of shared signal across the whole genome, it may fail to identify scenarios where the signal is restricted to particular genomic regions or in opposing directions at different loci. We thus estimated the pairwise local genetic correlation using software SUPERGNOVA  exists.Genetic correlation reflects either horizontal pleiotropy (pleiotropy) or vertical pleiotropy . In horizontal pleiotropy, a genetic variant has independent effects on multiple traits, whereas in vertical pleiotropy, a genetic variant has an effect on a trait through its genetic effect on an intermediate trait. We next conducted a cross-trait meta-analysis to identify pleiotropic variants that simultaneously influence both traits using software Cross-Phenotype Association (CPASSOC)  the SNP reached genome-wide significance (PCPASSOC < 5 × 10–8) in CPASSOC; (2) the SNP did not reach genome-wide significance (5 × 10–8 < Pmigraine or CKD or kidney function < 1 × 10–5) in original single-trait GWAS; (3) the SNP was not in LD . Significant index SNP was defined as https://grch37.ensembl.org/info/docs/tools/vep/index.html) was used to map the shared SNPs identified by CPASSOC to its nearest gene.Ensembl Variant Effect Predictor  within each tissue was used to identify significant expression–trait associations. We then performed joint/conditional tests for loci with multiple associated features to determine independent genes at each locus. Colocalization analysis was further conducted to examine whether GWAS signals and GTEx expression quantitative trait loci (eQTL) signals were colocalized at the same causal variant. We then integrated these results across traits to identify shared gene–tissue pairs.Cross-trait meta-analysis identifies pleiotropic variants without considering gene expression and tissue specificity while many genetic variants lead to complex traits via regulating tissue-specific gene expressions. We performed a transcriptome-wide association study (TWAS) analysis using FUSION . We further conducted CAUSE  as a complementary analysis to detect causal relationships while accounting for both correlated and uncorrelated pleiotropic effects  analysis to assess putative causal relationships via software TwoSampleMR .We computed the phenotypic variance explained by IVs , during which 97 migraine patients and 2,461 migraine-free individuals developed CKD (Table P = 0.84) was found. For kidney function, no significant global genetic correlation was observed for migraine with either eGFR (P = 0.75) or UACR (P = 0.82).As shown in Fig. P < 2.12 × 10–5), no significant local signal was identified between migraine and CKD  transcription factor, known to associate with migraine  in cross-traits and suggestive significance (Pmigraine/CKD/kidney function < 1 × 10–5) in single traits, including one locus shared between migraine and CKD (rs1047891), seven loci shared between migraine and eGFR , and three loci shared between migraine and UACR . Of note, rs1047891 was shared across all traits. This SNP is located near CPS1, previously reported to associate with migraine in women  or were in LD  associated with pain perception  was determined, including a median of 22 variants (ranges: 1–197). Notably, at the locus of index SNP rs1047891, the 99% credible set consisted of only one single variant (rs1047891 itself) for migraine–eGFR and migraine–UACR, and of only two variants (rs1047891 and rs715) for migraine–CKD, stressing again its putative causal role.Furthermore, for the 11 shared loci, a majority  colocalized at the same candidate causal variant (PPH4 > 0.7), while four colocalized at different candidate causal variants (PPH3 > 0.7). Of note, both fine-mapping and colocalization analyses supported a shared causal variant for migraine with CKD, eGFR, and UACR at rs1047891 (Supplementary Table 14).TREX1, SHISA5, PRR13, TMA7) mainly expressed in tissues of the nervous and cardiovascular system  mainly expressed in tissues of the nervous and cardiovascular system. Among these genes, ICA1L remained significant using CMC brain tissues, which was also identified by our cross-trait meta-analysis and the previous UACR GWAS . No overlapping tissue–gene pair was found for migraine and CKD using either tissue. For kidney function, 19 significant tissue–gene pairs were found for migraine and eGFR using GTEx tissues, including four genes (P = 0.28). Conversely, genetically predisposed CKD also did not seem to influence migraine onset . For kidney function, genetically predisposed migraine was significantly associated with a higher level of UACR , while the effect attenuated to null when accounting for correlated and uncorrelated pleiotropy  or adjusting for systolic blood pressure . Conversely, genetically predicted UACR was not associated with migraine . There was no significant association between migraine and eGFR. The results remained consistent when restricting analyses for MA and MO .Finally, we performed a bidirectional two-sample MR to make causal inference Fig. . GeneticThe mean F-statistics of our IVs were larger than 50 (Supplementary Table 7), indicating strong instruments. With the current sample size of outcome, assuming 0.81% (migraine) and 0.32% (CKD) of phenotypic variance explained by IVs based on the data we used, our study had more than 80% statistical power to detect an OR of 1.16 for migraine on CKD and 1.24 for CKD on migraine, respectively.To the best of our knowledge, this is the most comprehensive observational and genetic analysis that systematically investigates the phenotypic association, genetic correlation, pleiotropic loci, expression–trait association, and causal relationship between migraine, CKD, and kidney function. In observational analysis, we found no strong phenotypic link between migraine and CKD. Genetic analysis suggested a weak genetic relationship between migraine and CKD with merely one candidate pleiotropic variant identified, while four specific genomic regions showing significant local signals were found for migraine and eGFR, relaxing the binary disease status to the continuous physiological measure. Such genetic overlap was further substantiated by 10 pleiotropic loci and 28 shared expression–trait associations for migraine and kidney function, primarily tagging tissues of nervous and cardiovascular systems. However, we found limited evidence to support a causal effect of migraine on CKD and kidney function. These findings advance our understanding of the relationship underlying migraine and CKD, providing potential implications for disease prevention strategies.In contrast to previous observational studies, we found a minimal phenotypic and genetic link underlying migraine and CKD. In observational analysis, the age and sex-adjusted hazard of CKD was 1.32 (95% CI = 1.07–1.61), which was largely consistent with one (and the only) existing observational study reporting a relatively small effect   shared for migraine with kidney function as well as with CKD. This pleiotropic SNP is located near TREX1 and ICA1L) replicated by using the CMC brain tissue. TREX1, shared by migraine and eGFR, and expressed in the brain, artery, spleen, and many other tissues, encodes a 3’ to 5’ DNA exonuclease known to regulate immunity and repair DNA. In human neural cells, deficiency of TREX1 contributes to the accumulation of extranuclear DNA, thereby inducing neurotoxicity through increased type I interferon secretion  protein that is involved in protein domain specific binding activity and regulation of transport. Findings from cell-type specificity analysis in the brain have identified enrichment in the ICA1L expression in glutamatergic excitatory neurons  should be treated as clinical guideline recommendations. Avoiding unnecessary intervention makes sense for individuals with migraine because triptans as a first-line treatment for moderate or severe migraine attacks have the potential kidney toxicity to do harm  exists across GWAS of migraine and GWAS of UACR. However, the lower end of the one-sided 95% CI for F-statistic remained high (55.6 for migraine IVs and 48.1 for UACR IVs), thus considerable weak instrument bias in our two-sample MR was not expected Below is the link to the electronic supplementary material.


Genome-wide association studies (GWAS) have underrepresented individuals from non-European populations, impeding progress in characterizing the genetic architecture and consequences of health and disease traits. To address this, we present a population-stratified phenome-wide GWAS followed by a multi-population meta-analysis for 2,068 traits derived from electronic health records of 635,969 participants in the Million Veteran Program (MVP), a longitudinal cohort study of diverse U.S. Veterans genetically similar to the respective African , Admixed American , East Asian , and European  superpopulations defined by the 1000 Genomes Project. We identified 38,270 independent variants associating with one or more traits at experiment-wide  To address the underrepresentation of non-European individuals in genome-wide association studies (GWAS), we conducted a population-stratified phenome-wide GWAS across 2,068 traits in 635,969 participants from the diverse U.S. Department of Veterans Affairs Million Veteran Program, with results expanding our knowledge of variant-trait associations and highlighting the importance of genetic diversity in understanding the architecture of complex health and disease traits. Among published GWAS, 95% of participants are genetically similar to individuals from European reference populations . The lacElectronic health record (EHR)-linked biobanks have played a pivotal role in genomic discovery by providing information on the genome and the phenome in large numbers of individuals –12. HistThe Department of Veteran Affairs (VA) Million Veteran Program (MVP) is a longitudinal health, genomic, and precision medicine cohort established in 2011. MVP’s goal is to enroll at least one million Veterans from diverse populations: as of this writing, over 950,000 Veterans have volunteered for the program. The MVP database contains array-based genome-wide genotyping as well as longitudinal EHR data and questionnaire data. Here, we present a multi-population phenome-wide set of GWAS in 635,969 Veterans, of whom 29% are genetically similar to non-European population groups inferred from the 1000 Genomes Project reference panel. We characterize the genetic architecture of 2,068 traits across a comprehensive catalog of phenotypes representing EHR-derived diagnosis codes, clinical laboratory tests, and vital signs, as well as survey responses. We identify independently associated signals using contemporary fine-mapping methods, characterizing pleiotropy across traits and populations, highlighting signals found in non-European population groups .Methods). The frequency and imputation quality scores of single nucleotide polymorphisms (SNPs) among the population groups are provided (See Data availability).In this study, we analyzed data from 635,969 participants (MVP Genomics Release 4 ), aggregulations . After iMethods, We extracted phenotypic trait data from the VA EHR, which consisted of diagnosis codes, laboratory measures, and vital signs. Additionally, we included responses to survey questions on health and behavior administered at MVP enrollment. After trait QC, 1,854 binary and 214 quantitative traits were included in the downstream analysis in at least one population group (Methods). The actual analysis took 14,286 GPU hours , leading to an overall 160-fold reduction in the core hours required.We next turned to the substantial computational task of generating the >350 billion variant-trait associations across population groups. Unfortunately, the current implementation of the Scalable and Accurate Implementation of GEneralized mixture model (SAIGE) algorithm  – ideal Methods, After multi-population meta-analysis, we identified 98,485 associations  with a study-wide significance of Methods, ; 1,096 bMethods,  and 178 Methods,  exhibiteMethods, . ConsistMethods, ; 85.6%  were only available in AFR . The incanalysis . This lee cancer . This sifindings –28. We at levels  and a mi disease  30)..P>4.6×10FAM234A associated with iron deficiency anemias , a well-established variant at increased frequency in African populations due to balancing selection as it is protective against malaria but causes sickle cell anemia risk allele . The 1% of locus-trait pairs that failed to map were primarily due to computational constraints  contained a single variant . To compWe next analyzed the distribution of effect sizes and allele frequencies for lead variants and finemapped signals for the 15,822 variant-trait-population combinations with high confidence (PIP > 0.95) fine-mapped signals. Consistent with previous reports , 37, we APOE gene is linked to 24 different traits, including those previously identified conditions such as macular degeneration, abdominal aortic aneurysm, dementia, Alzheimer’s disease, and HDL levels. We observed new associations between this variant and chronic liver disease and cirrhosis.Next, we investigated the associations of high-confidence fine-mapped variants (PIP > 0.95) with two or more traits. Filtering the 15,045 high-confidence fine-mapped variant-trait pairs, finemapped above to include only traits with a phenotypic correlation coefficient > |0.2| resulted in 3,955 variant-trait pairs across 3,201 variants and 377 traits , fig. S9To characterize phenotypic variation attributable to common genetic variants across the four major population groups, SNP heritability was calculated using linkage disequilibrium score regression (LDSC) with population-specific GWAS results and in-sample LD reference panels . This anR groups . Height R groups .We then examined the genetic correlation between pairs of traits with significant heritability within each population group using LDSC and MVP-derived LD reference panels. We identified significant correlations  in all populations: 6,424 pairs (671 traits) in AFR, 3,031 pairs (494 traits) in AMR, and 154,503 pairs  in EUR populations. Although there was considerable overlap in trait pairs across populations, 1,267 unique trait pairs were identified among non-EUR participants. Classifying variables according to genetic correlations and seeking groups with robust correlations fluences . DespiteWe finally analyzed the genetic correlation of each trait between the population groups using Popcorn . With EUulations . We alsoABCG2   were unique in the non-EUR population groups . Althouguricemia  and suscuricemia , with an2231142) . In MVP,We noted that the majority of population-specific signals were in non-coding regions. To gather insights into these variants, we used functional prediction scores from RegulomeDB , identifAPOE-e4 associated with a 30% lower risk of dementia in the AFR compared to the EUR population  at 1,888 finemapped loci  with overlapping credible sets in multiple populations. This identified 16 heterogeneous variant-trait associations when comparing the AFR to the EUR population and 11 when comparing the AMR to the EUR population . Focusinpulation ; there wpulation .Here, we present a comprehensive, phenome-wide atlas of GWAS analyses in the largest multi-population biobank to date. Analyzing approximately 44.3 million variants across 2,068 traits in 635,969 US Veterans representing four diverse populations, we identified 98,485 independent variant-trait associations. The summary statistics from this effort comprise a freely accessible resource for the community to dissect the genetic basis of health and disease and foundational data to support discovery, bridging the knowledge gap in the underrepresented populations. Additionally, we highlight the essential role of efficient software operating at exascale supercomputing capabilities to perform analyses at this scale, made possible through a collaboration between the VA and DOE.a priori are likely causal. Despite this, 90.8% of approximate credible sets that mapped to a single variant carried only “‘non-coding” functional annotation, with the majority mapping to “introns”  or “non-gene”  annotations. This suggests the presence of large numbers of biologically important variants within proximal or distal elements acting on genes to regulate their expression, where high-throughput functional assays are well positioned to systematically test this set of variants for function  that function .Our analysis expands on previous, large-scale fine-mapping experiments , 50, 51 ABCG2 may represent an independent signal for gout risk, in addition to the known AFR-specific variant rs2231142 in ABCG2 , could result in missing true signals. Similarly, our preference for precision over recall (sensitivity) meant we limited the fine-mapping to a maximum of five signals per locus. This approach can lead to an underestimation of the number of signals at certain highly significant loci. Future research may consider these constraints and propose alternative approaches to further enhance the validity and comprehensiveness of the results.Diversity is a critical feature in advancing precision medicine important in genomic studies because it helps to ensure that the results are generalizable across different populations. Despite large population biobank efforts such as UK Biobank, FinnGen, and Biobank Japan, the limited diversity in the published GWAS literature is quite evident. In recent years, data from more diverse biobanks are becoming become available, such as the All of Us Study Research Program, America Latino Research Biobank, and Human Hereditary and Health in Africa (H3Africa), as well as hospital and institutional biobanks , 10, 58.The VA Million Veteran Program (MVP) is a national cohort launched in 2011 to determine the contributions of genetics, lifestyle, and military exposures to health and disease among US Veterans . Blood bGenotyping and imputation methods for the MVP were described previously . In brieWe used the reference dataset from the 1000 Genomes Project for genetically inferred population estimation with the smartpca module in the EIGENSOFT  package Clinical outcomes from EHR were defined by Phecodes , which aWithin each genetically-inferred population group, we performed a GWAS for each trait of interest to determine the association with each imputed DNA variant. We used the generalized linear mixed model framework to account for participant relatedness and unbalanced case-control ratios with a GPU-optimized version of the SAIGE package implemented on the US Department of Energy’s Summit supercomputer. Directly genotyped variants were used for step 1 of SAIGE. Imputed genetic dosages were used for step 2 of SAIGE. Only variants with an imputation quality > 0.3 and MAC > 20 within the relevant genetically-inferred population groups were included in the GWAS. Analyses were adjusted for age, sex, and ten population-specific genetic PCs.P-values or allele frequencies > 1 or < 0). Variants that were monomorphic, poorly imputed GWAS results were filtered using a custom R script based on EasyQC . QualityMulti-population meta-analysis was performed using the fixed-effect, inverse-variance weighted method implemented in GWAMA . Meta-anP-value significance thresholds were then determined by dividing the traditional genome-wide threshold of 5 × 10−8 by the number of independent traits: 5 × 10−8 / 1083, resulting in our study-wide significance of 4.6 × 10−11.We calculated Pearson pairwise correlations for the phenotype residuals derived during step 1 of SAIGE to determine the number of independent traits tested. Calculations were made for each population separately and only for the meta-analyzed traits . PCs were calculated from the correlations as well as the variance explained by each of the PCs. The number of independent traits for each population was determined by the number of PCs required to explain a variance of 0.99. For the meta-analysis, population-specific residuals were combined before calculating PCs. This approach resulted in 1,083 independent traits. The population-specific and meta-analysis P-values and counted the number of independent SNPs. The first clumping round grouped SNPs significant at a study-wide P-value threshold  , 65 withWe set the maximum number of signals per locus to five instead of the default setting of ten because, during testing, we observed multiple instances of loci with suspicious credible sets at the higher setting. We tested by calculating the residual association for each signal after removing the effects of the other signals according to the following equation:Here atistics ), N is tThe suspicious credible sets were non-primary signals at loci for phenotypes with suspected highly polygenic architecture including, most notably, height-related traits. These signals generally manifested as single-variant credible sets whose signal-level residual associations appeared as strong outliers in what would have otherwise been loci with the null residual association for the given signals. Reducing the number of signals mapped per locus from ten to five reduced the frequency of these suspicious credible sets.et al.   to deterWe determined the identities of the ancestral and derived alleles for all variants that were fine-mapped with high confidence in any population (PIP > 0.95) by referencing the parsimony-derived ancestral allele identities in the 1000 Genomes (1000G) Phase III variant call format files . Given oWe compared the lead and fine-mapped variants and their proxies . We used a paired Wilcoxon sign-rank test to identify significant differences in the credible set sizes for signals mapped in AFR/AMR, AFR/EUR, and AMR/EUR populations.We focused on characterizing novel SNPs in the non-EUR population fine-mapped to a trait by identifying variants mapped with high confidence (PIP>0.95) in the non-EUR populations and either unmapped or mapped with low confidence in the EUR population . We furtScreening for heterogeneous effects across populations was performed on variants fine-mapped to a trait, specifically for Phecode only, from any population with a MAF>0.05. The quantitative traits were not tested for heterogeneity due to the potential discrepancy in their scales across different population groups. The variant-trait pair must have been fine-mapped with high confidence (PIP>0.95) in both populations being compared  with MAF>0.05. To adequately control for the false discovery rate (FDR), the heterogeneity analysis performs an adaptive multiple testing procedure on the heterogeneity effect  Supplem on the fP-value, (b) the most significant population-specific P-value starting with the largest population size , or (c) the trait with the largest absolute meta-analysis effect estimate. Next, all associated traits with an absolute phenotypic correlation coefficient >0.2 with trait #1 were flagged as correlated. We iterated over these steps until only uncorrelated traits remained.  was selected for comparison with all others based on the largest PIP value (0.95–1). If there was a tie, we selected trait #1 as (a) the trait with the most significant meta-analysis emained. .Supplement 1


Principal component analysis (PCA) is widely used in various genetics studies. In this study, the role of classical PCA (cPCA) and robust PCA (rPCA) was evaluated explicitly in genome-wide association studies (GWAS). We evaluated 294 wheat genotypes under well-watered and rain-fed, focusing on spike traits. First, we showed that some phenotypic and genotypic observations could be outliers based on cPCA and different rPCA algorithms . Hubert’s method provided a better approach to identifying outliers, which helped to understand the nature of these samples. These outliers led to the deviation of the heritability of traits from the actual value. Then, we performed GWAS with 36,000 single nucleotide polymorphisms (SNPs) based on the traditional approach and two robust strategies. In the conventional approach and using the first three components of cPCA as population structure, 184 and 139 marker-trait associations (MTAs) were identified for five traits in well-watered and rain-fed environments, respectively. In the first robust strategy and when rPCA was used as population structure in GWAS, we observed that the Hubert and Grid methods identified new MTAs, especially for yield and spike weight on chromosomes 7A and 6B. In the second strategy, we followed the classical and robust principal component-based GWAS, where the first two PCs obtained from phenotypic variables were used instead of traits. In the recent strategy, despite the similarity between the methods, some new MTAs were identified that can be considered pleiotropic. Hubert's method provided a better linear combination of traits because it had the most MTAs in common with the traditional approach. Newly identified SNPs, including rs19833 (5B) and rs48316 (2B), were annotated with important genes with vital biological processes and molecular functions. The approaches presented in this study can reduce the misleading GWAS results caused by the adverse effect of outlier observations. Triticum aestivum L.) is vital to the world's agricultural economy. Understanding the basis of its genetic and phenotypic diversity is essential to increase grain yield. Such a goal requires statistical methods with the correct application1. In this regard, cPCA has been one of the most important, simplest, and most widely used statistical tools for breeders. PCA aims to reduce data complexity in several principal components (PC). This multivariate method, in addition to studies of phenotypic and molecular diversity3, has been used in confirming population structure5, genotype selection6, understanding the pattern of genotype-by-environment interactions8, and selection of traits for yield modeling9. Despite its widespread use, the results of this technique can be highly biased in population genetic research10 and GWAS11, which have been cited as potential pitfalls12.Bread wheat  algorithm21.Most of the problems of PCA are due to the high sensitivity of this method to the presence of outliers in the data. Phenotypic and genotypic data are susceptible to outlier samples, regardless of the cause. Outlier observations have been observed in single-site and multi-environment trials26. Meanwhile, various QTLs distributed in almost all chromosomes have been identified for important wheat traits such as spike weight, grain number, thousand kernel weight, and grain yield31. It was also concluded that many candidate genes for wheat grain yield under rainfed environments are in the form of gene clusters32. In some GWAS studies based on gene annotation, it has been determined that SNPs identified for yield and yield components under drought stress are linked to genes that play an important role in plant growth and survival35. Statistical methods are the core of GWAS36. Although several of these methods have been developed for GWAS, most of them are sensitive to phenotypic outliers, making their results unreliable11. Population structure is used as a covariate in GWAS to avoid false positive rates. Due to the high dimensionality, determining complex population substructures using SNPs is challenging37. PCA is used as a simple method in setting population classification in these types of studies, and usually, its first few PCs are included as covariates of the population structure in the model. This method may not be suitable for properly diagnosing the population structure in the presence of outlier data21. Such PCA can wrongly consider linkage disequilibrium (LD) structure instead of population structure, and principal component scores may capture outliers12. Therefore, the linear combinations of the first three PCs, included as covariates in the model, can affect the GWAS results. On the other hand, sometimes, instead of phenotype variables, the PC obtained from them is used for GWAS41. Therefore, the contamination of phenotypic data with outlier observations may also distort the GWAS results. In general, cleaning outliers and selecting robust statistical models in GWAS reduces the false positive and negative rates of QTL detection42. In addition to GWAS, it has been reported that different methods of genome-wide QTL mapping studies are also susceptible to outliers, and in their presence, they bring misleading results43.Over the past years, GWAS has proven its power in quantitative trait locus (QTL) mapping. Many researchers have tried deciphering and dissect the genetic basis of various wheat traits using this approachThis study has three specific aims: (i) to identify phenotypic and genotypic outlier observations using PCA and rPCA; (ii) to identify novel putative alleles associated with important spike traits under well-watered and rain-fed environments using GWAS; and (iii) to determine the power of PCA and rPCA linear combinations obtained from phenotypic and genotypic data to reduce the effect of outlier samples in GWAS analysis.44. The broad-sense heritability of these traits was calculated through the following equation:A total of 294 Iranian bread wheat genotypes, including 90 cultivars released during the last century and 204 landraces collected from different locations  technique, the details of which have been described previouslyr2) for all pairwise comparisons. The LD decay pattern for the whole genome and separately for A, B, and D genomes was displayed by plotting pairwise r2 values against genetic distance (bp).Genome-wide linkage disequilibrium (LD) analysis was checked by calculating pairwise marker allele squared correlation coefficient  techniques, to compute the robust loadings52. This rPCA method is resistant to outliers in the data and uses the MCD method for low-dimensional data sets. It is also very suitable for high-dimensional data53. ROBPCA yields more accurate estimates of noncontaminated datasets and more robust estimates of contaminated data. In addition, the Hubert model produces a diagnostic plot that displays and classifies outliers52. The spherical principal components procedure, called the Locantore method, is a functional data analysis method. This method performs cPCA on the data but is projected onto a unit sphere. The Locantore approach is very fast, and the estimates of the eigenvectors are consistent. This method is intended to explore the structure of populations of complex objects54. Finally, the Proj approach, which is as fast as the previous method, was used. This approach includes a simple algorithm for approximating the PP-estimators for PCA whose PCs can be sequentially computed. In other words, the Proj approach uses PP to calculate the robust eigenvalues and eigenvectors without going through robust covariance estimation55. The cPCA and rPCA analyses were performed using the rrcov package in the R program56. We used the outlier plots provided by these methods to identify outlier observations. Also, The first and second PCs were plotted to obtain a biplot.We used classical PCA analysis and four robust PCA  methods to evaluate the population structure and identify outliers. Multivariate detection of outlier observations includes examining each observation based on a combination of variables. Usually, researchers deal with more than two variables in their data, so it is necessary to determine outlier observations in terms of a combination of variables. PCA uses the distance of the sample scores as a criterion for investigating outlier observations. The greater the distance between the observed scores, the higher the possibility of outliers. Most rPCAs use the Projection-Pursuit (PP) principle. PP methods are suitable for analyzing data sets with many variables, and they aim to find structures in multivariate data by projecting them on a low-dimensional subspace. These methods maximize a robust measure of spread to obtain consecutive directions on which the data points are projected57 and has better control over confounding effects25, we used this model. In the MLM model, two covariates are used to prevent false positives: (i) matrix k, which represents kinship relations or family relatedness, and (ii) the first three PCs of cPCA, which are considered as the population structure (stratification) in the model. Simply put, the equation of this model is as follows:Y represents the studied trait, SNP provides genotypic information, PCs are the population structure, and the kinship represents the relationship between individuals in the population using genotypic information, and e is the residual error57. In the MLM model, individuals are considered random effects, and the relatedness among individuals is conveyed through a kinship matrix.First, GWAS analysis was performed between SNP markers and average phenotypic data for each individual trait in each environment. Since the mixed linear model (MLM) is a standard method in GWAS for various wheat traitsAs we mentioned earlier, classical PCA may not correctly represent the population structure. Therefore, in the second GWAS scenario, we used the four described rPCA methods as population structure. This work was done with the aim of obtaining different linear combinations of genotypic data to moderate the effect of genotypic outliers on GWAS results. Because rPCAs perform better in the presence of outlier observations.PCs have been used instead of phenotype variables in GWAS in recent years. Since GWAS for PCs obtained from phenotypic data can be more valuable than traditional single trait-GWAS, we used two PCs instead of the traits themselves in the third scenario. The first two PCs were used because they explained more than 90% of the phenotypic changes, and the remaining PCs did not provide specific information. We also used the PCs obtained from cPCA and four rPCA methods. This work was done to reduce the effect of outlier observations from phenotypic data.10 (p) > 3 was used to state statistically significant marker-trait associations (MTAs). Confidence intervals (CIs) for MTAs were calculated using the linkage disequilibrium (LD) decay. GWAS analyses were performed using genome association and prediction integrated tool (GAPIT) R-package58, but the necessary PCs were extracted through the rrcov package in the R program56. The quantile–quantile (Q-Q) plots of the observed and expected P values were plotted at − log10 (p) values to assess the adequacy of a fitted normal straight line to the markers. Finally, Venn diagrams were drawn using an online tool (https://bioinformatics.psb.ugent.be/webtools/Venn/) and the t-test was performed between the alleles of each SNP to compare the results.In all three scenarios above, the threshold of − loghttp://plants.ensembl.org/index.html) database were annotated using basic local alignment search tools (BLAST) and aligned with IWGSC v2.1  reference genome59. After aligning the SNP sequences with the reference genome, overlapping genes with the highest percentage identity (%ID) and the lowest expected value  were selected for further processing and interpretation. Then, the ontology of genes, i.e., molecular function, biological process, and their cellular component, was extracted from the ensemble-gramene database. It should be noted that markers with almost identical sequences were filtered. Finally, the gene network was analyzed using the genes identified in the database for annotation, visualization, and integrated discovery (DAVID) bioinformatics resources (https://david.ncifcrf.gov/). This tool examines gene pathways based on the Kyoto Encyclopedia of Gene and Genomes (KEGG) enrichment analysis62 .The sequences surrounding all associated SNPs in the EnsemblPlants . The amount of error variance also remained almost constant. The highest and lowest heritability were related to SIL and GY traits, respectively. Removing two outlier observations caused the heritability to increase by about 2% in some traits  versus the observed − log10 (p) for PCA covariates were almost the same in both well-watered , it was found that no outlier sample had high scores and orthogonal distances based on genotypic data. If the number of accessions is high, the outlier status of some samples will change. Genotype No. 161 was present in a core set designed from among 2403 Iranian wheat landraces, and 12% of other genotypes were in outlier groups16. In analyzing the diversity of 80,000 wheat accessions worldwide, it was found that some are outliers. A closer examination indicated that some samples were misclassified in their passport information66. This is an example of the application of identifying outlier samples. Also, tools have been developed based on PCA analysis to detect outliers67 to, e.g., determine the SNPs under selection, and involved in biological adaptation, and have been used in various crops69.In the present study, phenotypic data compared to genotypic data, different methods identify the same samples as outliers. This is probably due to the high dimensionality in the genotypic data. Determining outliers in high-dimensional genomic data is difficult4 have discussed the possibility of mistakenly collecting exotic germplasm instead of landraces in Nepalese wheat during the 1970s to 1990s. According to our results, it has been reported that PCA based on SNPs can divide wheat accessions into separate groups according to breeding origin70. In our study, the distribution of landraces was not strictly based on their geographical origin where they were collected. The subgroups identified as population structure can represent different wheat breeding programs33. Therefore, using PCs as a population structure in GWAS can avoid false positive associations.A good separation of cultivars from landraces based on PCA was expected because there are traces of foreign origin in the pedigree of many Iranian wheat cultivars. Some of the cultivars mixed with the landraces are old and the detailed information about their pedigree is not available, but they are most likely of landraces origin. In this regard, Khadka et al.73. As it was apparent, the traits studied under well-watered showed a decrease in average. SIL was an exception to this rule because the number of nodes decreased in parallel with the reduction in spike length. Heritability range varied from 50% in GY to 75% in SIL. The heritability estimated in this study for SIL is almost equal to that reported in a similar study44. The high heritability of this trait might be due to being mainly controlled by genetic effects. While for GY, which has complex control, heritability was low74. Our results demonstrate the distorting effect of outlier samples in estimating heritability, as previously mentioned65. Due to the incorrect estimation of heritability in the presence of outliers, it is suggested to use the robust estimation of heritability and to pay attention to these methods along with the classical approach18. In another study, the robust DF-REML framework for estimating variance components was proposed, which could provide a robust estimate of heritability75. However, many reports still do not pay attention to outlier data, which seems to be due to a lack of deep understanding of the distorting effects of this data.Efforts to increase wheat yields continue to meet human needs. In this regard, evaluating spike traits is critical due to their direct relationship with the grain. Several studies have emphasized the importance of spike traits10 (p) > 3. Such changes in GWAS results are because genomic data are rarely of good quality and are contaminated with outliers, missing values, and noise20. Q-Q plot is a convenient tool that shows control of type I error in MTA detection and can be used for model selection in GWAS78. Population stratification or cryptic relatedness leads to systematic deviation from the diagonal at the upper-right end of the Q-Q plots79. Based on this plot, there was not much difference in the results. This result is probably why we did not have outlier observation in SNP data of the third type . However, it seems that using PCs obtained from Hubert's approach can be useful in data with outlier observations of the first and second type. Also, other rPCA methods need to be investigated in diverse populations because we saw slight differences in the deviation from the diagonal at the Q-Q plots of different methods. Finally, using cPCA in genotyping data that are not contaminated by outlier observations is better.We performed GWAS based on three approaches. Although these methods had a lot in common in highly significant MTAs, there was a difference between the methods in terms of significant SNPs at the level of − log80. 4A was the chromosome that contained MTAs for GY in both environments; even SNP rs12851 on this chromosome showed its significant association in both environmental conditions. The same result was reported in similar studies that observed a stable association between chromosome 4A and yield under drought stress82. In addition, SNP rs5823, associated with GN and PC1 in all methods, was located on chromosome 4A. Interestingly, it was present in the carotenoid biosynthesis pathway and supported the cellular anatomical entity. When we used Hubert's PC for population structure, chromosome 7A was most associated with GY. According to the annotation, SNP rs30826 on this chromosome played a role in the membrane structure and was present in the plant-pathogen interaction pathway. It has been proven that there are crosstalks between responses to biotic and abiotic stresses, and some stress-resistant genes can respond to biotic and abiotic stresses83. Also, the plant-pathogen interaction pathway was involved in the drought stress resistance of transgenic wheat84. In a robust GWAS analysis, to overcome the problems of outlier observations, the linear mixed model approach was strengthened using the β-divergence method. This method performed better than the linear regression and mixed model approaches in the presence of outlier data and identified new SNPs that can be used in breeding programs11. The combination of GWAS and t-tests help identify significant SNPs85, confirming CAPS markers86, and identifying favorable SNP alleles87. Hence, we tracked the t-test for a more accurate assessment of the changes in phenotypic data due to allelic variation. The Hubert and Proj method had the highest percentage of significant SNPs in some traits compared to the classical method. The non-significant SNPs between the two alleles in terms of the t-test were distributed in most traits in a range of chromosomes; however, 2B and 7A had the highest number of these SNPs for SIL and GN traits, respectively.The distribution of GY-related markers in different chromosomes has been observed before39. If the first two PCs explain a high percentage of trait variation, they can be suitable enough for GWAS41. In the present study, these two PCs captured more than 90% of the variation. Chromosome 7A had a high percentage of MTAs related to PC1 in all methods. The mentioned chromosome is important due to its association with multiple agronomic traits88 and contains pleiotropic QTL90. Chromosome 2B was among the other regions associated with PCs in both environments. Pleiotropic loci have been reported in chromosome 2B91. Interestingly, under well-watered, SNP rs7805 located on chromosome 3B was associated with PC1 in all methods, while it was not significantly associated with any trait. 3B is a chromosome that simultaneously controls several yield components92. Such QTLs controlling two or more traits lead to high genetic correlation in many traits. The presence of such QTLs in the present study is not far from expected because the correlation between spike traits is certain44.Principal component-based GWAS is statistically more powerful than single-trait GWAS and requires less computational time than multi-trait GWAS. Therefore, it is an efficient method to identify pleiotropic markers94, the presence of even a single outlier has a negative effect on PCA results95. The impact of outlier samples on GWAS results has already been discussed. It has been stated that the number and identity of QTLs identified through GWAS are influenced by the curation and preparation of phenotypic data. If the phenotypic data is contaminated with outliers, the number of suspicious QTLs will increase, especially in loci with unbalanced allelic frequency64. Therefore, it seems necessary to identify the outliers and then enter the next steps for the accuracy and precision of GWAS. For this reason, we used rPCA to obtain other linear combinations of traits that moderate the effect of outliers as input for GWAS. As far as we searched, such an approach has not been investigated in any GWAS. Under well-watered, SNP rs19833 on chromosome 5B, associated with PC1 in Grid and Proj methods, was involved in protein processing in the endoplasmic reticulum. There is evidence of the consequences of protein processing in the endoplasmic reticulum on the final grain size of wheat96, and we know that spike traits strongly affect the final grain size. In addition, based on the above two methods, other markers were identified that play a role in essential candidate genes, such as protein binding, protein phosphorylation, and lipid metabolic process. We saw a similar situation in the well-watered environment where SNP rs48316 located in chromosome 2B, was not associated with any trait but was significantly associated with PC1 in different methods. According to KEGG results, this SNP overlapped with the TraesCS2B02G098500 gene and was present in pathways such as the phosphatidylinositol signaling system, inositol phosphate metabolism, and metabolic pathways. All three of these pathways play a role in tolerance to drought stress99.Although PC-GWAS increases statistical power and has led to the identification of new SNPs in some GWAS studiesWhen phenotypic and genotypic data are contaminated with outlier observations, PCA and different rPCA algorithms provided promising results in identifying them. We have shown that in such a situation, cPCA should be used cautiously in GWAS due to its sensitivity. Using robust strategies in GWAS, putative alleles for important agronomic traits in wheat were identified that were not found in conventional GWAS. Linear combinations of Hubert and Proj methods moderated the effect of phenotypic outliers to a great extent and effectively identified pleiotropic markers. Also, in GWAS results, the population structure provided by rPCA methods discovered several new QTLs associated with traits. Robust strategies in GWAS reduce the risk of missing interesting rare alleles. Finally, it is necessary to pay more attention to the effect of outlier samples and the above methods in future GWAS studies.Supplementary Information 1.Supplementary Information 2.Supplementary Information 3.Supplementary Information 4.