E, (ii) deals with different types of G–E relationships, and (iii) is computationally efficient.Accurate power and sample size estimation is crucial to the design and analysis of genetic association studies. When analyzing a binary trait via logistic regression, important covariates such as age and sex are typically included in the model. However, their effects are rarely properly considered in power or sample size computation during study planning. Unlike when analyzing a continuous trait, the power of association testing between a binary trait and a genetic variant depends, explicitly, on covariate effects, even under the assumption of gene–environment independence. Earlier work recognizes this hidden factor but the implemented methods are not flexible. We thus propose and implement a generalized method for estimating power and sample size for (discovery or replication) association studies of binary traits that (i) accommodates different types of nongenetic covariates Extensive simulation studies show that the proposed method is accurate and computationally efficient for both prospective and retrospective sampling designs with various covariate structures. A proof-of-principle application focused on the understudied African sample in the UK Biobank data. Results show that, in contrast to studying the continuous blood pressure trait, when analyzing the binary hypertension trait ignoring covariate effects of age and sex leads to overestimated power and underestimated replication sample size.https://www.ukbiobank.ac.uk. The R package SPCompute that implements the proposed method is available at CRAN. The genome-wide association studies are carried out using the software PLINK 2.0 [Purcell et al. ].The simulated datasets can be found on the online web-page of this manuscript, and the UK Biobank application data can be accessed at  Gs) that are truly associated with the phenotype of interest (Y)  of complex and heritable human diseases and traits . It is wrest (Y) . Additiorest (Y)  has showY on G and important nongenetic covariates Es. It is then straightforward to show that the power of the corresponding genetic association test only depends on the effect size and minor allele frequency (MAF) of the SNP, sample size, and the unexplained phenotypic variance  allows for different types of G–E relationship, and (iii) has good computational efficiency for large-scale studies. The utility of the proposed method is illustrated and compared with the existing methods through extensive simulation studies and an application study of the UK Biobank data  takes into account different types of nongenetic covariates ank data . The proE; the method implementation and the application allow for multiple Es. To study the relationship between a trait Y and an SNP G of interest, conditional on the nongenetic covariate E, we consider the following generalized linear model .To compute the unconditional power, naturally we replace the conditional Fisher information matrix n isOnce The unconditional power is thenwhereis based on the unconditional Fisher information matrix, α level, the sample size n required to achieve a desirable power can be computed by simply inverting the power function, which is monotonic with respective to n. Although the sample size computation is for a specific genetic effect Gβ, it is clear that, similar to the conditional Fisher information, the unconditional Fisher information in Eβ. Thus, this hidden factor must be explicitly accounted for when performing sample size calculation for a binary trait.To plan a successful replication study at the iG, iE) from the corresponding covariate space G and E, while conceptually simple enough so that that practitioners can make use of their domain knowledge.To compute the unconditional Fisher information matrix G and E, requiring only the marginal distributions of G and E. Although this makes the method easy-to-implement, the assumption may not hold in practice  and a binary E, and its generalization to different types of G and E is nontrivial.The work of E as a covariate in the second-stage regression, we consider it to be the response variable such that,where g2 is the link function, being identity when E is continuous and logit when E is binary.Here, we utilize the idea of second-stage regression  but exteE in a unified framework. When E is continuous, the regression model also requires p.Compared with the second-stage regression model in Since the intercept parameters (for both Stages 1 and 2) do not have clear interpretations in logistic regression, particularly for case–control studies , the defEs by specifying the corresponding g2 function for each E considered. Later, we will demonstrate the utility of our approach in a UK Biobank data application of hypertension, for which both age and sex are important covariates to consider for power and sample size computation. In the rest of this section, we assume there is only one covariate E to simplify the presentation.We note that the proposed method can account for multiple G and E are binary, The estimation of the unconditional power heavily depends on the computation of β) in Fx . Thus, tB, we simulate independent observations Specifically, for a large integer B grows.By a simple application of the law of large number, the sample estimate,converges almost surely to the true expected matrix B (e.g. >10 000). Furthermore, the proposed semi-simulation method is scalable, as for each B but is independent of the target sample size n. Once As we will illustrate later in the simulation studies, n, a full-simulation approach requires simulating B independent datasets, b, and then calculating the empirical power which is the proportion of significant tests among all simulated datasets  observations. Standard MLE of Thus, the original representative dataset It remains to be discussed what is a representative For the unconditional power analysis, E is binary and the link function in i = 0, 1, and 2, and j = 0 and 1, asusing the available information such as MAF and the inheritance mode, with appropriate rounding to ensure that n.When E is continuous and the link function is identity with G such that i = 0, 1, and 2. Then for each of the When Although SPCompute available at CRAN) with those computed using Quanto of We compared the power and sample size computed using the proposed P1.SS and P2.RD methods , E being binary [as the method of E], and E being continuous. Although we only considered one E in the simulation studies for method comparison, our implemented SPCompute R package allows for multiple Es, as demonstrated in our UK Biobank application study in Section 5. Finally, for the simulation studies we also considered three study designs, where S1 is case–control retrospective , while S2 and S3 are prospective to reflect the design of the emerging biobank-sized data such as the UK Biobank data used in our application.We considered three different scenarios for Gβ) was fixed at In the power computation, the log odds ratio (OR) for the genetic effect was fixed at The accuracy of each method was then assessed by comparing the computed power with the empirical value, obtained through a large number of independent replications for a range of sample sizes (600–10 000). First, for each given sample size, we obtained the computed power for each method considered. Second, we simulated 1000 independent replications to obtain the empirical power, which was then used as the oracle value to benchmark and obtain the absolute error (AE). Finally, we summarized the AE values with their averages and maximums across the range of sample sizes considered .Quanto of The choice of no covariate effect was to accommodate the implementation of Gβ ranging from G. Finally, we used The associated SNP has a MAF of 0.1, with a dominant effect Gβ ranging from E has a population exposure rate of G and E as defined in Similar to S1 above, in the second scenario the disease prevalence is also 20%, and the associated SNP with MAF of 0.1 has a dominant effect Quanto of G main effect (as opposed to G × E interaction effect), Quanto does not consider the presence of E. Thus, we only input the information about G in the implementation of Quanto. The method of E for the power (and sample size) computation; G must be binary, hence the dominant genetic model was assumed for method implementation.To implement E was assumed to follow the standard normal distribution conditional on G. The dependency between G and E was set to For this last scenario, without loss of generality, the covariate E for the implementation of Quanto. For the method of E, we considered two approaches. We first omitted the continuous covariate E (corresponding results*), and we then dichotomized E by defining As in the previous scenario, we ignored the information on E to obtain Y on G and G to obtain sample estimates of As the parameter values specified for the true models (1) and (5) cannot be directly used for the two mis-specified models, we used estimated at the (replication) study planning stage, can lead to overestimated power and hence underestimated replication sample size for studying a binary trait.Quanto tends to overestimate the power of an association study, while both Demidenko and the proposed two methods provide power estimates close to the Oracle values. However, if the influential covariate is continuous , only the proposed two methods (P1.SS and P2.DD) perform well.In the presence of a binary covariate (S2), underestimate the necessary sample size for a successful replication study in the presence of influential covariate, while the proposed P1.SS and P2.RD methods are accurate.In the right panel of To examine the sensitivity of the proposed methods to the choice of MAF, we also computed the average and maximum AE of the two proposed methods under the same setting in Scenario 3 (S3) above, for a range of MAF from 0.05 to 0.5. As shown in To select between the two proposed methods, P1.SS and P2.RD as, respectively, described in Sections 3.2 and 3.3, here we study factors influencing the computational efficiencies of the two methods and make recommendations to practitioners.B, the number of independent observations drawn from B replicates of one-sample n does not have a direct impact on computational time. In contrast, the computational time of the P2.RD method depends on n, as the method first creates a representative dataset of size n from n observations as in Conceptually, the computational efficiency of the semi-simulation P1.SS method depends on n, while that of P1.SS is independent of n.To numerically demonstrate the computational properties of the two methods, without loss of generality, we considered simulation Scenario S2 in Section 4.1.2 and used B; we used B in our method implementation is 10 000. Interestingly, the relationship between B and SE appears to be approximately log-log linear.However, the accuracy of P1.SS depends on large Y-axis in n is larger than 25 000, P1.SS is preferred over P2.RD. Although both the RD and SS methods are included in our software SPCompute, the RD approach is not scalable. Thus, RD is only suggested for power computation at medium sample size, and SS is set as the default approach in our software.We note that To illustrate the practical utility of the proposed power and sample size computation methods, we applied them to the UK Biobank data , focusinWe started with the 3460 participants with self-reported ancestry being African. First, we followed the standard practice  to filteK-mean algorithm with K = 4  using the overall principle components (PCs) provided by UKB (Data-Field 22009). th K = 4  to the 3th K = 4  using thth K = 4 . Followith K = 4 . Among tP-value <1e−10, MAF < 0.01, and missing rate >0.2. The X chromosome was not included in our analysis due to the recent report of previously unrecognized data quality issue of the X chromosome , and we then filtered out SNPs based on the thresholds of HWE romosome . In totan = 2510 analyzed individuals, the prevalence rate of hypertension  is 39.48%, and the diastolic blood pressure has mean 85.35 and SD 10.75.We considered two phenotypes, one binary (hypertension) and the other continuous (diastolic blood pressure). In this application, we only considered their measurements at the initial assessment, as longitudinal data analysis is beyond the scope of this work. Additionally, for blood pressure we considered the automated reading (Data-Field 4079) instead of the manual reading. There are two automated measurements of blood pressure during the initial assessment, and we used the average. Among the The GWAS of both traits included age and sex as covariates, and are carried out using the software PLINK 2.0 . Of the To illustrate the importance of including covariates in power and sample size computation for a binary trait, as a proof-of-principle, we focused on the top five-ranked SNPs from each GWAS. The effect size estimates of both SNPs and covariates were used for the corresponding power and sample size computation, though we recognize the potential issue of winner’s curse ; this isQuanto; the method of SPcompute. Finally, in addition to discovery GWAS to achieve 80% power. For comparison, we also analyzed the continuous trait of blood pressure, where the covariate effects are implicitly incorporated through the specification of the residual variance.To show the important role of age and sex in study planning of the binary trait of hypertension, we computed powers and required replication sample sizes twice. We first ignore the two covariates as commonly done (without E), which is equivalent to using underestimated replication sample size  must be explicitly specified and included in power and sample size computation, in addition to the genetic effect of interest (Gβ).Explicitly adjusting for covariate effects is a standard practice in GWAS, but it is rarely done at the study planning stage. When performing power estimation or replication sample size calculation for a continuous trait through linear regression, covariate effects are implicitly accounted for through residual variance. However, when analyzing a binary trait through logistic regression, covariate effects , which affects the power of an association study (However, there are still several limitations of the proposed method that require future work to address. For example, winner’s curse where the effect size estimates of significant SNPs are biased upward is known to be a common problem in GWAS . Therefoon study . Additioon study , 2022. FSPCompute, such as its ability to handle both binary and continuous covariates. We made some simplifying assumptions to make the example easier to understand. For example, we accounted for the covariate effects of age and sex simultaneously by introducing two separate models in the second-stage regression of G, an assumption that might be unrealistic in more complex settings. In general, the proposed methods can also handle multiple Es that are correlated conditional on G, but at the cost of user’s specifying nested second-stage GLMs; see user manual of SPCompute v1.0.3 for additional details. Finally, the framework of the proposed method can be generalized to incorporate gene–gene and gene–environment interaction effects, which we will provide as future software updates.Our UKB application in Section 5 only serves as a proof-of-principle and highlights the practical utility of btad139_Supplementary_DataClick here for additional data file.


Introduction: In this study estimated genetic and phenotypic correlations between fifteen complete blood count (CBC) traits and thirty-three heritable plasma metabolites in young healthy nursery pigs. In addition, it provided an opportunity to identify candidate genes associated with variation in metabolite concentration and their potential association with immune response, disease resilience, and production traits.Methods: The blood samples were collected from healthy young pigs and Nuclear Magnetic Resonance (NMR) was used to quantify plasma metabolites. CBC was determined using the ADVIA® 2120i Hematology System. Genetic correlations of metabolite with CBC traits and single step genome-wide association study (ssGWAS) were estimated using the BLUPF90 programs.Results: Results showed low phenotypic correlation estimates between plasma metabolites and CBC traits. The highest phenotypic correlation was observed between lactic acid and plasma basophil concentration . Several significant genetic correlations were found between metabolites and CBC traits. The plasma concentration of proline was genetically positively correlated with hemoglobin concentration  and L-tyrosine was negatively correlated with mean corpuscular hemoglobin . The genomic regions identified in this study only explained a small percentage of the genetic variance of metabolites levels that were genetically correlated with CBC, resilience, and production traits.Discussion: The results of this systems approach suggest that several plasma metabolite phenotypes are phenotypically and genetically correlated with CBC traits, suggesting that they may be potential genetic indicators of immune response following disease challenge. Genomic analysis revealed genes and pathways that might interact to modulate CBC, resilience, and production traits. Immunity refers to the immune system’s capacity to protect individuals from disease by recognizing and eliminating potentially pathogenic agents, including bacteria, bacterial toxins, viruses, parasites and fungi . The earOther component of blood such as platelets, possess immune receptors and produce inflammatory molecules . PlateleIn humans, metabolic reprogramming of immune cells has a critical influence on their function . For exaTherefore, understanding the impact of different metabolites on metabolic reprogramming of immune cells is important to improve diagnosis, prognosis, and therapeutic personalized medicine strategies in humans . In thisIn the last decade, metabolomics has been used to discover biomarkers of disease in different livestock species as well as in animal genetic studies because it provides the potential to identify new phenotypes or traits which can be used to select for more efficient and resilient animals . It is tThe importance of health and the immune system in relation to productivity in pigs facing disease challenge has been described . Bai et The present study is part of a larger project which has identification of predictors of disease resilience in young healthy pigs prior to a disease challenge as its main objective. For this purpose, a natural polymicrobial disease challenge model  was estaThe purpose of this study was to estimate the phenotypic and genetic parameters between CBC traits and plasma metabolite concentrations in plasma samples collected on young healthy pigs, prior to the disease challenge. Furthermore, we attempted to identify genomic regions that control the genetic variance of metabolites that are genetically correlated with CBC, resilience, and production traits.In Vivo Experiments guidelines ARRIVE; https://arriveguidelines.org;  tubes  from all pigs in the quarantine nursery 5 days post-arrival at average 26 days of age  for CBC All animals were genotyped using a 650 k Affymetrix Axiom Porcine Genotyping Array at Delta Genomics . Raw Affymetrix SNP data were processed by Delta Genomics, separately for each cycle, using the Axiom Analysis Suite. All the details of genotyping and quality control have been previously described . A total® 2120i Hematology System . A total of 15 CBC traits were included: concentration of total white blood cell concentration , neutrophils , lymphocytes , monocytes , eosinophils , basophils , red blood cells , hemoglobin , hematocrit , mean corpuscular volume , mean corpuscular hemoglobin , mean corpuscular hemoglobin concentration , red blood cell distribution width , platelet concentration , and mean platelet volume . Descriptive statistics including mean and standard deviation values of CBC traits by batch, for the pigs included in the analysis, are shown in In this study we used CBC and metabolomics data obtained from blood samples collected in the quarantine nursery from 968 pigs. Details of the CBC and metabolomic data have been described by 2O and centrifuged  to remove residual glycerol bound to the filter membranes. To remove macromolecules from the sample (primarily protein and lipoproteins), aliquots of each sample were transferred into the centrifuge filter devices and spun at 10,000 rpm during 20 min (2PO4 buffer (pH 7) was added and the dilution factor was annotated and metabolite concentrations were corrected in the subsequent analysis. Thereafter, 46.5 µL of a standard buffer solution , 5.84 mM 2-chloropyrimidine-5 carboxylate, and 0.1% NaN3 in H2O) was added to the sample (1H-NMR spectra were collected on a 700 MHz Avance III (Bruker) spectrometer equipped with a 5 mm HCN Z-gradient pulsed-field gradient (PFG) cryoprobe (1H-NMR spectra were acquired at 25°C using the first transient of the NOESY pre-saturation pulse sequence (noesy1dpr), chosen for its high degree of quantitative accuracy , short chain fatty acids (SCFA), sugars, alcohols, organic acids, amines, TCA cycle intermediates and urea cycle intermediates . In addiΥijk is the phenotype for the trait  for one of the 968 analyzed pigs; Batchi is the fixed effect ; Ageijk is the covariate of age when the pig entered the quarantine nursery; Penj is the random effect of nursery pen by batch, with Penj∼ N , where σ2P is pen variance; Litterijk is the common environmental effect associated with litter, with Litterijk∼ N , where σ2L is the litter environmental variance; uijk is the random additive genetic effect, with the vector u ∼ N , where G is the genomic relationship matrix and σ2A is the additive genetic variance; and eijk is the residual effect, with eijk ∼ N , where σ2e is the residual variance  were available for 968 F1 crossbred pigs and genotypic data were available for 3,205 F1 crossbred pigs. The complete pedigree for 3,205 pigs was unavailable due to the use of pooled semen in some batches , howeverH matrix; H matrix needed for mixed model equations is given by:A−1 is the inverse of the numerator relationship matrix; A22−1 is the inverse of the pedigree relationship matrix; and G1− is the inverse of the genomic relationship matrix. The genomic relationship matrix (G) was constructed as: G = ZDZ′q , and q is a weighting factor. The weighting factor was as in 22. The genomic estimated breeding value  was calculated by ssGBLUP and the solutions of the SNP effects (û) were obtained using the AIREMLF90 , was performed using the programs of BLUPF90 software family , modifie = ZDZ′q ; where ZIREMLF90  algorithi)/σ2a] x 100%, where ai is the genetic value of the ith SNP window and σ2a is the additive GV (Y is the vector of the phenotypes (metabolite concentration); b is the vector of fixed effects (batch and covariate of age when the pig entered the quarantine nursery); X is the incidence matrix relating observations to the fixed effects, c is the vector for the random pen effect; W is the incidence matrix of the random pen effect; l is the vector of for the random litter effect; U is the incidence matrix of the random litter effects; a is the vector of direct additive genetic effects; Z is the incidence matrix of random animal effects; and e is a vector of the random residuals.In this study, SNPs located within 0.5 Mb were grouped as a single window, and the percentage of genetic variance (GV) explained by each window was calculated using the postGSF90 module as: [Var. Genecards (https://www.genecards.org/) was used to investigate the gene function based on orthologous genes of humans. Candidate genes were also compared with the information about QTLs reported in QTLdb .The identification of candidate genes was performed using p ≤ 0.05) genetic correlations with traits of interest  were used for network visualization. In order to generate a gene-compound network, a file containing the list of KEGG elements was loaded into Metscape following instructions provided by (The Metscape plugin  in Cytosvided by . In a gevided by .p < 0.05). Pyruvic acid showed positive phenotypic correlation estimates with HCT, MCV, MCH (p < 0.05), and negative correlations with PLT, RDW, and MPV (p < 0.05). D-glucose showed negative phenotypic correlation estimates with NEU, BASO, EOS, MONO, LYM, and MPV. Furthermore, L-alanine showed negative phenotypic correlation with MCHC (p < 0.05). Finally, oxoglutarate was positively correlated with HGB (p < 0.05). A scatter plot showing the negative correlations between pyruvic acid, D-glucose and CBC traits is shown in In general, estimates of phenotypic correlations of the metabolites with CBC were small . The estThe phenotypic correlation between metabolites that are involved in the same pathway  are shown in p < 0.05) with white blood cell traits. For example, a high negative genetic correlation between NEU and plasma L-lysine was observed (p < 0.05). L-glutamine was positively correlated with NEU (p < 0.05) and L-aspartate was positively correlated with MONO (p < 0.05). 2-hydroxybutyrate, 3-methyl-2-oxovaleric acid and L-alpha aminobutyric acid had positive genetic correlation estimates with EOS, while dimethylglycine was negatively correlated with EOS concentration (p < 0.05). Positive genetic correlations were estimated for WBC with the amino acids L-asparagine and L-glutamic acid (p < 0.05). Lymphocyte concentration was positively correlated with isobutyric acid and L-histidine (p < 0.05), while LYM was negatively correlated with hypoxanthine and L-ornithine  and HCT (p < 0.05). A high negative genetic correlation was observed for L-tyrosine with MCV (p < 0.05) and MCH (p < 0.05). In addition, L-glycine was positively correlated at the genetic level with MCH (p < 0.05). L-alanine (-p < 0.05) and L-alpha-aminobutyric acid (p < 0.05) were negatively correlated with RDW. Furthermore L-alanine was positively correlated with PLT (p < 0.05). Finally, the amino acid L-methionine was negatively correlated with MPV (p < 0.05). Basophils, RBC, platelets, MCHC, and MCV were not genetically correlated with any of the metabolites. The genetic correlation between metabolites that are involved in the same pathway are shown in Estimates of genetic correlations between metabolites and RBC and platelet traits are shown in GWAS was performed for L-alpha aminobutyric acid, L-aspartate, L-asparagine, L-glutamic acid, L-glutamine, L-glycine, L-histidine, L-lysine, L-methionine, L- ornithine, L-serine, betaine, creatinine, dimethylglycine, hypoxanthine, isobutyric acid, oxoglutarate, 2-hydroxybutyrate and 3-methyl-2 oxovaleric acid because in the present study they were estimated to be genetically correlated with CBC, and in a previous study they were genetically correlated with resilience, or production traits .For L-glutamic acid, the five most important windows were located on SSC14 and explained 7% of the genetic variance . In addiSPECC1L, ADORA2A, UPB1, GUCD1, LRRC75B, GGT5, SUSD2, CABIN1, DDT, GSTT4). Another window on SSC2  was found to explain genetic variance for both betaine and dimethylglycine. Four genes were located in this window . In addition, one window on SSC1  was found to explain some of percentages of the genetic variance for L-ornithine, L-proline, and L-tyrosine. A total of 5 genes were found in this region .The results of GWAS showed that some windows overlapped for some of the metabolites. For example, the window on SSC14  explained some of the genetic variance for both L-glutamic acid and glutamine. In this window a total of 10 genes were found (p < 0.05) genetic correlations with traits of interest , and for which had overlapping genomic windows that explained genetic variance. DMGDH, BHMT2, BHMT), are associated with both metabolites, suggesting pleiotropic effects of genes on multiple metabolites.Discovery of common genomic regions for different metabolites led us to further investigate some genes that control the genetic variance of different metabolites. Thus, a compound-gene network of metabolites that had significant  genetic correlations between thirty-three heritable metabolites with CBC traits in healthy young pigs, and 2) identify genomic regions controlling the genetic variance of metabolites that were genetically correlated with CBC and production and disease resilience traits. Identification of genetic predictors/markers of resilience and production traits under disease challenge by using samples from healthy pigs is necessary for genetic selection programs in high health nucleus farms. This study contributes to our understanding of the relationship of metabolites and immune response cells in pigs. The results of phenotypic and genetic correlations increase our understanding of the crosstalk between metabolites and immune cells in healthy animals, which might help design nutritional and selection strategies to improve resilience. Meanwhile, it is possible to estimate the genetic correlations between different traits, it is often not clear what molecular processes contributes to these genetic correlations. Thus, this study deepens our understanding to what contributes to the genetic correlations at a molecular level in young healthy pigs.Phenotypic correlations of metabolites with CBC traits were generally very low. D-glucose had negative phenotypic correlation estimates with NEU, LYM, MONO, EOS, BASO, and MPV, while lactic acid was phenotypically positively correlated with WBC, NEU, LYM, BASO, EOS, RBC, HGB and MPV. Lactic acid is a hydroxycarboxylic acid and is mainly produced in muscle cells and red blood cells during anaerobic glycolysis . During Overall, estimates of genetic correlations between metabolites and CBC traits ranged from moderate to high. We found high negative genetic correlation between plasma L-lysine and NEU (−0.81 ± 0.4), which is in agreement with previous studies reporting that lysine can modulate the neutrophil metabolism . L-LysinWe found that L-glutamine was genetically positively highly correlated with NEU and L-aspartate was positively correlated with MONO. Positive genetic correlation estimates were observed for the amino acids L-asparagine and L-glutamic acid with WBC. Lymphocyte concentration was negatively correlated with hypoxanthine and L-ornithine. Extensive research conducted in human and animal studies have demonstrated the role of amino acids in immune cell maturation, modulation, and function. For example, amino acids such as glutamic acid, glutamine, histidine, methionine, leucine, isoleucine, and valine are functional regulators of macrophages, dendritic cells, and T cells .One of our most interesting results is the high positive genetic correlation between L-proline and hemoglobin concentration (0.94 ± 0.03). Using NMR spectroscopy and mutagenesis In addition, isobutyric acid was found to be positively genetically correlated with LYM concentration (0.69 ± 0.35) in healthy pigs. Previously, Other metabolites such as 2-hydroxybutyrate, 3-methyl-2-oxovaleric acid and L-alpha aminobutyric acid were estimated to have positive genetic correlations with LYM and EOS concentration meanwhile dimethylglycine was negatively correlated with EOS. Furthermore, we found that the amino acids L-alanine and L-alpha-aminobutyric acid, also called homoalanine, are negatively genetically correlated with RDW. The red blood cell distribution width is a measure of size variability and heterogeneity of erythrocytes in the pheripheral blood and reflects the degree of anysocytosis. At present it is not clear why L-alpha aminobutyric and L-alanine are genetically correlated with RDW, but it is worth further investigation. For many other metabolites such as 2-hydroxybutyrate and 3-methyl-2-oxovaleric acid, literature on genetic correlations is lacking, making the interpretation of our results difficult.RAB32) located on SSC1 as a candidate gene for RBC concentration. In the present study we found Member RAS Oncogene Family (RAB27A), located on SSC1 as a candidate gene for L-proline. In addition, proline was found to be genetically correlated with HGB concentration and HCT. These results might suggest that member RAS oncogene family (RAB32 and RAB27A) and proline modulate RBC traits, however further functional studies are necessary to validate our results. In addition, 3/μL) suggesting a possible role of L-alanine and tubulin superfamily in platelets concentration.We performed a GWAS for 22 metabolites in young healthy pigs that were genetically correlated either with production or resilience traits or with CBC traits and investigated the genomic regions that explained a sizeable proportion of the variance for each metabolite. GWAS with CBC traits, were previously reported by SEC63, OSTM1, NR2E1, SNX3 and AFG1L), explained 1.02% of genetic variation of L-lysine concentration which was negatively genetically correlated with NEU concentration. Interestingly NR2E1  functions as a repressor and activator of gene transcription . PLA2G3 is involved in L-serine metabolism and lipid metabolism. It catalyzes the calcium-dependent hydrolysis of the sn-2 acyl bond of phospholipids to release arachidonic acid and lysophospholipids. Phosphatidylserine is a phospholipid that consists of two fatty acids attached in ester linkage to the first and second carbon of glycerol and serine attached through a phosphodiester linkage to the third carbon of the glycerol , dimethylglycine dehydrogenase (DMGDH), betaine-homocysteine S-methyltransferase (BHMT), and betaine-homocysteine S-methyltransferase 2 (BHMT2). DMGDH is involved in the catabolism of choline, catalyzing the oxidative demethylation of dimethylglycine to form sarcosine. BHMT and BHMT2 are methyl transferases. BHMT encodes a cytosolic enzyme that catalyzes the conversion of betaine and homocysteine to dimethylglycine and methionine, respectively. BHMT2 can catalyze the transfer of the methyl group from betaine to homocysteine to create methionine  for all metabolites. For L-glutamic acid, there were five important neighboring windows on SSC14 that together explained 6.9% of the genetic variance. Interestingly, we found overlapping windows on SSC14 that explained variance for L-glutamic acid, L-glutamine, L-serine, and oxoglutarate . These overlapping genomic windows might explain the positive genetic correlation between L-glutamic acid and oxoglutarate. Other overlapping windows were detected on SSC1 for L-lysine, L-ornithine, L-proline, and L-tyrosine , on SSC2 for betaine and dimethylglycine , on SSC6 for L-asparagine, L-proline, and L-serine , and on SSC12 for creatinine and isobutyric acid . These overlapping windows on SSC2 might contribute to the positive genetic correlation observed between betaine and dimethylglycine. These results suggest pleiotropic effects of loci on metabolite concentrations, i.e., that the same gene may control variation in more than one metabolite. Pleiotropy effects of loci on metabolites have been previously described in human studies . To furtglycerol . In a prthionine . The metr litter  and BHMTnit area . InteresF-box protein 38 (FBXO38) and 5-hydroxytryptamine receptor 4 (HTR4). 5-hydroxytryptamine receptor 4 is a member of the family of serotonin receptors, which are G protein coupled receptors that stimulate cAMP production in response to serotonin (5-hydroxytryptamine). Interestingly HTR4 to be associated with RFI in dairy cattle using the Random Forests (RF) algorithm. In addition, GWAS performed by HTR4 as a candidate gene for residual concentrate intake (RCI) in dairy cattle. In pigs there is no evidence in the literature to connect isobutyric acid with HTR4 and RFI, making interpretation of our results challenging. However, 5-hydroxytryptamine receptor 2B, (HTR2B), which belongs to the same family of serotonin receptors as HTR4, was proposed as functional candidate gene for feed conversion ratio (FCR) in pigs , Hypor Canada , Topigs Canada , Alliance Genetics , Fast Genetics , DNA Genetics , Genesus Genetics .


Understanding human genetic influences on the gut microbiota helps elucidate the mechanisms by which genetics may influence health outcomes. Typical microbiome genome-wide association studies (GWAS) marginally assess the association between individual genetic variants and individual microbial taxa. We propose a novel approach, the covariate-adjusted kernel RV (KRV) framework, to map genetic variants associated with microbiome beta-diversity, which focuses on overall shifts in the microbiota. The KRV framework evaluates the association between genetics and microbes by comparing similarity in genetic profiles, based on groups of variants at the gene level, to similarity in microbiome profiles, based on the overall microbiome composition, across all pairs of individuals. By reducing the multiple-testing burden and capturing intrinsic structure within the genetic and microbiome data, the KRV framework has the potential of improving statistical power in microbiome GWAS.IL23R, reported in a previous microbiome genetic association study and discovered 3 other novel genes, 2 of which are involved in immune functions or autoimmune disorders. In addition, simulation studies show that the covariate-adjusted KRV has a greater power than other microbiome GWAS methods that rely on univariate microbiome phenotypes across a range of scenarios.We apply the covariate-adjusted KRV to the Hispanic Community Health Study/Study of Latinos (HCHS/SOL) in a two-stage  genome-wide association analysis for gut microbiome beta-diversity. We have identified an immunity-related gene, Our findings highlight the value of the covariate-adjusted KRV as a powerful microbiome GWAS approach and support an important role of immunity-related genes in shaping the gut microbiome composition.Video AbstractThe online version contains supplementary material available at 10.1186/s40168-023-01530-0. Bifidobacterium, a genus of beneficial gut bacteria that utilizes lactose as an energy source, has been associated with a non-persistence genotype of the human lactase gene (LCT), which typically results in lactose intolerance [The human microbiome plays an important role in host health and is involved in fundamental body functions such as metabolism and immune response , 47. Whiolerance , 26, 38.Many studies have sought to identify genetic variants that influence microbial composition, and most of them incorporate microbiome characteristics as phenotypes in genome-wide association studies (GWAS). Typical analyses marginally test the association between abundances of individual taxa and genotypes of individual genetic variants , 33, 38.As the microbiome functions as a community, an alternative microbiome phenotype is beta-diversity, the dissimilarity in overall microbiome profiles between individuals. Beta-diversity analysis represents a standard mode of analysis in microbiome profiling studies as it focuses on discovery of concerted shifts in the community rather than individual taxa. However, few studies have considered beta-diversity as a trait of interest in microbiome GWAS and there is no standard strategy. Some studies , 62 haveHere, we propose to assess the association between groups of variants at the gene level and the overall microbiome composition, characterized by beta-diversity, at the community level. Community-level analyses and multi-variant testing have been shown to be powerful in microbiome , 70 and Although the KRV is a potentially powerful approach for microbiome GWAS, the KRV framework lacks a general strategy to control for covariates such as population structure, which is imperative for any genetic association analysis. Here we extend the original KRV framework to allow for flexible covariate adjustment.IL23R) reported in a previous microbiome genetic association study and discovered other novel genes related to immune functions. Furthermore, we have identified individual genetic variants and specific microbial taxa involved in these gene-microbiome associations. In addition, our simulation results show that the covariate-adjusted KRV maintains valid type I error rates in the presence of confounding and has a much greater power than other single-trait-based competing methods across a range of scenarios. Together, our proposed approach demonstrates good statistical properties and provides a powerful way to study the effect of human genetic variation on microbiome composition.We apply the covariate-adjusted KRV to the Hispanic Community Health Study/Study of Latinos (HCHS/SOL) , 60 via We aim to assess the covariate-adjusted association between genotypes of multiple genetic variants within a gene and abundances of microbial taxa at the community level, using the previously developed KRV framework. We now give an overview of the original KRV framework and extend it to allow for flexible covariate adjustment. The overall procedure for covariate-adjusted KRV in the context of microbiome GWAS is shown in Fig. G, and a group of traits, Y. Suppose we have genotype data of m genetic variants and phenotype data of q traits available for n unrelated individuals. For the i-th subject, let l-th variant; let m genetic variants within a particular gene, and q microbial taxa that form the microbiota.The KRV framework has been proposed by Zhan et al. , 69 to e pathway . In the i and j. Let i and j. Specific choices of kernel functions in the context of microbiome GWAS are discussed in Methods: i, j)-th entry of Let p-value and assess the significance of the association at a given significance level.Intuitively, the KRV coefficient compares genotypic similarity to phenotypic similarity across all pairs of individuals. A large KRV coefficient indicates that the pairwise similarity pattern in genetic profiles well resembles the pairwise similarity pattern in phenotypic profiles, which implies that the genetic variants are associated with the traits in a certain way. To perform hypothesis testing, the permutation distribution of the KRV statistic under the null hypothesis of no association between genetics and phenotypes can be approximated by a Pearson Type III distribution , allowini, we have a set of covariates i-th row of The above framework does not take into account any covariates that might be involved in a typical genetic association study. Now suppose that, for each individual approach , 69, wheTo adjust for covariates in a general way, we propose a novel adjustment approach that applies to all possible kernel types, regardless of the requirement for input data. Our approach is based on kernel principal component analysis (kernel PCA) , a genermentclass2pt{minimp-value. In this case, the null hypothesis is that there is no association between the genetics and the phenotypes after adjusting for the effects of the covariates.The usual hypothesis testing procedure in the KRV framework can be applied to the adjusted KRV statistic to obtain a In the KRV framework, kernel functions are used to summarize pairwise similarities in genotype and phenotype profiles among the subjects. In order to improve the statistical power in hypothesis testing, we would like to choose kernels that better reflect the actual structure within the genetic and phenotype data as well as the patterns of association , 70. ForFor genotype data, popular kernel functions include the linear kernel variants . Dependivariants .For microbiome data at the community level, the kernel matrix can be obtained by transforming known ecological or phylogenetic dissimilarity measures . For example, Bray-Curtis dissimilarity quantifies the dissimilarity between two microbial communities based on the difference in counts at each taxon between the two communities. The UniFrac distances are dissimilarity measures based on the phylogenetic structure of the taxa , 45, 46:While the Bray-Curtis dissimilarity and UniFrac distances take scaled or rarefied microbial counts or presence/absence information as input, microbial dissimilarity can also be calculated from other types of transformed abundance data. For example, the centered log-ratio (CLR) transformation , 24 and Given a pairwise dissimilarity matrix  package , where wWe note that taking Euclidean distances followed by kernel matrix transformation is equivalent to constructing a linear kernel matrix based on the same data  is a community-based prospective cohort study aimed to identify risk factors for health outcomes in Hispanic/Latino populations in the USA. The study recruited 16,415 Hispanic/Latino adults aged 18–74 years, representing diverse ethnic background, at four US field centers , using a two-stage probability sampling design .N is the sample size and v is the ratio of observed variance of imputed dosages to the expected binomial variance [12,803 participants consented to genetic studies. Genotyping was performed on an Illumina custom array, SOL HCHS Custom 15041502 B3, which consisted of the Illumina Omni 2.5M array (HumanOmni2.5-8v1-1) and As an ancillary study, the HCHS/SOL Gut Origins of Latino Diabetes (GOLD) study was further conducted to investigate the role of gut microbiome composition in diabetes and other health outcomes in Hispanic/Latino individuals . Gut micThe HCHS/SOL study was approved by the Institutional Review Boards of all participating institutions, and written informed consent was obtained from all participants.To identify genetic variants associated with the overall gut microbiome composition in Hispanic/Latino individuals, we applied the covariate-adjusted KRV test to the HCHS/SOL study in a genome-wide association analysis for gut microbiome beta-diversity.We considered genetic variants  within For each gene, we assessed the association between common variants  kernel PCs derived from the kernel matrices, as mentioned in Methods: Our investigation of the genetic effect on the microbiome involved two stages. In the first stage, we tested the association between the variants in each gene and the microbiome profile at the community level. In the second stage, for any genes called significant in the first stage, we marginally assessed the association between each of the individual variants within those genes and the community-level microbiome profile to look for significant variants, again using the covariate-adjusted KRV. Bonferroni correction was applied in both stages. Since this was a nested hypothesis testing approach, the second-stage test only required correction for the number of variants in the genes that were called significant in the first stage. All analyses were performed on unrelated individuals  , a kernementclass2pt{minimWe conducted simulation studies to further evaluate the type I error rate and power of the covariate-adjusted KRV test. We simulated genotype data and microbial OTU count data under realistic settings, and introduced population stratification as a confounder that affected both genetic and microbiome data.cosi2 program [The general simulation setting is as following. We considered a sample size of 1000. SNP genotype data over a 1-Mb chromosome were simulated for 500 individuals of African ancestry and 500 individuals of European ancestry. Specifically, we first generated 10,000 haplotypes of African ancestry and another 10,000 haplotypes of European ancestry over a 1-Mb chromosome according to coalescent theory using the  program . To formWe used a Dirichlet-multinomial distribution to generate microbial OTU counts for each individual in the sample, as this distribution well accommodates the over-dispersion of microbiome count data , 70. To Both unadjusted and adjusted KRV tests were performed to test the association between the overall microbiome composition (composed of 856 OTUs) and common SNPs . In Type I Error Scenario 1, we increased the abundance of the 10 most common OTUs by 10% in African individuals and then rarefied the abundance back to 1000 total counts per individual. In Type I Error Scenario 2, we increased the abundance of 10 rare OTUs (chosen randomly from the top 40 rarest OTUs) in African individuals by adding a unit count before rarefying the abundance back to 1000 total counts per individual. These two scenarios were not meant to reflect the microbiome difference between African and European individuals in reality, but they served as hypothetical situations to introduce confounding effect into the genetics-microbiome relationship. Here we used the estimated mean proportion parameters of the Dirichlet-multinomial distribution as a measure of OTU prevalence. 10,000 simulations were performed for each type I error scenario.i at a chosen common SNP. In Power Scenario 1, for each individual i, we increased the counts of the 11th–20th most common OTUs by a factor of i, where i, we increased the counts of 5 rare OTUs (chosen randomly from the top 40 rarest OTUs) by an addition of To evaluate the power of the covariate-adjusted KRV, we based our simulation setting on Type I Error Scenario 1 and further introduced genetic effect on the microbiome in three different power scenarios, where a single SNP affected the abundance of multiple microbial OTUs . Let 856 OTUs , we incrIn the power simulation, we also considered two competing methods that analyze the association between a group of variants and the overall microbiome composition but rely on univariate microbiome phenotypes, as described in Methods: We estimated the computation time of the covariate-adjusted KRV test for different sample sizes. For each sample size, we simulated 10 data sets and reported the average computation time. Given constructed genotype and microbiome kernel matrices and 10 covariates, the average computation times are 0.09, 1.23, 12.58, and 97.57 s on a laptop (2.7 GHz CPU and 16 GB memory) for sample sizes of 200, 500, 1000, and 2000, respectively. The gene-level analysis of the HCHS/SOL data set  took approximately 8 hours on a high-performance computing cluster , with computing jobs divided by chromosome.p-value QQ-plots of the first-stage gene-level analysis results. For all microbiome kernels, the unadjusted KRV produces highly anti-conservative p-values (with large genomic inflation factors), while the PC-adjusted KRV has well-controlled type I error rates  where additional covariates  are available and adjusted, IL23R and C1orf141 are no longer genome-widely significant  and the order of magnitude of their p-values (Table nt Table . Similarmentclass2pt{minimIL23R is of considerable interest: it encodes one part of the receptor for interleukin-23 (IL-23), a pro-inflammatory cytokine closely involved in autoimmunity [IL23R gene has been associated with inflammatory bowel diseases (IBD) including Crohn’s disease and ulcerative colitis [IL23R gene (rs11209026) was associated with a higher microbiome diversity and richness and a higher abundance of beneficial gut bacteria in the ileum of healthy individuals, suggesting the influence of host genetics on the microbiome prior to onset of IBD. In addition, a mouse-based experimental study [IL23R expression had altered gut microbiota and were susceptible to colonic inflammation, where increased disturbance of gut microbiota exacerbated the disease activity. Coupled with these results, our finding further supports that the gut microbiome may mediate the host genetic effect on the development of inflammatory diseases like IBD. In its normal function, the IL23R gene likely helps shape the overall gut microbiota towards a healthy composition, which may in turn support normal immune activities and prevent gut inflammation.Among these genes, immunity . The IL2 colitis , 58. In  colitis , the proR gene rs1209026 wC1orf141 gene, with uncharacterized protein function, has overlapping regions with IL23R. Variants in the IL23R-C1orf141 region have been associated with susceptibility to Vogt-Koyanagi-Harada disease, a multi-system autoimmune disorder that affects pigmented tissues, in Chinese and Japanese populations [ZFR gene encodes the highly conserved zinc finger RNA-binding protein, which is shown to prevent excessive type I interferon activation by regulating alternative pre-mRNA splicing [MTMR12 gene encodes an adapter protein for myotubularin-related phosphatases and is likely involved in skeletal muscle functions [The other genes are also interesting to further explore. The ulations , 54. Thesplicing . Preventunctions . OverallMTMR12 is more significant with the unweighted UniFrac kernel than with the CLR-linear kernel, we focus on unweighted UniFrac for our subsequent analysis of MTMR12. Figure IL23R and C1orf141 genes were combined into a single IL23R-C1orf141 region due to overlapping variants. Based on the analysis using the Bray-Curtis kernel, there are 72 significant variants (out of 557 common variants) in the IL23R-C1orf141 region (ZFR and 125 significant variants (out of 174 common variants) in MTMR12  variant from each identified gene. This is similar to a PCoA analysis. Figure R12 Fig. .Fig. 4PCTo further understand how the discovered genes drive differences in gut microbiome composition, we conduct an exploratory analysis to identify specific microbial taxa involved in the microbiome GWAS associations. Our strategy is to perform dimension reduction on both genetic and microbiome data and use correlation analyses to complement and help interpret our community-level analysis results.p-value < 0.05 from linear regression): these kernel PCs represent the microbial community profiles that mainly drive the gene-microbiome associations. In Step 2, we inspect genus-level microbial abundance data and identify taxa that contribute the most to the significant kernel PCs from Step 1  of the top variant, rs10789226, from IL23R is positively associated with the abundance of Bacteroides and Blautia, while being negatively associated with the abundance of Prevotella. Bacteroides and Prevotella are the most abundant genera in this study  and dominate the first PC of the Bray-Curtis kernel. These two genera have been studied extensively as metrics for dietary patterns [Prevotella-to-Bacteroides ratio is associated with greater obesity in Hispanic/Latino populations based on a previous study using HCHS/SOL data [Bacteroides compared to healthy individuals, although mixed roles of Bacteroides have been reported in other studies [Prevotella species are classically considered as commensal bacteria, increased abundance of certain Prevotella strains has been associated with mucosal inflammation and linked to chronic inflammatory diseases [The microbial taxa identified for each gene-microbiome association signal are listed in Table patterns , 27. IntSOL data . In termSOL data  suggests studies . On the diseases . Based oZFR and the unweighted UniFrac kernel. Allele T (vs. Allele A) of the top variant, rs2113093, from ZFR is positively associated with the abundance of two unidentified genera from Clostridiales and Ruminococcaceae. As Ruminococcaceae is an order that belongs to the Clostridiales family, this result is consistent with the strength of the unweighted UniFrac kernel in utilizing phylogenetic information. Ruminococcaceae helps maintain the gut health by producing short-chain fatty acids (SCFAs) [Ruminococcaceae has been associated with IBD disorders [Clostridiales strains have been shown to mediate effective immune response against colorectal cancer in mouse models [Clostridiales and Ruminococcaceae bacteria in mediating the effect of ZFR in regulating innate immune response, and Allele T of rs2113093 is likely associated with a more favorable gut microbiome composition.We next look at the taxa involved in the association between  (SCFAs) , and a disorders  and inflisorders . On the e models . These fOverall, the above findings offer us a better understanding of the identified community-level associations. Nevertheless, due to heterogeneity in functions of individual bacterial species and strains, a higher study resolution will be required to further elucidate the mechanisms underlying the association between the identified genes and the gut microbiome.As a comparison to our proposed covariate-adjusted KRV approach, we applied additional competing methods of microbiome GWAS to the same set of HCHS/SOL data , the CLR-linear kernel  and the PhILR-linear kernel , but not significant at the genome-wide level.At a study-wide significance level  based on various microbiome kernels: BANK1 , MAST3 , POMC (CLR-linear), C1orf21 (CLR-linear) and AHSA2 (PhILR-linear). Among these genes, POMC produces peptides involved in anti-inflammatory actions [BANK1 is associated with systemic lupus erythematosus [MAST3 and AHSA2 are associated with IBD [We next investigate the replication of signals found by previous gut microbiome GWAS studies in our analysis. We have examined the significance of 63 previously reported genes that harbor variants associated with gut microbiome beta-diversity , 62, 64  actions , BANK1 iematosus , and MASwith IBD , 66, corWe have conducted simulation studies to further evaluate the performance of our proposed covariate-adjusted KRV test in terms of type I error rate and power. Table Under Type I Error Scenario 2 Table , where pFigure Under large effect sizes Fig. , while tGiven the importance of the microbiome in human health, there is an emerging interest in studying the relationship between host genetic variation and human microbiome. Our methodological contribution in this work is twofold. First, we have proposed a novel microbiome GWAS approach to evaluate the association between gene-level genetic variation and community-level microbiome composition. Second, we have proposed a novel multivariate statistic, the covariate-adjusted KRV, to implement this approach with flexible covariate adjustment. By reducing the multiple-testing burden and aggregating small effect sizes between the genetics and the microbiome, our proposed approach improves statistical power and thus requires fewer samples to detect associations compared to the traditional marginal testing approach. Simulation studies show that the covariate-adjusted KRV maintains valid type I error rates in the presence of confounders and has a much higher power compared to other microbiome GWAS methods that rely on univariate microbiome phenotypes. In a genome-wide analysis of the HCHS/SOL data, we have identified four genes associated with gut microbiome beta-diversity. We have also identified individual variants within these genes and specific microbial taxa involved in the associations, which will be useful for future investigation of the mechanisms underlying the genetics-microbiome relationships.IL23R gene is especially interesting for future study, due to its recognition in previous microbiome genetic association studies [Most of the identified genes based on the HCHS/SOL data have been previously implicated in immune functions or immunity-related disorders. This is consistent with the works by Blekhman et al.  and Rühl studies  and its  studies , 34. Fur studies , 50, and studies  in patieIL23R-C1orf141 region, identified using Bray-Curtis, mainly associate with abundances of Bacteroides and Prevotella  in a reduced sample revealed similar results. However, the signal from the LCT locus and Bifidobacterium abundance at a study-wide significance in the taxon-level analysis, the LCT gene was not genome-widely significant in the community-level analysis. Bifidobacterium was a relatively common genus  in the HCHS/SOL data. However, when we analyzed the microbiome as a whole and used microbiome kernels that are efficient in detecting abundance changes in common taxa, such as Bray-Curtis and weighted UniFrac, abundance differences in Bifidobacterium were likely overshadowed by those in the most abundant genera such as Bacteroides and Prevotella. This discrepancy in results reflects the inherent difference between taxon-level and community-level analyses. On the other hand, none of the genes identified in our community-level analysis was replicated in the taxon-level analysis, highlighting the value of our proposed approach in discovering gene-microbiome associations that involve concerted shifts in the microbial community. Nevertheless, our proposed KRV framework is not meant to replace the existing taxon-level microbiome GWAS approaches, as the two modes of analysis focus on distinct types of genetic features. If one is interested in identifying both loci associated with individual taxa and loci associated with the overall microbiome composition, our proposed framework can be applied in conjunction with existing taxon-level GWAS approaches to provide comprehensive results.We have compared our gene-based community-level analysis to a traditional variant-based taxon-level microbiome GWAS conducted on the same data. While we identified an association between the We have also investigated the replication of signals from previous gut microbiome GWAS studies. Five previously reported beta-diversity-associated genes  have beeWhile we have focused on the application of our proposed approach to microbiome GWAS in this work, the covariate-adjusted KRV can also be applied to investigate the relationships among other types of multivariate omics data. For example, we can investigate microbiome-metabolome relationships by examining the association between microbiome composition and groups of host metabolites that belong to distinct metabolic pathways. Such an analysis was described in one of our previous works , where wWe have proposed a promising approach, the covariate-adjusted KRV framework, to study the covariate-adjusted association between host genetic variation and community-level microbiome composition, which demonstrates good performances in both simulations and real data analysis. The genes and loci identified using our approach will help elucidate the complex interactions among host genetics, gut microbiome and host immune systems. With the increasing collection of various omics data and high-dimensional traits, we expect the covariate-adjusted KRV to bring more discoveries by taking advantage of the innate structure within the omics and phenotypic data.Additional file 1. A PDF file that includes additional methods and results (Section S1-S3), supplemental figures  and short tables (Table S1-S2).Additional file 2. An XLSX file that includes supplemental long tables (Table S3-S5).


Oryza sativa data set is analyzed by SFDAT. It is shown that SFDAT can better perform gene association analysis and eliminate the false positive of gene localization. This study showed that SFDAT can lower the interference caused by noise while maintaining high power. SFDAT provides a new method for the association analysis between gene regions and phenotypic quantitative traits.Functional linear regression models have been widely used in the gene association analysis of complex traits. These models retain all the genetic information in the data and take full advantage of spatial information in genetic variation data, which leads to brilliant detection power. However, the significant association signals identified by the high-power methods are not all the real causal SNPs, because it is easy to regard noise information as significant association signals, leading to a false association. In this paper, a method based on the sparse functional data association test (SFDAT) of gene region association analysis is developed based on a functional linear regression model with local sparse estimation. The evaluation indicators CSR and DL are defined to evaluate the feasibility and performance of the proposed method with other indicators. Simulation studies show that: (1) SFDAT performs well under both linkage equilibrium and linkage disequilibrium simulation; (2) SFDAT performs successfully for gene regions ; (3) With power and type I error rates comparable to OLS and Smooth, SFDAT has a better ability to handle the zero regions. The  In recent years, with the development of high-throughput sequencing technology and the application of second-generation and third-generation sequencing platforms, unprecedented large-scale and high-dimensional genetic variation data have been generated. SNP (single nucleotide polymorphism) or CNVS (copy number variation) have become common genetic markers for studying the genetic mechanism of traits. Linkage disequilibrium-based association analysis has achieved great success in detecting the pathogenic genes of human diseases and the genetic structure of complex traits of animals and plants ,2,3. GenUnivariate association detection is an effective method for common variants in gene association analysis. This analysis method has many advantages and has achieved good results through the improvement of many experts and scholars. The variants in the gene region are detected one by one while using this method. This approach can be adopted for common variants, while for rare variants, other important information contained in their genetic region may be overlooked, such as the location of individual variants, the correlation between variants, etc., so it is easy to underestimate or overestimate the power of a rare variant. To overcome this problem, many association analysis methods based on the genomic region have been proposed, including: OMNI , eSCAN , SKAT 1, SKAT-O There are so many association analysis methods based on genomic regions, but they could be generally divided into three kinds. The first type of method is based on merging ideas ,17,18,19The second type of method is based on the variance component test of the mixed model ,22,23,24The third type of method is based on the functional data analysis (FDA) ,27,28,29Lin et al.  proposedO. sativa was analyzed by SFDAT to demonstrate the applicability of real data of SFDAT.In consideration of these advantages of fSCAD and the problems of gene association analysis methods based on FDA, a new gene association analysis approach called sparse functional data association test (SFDAT) which is based on FDA  was propith individual. For i-th individual, the traditional linear genetic model can be expressed as:T] represents the genomic region under consideration, that is, a DNA fragment that contains multiple SNP loci, among which there may be SNP loci that can affect the target quantitative trait. The discrete genetic markers in Equation (1) are converted into the continuous genetic marker function, and the effects of genetic markers Let For Equation (2), the B-spline function is used to fit the genetic variants and the genetic effects. According to the functional data analysis method ,34: FirsLet The coefficient Let The functional linear model of Equation (2) can be rewritten asLet The form of the linear regression equation is:In the actual operation, the integral interval It can be seen from the equations established above that the genetic variants and effects in the functional linear genetic model are transformed into a continuous function through B-spline. Finally, the functional genetic model is transformed into the traditional linear regression model. In order to obtain the local sparse estimation of n et al. . Lin et n et al.  proposedand Li’s  pλ(•) isIts domain is n and Li  and the For Equation (9), when Another major problem in the genetic study for quantitative traits is whether the association between genetic regions and phenotypic traits is real existence. In general, we consider the following hypothesis-testing questions:Since the genetic effect function is the expansion of the basis function, the above assumption is equal to the following assumptions:ForThe statistic can be defined as:The above statistical test is for the entire gene region tor. Lin  have proTherefore, it is necessary to establish indicators for SFDAT to estimate the effect function in zero or non-zero regions. On the one hand, it can measure the accuracy of the model estimation; on the other hand, it can provide a reference for a more accurate analysis of functional linear model regional association.There are numerous SNP loci in the gene region, and the identified causal SNP loci will inevitably have location deviation, so we regard the region with a total of 200 loci centered on the causal SNP loci as the region of acceptable deviation (Abbr. RAD), that is, we can accept that the identified causal SNP is within the RAD. Then, on the basis of being closer to reality, in order to evaluate the ability of the function to compress the zero regions on the one hand, and measure the accuracy of the function to identify the non-zero region on the other hand, we evaluate the identification ability and the region-selection ability of the model through the correct selection ratio (Abbr.CSR) of zero regions outside RAD and the discovery length (Abbr. DL) for non-zero regions in RAD, which was defined, respectively, by0 and ISE1 can be used to estimate the error between estimated test is the test individual set, For areas with zero or non-zero effects in the integral region, the following integral squared errors (ISE) are defined by Lin :(15)ISE00, ISE1 and PMSE as criteria for evaluating the accuracy of effect estimates for gene regions. To determine the degree of fitting on zero effects, we defineAccording to the above definition, we can define ISE0, the more accurate estimation of zero effects. To determine the degree of fitting on the non-zero effects, we define1, the more precise estimation of non-zero effects. To determine the degree of fit for the genetic model, we defineIn the SFDAT method, the choice of parameter mportant  as long In order to verify the feasibility and effectiveness of the SFDAT method, a computer simulation was carried out. The simulated SNP genotype data were used to study the power, type I error rate and estimation accuracy of the method. To compare the advantages of the SFDAT method, the OLS and Smooth methods were also adopted. The computer simulation code was written in R language.p value of the genetic model under different assumptions; secondly, count the number of p values less than a certain threshold; thirdly, the counted number divided by the total number of simulations, and then the ratio under the non-zero hypothesis is the power and the ratio under the null hypothesis is the type I error rate. The reason for calculating in this way is: under a non-zero hypothesis, there is an associated variant in the region, if the p value is less than threshold p value is still less than threshold The power of the model and type I error rate can be obtained by the following steps: firstly, test Equation (2) to obtain the At last, a test set for each simulation  was generated to calculate the PMSE.In the simulation, we consider the linkage equilibrium and linkage disequilibrium simulation. For the linkage equilibrium simulation, the simulated SNP genotype dataset consists of many simulated gene regions, each of which contains 900 SNPs, and the MAF of SNPs within each region is generated by uniform distribution  and Pan ,38 and sIn the simulation, the number of basis functions For linkage equilibrium and linkage disequilibrium simulation, four kinds of gene regions will be discussed: rare variants gene regions, low-frequency variants gene regions, common variants gene regions and mixed variants gene regions. The rare variant's gene region is constituted by rare variants of which MAFs are generated by uniform distribution Simulated phenotypic trait values were generated byCase I: A total of three scenarios will be considered: Scenario I: setting a positive causal SNP at locus 450 in the gene region; Scenario II: setting a positive causal SNP at locus 100 and 800 in the gene region, respectively; Scenario III: setting a positive causal SNP and a negative causal SNP at locus 100 and 800 in the gene region, respectively. The effect size of each scenario is fixed at 5 . In general, the DL of linkage disequilibrium simulation is smaller than that of linkage equilibrium, that is, the location of the identified causal SNPs is more concentrated.0 and its standard deviation of three methods for linkage equilibrium and linkage disequilibrium under Case II are shown in 0 value or standard deviation of the OLS method is the largest among three methods, while there are smaller and similar results for the Smooth and SFDAT methods; the ISE0 standard deviation of the Smooth method has a larger deviation than that of SFDAT method when the number of causal SNPs in the gene region is small; the ISE0 values are similar (in other words the degree of the fitting is close) when the number of the causal SNPs and the effect size are the same regardless of the proportion of the negative effect; the ISE0 and its standard deviation increase while the number of the causal SNPs and the effect size increase. Compared to the simulation of linkage equilibrium, ISE0 decreased significantly in the regions of common variants and mixed variants under linkage disequilibrium, and slightly increased in the regions of low-frequency variants and rare variants. It is also verified that the models can better fit the zero region of common variants.The ISE1 and its standard deviation of three methods under linkage equilibrium and linkage disequilibrium based on Case II. In the situation of linkage equilibrium, the standard deviation increases as MAF decreases which indicated that three methods fitted better on the common variants in the non-zero region; the ISE1 and its standard deviation of the three methods were similar: as the effect size 1 of linkage disequilibrium simulation is significantly lower than that of linkage equilibrium when the rare variants region exists negative causal SNPs.PMSE and its standard deviation of three methods under linkage equilibrium and linkage disequilibrium in Case II are shown in We set five sample sizes of 500, 1000, 1500, 2000 and 2500, each sample size is simulated 10,000 times. Simulated traits are generated by model 0, the standard deviation of ISE0 and type I error rates are larger than those of Smooth and SFDAT methods, which declares that there may be a false correlation in the association analysis using OSL method, and the zero effect may be recognized as a non-zero effect. In addition, although Smooth has a similar performance to SFDAT in power, ISE1 and PMSE, it does not have the capacity to shrink sparse regions, which leads to noise fluctuations in the application of real data usually and further causes false association. Therefore, if we consider the SFDAT’s performance of the power, type I error rates and combine its performance of other indicators , the SFDAT method would be an excellent method which has extraordinarily high power and has a marvelous ability to reduce false positives.Combining O. sativa) varieties from 82 countries [We apply SFDAT to the data set of 413 diverse rice  method. SFDAT can compress unassociated SNP loci in gene regions without reducing the power too much, and reduces false positives in association analysis. Our simulation studies and real data analysis also show that SFDAT can detect non-effect SNP loci more accurately and compress their coefficients to zero compared to OLS and Smooth, while maintaining higher power and lower false positives. Thus, SFDAT is a powerful tool for GWAS using next-generation sequencing data.