Fusarium Head Blight (FHB) resistance, softness equivalence (SE), and flour yield (FY). Four TP data sampling schemes were tested: (1) use all TP data, (2) use subsets of TP lines with low genotype-by-environment interaction, (3) use subsets of markers significantly associated with quantitative trait loci (QTL), and (4) a combination of 2 and 3. We also correlated the phenotypes of relatives of the TP to their GEBVs calculated from TP data. The GS accuracy within the TP using all TP data ranged from 0.35 (FHB) to 0.62 (FY). On average, the accuracy of GS from using subsets of data increased by 54% relative to using all TP data. Using subsets of markers selected for significant association with the target trait had the greatest impact on GS accuracy. Between-environment prediction accuracy was also increased by using data subsets. The accuracy of GS when predicting the phenotypes of TP relatives ranged from 0.00 to 0.85. These results suggest that GS could be useful for these traits and GS accuracy can be greatly improved by using subsets of TP data.Genomic selection (GS) is a breeding tool that estimates breeding values (GEBVs) of individuals based solely on marker data by using a model built using phenotypic and marker data from a training population (TP). The effectiveness of GS increases as the correlation of GEBVs and phenotypes (accuracy) increases. Using phenotypic and genotypic data from a TP of 470 soft winter wheat lines, we assessed the accuracy of GS for grain yield,  Fusarium Head Blight , and various quality traits. While QTL have been identified for these traits in soft red winter wheat , which is a marker-based breeding tool that estimates all marker effects simultaneously and uses all markers to model the genomic estimated breeding value (GEBV) of individuals  lines and markers while little research has been done on optimizing GS accuracy by systematically selecting or eliminating TP lines or markers. There has been research in animals comparing GS accuracy using high- and low-density SNP chips in GS as the cost of the high-density chips can limit population size (A few studies have been conducted to determine the prediction accuracy of GS models built using the TP data to predict the phenotype of lines from independent data sets. Genomic selection will have the greatest impact on plant breeding when the TP has been optimized to produce the greatest GS accuracy and when phenotypic data from one set of environments can predict performance in a different set of environments. Our objectives were to (1) determine the prediction accuracy of different GS models for four economically important traits of SRWW, (2) determine the ability of the GS model built on TP data to predict the phenotype of different populations of SRWW with varying relationships to the TP, (3) determine the effect of using subsets of TP lines and markers on GS accuracy, and (4) assess the accuracy of a GS model built on data from one environment to predict performance in a different environment.4-derived lines from The Ohio State University SRWW breeding program and is derived from 47 biparental crosses involving 23 parental lines that were selected for desirable GY, FHB resistance, quality, and pedigree diversity . Seed was available for 22 of the 23 parental lines and these 22 lines comprise the parental population (PP) (Table S2). The third population consisted of 94 F4-derived lines from The Ohio State University SRWW breeding program and is called the validation population (VP) (Table S3). Of the 94 VP lines, 85 share some pedigree relationship to the TP: these 85 are termed the VP2 set. Seventeen VP lines were half sibs with some of the TP lines and these 17 are termed the VP3 set.Three populations were used in this study. The first population is the TP and was previously described by ° 46.2’ W 81° 55.8). Grain yield was obtained using a plot combine and seed weight per plot was adjusted to 13% moisture. The FHB index ratings were collected from an inoculated and misted nursery during June 2010 and 2011 in Wooster, Ohio from a randomized complete block design of single row plots with three replicates each year. Index was determined by visually estimating the percentage of symptomatic spikelets in a sample of spikes at about Feekes stage 11, which was about 21 d after heading (Feekes 10.3). A sample consisted of a handful of spikes (∼15 heads per handful) and three areas per plot were sampled. The SE and FY traits were analyzed using the methods of Phenotypic data for the TP were previously described by Phenotypic evaluation of the PP was conducted during 2010–2011 and 2011–2012 growing seasons. The PP lines were included in part of a larger trial that was grown in an augmented design with either one or two replications at the same three locations as the TP . In 2010–2011 there was one replicate at each location and in 2011–2012 there were two replicates in Custar and one replicate in Wooster, Ohio. The augmented design consisted of five blocks per replication each with 38 unique lines and two checks . Planting and harvest dates as well as nitrogen application are the same as described by Best linear unbiased predictions (BLUPs) of line effects were obtained as described by http://www.triticarte.com.au). The genotyping produced 4858 biallelic SNP markers and 28,311 dominant DaRT markers that were scored in the TP. For most of the GS work we only used the 4858 SNPs. Of the 4858 SNPs, 2442 SNP markers were scored in common between the PP, VP, and the TP. When using the TP data to develop GEBVs for the VP and PP lines, we only used the 2442 common markers. All markers used in the analysis had a call rate of at least 70%. Missing data in the TP were imputed based on the average marker score of lines from the same cross. Missing values were imputed as 1 if the average genotype score for other lines from that family was greater than 0 or as −1 if the average was <0. Missing data in the PP and VP populations were imputed as the common allele.DNA for genotyping was extracted from a sample of lypholized leaves collected from two 2-wk-old seedlings per line using a 96-well format . All three populations were genotyped using genotyping-by-sequencing technology by Triticarte Pty Ltd Yarralumla, ACT, Australia . Marker subset 4 varied by trait and included markers associated with each trait at a P < 0.01. For GY, this subset included 604 markers with a P < 0.01 for GYN or GYW. Marker subset 5 varied by trait and contained markers with a P < 0.005 for each trait. Finally, marker subset 6 was created for grain yield only and included 362 markers with P < 0.01, a low residual variance, and the average of the absolute value of allele effects for GYN and GYW greater than 30 kg hectare-1. The number of markers in each set for each trait is shown in Unique subsets of the 4858 SNPs and the 28,311 DaRT markers from the TP were made for each trait using results from an association analysis  conducted in R 3.0.2 using the function ‘eigen’. The scores of the first and second principal components were plotted to create a PCA graph to show how the VP lines grouped with the TP lines.Three GS models were used in the TP with the 4858 SNP markers: Ridge-Regression BLUP (RRBLUP), Bayesian LASSO, and Random Forest. For each model ten-fold cross-validation was used to estimate GEBVs and the accuracy of GS. For cross -validation the TP lines in the prediction set were randomly selected without replacement allowing GEBVs of all 470 lines to be predicted within one cycle. Each model was implemented in R 3.0.2 (R Development Core Team 2011) using a Windows 2008 64-bit virtual machine with a 3.46 GHz Intel(R) Xenon(R) CPU processor and 32.0 GB of RAM.X is the design matrix for the fixed effects Z is the design matrix for the random effects u, u are the random effects, K is a positive semidefinite matrix that accounts for the relatedness among individuals based on markers, and A, the kinship matrix, and RRBLUP was conducted using the ‘rrBLUP’ package 4.2 in R . The funvariance . The resgenotype . The RRBc) was calculated as r is the accuracy of the model and H is the heritability of the trait (y) was determined by multiplying the REc by the ratio of years to complete one cycle of phenotypic selection vs. years to complete one cycle of GS for each trait. In our program it is estimated to take 7 yr for one cycle of phenotypic selection for grain yield and 5 yr for one cycle for FHB, FY, and SE. One cycle of GS can be completed in 1 yr in winter wheat. Finally, proc.time was used to determine the length of time to complete 300 cycles of 10-fold cross-validation for each GS model.The accuracy of a GS model was determined using a Pearson’s correlation between the GEBVs of all lines and their phenotypic BLUP. The relative efficiency per cycle of GS as compared to a cycle of phenotypic selection  of each of the PP lines could be calculated to assess the ability of the GS model to predict the TBVs. The TBV of the ith PP line was calculated for each trait using the equation:The RRBLUP model was retrained using the TP phenotypic and data from markers that were scored in both the TP and the VP to obtain GEBVs of each VP line using the same method as described for the PP population. The prediction accuracy was determined using a Pearson’s correlation between the GEBVs of the VP lines and their phenotypic BLUPs. Accuracy was determined using the entire VP data set, as well as for the VP2 and VP3 subsets.The authors state that all data necessary for confirming the conclusions presented in the article are represented fully within the article.Phenotypic data from the TP were previously described by Using only RRBLUP we obtained nearly identical accuracy using all 33,169 markers or just the 4858 SNPs. We decided to use just the 4858 SNPs to compare the accuracy of GS with different models as some models can take far too much time with 33,169. Using 10-fold cross-validation the RRBLUP and Random Forest models had the highest accuracies for all traits and produced nearly identical results . The Bayvs. phenotypic selection per cycle (REc) and per year (REy) was calculated. All assessments of relative efficiency showed GS to be more efficient than phenotypic selection. The greatest REy for any grain yield trait was found for GYW (4.8), which was the grain yield trait with the highest accuracy and the highest heritability.The relative efficiency of GS vs. phenotypes while the accuracy for SE and FHB was greatly reduced. The difference between the mean phenotype of the top three (T3) and bottom three (B3) PP lines showed that the T3 group was always superior to the mean of the B3 group for all traits and this difference was significant at P < 0.1 for GYW, SE, and FHB.We assessed the ability of GS to predict the phenotypes of related lines that were phenotyped in independent environments. We used RRBLUP and all TP data to calculate the GEBVs of the PP and VP lines and estimated accuracy by correlating those GEBVs with the phenotypes of the PP and VP lines using both unweighted and weighted correlations. The RRBLUP model was chosen because it was more efficient  than Random Forest or Bayesian LASSO. The accuracy of GS models based on the TP data to predict the PP phenotypes was considerably greater for all traits when we used a weighted correlation than an unweighted correlation . The accP < 0.1.In general all accuracies from using TP data to predict the GEBVs of the VP lines were low and all were lower than those observed when using the PP phenotypes and weighted correlations . AssessiThe results of the simple matching coefficient indicate the VP and the TP populations are related. The average genetic similarity within each population alone was 0.69, while the average genetic similarity between the VP and TP was 0.68. The PCA also shows a relationship between the VP lines and the TP lines .The accuracy of the GS model was determined using data subsets derived from the TP by (1) removing TP lines with high GEI from the TP for each trait and (2) selecting markers based on results from an association analysis conducted using the TP data .e.g., all markers minus the subset 2 markers) for each trait. These subsets of nonsignificant markers produced within-environment GS accuracies that were on average 20% lower than the accuracy obtained using all marker data, and 46% less accurate than using marker subset 2 (Table S4).The GS accuracy was increased when using data from all TP lines and subsets of significant markers for all traits except GYN . ExcludiThere was a positive interaction between using subsets of TP lines and subsets of markers for GYA, GYN, and FHB where the greatest accuracies were obtained using the combination of a subset of lines with low GEI and marker subset 2: these accuracies were 75% (GYA), 113% (GYN), and 121% (FHB) greater than the accuracy obtained using all TP data . For GYWe.g., GYW data or GYN data) were used to build a GS model that was then used to predict the phenotype of the TP lines in the other set of environments. The accuracies of these between-environment predictions were low and negative when using all TP data (r = 0.37) was found using the 400 low GEI lines and marker subset 6. This set contained 362 markers that had low residual variance, were significant for GYW or GYN, and the absolute value of allele effects for GYW or GYN were greater than 30 kg hectare-1. Similar, positive accuracies for between-environment predictions for grain yield were also found with the other marker subsets. The results were similar when using either GYW or GYN to train the model and predicting the other environment.Phenotypic data for grain yield in the TP from only one set of environments  were used to build a GS model that was used to predict the phenotype of the TP lines in the other year. When using all marker data the GS accuracy for between-year was low for FHB (range 0.13 to 0.16) and moderate for SE and FY (range = 0.24 to 0.59) when using either all TP lines or the subsets of lines with low GEI . The GS For SE and FY, removing lines with high GEI did not increase prediction accuracy between years regardless of marker subset . Using re.g., all markers minus the subset 2 markers) for each trait. These subsets of nonsignificant markers produced between-environment GS accuracies that were on average 15% lower than the accuracy obtained using all marker data, and 33% less accurate than using marker subset 2 (Table S4).We also evaluated GS accuracy using all nonsignificant markers  compared to GYW (H = 0.69) and likely explains why accuracy for GYN was lower than GYW. The accuracies for grain yield using all TP lines and marker data ranged from 0.41 to 0.57  environment alone . During  to 0.57  and are The GS accuracy for FHB using all TP data was 0.35, which is lower than most other reports for FHB resistance. In barley, the accuracy of GS for predicting the percentage of FHB infected kernels ranged from 0.41 to 0.67 . Heffnerc) of GS across traits mostly reflected the GS accuracy. The REc for SE and FY in this study  ranged from 2.4 (FHB) to 4.8 , the prediction accuracy was increased for all traits except GYN  was found using the subset of 400 lines with low GEI and marker subset 6 . The majority (99%) of the markers in subset 6 are not in linkage disequilibrium (LD) with one another suggesting these markers are likely mostly tagging independent QTL.Using data from one set of environments to predict the performance in independent environments is the crux of plant breeding. The GS prediction accuracy between environments for grain yield was very low  when usir = 0.42) was greater than the correlation of FHB phenotypes between environments (r = 0.32). However, for SE the highest accuracy between environments was lower than the correlation of phenotypes between environments (r = 0.81) and for FY was equal to the correlation between environments (r = 0.72).As with grain yield, the between-environment prediction accuracies for FHB, SE, and FY were lower than when using data from both years to build the model and it varied depending on which year’s data were used to build the model. For these traits using a subset of lines with low GEI had little impact on improving accuracy . Using sFor grain yield, removing lines with high GEI likely allowed the model to more accurately estimate genetic effects and GEBVs. A line’s mean phenotype within an environment is due in part to its genetic effect and in part to the GEI of that line with the environment: the calculated GEI is due in part to true GEI but also in part to experimental error that may be confounded with that line and that environment. It is interesting that the accuracy of GYA and GYW decreased  when using a subset of lines, but increased when using subsets of markers. In contrast, the GS accuracy for GYN and the between-environment GS accuracies only increased when using both the subset of lines and subsets of markers. This could be due to the error (noise) present in the phenotypic data for GYN, likely caused by the water damage to these plots. Most of the 70 lines with high GEI variance that were removed had negative GEI with the GYN environment and positive GEI with Wooster. This likely led to underestimating the true yield potential of these lines in the GYN environments while data from the Wooster environments were more indicative of their true genetic value. Including these high GEI lines in any analysis adds noise to the GYN data set and that reduces our ability to predict GYN, or the ability of GYN data to predict grain yield elsewhere. Thus GS accuracy is low for GYN and between-environment predictions when using data from all TP lines even with the reduced marker subsets. This is not a problem when using GYW or GYA data (GYW is a component of GYA) as the GYW phenotype data likely more accurately reflected true genetic values than did the GYN phenotypic data. Prediction accuracy for GYA and GYW increased using just subsets of markers as the markers were selected for significance for GYW or GYN, which means they were discerning genetic effects from noise.y observed for these traits in the TP indicate that GS could be very useful for improving these traits. This conclusion is further supported by the ability of the TP data and GS model to predict the performance of the parents of the TP. For all traits, the accuracy of GS can be greatly increased by using subsets of markers that are significant for the trait. The increase can be even greater when also using a subset of lines with low GEI for some traits. Increases of GS accuracy within the TP using cross-validation of up to 131% were attained by using data subsets. Even using marker subsets containing <7% of the total markers produced greater accuracies than using all markers. The increase in accuracy from using subsets of TP lines and/or markers is similar to what other studies have shown one would expect by increasing the TP size and number of markers . However, our results suggest that a small subset of selected markers can provide more accurate GS predictions than a large number of markers. It is important to note than one must have a large number of markers and TP lines to begin with to have accurate estimates of genetic effects and genome coverage. From the large set of markers you can systematically select lines and markers to form a small and more informative subset that produces the greatest accuracy for use when implementing GS. These small marker subsets may allow the use of alternative genotyping platforms that are less expensive and more repeatable than GBS in future cycles of GS initiated from the TP. In plant breeding it is difficult to add more lines to a TP to increase the accuracy of GS as this greatly increases phenotyping resources. The TP size must allow for efficient phenotyping over multiple environments in order to accurately estimate GEI and marker effects. This study removed 5 to 17% of the TP lines based on GEI: the remaining lines must form a TP of sufficient size to provide robust estimates of genetic effects. These results suggest that starting with a large number of lines and markers in the TP allows one to select for the most informative ones to use in generating GS models with improved accuracy that can then be used when implementing GS.


P-values” (ADA) method removes variants with larger P-values. However, when both rare and common variants are considered, it is not optimal to truncate variants according to their P-values. An alternative summary measure, the Bayes factor (BF), is defined as the ratio of the probability of the data under the alternative hypothesis to that under the null hypothesis. The BF quantifies the “relative” evidence supporting the alternative hypothesis. Here, we propose an “adaptive combination of Bayes factors” (ADABF) method that can be directly applied to variants with a wide spectrum of minor allele frequencies. The simulations show that ADABF is more powerful than single-nucleotide polymorphism (SNP)-set kernel association tests and burden tests. We also analyzed 1,109 case-parent trios from the Schizophrenia Trio Genomic Research in Taiwan. Three genes on chromosome 19p13.2 were found to be associated with schizophrenia at the suggestive significance level of 5 × 10−5.Multi-marker association tests can be more powerful than single-locus analyses because they aggregate the variant information within a gene/region. However, combining the association signals of multiple markers within a gene/region may cause noise due to the inclusion of neutral variants, which usually compromises the power of a test. To reduce noise, the “adaptive combination of  P-values” (ADA) method was proposed for the analyses of unrelated subjects2 and family data3.Multi-marker association tests can be more powerful than single-locus analyses because these tests combine variant information within a gene/region. Moreover, the multiple-testing penalty is moderate compared with that encountered in single-locus analyses. However, combining the association signals of multiple markers within a gene/region may cause noise due to the inclusion of neutral variants, which usually compromises the power of a multi-marker association test. To eliminate noise from neutral variants, the “adaptive combination of 2. While “rare” is frequently defined arbitrarily, here, according to Ionita-Laza et al.4, we defined variants with a minor allele frequency (MAF) n is the number of individuals in the study. The per-site P-values were first calculated for each individual variant site, and the ADA method was used to truncate larger per-site P-values that were more likely to be attributed to neutral variants. The P-value is the probability of obtaining a statistic as extreme as or more extreme than the observed statistic under the null hypothesis (H0) of no association. However, a P-value provides no information regarding the alternative hypothesis (H1). For example, a P-value of 10−9 may appear to provide strong evidence against H0; however, if the test is low-powered, it may be almost as unlikely under H1 as under H07. In genome-wide association studies (GWAS), the power to detect disease-associated single-nucleotide polymorphisms (SNPs) varies with MAFs. In this work, we show that truncating variants according to P-values is not optimal, when both rare and common variants are considered .The ADA method was originally proposed for rare-variant association testing8 have extended the ADA method to address both rare and common variants . However, the RC-ADA method also truncates neutral variants according to their P-values. In RC-ADA8, rare variants and common variants are weighted according to Beta and Beta4, respectively, where MAF is the MAF of the considered SNP. Compared with the commonly used weight function Beta, Beta decreases slowly as the MAF increases. RC-ADA preserves the associations of common variants by assigning them this weight function.Zhou and WangP-value is the Bayes factor (BF)10, which is the ratio of the probability of the data under the alternative hypothesis to that under the null hypothesis, as follows:H1 and H0 are the alternative hypothesis and the null hypothesis, respectively. In this work, we show that truncating variants according to BFs is superior to truncating variants according to P-values, because BFs quantify the “relative” evidence supporting H1. Here, we propose an adaptive combination of BFs (ADABF) method by extending our previous ADA method2 and the “adaptive rank truncated product” (ARTP) method12. As described in the “Methods” section, the highest k BFs in favor of H1 are combined, in the observed sample and in each of the resamples, respectively. The optimal k that achieves the strongest signal is allowed to vary in the observed sample and in each of the resamples. Then, the significance of the gene/region is assessed by comparing the strongest signal in the observed sample with its counterparts in the resampling replicates.An alternative summary measure to the 13. In the VT approach, Price et al. assume that a certain unknown MAF threshold, T, exists, and variants with MAFs lower than T are more likely to be disease-associated. Therefore, they compute the statistic for each MAF threshold and then search for the optimal MAF threshold with permutations. However, the MAF has little relevance to the association signals15. Disease-associated variants can be either rare or common. Here, we propose the ADABF method, which is based on the concept of VT, but we assume that a certain unknown BF threshold exists, and variants with BFs larger than this threshold are more likely to be disease-associated.The logic underlying this work can be traced back to the “variable-threshold (VT)” approach19. Various multi-marker methods and the single-locus transmission disequilibrium test (TDT)21 were then applied to the empirical data from the Schizophrenia Trio Genomic Research in Taiwan (S-TOGET)22.By performing extensive simulations with case-parent trios and unrelated case-control data, we find that our ADABF test is valid because the type I error rates match the nominal significance levels. Moreover, the ADABF test is more powerful than the other gene-based tests−6 (24). The power for each scenario was evaluated using 10,000 simulation replicates (100 replicates for each Cosi data set). The ADABF method outperformed the other multi-marker tests because it excluded the variants with smaller BFs.Table 6, the purpose of adding ADABF1 was to evaluate the sensitivity of the results to the prior setting. ADABF1 (standard deviation of the prior distribution = 0.1) performed similarly to ADABF . ADA also performed well because it truncated the variants with larger P-values. The popular kernel test (denoted by “TK”) was more powerful than the burden test . Because the percentage of causal variants When the haplotypes were generated according to the linkage disequilibrium (LD) patterns in Asians, the simulation results were similar to the abovementioned findings  simulated exome data28. The “Davies” method was used to compute the P-values29. VW-TOW was implemented using the R code downloaded from the authors’ website, i.e., http://www.math.mtu.edu/~shuzhang/software.html, and the number of permutations was set as 106. The rare variant threshold (RVT) used in VW-TOW was set as n is the sample size (697). Age and smoking status served as covariates adjusted in TLC, TK, and VW-TOW.TLC and TK were performed using the “SKAT” R package (version 1.2.1)2, we first considered the linear regression for each locus as follows:Y is the quantitative trait (Q4 or Q1) and Gl is the genotype score  of the lth variant . We obtained the maximum likelihood estimate (MLE) of βl  and the corresponding variance by fitting the linear regression (Eq. βl’s) was assumed to be N, where the prior variance was W = 0.22 = 0.04 for ADABF and W = 0.12 = 0.01 for ADABF1 .To perform ADABF, ADABF1, and ADAP-values of ADABF, ADABF1, and ADA2 were all obtained using the sequential resampling approach26 in which the minimum and maximum numbers of resampling were set as 102 and 107, respectively.The P-values for each multi-marker association method. Because Q4 did not depend on any variant, we assessed the type I error rates by calculating the percentages of the 641,000 P-values that were smaller than the significance level, i.e., To assess the type I error rates, for each replication, we sequentially tested the association of each gene with Q4. Summarizing 200 replications, we obtained 641,000 = 200 × 3205) 205 P-val27. Among the nine genes, the power for six genes  was smaller than 0.1 for all the tests and it was impossible to compare the different methods using this very low power. The second to fourth rows shown in Table KDR, FLT1, and HIF1A, respectively. For each gene and each method, we obtained 200 P-values after analyzing all the 200 replicates. We quantified the power by calculating the percentage of the 200 P-values that were smaller than the significance level . In contrast to the small causal percentage in the abovementioned simulations . We confirmed that all experiments were performed in accordance with the relevant guidelines and regulations.A portion of the Taiwanese case-parent trios obtained from the S-TOGET from 2009 to 2014 were subjected to GWAS genotypingTotally 3,374 subjects were genotyped using the PsychChip array, which was developed by the Psychiatric Genomics Consortium (PGC) and Illumina . After removing individuals with call rates < 98%, Mendelian errors, or sex inconsistency, 1,109 case-parent trios were used for analysis.P-value < 10−6 in controls), 325,994 autosomal markers were retained for analysis.The PsychChip array (PsychChip_15048346_B) included ~580,000 markers in total. After removing invariant markers, markers with call rates < 98%, and markers that were significant for the Hardy-Weinberg equilibrium test . We also included the 5’ and 3′ flanking regions of each gene. The 5′ flanking region may contain regulatory sequences such as promoters that control gene transcription. The 3′ flanking region may contain sequences that terminate transcription. Multi-marker analyses may include ±5 kb35, ±10 kb36, ±20 kb37, or ±30 kb38 flanking regions of a gene. Because incorporating additional flanking sequences increases the coverage of more distant regulatory elements, we grouped the variants within ± 30 kb flanking regions of a gene into a multi-marker analysis according to Song et al.38. In total, there were 24,769 autosomal genes.We then resorted to multi-marker analyses. Because the SNP positions of the S-TOGET data were based on the human genome GRCh37/hg19 assembly, we mapped variants into genes according to the same assembly in the UCSC Genome Bioinformatics database −6. Three genes on chromosome 19p13.2, including EVI5L , PRR36 (proline rich 36), and LYPLA2P2 (lysophospholipase II pseudogene 2), were detected to be associated with schizophrenia at the suggestive significance level of 5 × 10−5. This is a consistent result across all the five gene-based association tests except TLC.As shown in Fig. EVI5L-PRR36-LYPLA2P2 region are described in Table The 13 SNPs in the In this work, we proposed the “adaptive combination of Bayes factors” (ADABF) method, which is applicable to a mixture of common and rare variants and can be applied to GWAS or next-generation sequencing (NGS) data.39. Based on our analysis for the S-TOGET trio data, three genes in this region, including EVI5L, PRR36, and LYPLA2P2, were detected to be associated with schizophrenia at the suggestive significance level of 5 × 10−5. Four multi-marker tests including ADABF, ADABF1, ADA, and TK all suggest that PRR36 is the most significant gene. This gene encodes a large protein - Proline Rich Protein 36 (PRP36)40. The second significant gene identified by the four multi-marker tests is EVI5L. It is also a protein-coding gene, but its function remains unknown41. The third significant gene identified by the four tests is LYPLA2P2, which is a pseudo gene42.Chromosome 19p13.2 has been found to be associated with panic disorderEVI5L-PRR36-LYPLA2P2 region (7865161–7975117 base pair) is MAP2K7 . Knocking out MAP2K7 results in schizophrenia-like behavioral deficits in mice45. A substantial effect size was observed for common variants in a case-control sample from the Glasgow area and a replication sample of Northern European descent47.The gene next to the EVI5L gene, the most prominent signal was achieved by combining the top four significant SNPs , with a variance of W = 0.22 = 0.04] as the prior for ADABF. To evaluate the sensitivity of our results to this choice, we also considered another prior variance, i.e., W = 0.12 = 0.01. We found that our simulation and the S-TOGET results were very stable across these two settings. As noted by Stephens and Balding5, W can be chosen dependently on the MAF according to prior settings that are believed to best fit the underlying genetic architecture of a disease. Therefore, theoretically, we can develop better ways to prioritize SNPs.In this work, we used the prior in the WTCCC GWAS48, schizophrenia49, and type 2 diabetes50. Certain specialized arrays such as PsychChip were designed for the detection of both common and rare variants. There is a need to develop a powerful method for the joint analysis of rare and common variants. Compared with ADA2 and RC-ADA8, our ADABF method is recommended for its applicability to variants with a wide spectrum of MAFs. Compared with other multi-marker association tests such as TLC51, TK28, and VW-TOW18, our ADABF method is recommended for its robustness to the inclusion of neutral variants.With the advent of NGS technology, there has been a great interest in rare-variant association testing. However, both rare and common variants contribute to the etiology of complex diseases such as the Hirschsprung diseaseM1  and M2, the TDT tests whether the M1 allele is transmitted to an affected child more often than the M2 allele from heterozygous parents20.Here, we describe the method to analyze case-parent trios, but it can be generalized to unrelated case-control analyses. For a variant with two alleles, i.e., M1 compared with allele M2. We denote b be the number of transmissions of M1 from heterozygous parents to the affected offspring, and let c be the number of such transmissions of M2. We then obtain β~N. Throughout this work, we follow the WTCCC GWAS6 to specify the prior variance, i.e., W = 0.22 = 0.04. The prior distribution is presented in the left column of Figure Let OR be the odds ratio of allele W = 0.12 = 0.01  was generated according to the following model:Gc was the genotype score  of the causal variant, and the effect size was x-axis in Fig. P-value  the BF ranking was superior if RB < RP, (2) the BF ranking was identical to the P-value ranking if RB = RP, and (3) the BF ranking was inferior if RB > RP. According to Table P-value, across all ranges of causal-allele frequencies. As the MAF of the causal variant increased, the power to detect that causal variant also increased and both mean ranks improved. More replicates showed that the BF ranking outperformed the P-value ranking, across all ranges of causal-allele frequencies.Let P-value ranking, rare causal variants will benefit from the BF ranking  and a larger P-value but a smaller P-value = 0.2 may actually be a neutral variant, because this large P-value is obtained from reliable information , instead of P-values.Compared with the BFl be the BF of the lth variant. Denote the ordered BFs by BF(1) ≤ BF(2) ≤ … ≤ BFL)( for a region containing L variants. The summary score aggregating the highest k BFs is as follows:I(BFl ≥ BFk) is 1 if the lth variant is among the top k most significant variants according to BF, and is 0 otherwise. Because the natural logarithm of the BF is linked to log-likelihoods, log(BF) is considered the “weight of evidence”10. Therefore, in Eq. (L variants in the region of interest. Because log(BF) represents the “weight of evidence”10, we do not impose any additional weight according to the MAF. As previously mentioned, the MAF has little relevance to association signals15. Disease-associated variants can be either rare or common. If we believe that rare variants are more likely to be non-neutral, the Beta function can be used to weight the contribution of individual BFs.Let S1, …, SL for a region containing L variants. Then, we use the efficient sequential resampling approach proposed by Liu et al.26 to assess the significance of the association between the region and a disease. The procedure is performed as follows:(i)B = 100 sets of L × 1 vector of point estimates under the null hypothesis) from the multivariate normal distribution N, where the th element of VL × L is i, j = 1, …, L. Recall that ith variant, such as Eq. bth set of k , we compare Sk with Skb) and obtain the P-value of Sk by P-value across k , which is denoted by MinP. The minimum P-value of the bth resample is calculated similarly and denoted by MinPb)P-value based on 100 sets of B = 1,000) to increase the precision of the P-value. This procedure is repeated until the P-value is larger than If the adjusted Based on Eq. , we obtahttp://homepage.ntu.edu.tw/~linwy/ADABF.html.The R code of our ADABF method can be downloaded from W = 0.22 = 0.04) was compared with the ADABF1 (prior variance W = 0.12 = 0.01) and ADA tests2. To make a fair comparison, these three tests were all performed using the “adaptive rank truncated product” (ARTP) method12. Therefore, the highest k BFs  are combined, in the observed sample and in each of the resamples, respectively. The abovementioned sequential resampling approach26 was used to assess the significance of the association between the region of interest and the disease, and the minimum and maximum numbers of resampling were set as 102 and 107, respectively.The ADABF test (prior variance 16 and the “SKAT” R package (version 1.2.1)28, to analyze the case-parent trios and unrelated subjects, respectively. To make a fair comparison, we did not assign any MAF-weighting function to the TLC, TK, ADABF, ADABF1, or ADA tests.Furthermore, the TLC and TK tests were performed for comparison. These two tests were performed using the “rvTDT” R package (version 1.0)18. VW-TOW is a test used to detect associations of rare and common variants, and was proposed by Sha et al.18. These authors divided the variants into rare (if MAF < RVT) and common (if MAF ≥ RVT), and then searched for the optimal weights for the two groups of variants, separately. The statistics from the two parts of the variants were then combined, and the P-value was calculated with permutations. This test was performed using the R code, which was downloaded from the authors’ website at http://www.math.mtu.edu/~shuzhang/software.html, and the number of permutations was set as 10,000. The RVT was set as n was the sample size4. Because VW-TOW was proposed for the analyses of unrelated individuals18, it was not evaluated for case-parent trio data.For the analysis of unrelated subjects, we also compared ADABF with VW-TOW54, we generated 100 data sets following the LD patterns in Europeans. Each of the 100 Cosi data sets contained 10,000 chromosomes from a 20 kilo base (kb) pairs region. That is, totally 100 20-kb regions were considered. On average, ~150 variants could be observed in a 20-kb region. The distribution of the MAFs of the variants is shown in Figure 55.With the Cosi programY = 1 denotes disease) was generated according to the following model:α = −2.94. To study the power, the disease status was generated according to the following model:α = −2.94, d was the number of causal variants (d = 2 or 4), Gkc was the genotype score  of the kth causal variant, and the effect sizes were β was positive or negative depending on whether the causal variant was deleterious or protective, respectively. When All causal variants were deleterious andIn total, 50% of the causal variants were deleterious, and 50% of the causal variants were protective.To evaluate the type I error rates, the disease status (The following two data structures were simulated: (1) 2,000 case-parent trios and (2) 2,000 unrelated subjects, of which 1,000 were cases, and 1,000 were controls.Supplementary Information


Next-generation sequencing technology makes directly testing rare variants possible. However, existing statistical methods to detect common variants may not be optimal for testing rare variants because of allelic heterogeneity as well as the extreme rarity of individual variants. Recently, several statistical methods to detect associations of rare variants were developed, including population-based and family-based methods. Compared with population-based methods, family-based methods have more power and can prevent bias induced by population substructure. Both population-based and family-based methods for rare variant association studies are essentially testing the effect of a weighted combination of variants or its function. How to model the weights is critical for the testing power because the number of observations for any given rare variant is small and the multiple-test correction is more stringent for rare variants. We propose 4 weighting schemes for the family-based rare variants test (FBAT-v) to test for the effects of both rare and common variants across the genome. Applying FBAT-v with the proposed weighting schemes on the Genetic Analysis Workshop 19 family data indicates that the power of FBAT-v can be comparatively enhanced in most circumstances. Hypertension or high blood pressure is a chronic medical condition with unknown complex etiology . Blood pxim denote the genotype  of the ith individual at the mth variant. Both population-based and family-based methods for rare variant association studies are essentially testing the effect of a weighted combination of variants, ∑mwmxim, or its function. How to model the weights wm is critical for the testing power because the number of observations for any given rare variant is small and the multiple-test correction is more stringent for rare variants [However, existing statistical methods to detect common variants may not be optimal for detecting rare variants because of allelic heterogeneity and the extreme rarity of individual variants . Recentlvariants . Family-variants . To poweThe GAW19 data consists of a whole genome sequencing data set for a large-scale pedigree-based sample that includes 959 individuals. Among the 959 individuals, 849 have simulated phenotypes in all 200 replicates. Our analysis focuses on the family data of the 849 individuals. We applied FBAT-v with the proposed weighting schemes to the GAW19 family data. Our results indicate that the type I error rates for all the methods compared are under control and the power of the FBAT-v with an optimal weight outperforms the methods compared in most circumstances.n trios. Each individual in the sample has been genotyped at M variants in a genomic region. Denote yi as the quantitative trait for the ith offspring. Denote Xi = T as the genotypic score of the ith individual, where xim ∈ {0, 1, 2} is the number of minor alleles that the ith individual has at the mth variant.Consider a sample of p covariates. Let T denote covariates of the ith individual. We adjust both trait value yi and genotypic score xim for the covariates by applying linear regressions. That is,Suppose that we have ỹi and yi and xim, respectively. Denote ith individual.Let To test the null hypothesis of no association, the weighted family-based association test (FBAT) statistic for rare variants (FBAT-v)  can be dZ approximately follows N in large samples under the null hypothesis of no association. For large pedigrees, pedigrees are decomposed into nuclear families which are treated as independent unless a trait locus is known to be linked to the markers under test. The pedigree’s contribution to the tests statistic is obtained by summing over all nuclear families within the pedigree. However, in the case where linkage is present and the null hypothesis states “no association but linkage presents,” the genotypes of the different nuclear families derived from 1 pedigree are correlated. In this case, the variance of Ww): genotype risk value (grv); log odds ratio (lor); and optimal weight (ow).To increase the power of FBAT-v, we propose the following 3 weighting schemes that use only founders’ information. In the family data, founders are individuals who have no parents specified  weighting scheme is based on genotype frequencies and effect sizes for each single-nucleotide polymorphism (SNP) from the single-variant study. Comparing the continuous trait with a prespecified threshold, we can classify subjects into 2 categories: cases and controls. Assume that AA, AB, and BB  are genotypes for a SNP. Based on the log-additive model, the 3 genotypes have a relative risk of 1, odds ratio (OR), OR2, respectively. If the B allele has frequency p, then the average relative risk (ARR) in the population can be calculated as: ARR = (1 − p)2 + 2p(1 − p)OR + p2OR2. 1/ARR, OR/ARR, and OR2/ARR are assigned as weights for genotype AA, AB, and BB, respectively. This weighting scheme puts big weights on variants with more copies of the risk alleles.The log odds ratio (lor) weighting scheme is based on effect size for each SNP from the single-variant study. Similarly, comparing the continuous trait with a prespecified threshold , we can classify subjects into 2 categories: cases and controls. We can then build a logistic regression model by adjusting for covariates such as age, gender, and smoking status. The weight for each individual SNP is determined by the lor of its association with disease. This weighting scheme puts big weights on variants with large effect sizes associated with disease.The optimal weight (ow) wso was first proposed by Sha et al. [The a et al.  in a popρ is the correlation coefficient between trait value residuals ỹ of unrelated individuals and genotypic score residuals. This weighting scheme gives large weights to rare variants that have small allele frequencies and strong associations with the trait of interest.grv, lor, and ow—can adjust the direction of the association, which potentially can boost power of FBAT-v as FBAT-v only focuses on all the variants having effects in the same directions and can lead to lower power when there are variants with effects in the opposite directions. In addition to the aforementioned weighting schemes, we also propose to use functional prediction scores as weights in FBAT-v. By incorporating computational predictions of the functional effects of nonsynonymous variants into FBAT-v, it can avoid the loss of power that results from combining both functional and nonfunctional variants [All the aforementioned weighting schemes—variants .http://snpEff.sourceforge.net) [http://genetics.bwh.harvard.edu/pph2) [Price et al.  first inrge.net)  to predidu/pph2) . We assigrv, lor, ow, and functional prediction (fp)—to the GAW19 family data, which consists of a whole genome sequencing data set for a large-scale pedigree-based sample of 959 individuals. Among the 959 individuals, 849 have simulated phenotypes in all 200 replicates. Our analysis focuses on the family data of the 849 individuals. The genotype, phenotype, and other information of 108 founders  out of the 849 individuals are used to calculate the grv, lor, and ow weights.We apply the FBAT-v method incorporating the proposed weighting schemes—To evaluate type I error rates and the power of FBAT-v incorporating the 4 different weighting schemes, we employ the complete set of 200 replicates in the GAW19 family data. Significance is assessed in significance levels of 0.1, 0.05, and 0.01. For power comparisons, FBAT-v with the 4 weighting schemes is compared with FBAT-v with the weighting scheme based on allele frequencies as in De et al. . In our MAP4 of chromosome 3. Q1 in the family data set is simulated as a normally distributed quantitative trait that is correlated among family members (additive genetic heritability = 0.68), but not influenced by any of the genotyped SNPs. Therefore, any observed associations are false positives. Table grv weights using empirical variance (FBAT-v-e-grv); FBAT-v with lor weights using empirical variance (FBAT-v-e-lor); FBAT-v with ow weights using empirical variance (FBAT-v-e-ow); and FBAT-v with fp weights using empirical variance (FBAT-v-e-fp). The type I error rates of FBAT-v with all the 5 weighting schemes are under control.To estimate the type I error rates, using our proposed approaches, we test association between the simulated trait Q1 and a region including 28 SNPs selected from gene MAP4, TNN, NRF1, LEPR, and FLT3) influencing simulated SBP or DBP.To evaluate the performance of our approaches, we compare the power of FBAT-v-e, FBAT-v-e-grv, FBAT-v-e-lor, FBAT-v-e-ow, and FBAT-v-e-fp in detecting association between SBP or DBP and the top 5 genes (http://genome.ucsc.edu/). Table Genes were defined by transcription start and end positions obtained from the University of California Santa Cruz (UCSC) Genome Browser hg19 build  and the lower heritability (<5 %). We did notice that FBAT-v-e-fp performs better in gene TNN than other methods. One possible reason is that there are more functional variants residing on this gene.Table grv and ow weighting schemes can boost FBAT-v’s power when the proportion of rare variants is large  and total variance being explained is relatively big . However, when the total variance being explained is less than 5 %, all of the methods have almost no power to detect rare variants. One possible reason is that the FBAT is essentially a burden-type test. Although the proposed weighting schemes of grv, lor, and ow can adjust the direction of the association, it still can lose power when rare variants in a gene act in different directions on phenotypes. A variance-component based FBAT [In this article, we propose 4 weighting schemes for the FBAT-v. Simulation studies indicate that both the sed FBAT  could begrv and lor are based on the effect size estimates from the marginal association. However, estimates are not stable when the variants are rare. This can be reflected from the unstable power of FBAT-v-e-grv and FBAT-v-e-lor when detecting gene NRF1 in Table The proposed weights


A matrix (pedigree) was used and 0.14 ± 0.01 when H matrix (relationship matrix that combines pedigree information and SNP data) was used. A total of 147 candidate genes for stayability were identified on chromosomes 1, 2, 5, 6, 9 and 20 and on the X chromosome. New candidate regions for stayability were detected, most of them related to reproductive, immunological and central nervous system functions.Stayability, which can be defined as the probability of a cow calving at a certain age when given the opportunity, is an important reproductive trait in beef cattle because it is directly related to herd profitability. The objective of this study was to estimate genetic parameters and to identify possible genomic regions associated with the phenotypic expression of stayability in Nellore cows. The variance components were estimated by Bayesian inference using a threshold animal model that included the systematic effects of contemporary group and sexual precocity and the random effects of animal and residual. The SNP effects were estimated by the single-step genomic BLUP method using information of 2,838 animals  genotyped with the Illumina High-Density BeadChip Array . The variance explained by windows formed by 200 consecutive SNPs was used to identify genomic regions of largest effect on the expression of stayability. The heritability was 0.11 ± 0.01 when  There is growing concern regarding the increase in the world population and the consequent increasing global demand for food. One solution to mitigate a possible food crisis is to increase animal productivity. According to FAO estimates, by 2050, Brazil will be responsible for providing 40% of the global food demand. The country currently possesses about 219 million cattle 10] for SThe inclusion of single nucleotide polymorphisms (SNPs) in analyses has allowed more accurate genetic evaluations of different productive traits, with a special advantage for the evaluation of traits that are expressed late and that require the implementation of a progeny test for the evaluation of sires, as is the case of STAY . A simplThe objective of the present study was to identify and investigate genomic regions with the largest effect on the expression of STAY in Nellore cattle. The identification of these genomic regions will allow a better understanding and evaluation of this trait, in addition to identify candidate genes for future studies.This work was approved by the ethical committee on the use of animals (CEUA) of the School of Agricultural and Veterinarian Sciences (FCAV/UNESP). Protocol number 18340/16.The database used was obtained from the livestock archive of eight farms located in the following towns and states: Valparaíso/SP, Cotegipe/BA, Água Clara/MS, Itaquiraí/MS, Comodoro/MT, Jussara/MT, Tangará da Serra/MT, and Goianésia/GO. The farms to which these herds belong are dedicated to beef cattle farming and are part of the Aliança Nelore database, which combines data from the DeltaGen® and Paint® (CRV Lagoa) breeding programs.The reproductive management adopted by the farms included in this study refers to two breeding seasons: a) an anticipated breeding season from February to April during which heifers at about 14 to 18 months of age are challenged for 60 days in order to identify sexually precocious animals; b) a breeding season that starts in November and lasts 90 days in which all females of breeding age of the herd participate to the breeding season. Heifers that do not conceive in the anticipated breeding season have another opportunity in the second season. Females, heifers and cows that do not conceive in the normal breeding season (November) are culled.Records from 127,561 cows born between 1980 and 2009 were used. Stayability was defined as a binary trait, attributing value 1 (failure) or value 2 (success) to each female. The starting point adopted for STAY was the age at first calving (AFC), including females with AFC of more than 22 months and less than 45 months in the analysis. In this study, success was defined when the female remained productive in the herd for a period of 65 months or longer, as suggested by .The contemporary groups were defined as year, farm and season of birth of the cow. Season of birth was classified as dry (March to August) and rainy (September to February). Contemporary groups without variability and those with fewer than four animals were excluded from the analyses.The precocity of each cow was calculated as a function of AFC, attributing score 1 (precocious) to females with AFC ≤ 31 months and 2 (non-precocious) to females with AFC > 31 months.After data editing, 96,811 animals remained for further analysis. Among these, 20,757 (21.44%) were precocious and 25,532 (26.37%) received value 2 (success) for STAY . The pedThe genotype file contained information for 2,020 females and 930 sires from the Aliança Nelore database genotyped with the Illumina High-Density BeadChip Array  that contains 777,962 SNPs. SNPs located on autosomes and on the X chromosome were considered. For analysis, the genotype of the female sex chromosome was coded as 0 for females homozygous for the first allele (A), as 1 for heterozygous females, and as 2 for those homozygous for the second allele (B). On the other hand, SNPs of the male X chromosome were coded as 0 or 2, where 0 = A_ and 2 B_. The same methodology was adopted by  in a GWAThe preGSf90 program  was usedη is the linear predictor; X and Z are incidence matrices of the systematic (contemporary group and precocity) and random effects, respectively; β is the vector of fixed effects; u is the vector of additive effect of the animal assuming H is the relationship matrix that combines pedigree information (matrix A) and SNP data (matrix G), as described by [e is the vector of residual effect assuming I is an identity matrix and An additive threshold animal model including the systematic effects of contemporary group and precocity was used to obtain the solutions of mixed model equations. A generalized linear mixed model with a probit link function was fitted using the Thrgibbsf90 software . The modribed by , and σu2A-1, was replaced with H-1, as described by [G-1 is the inverse of the genomic relationship matrix. Matrix G was obtained as follows [Z is the genotype matrix adjusted for allele frequencies; D is a diagonal matrix containing weights for the effects of SNPs , and q is a normalization factor. According to [G is close to In this model, the inverse of the numerator relationship matrix, ribed by :H−1=A−1rding to , these wA total of 500,000 Gibbs chains were generated in the analyses. One sample was removed every 10 iterations, considering a burn-in period of 30,000 iterations. Convergence was analyzed with the Postgibbsf90 software  and the ûs is the vector with the effect of each SNP; D is a diagonal matrix containing weights for the SNP effect; Z is the genotype matrix, and ûg is the vector with the estimated breeding values for genotyped animals. In this study, ûg was computed once and ûs was obtained considering two iterations, in which matrix D was equal to an identity matrix in the first iteration, while in the second one it became a diagonal matrix containing the weights calculated in the previous iteration. The objective of these iterations is to increase the weight of SNPs with large effects and to reduce the weight of those with small effects [The SNP effects were computed iteratively using the postGSf90 program according to the procedure described by . The equ effects .www.ncbi.nlm.nih.gov/mapview/)—Bos taurus UMD 3.1.1, Annotation Release 104 (accession GCF 000003055.6). Functional analysis of the mapped genes was performed using the DAVID v6.7 software (https://david.ncifcrf.gov/). ClueGo, a Cytoscape plug-in (http://apps.cytoscape.org/apps/cluego), was used to construct a network of functionally grouped genes based on biological terms in order to identify associations with biological processes.The 10 windows of 200 SNPs based on the highest additive genetic variance were considered. The genes were identified using the NCBI Map Viewer tool (2) for STAY was higher when the genomic information was included in the analyses through matrix H  and on the X chromosome , correspBos taurus, but this gene is homologous in humans and mice. According to [On BTA1, some LOC regions and the IGSF11 gene (immunoglobulin family) were identified. No studies are available for rding to , the genThree of the 10 largest windows of genetic variance were identified on BTA5, which corresponded to about 3% of the total variance explained by the markers . RegionsCai et al.  describeBos indicus and Bos taurus [Regions on BTA5 have also been associated with productive and reproductive traits in s taurus  that ares taurus . AccordiInvestigation of the metabolic processes in which the genes mapped to the 10 largest windows of variance are involved (DAVID v6.7 software) showed an enriched pathway (KEGG database) with genes related to reproductive traits associated with STAY. This pathway is related to endocytosis and contains three genes  located in the window of BTA6. These genes play an important role in cellular processes such as cell regulation, proliferation and differentiation. As can be seen in in vitro study, Woad et al. [The PDGFRA gene on BTA6 is related to the PDGF gene and both PDGFRs. These genes are expressed in the ovary of different species, influencing the transition from primordial to primary follicles  and stimd et al.  showed tAnother expressed gene found on BTA6 is KIT. This gene controls key cellular processes, including the migration, proliferation, differentiation and survival of cells. The KIT gene, together with its cleavage products, is found in somatic, germ and gonadal cells of both sexes. KITL/KIT signaling promotes the growth, maturation and survival of germ cells in the gonads. In the ovary, the expression of KIT in the cellular stroma accompanies the development of the thecal layer around advanced follicles .The CD164 gene on chromosome 9 was studied by  and theiThe RAI14 gene on chromosome 20 has been associated with spermatogenesis in mice. According to , RAI14 iThe PDK3 gene located on the X chromosome was studied by , who conThe results of the present study revealed a list of 147 candidate genes for STAY in Nellore cattle. New candidate regions for STAY were detected, most of them related to reproductive, immunological and nervous system functions.


We further demonstrate the importance of these results by showing that previously recommended sample sizes for EWAS should be adjusted upwards, requiring samples between ∼10% and ∼20% larger in order to maintain type‐1 errors at the desired level.Epigenome‐wide association studies (EWAS) are designed to characterise population‐level epigenetic differences across the genome and link them to disease. Most commonly, they assess DNA‐methylation status at cytosine‐guanine dinucleotide (CpG) sites, using platforms such as the Illumina 450k array that profile a subset of CpGs genome wide. An important challenge in the context of EWAS is determining a significance threshold for declaring a CpG site as differentially methylated, taking multiple testing into account. We used a permutation method to estimate a significance threshold specifically for the 450k array and a simulation extrapolation approach to estimate a genome‐wide threshold. These methods were applied to five different EWAS datasets derived from a variety of populations and tissue types. We obtained an estimate of  The mosThe growth of EWAS can be at least partially attributed to the introduction of the Illumina Infinium HumanMethylation450k BeadChip (450k array) . The 450k array is a low‐cost, high‐throughput, platform that interrogates around 450,000 individual CpG sites across the genome, covering <2% of all known CpG sites, and 99% of RefSeq genes  of single nucleotide polymorphisms (SNPs), the development of standardised experimental design protocols and statistical methods is crucial for ensuring that reported findings are robust, reproducible, and biologically relevant  at genomic distances of up to 1–2 kb , which might be preferred over an individual site‐level analysis aiming to identify DMPs , accessed and downloaded using the R package marmal‐aid  . An Illumina GenomeStudio report was provided, which contained raw probe intensities, this was first processed using the marmal‐aid database for healthy controls from Caucasian or African populations, and then repeating the same search this time querying the GEO database directly. Two datasets were identified in marmal‐aid, the first, ‘Caucasian’, comes from a study into age‐related changes to methylomic state as profiled in peripheral blood samples from 426 Caucasian individuals, spanning a wide range of ages  consisting of 65 Caucasian‐American controls. For all of these marmal‐aid datasets, processed Beta values were used which had undergone quantile normalization and imputation of missing probes  as given in the 450k manifest , and α taken as the 5th percentile of the distribution of minimum P values.In order to estimate the significance threshold at the density of CpGs present on the 450k array, the maximum 3.3m required to obtain the observed α using the Bonferroni correction:P values. Under these assumptions, the minimum P values from the permutation replicates would be expected follow a beta distribution with parameters:a and b of the beta distribution can be estimated using the following method of moments estimators:x¯ and s2 are the sample mean and variance of the minimum P values over the permutations.The effective number of independent tests is the number a to be 1, the estimate for b is:Fixing the value of β was then performed using the optim function in R, using the methods of moments estimate as the starting point, to obtain a final estimate of m′, which was compared to the value of m obtained from the Bonferroni equation given above.Maximum likelihood estimation of 3.4P values were sampled over a uniform grid of 100 densities from 0 to 1, in increments of 0.01, and the minimum P value at each density recorded. This procedure was repeated 100 times, and for each of these 100 replicates, the 5% point at each density across all the permutations was recorded. The mean 5% point for each density across all 100 replicates was then used in subsequent analysis.For each set of permutation results, a subsampling procedure was used to extrapolate the findings to a theoretical array of infinite density  and genome‐wide (P=1×10−6) significance levels. We re‐calculated the sample sizes required for 80% power using our empirical estimates of genome‐wide α.Tsai and Bell  estimatet distributions giving rise to the estimates were inferred from the reported results , and th1−β = 0.8, F is the cumulative distribution function of the non‐central t distribution with n–1 degrees of freedom and non‐centrality parameter ncp, given by:where t(1−α/2) the critical value when α=1×10−6. Treated as an optimization problem, this was solved for σ across the range of sample sizes n and mean methylation differences δ. These estimates were then used in another optimization, this time solving to obtain sample sizes for each δ using the empirically derived estimates of α.and 44.1Beta) of pairs of CpG sites from chromosome 1 as a function of genomic distance. The relationship between these variables appears consistent across datasets. The curves show the same characteristic shape with pairs in close proximity having the highest average levels of correlation, tailing off sharply as distances approach 1 kb, and then decreasing more slowly from 1 to 2 kb, appearing to reach a limit just above zero – assumed to be the mean background level of correlation across the genome. In terms of the actual mean per bin correlation values, these appear comparable across the datasets, with the exception of the CRC set, with the approximate maximum per bin correlations of 0.3, 0.55, 0.4, 0.33, 0.4 and approximate background levels of 0.07, 0.12, 0.04, 0.05, 0.07 for Gambian, CRC, Caucasian, Afr‐Am‐GTP and Cau‐Am sets, respectively. There are also differences in the variability and spread of correlation values between neighbouring bins, perhaps indicating differences in apparent level of noise between sets.The correlation structure was assessed for each dataset. The plots in Figure 4.2p distributions vary between the different datasets. The αs obtained for Gambia, Caucasian, Afr‐Am‐GTP and Cau‐Am are larger than the Bonferroni adjusted 5% threshold of α=1.07×10−7, while for CRC, this is smaller by almost a factor of 10. Investigating further, Figure P distributions against the expected quantiles of the β distribution, which assumes the tests are independent. From these plots, it can be observed for the Gambia, Caucasian, Afr‐Am‐GTP and Cau‐Am sets that while Bonferroni correction produces uniformly distributed P values, these are also deflated over the entire range. For the CRC set, it appears that the observed data are not at all well modelled by the beta distribution, and there is not a clear pattern of over or under correction of P values, as they appear both deflated at low values and inflated at higher values.The results from the permutation testing scheme are given in Table m) does not adequately model the minimum P value distribution for m tests, and thus, while it is a useful modelling tool, there is not a true underlying effective number of independent tests. The results for CRC do not produce the expected distribution of min P values, and the estimated values for α, m and b show little resemblance to the values obtained for the other datasets, indicating potential problems with this particular set. This is perhaps not surprising given that this dataset is very different to the others, not only in disease status and tissue type, but also in having a much smaller sample size. To determine the effect of sample size on the success of the modelling strategy, we repeated the experiment with another small control dataset from an African American population (n=12) from GSE41826 (the same study from which the Cau‐Am set was drawn). This similarly was not well modelled by the beta distribution, also producing an unusually large estimate for the m parameter and resulting in α of the same magnitude as that obtained for CRC .Converting these 5% points to effective number of tests yields results that are not in close agreement to those obtained by fitting the beta distribution. This suggests that the beta distribution with parameters  to the minimum α=1.07×10−7. Assuming that the results and conclusions from the assessment of correlation within the different sets are more generally applicable, and that there are no major differences between different populations, then the results from these four sets can be combined to give a weighted mean of α=2.4×10−7. From permutation testing results, we conclude that a significance threshold of α=2.4×10−7 would be appropriate for the 450k, accounting for the subset of probes tested on the array but not the hypothetical set of probes that could be tested with saturated genome‐wide coverage.Looking now at the 5% values obtained, for the Gambian, Caucasian, Afr‐Am‐GTP and Cau‐Am sets, these are all larger than the Bonferroni adjusted 5% threshold of 6, that is, 1 million CpGs, which is four times the density of the 450k array. The consensus of the results from the four different sets was taken, yielding genome‐wide α=3.6×10−8. Interestingly, this figure is close to that typically used for GWAS: α=5×10−8, although it is not clear why this would be the case, considering these are distinct molecular measurements. It is unlikely that this coincidence is due to pervasive effects of methylation quantitative trait loci, thus simply reflecting LD, because similar results were seen in Caucasian and Afr‐Am‐GTP populations. Further investigation is required to determine whether there is some common mechanism at play or that this is merely coincidence.To address the issue of genome‐wide multiplicity, we used a subsampling method to extrapolate the results of permutation testing to an array of infinite density. The results of fitting the Monod function to the subsampling data revealed that the limit for the number of tests as the coverage on the array becomes saturated is in the region of 1 × 10−6, and would fall within the range considered stringent, 10−8 to 10−7 , WGBS (whole genome bisulphite‐sequencing) or RRBS (reduced representation bisulphite sequencing). In terms of cross‐tissue applicability, given the now wide‐spread availability of public 450k datasets, further work could be done in comparing thresholds derived for different tissues. In a similar vein, we could also repeat the study for different populations, or perhaps even perform a huge meta‐analysis using all healthy controls from every available study on GEO. Disease status is perhaps an important consideration, as wide‐scale disruption to the methylome such as that often observed in cancer could potentially invalidate some of the assumptions made, particularly regarding the level and extent of co‐methylation present, as the results we obtained here for the CRC data indicate. As for cross‐platform applicability, this is perhaps less certain, as arrays such as the 450k are designed to target genomic features such as promoter and enhancer regions and CpG sites in higher density contexts (Bibikova et al., α=2.4×10−7 threshold for the 450k array that we have estimated here takes into account both dependency between tests due to patterns of co‐methylation, and the multiplicity of the set of CpGs tested. As it is derived from results averaged over European, African and American populations, it could therefore find general application for 450k array data, offering an empirically derived, more permissive alternative to Bonferroni correction. One major limitation of this threshold is that it does not take into account genome‐wide multiplicity. The non‐random placement of probes and the current limited coverage of the 450k makes extrapolation to saturated probe coverage somewhat speculative, but we believe our estimated genome‐wide α=3.6×10−8 is a useful first step towards standardising levels of evidence in EWAS.As experience in GWAS has shown, the use of a standard significance threshold aids comparison and combination of results across experiments, and enables power calculations to inform the design of future experiments. The With the recent release of the EPIC array, the issue of significance in EWAS is as relevant as ever. Future work may then seek to apply the methods described here to similarly derive threshold estimates for the EPIC. In this regard, it is interesting to note that estimates for GWAS significance thresholds were based on early generation genotyping arrays, but remained unchallenged as denser arrays became available. We expect that comparison of future estimates of EWAS significance to the present results may go some way to addressing the question of whether it is possible to establish by extrapolation a universal, platform‐agnostic EWAS threshold for single site‐level differential methylation analysis.Supplementary InformationClick here for additional data file.Supplementary InformationClick here for additional data file.Supplementary Table 1. Permutation results for the additional small dataset consisting of samples from an African American population contained within GSE41826Supplementary Figure 1. Details of the permutation algorithmSupplementary Figure 2. Details of the subsampling algorithmClick here for additional data file.


Advances in experimental biology have enabled the collection of enormous troves of data on genomic variation in living organisms. The interpretation of this data to extract actionable information is one of the keys to developing novel therapeutic strategies to treat complex diseases. Network organization of biological data overcomes measurement noise in several biological contexts. Does a network approach, combining information about the linear organization of genomic markers with correlative information on these markers in a Bayesian formulation, lead to an analytic method with higher power for detecting quantitative trait loci?Block Network Mapping, combining Similarity Network Fusion  with a Bayesian locus likelihood evaluation, leads to large improvements in area under the receiver operating characteristic and power over interval mapping with expectation maximization. The method has a monotonically decreasing false discovery rate as a function of effect size, unlike interval mapping.http://lbm.niddk.nih.gov/vipulp/. Genotype data is available at http://churchill-lab.jax.org/website/GattiDOQTL.Block Network Mapping provides an alternative data-driven approach to mapping quantitative trait loci that leverages correlations in the sampled genotypes. The evaluation methodology can be combined with existing approaches such as Interval Mapping. Python scripts are available at The online version of this article (doi:10.1186/s12859-016-1351-8) contains supplementary material, which is available to authorized users. Quantitative variations in living organisms result from environmental factors and multiple segregating genes . The seaThe mapping problem for quantitative trait loci (QTL) is, briefly stated, to find the genetic markers that correlate with measured quantitative traits. Single marker regression , 5 was tThis led to the formulation of multiple IM methods and composite IM with the introduction of markers used as covariates –19. The The use of linkage maps, obtained using multi-point analysis of marker segregation data, is a major advantage of these IM methods compared to single marker regression, but is considered as a separate preliminary step before IM. In the present work, we report on a method, Block Network Mapping (BNM), that incorporates linkage through an experimental data-driven linkage network found using Similarity Network Fusion  combineTo develop BNM, we used synthetically generated phenotypes paired with real genotypes obtained in a study of white blood cells  in a speWe investigated the effect size and population size dependence of the false discovery rate (FDR), the power, and the receiver operating characteristic (ROC) obtained using our method, BNM, compared to the standard expectation maximization (EM) implementation of IM implemented in the R/qtl package .N subjects being studied , 1 , 2 , and 3 . We remove SNPs missing values on more than half of the mice and then use SNF to cluster the remaining SNPs based on both their distance matrix s and s′ by using the genetic distance between the SNPs, measured in centiMorgans: We define a distance matrix We also tried using the actual base position index along a chromosome to define the distance matrix, but the final results were not much different.wm is the phenotype of mouse m, we define a normalized phenotype ρm by s taking values α=0,1,or 2, the phenotype-weighted mutual information between two SNPs s and s′ is defined as We suppose that the phenotypes measured have been transformed into positive values by exponentiating. If where m, but in order to avoid bias due to the empirical distribution of phenotype values, we permute the phenotypes to obtain a phenotype-independent mutual information by averaging Note that ρperm is a permutation of ρperm replacing ρ, and Nperm is the total number of permutations. Note that with every permutation, the missing values of SNPs are randomly assigned a state independent of the previous permutation. In this way, our empirical I is independent of the actual phenotypes, but may possibly depend on the distribution of phenotype values. In more detail, suppose that the samples are drawn with unknown bias. Then, a uniformly weighted mutual information between SNPs would be a biased estimator of SNP-SNP mutual information, due to the unknown sampling bias in the observed samples. For example, if the phenotype values are skewed due to sampling bias, our empirical permutation formulation of I will maintain the skewed distribution, while reducing the effect of biased sampling on the estimated SNP-SNP mutual information. This may reduce the power to detect correlations, but it will not enhance correlations due to biased sampling, so this is a conservative approach. Permutation tests are often used in similar settings in QTL analysis [where analysis .I and D defined in this manner are sample-dependent and sample-independent, respectively. Moreover, the mutual information similarity is in no way constrained by contiguity on the chromosome, and indeed, the two similarity measures are defined in units that are not directly comparable. We want to find a principled approach to combining these similarity measures into a single unified similarity matrix. The Similarity Network Fusion (SNF) approach [D and the mutual information matrix I. Fusion using the SNF algorithm requires specifying two parameters: the number of neighbors κ and hyperparameter η. We elaborate on the choice of these parameters in the next subsection.The matrices approach  is a recapproach  is that approach   where the end branches are the final clusters to be used. This turns out to be mostly a binary tree for the present dataset. At each iteration, the splitting process is repeated for every “open” branch. An open branch is one that did not meet the stopping conditions. If a branch meets all the stopping conditions then the branch will be considered “closed”. For each open branch/cluster k, we first check if the size of cluster k, Sk, is smaller than κ. If it is, then branch k ends, i.e. cluster k is now closed. Otherwise, the splitting process starts: first, the similarity matrix for cluster k is constructed. Then, starting with setting the number of clusters n to n=2, cluster k is split into n new clusters via spectral clustering. If all the new clusters have contiguous members and none of them is smaller than a minimum size, Smin (here Smin=2), then the new clusters are accepted and considered open, i.e., they move on to the next iteration. If these conditions are not met, we incrementally increase n and repeat the splitting test until either the new clusters are accepted or n reaches a maximum number nmax in which case the new clusters are rejected and branch k ends. This process is illustrated in Fig. nmax depends on the size of the cluster being split, nmax= min where tmax is the maximum number of iterations allowed. The iterations stop when either all branches are closed or the maximum number of iterations is reached.We separate the SNPs into different clusters based on their fused similarity matrix in the following manner. We perform hierarchical clustering where we iteratively divide a cluster into two clusters, or more if the binary split did not satisfy the conditions described below . The optimal κ,η pair is the one that leads to the smallest cluster sizes, as we wanted to obtain higher resolution for the correct SNP. Note that in some examples where we selected for larger clusters, we found a tradeoff between SNP localization and phenotype prediction accuracy. As we focus in this paper on the SNP mapping problem, we chose smaller cluster sizes. In particular, we look at the biggest cluster at the end branches and choose the κ,η pair with the smallest biggest cluster (the minimax criterion in this context). If the size of these smallest biggest clusters is the same then we compare the number of big versus small clusters.We still need to decide the values of The likelihood of a block is the likelihood that at least one SNP in this block contributes to the overall phenotype value. If a block has an effect on the phenotype, then a regression model on this block should have a good predictive power relative to a null model  of regression/ testing simulations. For each trial t we randomly divide the data points into two equal halves, a training and a testing set. A data point is composed of a subject’s phenotype value and its block k genotype, i.e., its sequence of SNP states composing block k. Then, we test two models, one to obtain the predictive power of block k for trial t and another to serve as the null model for block k and trial t. For both models, we use the sequence phenotype inference approach described in [For each block ribed in . This aprk,t between t, block k. The sign of the SNP’s effect on the phenotype never appears in these calculations because we are always comparing the predicted phenotype values with the test set phenotype values. If the prediction is correct, whether the SNP enhances or decreases a phenotype, the value of rk,t will be positive.For the first model, we train its parameters on the data points in the training set and then use it to predict the phenotypes of the subjects in the test set. Comparing our predicted phenotypes, Np permutation trials [p, we permute the phenotypes of the data points in the training set before training the model parameters. Then, similar to the first model, we predict the phenotypes of the subjects in the test set to obtain the Pearson correlation k, from trial t and permutation trial p. The relative predictive power of block k for trial t can now be defined via the ratio For the second (null) model, we perform n trials . For eacrk,t or This algorithm is outlined in Fig. Lk of block k as the fraction of trials where k′≠k.We can finally define the likelihood s’, to find the probability of the SNP s as the model given the phenotype data, as is standard in applications of Bayes’ theorem.In formulating our approach in a Bayesian setting, we consider each SNP as a possible model for the observed phenotype. In particular, we assume that each chromosome has only one possible ‘true’ SNP. Our prior probability is that every SNP is equally likely to be causative. It remains then to define the likelihood of the ‘data given the model’ part of the Bayes computation, which in our context corresponds to ‘the phenotypes observed given the causative SNP k, Lk, suggests that at least one SNP in block k is contributing to the quantitative phenotype. As discussed above, these blocks are chosen such that SNPs in the same block are more correlated to each other than to SNPs in a different block. However, there are still correlations between SNPs from different blocks, albeit not strong enough to be included in the same block. Because of these inter-block correlations, we expect that even blocks that do not contain the causative SNP could have a high likelihood as well simply due to correlations that exist in the finite set of sampled genotypes, and we can quantify this as follows. Assuming that there is only one causative SNP on each chromosome, if SNP s is the one then the likelihood that a block b will show an effect should be proportional to the odds ratio, s and block b compared to its correlation to all other blocks in the same chromosome. We define To motivate our likelihood function for the data given the model, we first note that a higher likelihood value of a block M is the similarity matrix for the corresponding chromosome obtained by fusing its distance and information matrices as described in Section “κ,η pair values obtained while performing the hierarchical clustering.where I) and is simply a measure of the correlation between SNP s and block b based on the finite amount of data available. We also tried using L0 defined in terms of the mean instead of the maximum of M, but this did not materially affect the results.Note that s given the data as the Pearson correlation, rs, between the sequence of phenotype-independent likelihoods Nc is the number of blocks in chromosome c which contains the SNP s. If this Pearson correlation rs is negative, we define rs≡0. It should be emphasized here that rs<0 does not correspond to a SNP that has a negative correlation with the phenotype. What is being compared here is the correlation pattern between likelihoods of SNP blocks, phenotype-independent (which indicates genetic linkage independent of phenotype considered) and phenotype-dependent (which indicates linkage weighted by phenotype). A negative correlation rs<0 occurs when the genetic linkage of SNP blocks is exactly the opposite of the linkage suggested by the phenotype weighting. For small sample sizes, such negative correlations can appear by chance, but just as in the definition of rk,t in Section “rs, the pseudo-probability of s because it takes values between 0 and 1 as defined, with the ‘pseudo-’ prefix to emphasize that it is not, in fact, a probability. We will use R(s)≡1−rs in our calculations of power, false discovery rate and other measures of our methodology.Using the Pearson correlation again but in a completely different context, we use our definition of section “” \documeLk: The likelihood that a block k contains a SNP which has an effect on the phenotype, calculated using training/testing splits of the data and null trials with permuted training phenotypes.s is correlated with a block k, calculated from the SNF fused similarity matrix.rs: The Pearson correlation coefficient over all blocks k between Lk and R: For each SNP s, R(s)≡1− max.R is defined like this so that increasing FDR P-value thresholds correspond to increasing R-value thresholds.As we have given several definitions in the preceding Method subsections, we summarize the relevant information to make the “We demonstrate our method by applying it to simulated data with 742 genotypic sequences of Diversity Outbred (DO) Mice and 1000 phenotypes. We simulated phenotypes on the 19 autosomes and did not add a sex effect. We selected 19 genomic locations, one on each autosome, and generated 19 QTL effect sizes from an exponential distribution. Using the genotypes at each location, we created the QTL effects and scaled the variance to be 1. Then we added N noise and the QTL effects together.P-values calculations we run scanone with 1000 permutations (n.perm = 1000). The simulated data are obtained by choosing only one SNP that influences a particular phenotype on each of the 19 autosomes with varying effect sizes. These effect sizes range between 1.65×10−5 and 10.03  and their FDR-matching BNM R-values . In all cases BNM has a higher power  with expectation maximization from the R/qtl package. For the R/qtl simulations, we use scanone with the default settings and calc.genoprob with step = 0 and error.prob = 0. For the We also compare the ROC curves in 6 different effect size ranges Fig. . In thisd Mb from each other. For example, if one or more signals are obtained in a particular block, this counts as 1 true positive  or 1 false positive . We did the analysis at three different block sizes, d=2  thresholds, despite the fact that adding this freedom improves the IM R/qtl results much more than it does the results from BNM. Even with the use of blocks of varying sizes, IM shows a decreasing and then increasing FDR as effect sizes are increased while the BNM FDR continues to be a monotonically decreasing function of effect size  in the neighborhood of the “true signal”, it is considered a false positive. This is more stringent than the usual expectation of QTL mapping  so we reNext we examine how the power and false discovery rates change with the choice of different samples of phenotypes and with decreasing number of mice Fig. . To examThe effect of population size on QTL detection has been demonstrated , 31, so P-values , to linkage mapping and phenotype regression using Similarity Network Fusion  to definQTL locations and effects are specific to populations, and can only be detected when the population is polymorphic at the relevant loci. In light of this, BNM uses no information beyond the genotypes and phenotypes measured in the sample, besides the genetic distance. We did not find much difference between using the genetic distance and the distance measured in base pairs between markers.We found that the area under the receiver operating characteristic curve (AUROC) exceeded that of IM for all effect sizes, all allowed genome interval sizes  and all chosen numbers of mice . The power of our approach was considerably higher than that of IM in all circumstances, except when we allowed for some genomic distance between the true and predicted SNPs and simultaneously decreased the number of mice to 400. It is known , 31 thatAs our approach works block-by-block, it is somewhat similar to composite IM –19 but wOur work does not improve on simple IM with respect to effects of opposing sign associated with linked SNPs. It is not clear that our method could be modified to overcome this limitation, though our approach can detect nonlinear dependence on allele dosage. In its present form, we also made the assumption that only one block in a chromosome contributes to the phenotype. This is, of course, an external assumption from the viewpoint of the underlying mathematics. It can be relaxed by using only contiguous parts of chromosomes in the analysis, but these parts will have smaller numbers of blocks, which in turn will lead to lower power. In other words, multiple effects on a chromosome could be detected with BNM albeit with a worse AUROC. It would be more appropriate to investigate better approaches to solving the multiple locus problem  within aIn this study, we have presented a network approach to QTL analysis that uses sample genotype data to define covariates in a systematic and interpretable manner. Using the network of correlations between SNPs through SNF for finding covariate blocks was a central feature of our approach, along with a Bayesian approach to finding the likely SNPs within blocks using inter-block correlations. Network approaches may be more noise-tolerant and may scale well to larger sets of measured markers.