There is an unspoken assumption that imprecision of measurement of phenotypes will not have large systematic effects on the location of significant associations in a genome wide association study (GWAS). In this report, the effects of two independent measurements of the same trait, subcutaneous fat thickness, were examined in GWAS of 940 individuals.P < 0.0001) association in common to the two measurements. The correlation between allele effects was approximately equal to the square of the correlation between the trait measurements. An important quantitative trait locus (QTL) on BTA14 appeared to be shifted distally by 1 Mb along the chromosome. The divergence in GWAS was stronger with data coded into two discrete classes. Univariate trimming of the top and bottom 5% of data, a method used to control for erroneous trait values, decreased the similarity between the GWAS and increased the apparent shift of the QTL on BTA14. Stringent bivariate trimming of data, using only trait values that were similar to each other in the two data sets, substantially improved the correlation of trait values and allele effects in the GWAS, and showed evidence for two QTL on BTA14 separated by 1 Mb. Despite the reduction in sample size due to trimming, more SNP were significant. Using the mean of the two measurements of the trait was not as efficient as bivariate trimming.The trait values obtained by two independent groups working to the same trait definition were correlated with r = 0.72. The allele effects obtained from the two analyses were only moderately correlated, with r = 0.53, and there was one significant , two or more independent measurements of the same trait should be obtained for all samples, and individuals genotyped that have highly correlated trait measurements. It is usually assumed that a trait is measured with a degree of imprecision or error, but that the details of the measurement of a trait will not affect the results of a genome wide association study. Specifically, that 1) the particular details of how the trait is measured, 2) who measured it, and 3) whether the trait is subtly differently measured in a second sample will not i) materially affect the location of the most significant associations between a DNA marker and the trait of interest or ii) affect the confirmation of the results in a second sample, because it is assumed that the errors in measurement are not systematic. Genome wide association studies (GWAS) compare a large number of single nucleotide polymorphisms (SNPs) to a trait measurement and SNPs with strong associations are usually reported . For somrd sacral vertebra, but as fat layers are not uniformly thick there is clearly scope for variation in measurements performed by different individuals. These animals had been genotyped for a GWAS of body composition [Two measurements of subcutaneous fat thickness were collected on the same animals by two groups working independently  and thisposition  and one This analysis took previously collected genotypic data, additional unpublished phenotypes and then reanalysed the entire data set. The expectation was that there would not be systematic differences in the two measurements, that the underlying genetic basis for fat thickness would be evident in both GWAS, and that the differences in trait values might merely affect the degree of significance of the most significant SNP associations, which would largely be in common. The data were trimmed in two ways to remove outliers to determine whether this would be successful in controlling the differences between the GWAS. The fat thickness data were also coded as a threshold trait to determine how important such measurement error might be for discrete traits, where individuals may be coded as affected or unaffected.b = 0.89, s.e. = 0.03 , the correlation was r = 0.72 between them, and the regression coefficient of CHILLP8 on P8FAT was 03 Table  &1B both03 Table  &2B. UniP < 0.001) associated to the trait, which represents a false positive rate (FPR) = 76% (Table P < 0.001) associated to that trait measurement, and FPR = 86%. These associations showed a distinct excess of large t-test values compared to the theoretical expectation, consistent with the discovery of real associations  SNP in common  including BTB-01530836, which had P = 1.2 × 10-6 .The GWAS of the P8FAT measurement found 71 SNPs significantly . None of the significant (P < 0.001) SNPs were significant for both CHILLP8 and P8FAT . The number of significant (P < 0.001) associations decreased for CHILLP8 and P8FAT, but there was an increase in the number of SNPs that were significant in common. The CHILLP8 and P8FAT GWAS showed two clusters of SNP, one at BTA14:23 and one at BTA14:25 Mb, although there were more SNP in the BTA14:23 Mb cluster than in the BTA14:25 Mb cluster for both GWAS . The number of significant SNP nearly doubled  in both clusters . The number of significant SNPs were relatively low , which may reduce the number of highly divergent measurements and preserve as high a sample size as possible. Overall, the correlation between CHILLP8 and the P8MEAN allele effects was r = 0.84 and between P8FAT and P8MEAN allele effects was r = 0.88. These are approximately equal to the square of the correlations between the trait measurements of CHILLP8 and P8MEAN and P8FAT and P8MEAN (r = 0.91 gives rP < 0.001) SNPs in the CHILLP8 GWAS, 128 significant (P < 0.001) SNPs in the P8FAT GWAS. There were 22 significant (P < 0.001) SNPs common to both of the GWAS, four of these common SNPs were significant at the 1 × 10-5 threshold, and one of these SNPs was significant at the 1 × 10-7 threshold. Obviously, with discrete phenotypes it is possible to exclude all discrepantly coded individuals, and all +A and A+ individuals , two or more independent measurements of the same trait should be obtained for all samples, and individuals genotyped that have highly correlated trait measurements.b = 0.90) with a small standard error of estimation (s.e. = 0.01), which suggests that overall, there was little shrinkage in the fat thickness. Furthermore, the plot of divergence suggests that most of the difference is due to strongly divergent measurements for a minority of samples, implicating operator error rather than systematic differences due to the chiller. Nevertheless, given these factors of when, where and by whom the trait was measured, these measurement differences may be at the extreme end of divergence of measurement of the same trait, and studies of other traits may not be as strongly affected. However, until other analyses of independently performed repeated measurements are obtained one cannot be sure that the results obtained here are atypical or that they will represent a general phenomenon.The major differences in the trait measurements in this study were that 1) a different group of individuals performed the measurement (accredited AUSMEAT inspectors versus trained meat scientists), and 2) the P8FAT measurement was performed about an hour after slaughter on a warm carcass whereas the CHILLP8 measurement was performed after the carcass had been refrigerated, and would have been measured within 24 hours of the P8FAT measurement. Although one cannot explicitly disentangle the effects of warm vs chiller and inspectors vs meat scientists, because the comparison was warm+inspectors vs cold+scientists, the differences between the mean CHILLP8 and P8FAT were ~ 1 mm and the regression coefficient of one measure on the other was nearly 1 in the entire sample , two or more independent measurements of the same trait should be obtained for all samples. This threshold is suggested because the square of a decimal fraction begins to depart substantially from the original fraction below a value of 0.95, and the correlation between allele effects between two GWAS is approximately equal to the square of the correlation between trait values. For prospective individuals in a GWAS, only those with accurately measured trait values should be genotyped, such as those that have highly correlated trait measurements.The samples on which these analyses were based have been reported previously -23. Brierd sacral vertebra, using a cut and measure procedure with a specially designed ruler with 1 mm gradations . In this study we distinguish between the trait and the measurement of the trait. Here, P8 subcutaneous fat thickness is the trait and it was measured twice. The usual measurement is the warm dressed carcass measurement and is taken by an accredited AUSMEAT inspector and was called P8FAT in this study. There were 8,653 animals with P8FAT measurements. In addition to this measurement, the animals were also measured at the same location using the same instrument within 24 hours by a team of trained meat scientists in the chiller [In cattle in Australia, subcutaneous fat thickness measurements are taken at the P8 position, which is aligned with the crest of the 3 chiller  and is c chiller . FurtherIn total, 940 animals with P8FAT thickness measurements, of which 888 had CHILLP8 measurements, had been genotyped previously using the Illumina Bovine SNP50 Array  consistip/Op where Ep is the expected number of SNP with P values below a particular significance threshold, given the number of SNP in the panel and assuming that all tests are independent, and Op is the observed number of SNP with P values below that same threshold. The observed distribution of t-tests was compared to the theoretical distribution in a quantile-quantile (Q-Q) plot using the R program software [http://www.r-project.org/. The raw phenotypes, adjusted phenotypes and allele regression coefficients for different models were compared by calculating Pearson correlation coefficients.In this analysis the same analytical model and software was used to analyse the associations. In brief, analyses were performed using a mixed model implemented through the software ASReml  where thsoftware  downloadchillp8 - yp8fat)2. A second method, diff2 = (ychillp8 - yp8fat)2/0.5(ychillp8 + yp8fat), in which the difference between measurements is scaled by the size of the measurement, yielded essentially the same list of samples, so only diff1 was used in this study. Animals that had extreme trait values either due to univariate or bivariate trimming were excluded from data sets and the GWAS were rerun.Two forms of trimming of the data were performed. Univariate trimming was used to remove values from the top and bottom 5% of the distribution. Univariate trimming is a typical method to remove outliers or obviously incorrectly measured individuals  and mildTo determine how important the misclassification would be if discrete phenotypes were analysed, the fat thickness measurements were treated as if they were a threshold trait. It has been theorised that many discrete traits represent an underlying quantitative trait  and whenrd sacral vertebra; P8FAT: Rump fat thickness measured in millimetres on the warm carcass at the P8 position by AUSMEAT inspectors; Q-Q plot: quantile quantile plot of the observed distribution of a statistic against the theoretical distribution of the same statistic; QTL: quantitative trait locus; SNP: single nucleotide polymorphismBTA14: Bos taurus chromosome 14; CHILLP8: Rump fat thickness measured in millimetres on the chilled carcass at the P8 position by trained meat scientists; diff1 the squared difference between CHILLP8 and P8FAT; FPR: false positive rate; GWAS: Genome wide association study; P8: position aligned with the crest of the 3CHCHD7: coiled-coil-helix-coiled-coil-helix domain containing 7; LOC787404: similar to ribosomal protein S20; LYN: v-yes-1 Yamaguchi sarcoma viral related oncogene homolog; MOS: v-mos Moloney murine sarcoma viral oncogene homolog; NSMAF: neutral sphingomyelinase (N-SMase) activation associated factor; PENK: proenkephalin; PLAG1: pleiomorphic adenoma gene 1; RPS20: ribosomal protein S20; SDR16C5: short chain dehydrogenase/reductase family 16C, member 5; TGS1: trimethylguanosine synthase 1; TMEM68: transmembrane protein 68; TOX: thymocyte selection-associated high mobility group box; XKR4: XK, Kell blood group complex subunit-related family, member 4WB planned and performed the analyses, and drafted the manuscript.


MSH6 (P = 1.9 × 10−9), which was also associated with altered expression levels of MSH6 mRNA in multiple tissues. This study contributes to the growing evidence that DNA repair processes play a key role in ovarian ageing and could be an important therapeutic target for infertility.The length of female reproductive lifespan is associated with multiple adverse outcomes, including breast cancer, cardiovascular disease and infertility. The biological processes that govern the timing of the beginning and end of reproductive life are not well understood. Genetic variants are known to contribute to ∼50% of the variation in both age at menarche and menopause, but to date the known genes explain <15% of the genetic component. We have used genome-wide association in a bivariate meta-analysis of both traits to identify genes involved in determining reproductive lifespan. We observed significant genetic correlation between the two traits using genome-wide complex trait analysis. However, we found no robust statistical evidence for individual variants with an effect on both traits. A novel association with age at menopause was detected for a variant rs1800932 in the mismatch repair gene  Female reproductive lifespan starts just prior to menarche, the onset of the first menstrual bleed and finishes when oocyte supply becomes exhausted at menopause. Both processes are governed by genetic and non-genetic factors and the timing of these events is associated with multiple adverse health outcomes, including breast cancer, cardiovascular disease, osteoporotic fractures and infertility . Recent ReproGen consortium meta-analyses of 87 802 individuals for menarche and 38 968 individuals for menopause  to test for genome-wide genetic correlation between timing of menarche and menopause. Using 329 966 autosomal SNPs we observed a positive correlation of rgenetic = 0.138 . This result remained similar after adjustment for the top 10 principal components of population stratification.We performed a restricted maximum likelihood (REML) bivariate analysis ,19 withiP values <5 × 10−8 and a further four independent signals with P values <1 × 10−7 (Table r2 > 0.05), had been previously identified in the GWAS for one of the traits individually. The strongest bivariate signal was near GAB2, a known locus for menarche  found an enrichment in the ovarian cancer signalling pathway (P = 7.67 × 10−4), with three of the six genes closest to the top variants being in that pathway .The bivariate meta-analysis for menarche and menopause generated two signals with genome-wide significant 7 Table r > 0.05, enopause . There win silico replication cohorts, including up to 28 470 individuals from 22 studies for menarche and up to 19 851 individuals from 22 studies for menopause (Table P = 2 × 10−9). This variant was in the MSH6 gene on chromosome 2 and was associated with a 1.3 months (se = 0.38) reduction in menopause age per common allele in the replication cohorts alone   was associated with expression of MSH6 (P = 3.9 × 10−6–3.1 × 10−20). In monocytes, whole blood and liver, rs3136247 was the SNP most strongly associated with expression of MSH6, but in lung tissue the best SNP was rs2047681 (r2 = 0.6 with rs3136247).We investigated the functional significance of the novel locus associated with age at menopause by determining whether the top variant, or SNPs in LD with it, were associated with expression levels of any genes in the genome. We accessed data from four tissue types  and in all tissues rs1800932 or rs3136247 (r2 > 0.8) with the lead bivariate SNP , which is a known signal for menopause and reached P = 5 × 10−5 for menarche, following replication. This genomic region has also been associated with other phenotypes from GWAS scans, e.g. type 1 diabetes, multiple sclerosis and lupus (http://www.genome.gov/gwastudies/). This would be a good candidate to follow-up in additional cohorts with menarche data and if substantiated would provide evidence for an immunological pathway involved in both phenotypes. Despite finding no individual locus associated with both age at menarche and age at menopause, the positive although modest genetic correlation (rgenetic = 0.138) suggests that common genetic loci do exist, likely with very subtle effects. Our pathway analysis also suggests that there be one or two pathways of shared aetiology between the two traits, with many others uniquely involved.Female reproductive lifespan starts at menarche and ends at menopause and we therefore performed a bivariate analysis of the two traits. Two signals reached genome-wide significance in this analysis, but these were both heavily driven by low enopause . We sougP values in the original analysis. One of the limitations of the bivariate meta-analysis is that very strong signals in individual traits can drive the bivariate statistic over the P < 5 × 10-8 threshold. The method is therefore best applied to signals that are sub-genome-wide significant in individual traits, or to use in pathway analyses than can highlight biological processes common to both traits.Future studies could include increasing the sample size in the discovery meta-analysis or replication of the top signals in additional cohorts. This is important since most of our participating studies were Caucasian, therefore other ethnic groups need to be similarly analysed. Studies are ongoing which include individuals of multiple ethnicities, which should narrow down the association further. Also, other than adjusting for birth year in menarche analysis, we did not correct for environmental factors which may influence reproductive life span (such as early obesity or adult-age smoking). A further limitation of our study is that the cohorts included in the analysis were predominantly the same as those used in the meta-analyses for the individual traits ,3. Thus,MSH6 gene on chromosome 2. The SNP had a minor allele frequency of ∼18% and the rare allele increased menopause age by ∼1.3 months per allele. MSH6 heterodimerizes with MSH2 to form the MutS alpha protein complex, which is involved in mismatch repair (MMR), predominantly of single base mismatches and small dinucleotide insertion/deletion loops  . EXO1 has 5′–3′ exonuclease activity and interacts with several of the MMR proteins, including MSH2, MLH1, MSH3, PCNA and WRN for its role in MMR and recombination  . MSH6 mul cancer ,23. No rbination . UIMC1 rbination . MCM8 isbination . Finallybination . Thus, vn ageing . It has enopause –32. We ds et al. , where dBRCA1 MMR gene have marked depletion of germ cells   to test for genome-wide genetic correlation between timing of menarche and menopause. The total joint contribution of common SNPs to both age of menarche and age of menopause in the WGHS was estimated using the REML method implemented in GCTA . Women with recalled age at menarche between 9 and 17 years were included in the analysis. Age at natural menopause was defined as the age at the last menstrual period that occurred naturally between the ages of 40 and 60 years. Women were excluded with menopause due to hysterectomy and/or bilateral ovariectomy, or chemotherapy/irradiation, if validated by medical records, and women using HRT before menopause. All studies were approved by local ethics committees and all participants provided written informed consent. Each study performed genome-wide association testing for age at menarche or menopause across ∼2.5 million imputed SNPs, based on linear regression under an additive genetic model. Individual study data were meta-analysed using the METAL software package; genomic control (GC) adjustments were applied. We considered P-values of <5 × 10−8 to indicate genome-wide significance.Full details of the individual GWAS can be found in the original publications, but briefly: the menarche GWAS included 32 studies, comprising 87 802 women and the menopause GWAS included 22 studies, comprising 38 968 women: all were of White European ancestry. Nineteen studies were included in both GWAS meta-analyses, although the number of women from each study differed (Z test statistics) from each univariate GWAS meta-analysis  of age at menarche and natural menopause using our newly developed algorithm, empirical-weighted linear-combined test statistics (eLC)  ,35. BrieP value of <1 × 10−7 in the bivariate analysis were taken forward for replication in 22 additional cohorts with in silico data, which included data from the iCOGs meta-analysis, which incorporated 16 individual studies. We also determined for each SNP whether any SNPs in LD with the lead SNP (<1 Mb away and r2 > 0.8) were more strongly associated with each of the traits in the individual menarche or menopause GWAS studies. There were 10 proxy SNPs with a lower P value in the individual trait and these were also taken forward for in silico replication. Therefore, in total 16 SNPs were tested in replication cohorts .All SNPs with a Access to data is available via the GREAT database https://ifar-great.hsl.harvard.edu/ or by contacting the authors directly.r2 > 0.9) were searched against a multi-tissue eQTL database of expression of SNP results  the SNP most strongly associated with expression of MSH6 was our top GWAS SNP or one in strong LD with it (r2 > 0.95).The novel genome-wide associated SNP for age at menopause rs1800932) and SNPs in LD with this SNP  and A.F. is funded by a UK Medical Research Council Post-doctoral research fellowship (0701594). Further information on funding for individual studies is provided in supplementary information. Funding to pay the Open Access publication charges for this article was provided by the Wellcome Trust.J.R.B.P is a Sir Henry Wellcome Postdoctoral Research Fellow (092447/Z/10/Z). D.A.L. and A.F. work in a centre that receives infrastructure funding from the


LDLR and systolic blood pressure was identified, which is supported by pharmacogenetic studies. In summary, for sequencing studies, STAR is an important tool for detecting secondary-trait RV associations.Next-generation sequencing has made possible the detection of rare variant (RV) associations with quantitative traits (QT). Due to high sequencing cost, many studies can only sequence a modest number of selected samples with extreme QT. Therefore association testing in individual studies can be underpowered. Besides the primary trait, many clinically important secondary traits are often measured. It is highly beneficial if multiple studies can be jointly analyzed for detecting associations with commonly measured traits. However, analyzing secondary traits in selected samples can be biased if sample ascertainment is not properly modeled. Some methods exist for analyzing secondary traits in selected samples, where some burden tests can be implemented. However p-values can only be evaluated analytically via asymptotic approximations, which may not be accurate. Additionally, potentially more powerful sequence kernel association tests, variable selection-based methods, and burden tests that require permutations cannot be incorporated. To overcome these limitations, we developed a unified method for analyzing secondary trait associations with RVs (STAR) in selected samples, incorporating all RV tests. Statistical significance can be evaluated either through permutations or analytically. STAR makes it possible to apply more powerful RV tests to analyze secondary trait associations. It also enables jointly analyzing multiple cohorts ascertained under different study designs, which greatly boosts power. The performance of STAR and commonly used RV association tests were comprehensively evaluated using simulation studies. STAR was also implemented to analyze a dataset from the SardiNIA project where samples with extreme low-density lipoprotein levels were sequenced. A significant association between  LDLR was identified to be significantly associated with systolic blood pressure, which is supported by a previous pharmacogenetics study. In conclusion, STAR is an important tool for sequence-based association studies.Next-generation sequencing has greatly expanded our ability to identify missing heritability due to rare variants. In order to increase the power to detect associations, one desirable study design is to combine samples from multiple cohorts for mapping commonly measured traits. However, many current studies sequence selected samples (e.g. samples with extreme QT), which can bias the analysis of secondary traits, unless the sampling ascertainment mechanisms are properly adjusted. We developed a unified method for detecting secondary trait associations with rare variants (STAR) in selected and random samples, which can flexibly incorporate all rare variant association tests and allow joint analysis of multiple cohorts ascertained under different study designs. We demonstrate via simulations that STAR greatly boosts the power for detecting secondary trait associations. As an application of STAR, a dataset from the SardiNIA project was analyzed, where DNA samples from well-phenotyped individuals with extreme low-density lipoprotein levels were sequenced.  Next-generation sequencing has already revolutionized the study of complex traits, and made possible the detection of rare variant associations. Many sequence based association studies are currently being performed, some of which have already lead to the discovery of associations with clinically important traits, such as lipids levels Many methods have been developed for detecting rare variant associations secondary phenotypes using regression models (SPREG) in case control studies Several methods exist for detecting secondary trait associations in selected samples. For example, a retrospective likelihood method was developed for mapping However none of these methods for detecting secondary associations incorporate sequence kernel association test (SKAT), a powerful variance component score test based method. This method can be more powerful when causal variants have bidirectional effects and/or a large proportion of the variants within gene region are non-causal.Standard permutation algorithms cannot be applied to obtain empirical p-value. This is because when the primary and secondary traits are correlated and the genetic region is associated with the primary trait, neither the secondary trait residuals nor the locus genotypes are interchangeable under the null hypothesis. Therefore, the statistical significance can only be evaluated via asymptotic approximations, which has several notable limitations: 1.) Due to the low frequency of rare variants, asymptotic approximation for some tests may be violated, which can lead to either inflated type I error or loss of power. 2.) For some rare variant association methods, the analytical distribution for the test statistics is unknown and therefore the statistical significance has to be evaluated empirically. These rare variant tests that require evaluating p-values via permutation are often more powerful than the methods implemented in MTA, e.g. CMC or GRANVIL. It is therefore desirable that these tests can be applied to analyze secondary traits.To overcome the limitations of existing methods, a unified model was developed to detect secondary trait associations using selected samples. In the samples with extreme primary quantitative traits, through re-parameterizing the likelihood functions, interchangeable residuals for the secondary traits can be obtained under the null hypothesis. The residuals are approximately independent, and normally distributed. We proved theoretically that the analysis of secondary trait associations can be equivalently implemented by analyzing the correlation between the secondary trait residuals and the gene/genetic region. Therefore, any rare variant association test that can analyze QT in random population based studies can be incorporated in STAR. In addition, multiple cohorts can be jointly analyzed through conventional mega-analysis methods that use individual participant data or meta-analysis methods that use summary level statistics.A variety of popular rare variant tests have been implemented in the STAR framework and the power to detect secondary trait associations was evaluated. Specifically, we considered the weighted sum statistic (WSS) The performances for these methods were compared using extensive simulation studies. Genetic data were simulated under a realistic population genetic model as described by Kryukov et al LDLR and SysBP, which is statistically significant after applying a Bonferroni correction for testing multiple genes and traits. This association has strong biological support from pharmacogenetics studies LDLR gene, and established the importance of our method in sequence based association studies.The STAR method was also used to analyze a published sequence dataset from the SardiNIA project http://cran.r-project.org/web/packages/STARSEQ/. Additional companion softwares are deposited at http://code.google.com/p/starseq/.An R-package, STARSEQ which implements the STAR method is available through the Comprehensive R Archive Network (CRAN) at STAR model can be used with any rare variant test to detect associations with secondary traits in studies that use extreme sampling. The multi-site genotype for individual Under the null hypothesis of no gene/secondary trait associations, following the MTA framework, a multivariate generalized linear model can be implemented to estimate nuisance parameters The residual terms for the secondary traits, i.e. In order to obtain unbiased results, sampling schemes have to be properly modeled. Ascertainment corrected likelihood can be used, which jointly models sample ascertainment status found in .The likelihood function in shown in , the Jacussed in .In this model, the residual errors Burden tests, such as CMC and WSS, aggregate multiple rare variants across a genetic region and analyze them jointly. The following model can be used to obtain score statistics for a burden test:Score tests can be formally constructed from the joint likelihood for testing the null hypothesis of no gene/secondary trait associations, i.e. It is clear from formula (9) that Using similar ideas, we show in , that thThe KBAC test was previously developed for the analysis of binary trait associations −4, 50% are randomly chosen to be causal for the primary trait, and another 50% of the variants are independently chosen to be causal for the secondary trait. The set of causal variants for the primary trait are denoted by Type I error and power were evaluated for the following rare variant association tests that were extended in STAR, i.e. CMC, KBAC, WSS, SKAT and VT. Genetic data were generated according to a four parameter demographic model for Europeans Data for selective sampling studies are simulated, where for each dataset, a total of 5,000 individuals with extreme primary trait values are selected from a cohort of 100,000 individuals. Two-sided alternative hypothesis was tested for each method. Although p-values for CMC and SKAT can be obtained analytically, they can either be conservative or anti-conservative In order to illustrate the application of STAR for combining multiple cohorts, a meta-analysis of three studies was simulated. The primary trait for each study is different and a common secondary trait is measured for all studies. In the first study, the gene region is associated with the primary trait, and causal variants have an effect of −0.5. The correlation between the primary and secondary traits is 0.6. In the second study, the primary trait is associated with the gene region, and causal variants have an effect of 0.25. The primary and secondary traits are correlated with coefficient 0.4. In the third study, the gene region is not associated with the primary trait, and the correlation between the primary and secondary traits is −0.2. In each study, a different pool of 50,000 samples was simulated and 2,500 individuals with extreme primary trait were selected and analyzed for association. P-values for all rare variant tests in each study were obtained based upon 5,000 permutations. Meta-analysis is performed by combining Z-score statistics, which are transformed from p-values and weighted by the square root of the sample sizes in each study In order to evaluate type I errors, data were simulated under the assumption that the secondary trait effects for all variants were 0. The empirical distribution of p-values was obtained using 10,000 replicates. For evaluating power, two scenarios were considered, i.e. (A) causal variants have an unidirectional effect of 0.5; (B) causal variants have bidirectional effects, where 80% of the causal variants have effect 0.5 and the other 20% of the causal variants have effect −0.5.The power for analyzing each individual study and meta-analysis was evaluated using 10,000 replicates under a significance level of α = 0.05.APOB, B3GA4, LDLR and PCSK9 were tested for associations with the eight metabolic QTs. The genes APOC1, APOC2, APOE, B4GA4 contain no variants with MAF<1%, and SORT1 contains only 1 rare variant site. Gene-based association analysis was not performed for these five genes. Among the 256 individuals, 33 were taking blood pressure (BP) lowering medications; and their BP levels were adjusted by adding 10 mm Hg to their SysBP and 5 mm Hg to DiasBP levels APOB, B3GA4, LDLR and PCSK9. The five rare variant association tests incorporated in STAR were used to analyze the data. In addition to the secondary traits, the associations with the primary trait (i.e. LDL levels) were also analyzed. For the rare variant tests that use fixed MAF thresholds , variants with MAF<1% were analyzed. For VT test, variants with MAF<5% were used in the analysis. The secondary traits were also analyzed using standard linear regression that ignores the ascertainment mechanism, as a comparison to the analysis using the STAR method.Association analyses were performed for the nine genes that were sequenced from the SardiNIA project Type I error for STAR was investigated when 1.) the gene region is neither associated with the primary trait nor the secondary trait. 2.) the gene region is associated only with the primary trait but not the secondary trait. The quantile-quantile plots of empirical p-values and their theoretical expectations are displayed for different rare variant tests. It can be seen that all tests incorporated in the STAR method have well controlled type I error. The p-values for the five tests are slightly conservative even when permutation is used to evaluate significance. This can occur when either the aggregate variant frequencies are low or the sample size is not sufficiently large. For example, when the primary trait effect is nd 0.047 .As a comparison, we also evaluated type I errors of linear regression analysis that ignores sample ascertainment mechanisms. When the gene region is not associated with the primary trait, type I errors for all rare variant tests are well controlled. However, if the gene region is also associated with the primary trait, the distribution of p-values under the null hypothesis is highly skewed and the type I errors for all tests are seriously inflated , which iThe power of detecting secondary trait associations was compared for a variety of rare variant tests ( (71.5%) . If the  (71.5%) .VT can be more powerful than methods that use fixed variant frequency threshold, when the secondary trait effects are unidirectional. This is because using a fixed variant frequency threshold may result in the inclusion of higher frequency non-causal variants or the exclusion of more frequent causal variants from the analyses. For example, when the primary trait effect is  (71.5%) . HoweverThe variance component score test SKAT is less powerful than burden tests when causal variant effects are unidirectional. For example, when han KBAC . However (60.3%) .When the gene region is associated with both the primary and secondary traits, the power to detect secondary trait associations can be greater than when the gene region is only associated with the secondary trait. This is because variants with pleiotropic effects can be more enriched through extreme sampling. For example, when secondary trait effects are nd 49.7% . Howeverectively . TherefoThe power and type I errors for STAR were evaluated for a simulated meta-analysis of three studies. As shown in , the empWe also evaluated the power of the STAR method under the alternative hypothesis . It can APOB was found to be nominally significantly associated with LDL . When QT values are analyzed instead of the dichotomized trait and more powerful association methods are used, the power to detect associations with the primary trait can be increased. For the association with APOB, the p-values for the five tests are LDLR that was not previously detected was also observed . In this case, the CMC test gives the most significant p-value.Sequence data from the SardiNIA project were analyzed to detect associations with multiple lipids and metabolic traits. First, association analyses were carried-out for the primary trait LDL levels . In the APOB, B3GA4, LDLR and PCSK9 .Currently, many sequence based genetic studies are being performed to detect associations with complex traits. Due to the high cost of sequencing, the sample sizes for many of these studies are small. It was previously shown that in order to have sufficient power (e.g. >80%) to detect association with rare variants in an exome-wide study, in some cases it is necessary to sequence at least 10,000 samples with extreme traits from a cohort of 100,000 Previously CMC and GRANVIL tests were extended for analyzing secondary traits with p-value being evaluated analytically Permutation algorithm is often a necessary ingredient for rare variant association tests. Even if asymptotic approximations exist for some rare variant association tests such as SKAT and CMC, they may not be accurate and type I errors may be inflated or deflated Under the STAR framework, we compared the power of several rare variant tests for analyzing secondary traits in selected samples. It is clear from our comparisons that when causal variants have unidirectional effects, burden tests perform better than SKAT. However, when variants with effects in opposite directions are present, SKAT can be more powerful than burden test based methods. Given that the goal of the article is to introduce a method for analyzing secondary traits in selected samples, rather than to compare different rare variant tests, our simulations are not as comprehensive as some existing reviews, such as Basu and Pan LDLR and secondary trait SysBP, where carriers of rare variants in the LDLR gene tend to have lower SysBP levels. In fact, the LDLR gene has also been shown to be strongly associated with reductions of SysBP among the patients that receive atenolol, an antihypertensive drug LDLR gene may influence the etiology of SysBP. LDLR is potentially an important gene target for blood pressure treatment. In order to replicate signals In the analysis of the SardiNIA dataset, we adjusted the blood pressure for individuals undergoing antihypertensive therapy. The rank of sample blood pressure traits was only slightly changed after the adjustment. Given that we quantile-normalized the trait prior to the association analysis, the impact of the adjustment on the result is very minimal. In order to evaluate the robustness of the results, we also analyzed the associations with blood pressure when no adjustments were made, and the results are very similar (data not shown). A significant association was identified between rare variants in With the large scale application of next generation sequencing to study complex traits, samples from many existing cohorts will be sequenced. There can be insufficient power for analyzing associations in each individual study. It would be highly beneficial if samples from multiple cohorts can be combined for analyzing commonly measured traits. STAR is thus important and will greatly accelerate the process of identifying genes involved in complex trait etiology.Figure S1Conditional distribution of the secondary trait for individuals with extreme primary trait values in the upper and lower 5% tails. The density function of the secondary traits is plotted when the primary trait effect (TIF)Click here for additional data file.Figure S2Biases of the secondary trait effects due to extreme sampling under the null hypothesis. The bias in the secondary trait effects i.e. (TIF)Click here for additional data file.Figure S3Quantile-Quantile plot of p-values for rare variant tests in linear regression models under the null hypothesis of no gene/secondary trait associations. Sample ascertainment mechanism was ignored in the linear regression analysis. Five tests were evaluated, i.e. CMC, WSS, KBAC, VT and SKAT. Empirical p-values for each test were plotted against their theoretical expectations. A variety of scenarios with different primary trait effects and trait residual correlations were examined, which include (A) (TIF)Click here for additional data file.Figure S4The power for detecting association with secondary traits in selected samples. The power is shown for CMC, WSS, KBAC, VT, and SKAT implemented in the STAR framework. It is assumed that the secondary trait effects for causal variants are unidirectional, and their magnitudes are inversely proportional to the minor allele frequencies with (TIF)Click here for additional data file.Figure S5The power for detecting association with secondary traits in selected samples. The power is shown for CMC, WSS, KBAC, VT, and SKAT implemented in STAR framework. It is assumed that 80% of the causal variants increase the mean secondary trait value, and the remaining variants decrease the mean secondary trait value. The magnitudes of the secondary trait effects are inversely proportional to the minor allele frequencies, with (TIF)Click here for additional data file.Figure S6The power for detecting associations with secondary traits in selected samples. Power is shown for CMC, WSS, KBAC, VT, and SKAT implemented in STAR framework. Secondary trait effects are assumed to be fixed and unidirectional with (TIF)Click here for additional data file.Figure S7The power for detecting association with secondary traits in selected samples. Power is shown for CMC, WSS, KBAC, VT, and SKAT implemented in STAR framework. It is assumed that secondary trait effects are bidirectional with fixed magnitude (i.e.(TIF)Click here for additional data file.Figure S8Quantile-Quantile plot for meta-analysis p-values under the null hypothesis. Meta-analysis for three studies was simulated. The primary trait in each study is assumed to be different and a common secondary trait is measured in all studies. The gene region is not associated with the secondary trait. In the first study, the gene region is associated with the primary trait, and causal variants have an effect of −0.5. The correlation between the primary and secondary traits is 0.6. In the second study, the primary trait is also associated with the gene region, and causal variants have an effect of 0.25. The primary and secondary traits are correlated with coefficient 0.4. In the third study, the gene region is not associated with the primary trait, and the correlation between the primary and secondary traits is −0.2. CMC, WSS, KBAC, VT and SKAT were used to detect associations. In each study, a pool of 50,000 samples was simulated and 2,500 individuals with extreme primary trait were selected and analyzed. P-values for all rare variant tests were obtained based upon 5,000 permutations. The empirical distribution of p-values was obtained using 10,000 replicates.(TIF)Click here for additional data file.Figure S9Power for meta-analysis using CMC, WSS, KBAC, VT and SKAT. Meta-analysis for three studies was simulated. The primary trait in each study is assumed to be different and a common secondary trait is measured in all studies. Power for the five tests was displayed when (A) causal variants have unidirectional effect of 0.5, and (B) causal variants have bidirectional effects, i.e. 80% of the causal variants have effect 0.5 and the other 20% have effect −0.5. In the first study, the gene region is associated with the primary trait, and causal variants have an effect of −0.5. The correlation between the primary and secondary traits is 0.6. In the second study, the primary trait is also associated with the gene region, and causal variants have an effect of 0.25. The primary and secondary traits are correlated with coefficient 0.4. In the third study, the gene region is not associated with the primary trait, and the correlation between the primary and secondary traits is −0.2. In each study, a different pool of 50,000 samples was simulated and 2,500 individuals with extreme primary trait were selected and analyzed. P-values for all rare variant tests were obtained based upon 5,000 permutations. The power for analyzing each individual study and meta-analysis was evaluated using 10,000 replicates.(TIF)Click here for additional data file.Table S1Correlations of phenotypes from the SardiNIA cohort. Eight traits that were analyzed for associations are included, i.e. high density lipoprotein (HDL), low density lipoprotein (LDL), triglyceride (TG), total cholesterol levels (TCL), diastolic blood pressure (DiasBP), systolic blood pressure (SysBP), insulin levels (INSULIN), and body mass index (BMI). Correlations were estimated using 2044 unrelated individuals extracted from the SandiNIA pedigrees.(DOC)Click here for additional data file.Table S2Analysis of secondary trait associations using standard linear regression. Sample ascertainment mechanisms were ignored in the analysis. Seven secondary traits were analyzed, including total cholesterol levels (TCL), high density lipoprotein (HDL), body mass index (BMI), diastolic blood pressure (DiasBP), systolic blood pressure (SysBP), triglyceride (TG) and insulin levels (INSULIN). Gene-based association analysis was performed using CMC, WSS, KBAC, VT and SKAT.(DOC)Click here for additional data file.Text S1Extension of Kernel Based Adaptive Cluster to the Analysis of Quantitative Traits.(PDF)Click here for additional data file.Text S2Biases of Naïve Inferences of Secondary Trait Associations in Selected Samples.(PDF)Click here for additional data file.Text S3Details for the Null Likelihood Model.(PDF)Click here for additional data file.Text S4Practical Issues for Inferences under the Ascertainment Corrected Likelihood.(PDF)Click here for additional data file.Text S5Constructing Variance Component Score Tests from Ascertainment Corrected Likelihood.(PDF)Click here for additional data file.


Typically twin studies are used to investigate the aggregate effects of genetic and environmental influences on brain phenotypic measures. Although some phenotypic measures are highly heritable in twin studies, SNPs (single nucleotide polymorphisms) identified by genome-wide association studies (GWAS) account for only a small fraction of the heritability of these measures. We mapped the genetic variation (the proportion of phenotypic variance explained by variation among SNPs) of volumes of pre-defined regions across the whole brain, as explained by 512,905 SNPs genotyped on 747 adult participants from the Alzheimer's Disease Neuroimaging Initiative (ADNI). We found that 85% of the variance of intracranial volume (ICV) (p = 0.04) was explained by considering all SNPs simultaneously, and after adjusting for ICV, total grey matter (GM) and white matter (WM) volumes had genetic variation estimates near zero (p = 0.5). We found varying estimates of genetic variation across 93 non-overlapping regions, with asymmetry in estimates between the left and right cerebral hemispheres. Several regions reported in previous studies to be related to Alzheimer's disease progression were estimated to have a large proportion of volumetric variance explained by the SNPs. The heritability of brain structure and function has received extensive attention for many years, and it continues to be an area of active research Genome-wide association studies (GWAS) have discovered hundreds of single-nucleotide polymorphisms (SNPs) that are significantly associated with variation in brain structure and function Here we estimate the proportion of variance of 93 regional volumes, as well as ICV, GM, WM, and cerebro-spinal fluid (CSF) volumes, explained by 512,905 SNPs across the 22 autosomes genotyped on 747 adult participants from the ADNI study.http://adni.loni.ucla.edu/). This initiative is a collective effort led by Principal Investigator Michael Weiner, M.D., VA Medical Center and University of California – San Francisco, involving many co-investigators and recruitment of participants from over 50 sites in the United States and Canada. More information on the study can be found at www.adni-info.org.The NIH ADNI is an ongoing public-private partnership to test whether genetic data, structural and functional neuroimaging, and clinical data can be combined to measure the progression of mild cognitive impairment (MCI) and early Alzheimer's disease (AD). The structural brain MRI data and corresponding clinical and genetic data from baseline and follow-up were downloaded from the ADNI publicly available database  was used to genotype 818 participants in the ADNI database, which resulted in a set of 620,901 SNP and copy number variation (CNV) markers. Since the Apolipoprotein E (APOE) SNPs, rs429358 and rs7412, are not on the Human 610-Quad Bead-Chip, they were genotyped separately. These two SNPs together define a 3 allele haplotype, namely the e2, e3, and e4 variants, and the presence of each of these variants was available in the ADNI database for all the individuals; the APOE gene has been the most significant risk locus in GWAS of AD 3. All original uncorrected image files are available to the general scientific community, as described at http://www.loni.ucla.edu/ADNI.The MRI data were collected across a variety of 1.5 Tesla MRI scanners with protocols individualized for each scanner, including volumetric 3-dimensional sagittal MPRAGE or equivalent protocols with varying resolutions. The typical protocol included: repetition time (TR) = 2400 ms, inversion time (TI) = 1000 ms, flip angle = 8°, field of view (FOV) = 24 cm, with a 256*256*170 acquisition matrix in the x-,y-, and z-dimensions yielding a voxel size of 1.25*1.26*1.2 mmThe MRI data were preprocessed using standard procedures that included realignment to the anterior commissure and posterior commissure by using MIPAV software, skull-stripping by using Brain Surface Extractor (BSE) and Brain Extraction Tool (BET), cerebellum removal, intensity inhomogeneity correction, segmentation using the FSL-FAST software, and spatial co-registration by using HAMMER GCTA  An R package, called APCluster, was used to group standardized volumes into groups of similar regions based on the GCTA measures. Affinity propagation (AP) clustering 10p-values from the likelihood ratio tests (top right) for the standardized volumes of each non-overlapping region as explained by the 512,905 SNPs across the entire genome, after adjusting for covariates. The AP cluster method identified 9, 10, and 10 clustering groups within the 93 non-overlapping regional volumes for the Control, MCI, and AD groups, respectively. Fisher's exact tests of independence yielded p<0.001 for each of the pairwise comparisons of clustering membership, indicating similarity between the volumetric clustering results across the three groups. Subsequently all participants were combined into a single analysis, yielding 9 clusters of regional volumes. In addition, AP clustering identified 6 groups of (non-overlapping) regions based on genetic contributions to variation in their standardized, covariate-adjusted volumes see . Figure GCTA findings showed that about 85% of intra-cranial volume (ICV) variability and 57% of cerebrospinal fluid (CSF) volume variability were explained by genetic variation within these participants, with likelihood ratio tests (LRT) for the significance of the random component yielding p-values of 0.04 and 0.12, respectively. However, the genetic variation estimates for total grey matter (GM) and white matter (WM) volumes (after adjusting for ICV and other covariates) were both near zero. Previous studies of adults reported similar estimates for ICV heritability 73% in , likely In regional analyses, we found estimates that were asymmetric across hemispheres, with no clear systematic difference between left hemisphere and right hemisphere volumes. This is in agreement with one prior report The AP cluster analyses indicated the presence of 6 groups of brain regions within the genetic variation estimates; the largest group was comprised of those regions with little to no volumetric variability explained by the SNPs. The clusters of regional volumes differed significantly from the clusters of the corresponding genetic variation estimates, but average regional volumes were not associated significantly with genetic variation estimates. Thus, the regions that were similar in size were not necessarily similar in genetic variation, and there was no apparent relationship between a region's size and the genetic variation of the region.In the current study, we systematically estimated the variability of 93 non-overlapping regional volumes, ICV, and GM, WM, and CSF volumes explained by 512,905 SNPs across the 22 autosomes genotyped on 747 adult participants from ADNI. These results give some evidence for a genetic component of the variation between individuals in several functional brain systems.First, there were several medial/mid-line brain structures with high genetic variation estimates, including the bilateral medial frontal-orbital gyrus, left medial frontal gyrus, bilateral precuneus, right perirhinal cortex and right entorhinal cortex. These structures, along with other medial neural regions, have been characterized as being part of the default mode network (DMN) - defined as a set of functionally connected brain regions that exhibit task-induced deactivation and increase activity at rest Second, many subcortical nuclei, as well as white matter tracts, had large genetic variation estimates, including the right insula, bilateral globus pallidus, bilateral putamen, bilateral caudate and left nucleus accumbens. Many of these structures make up the basal ganglia , a group of nuclei that act as a cohesive functional unit. The basal ganglia are associated with a variety of functions, including motor control, procedural learning relating to routine behaviors or “habits”, eye movements, and emotional functions Finally, large genetic variation estimates were observed for two prominent perceptual cortical pathways, namely the dorsal “where” pathway and the ventral “what” pathway. First described by Ungerlieder and Mishkin Due to a lack of power in the likelihood-ratio testing procedure and a sample size that was not sufficiently large to make standard errors small, we did not find estimates to be highly statistically significant. We did not perform multiple comparisons adjustments on the p-values from these analyses, in order to preserve the ability to compare results across different brain regions. Here our goal is to map genetic variation across the entire brain, where the results of particular interest are the comparisons of genetic variation among different regional volumes. The mixed model approach utilized by GCTA allows for an approximation to total heritability based on a large number of SNPs; this methodology is validated by the comparison of our results to published twin studies that estimate “true” heritability and have similar findings. Estimates of 0.999 for three regions do not imply that over 99% of variation in those volumes is explained by genetic variability, but they likely indicate large true parameter values (i.e. volumetric variance explained by the SNPs) and some additional variation due to the (case-control) sampling scheme, as well as noise in the volumetric data.Although our findings agree with those from a number of published twin studies, some of our findings could derive from our study population, in that some of the genetic contribution to the progression of AD could have contributed to the genetic variation we detected. We found significant but asymmetric genetic variation estimates in regions previously reported to be related to AD, and we found that much of the heritability of overall GM and WM volumes may be due to the heritability of total ICV rather than from specific genetic contributions to GM or WM volumes. In the future, large twin studies in elderly patients could compare these regions in their heritability and assess their relationship with the progression of Alzheimer's disease.


Polygenic scores have recently been used to summarise genetic effects among an ensemble of markers that do not individually achieve significance in a large-scale association study. Markers are selected using an initial training sample and used to construct a score in an independent replication sample by forming the weighted sum of associated alleles within each subject. Association between a trait and this composite score implies that a genetic signal is present among the selected markers, and the score can then be used for prediction of individual trait values. This approach has been used to obtain evidence of a genetic effect when no single markers are significant, to establish a common genetic basis for related disorders, and to construct risk prediction models. In some cases, however, the desired association or prediction has not been achieved. Here, the power and predictive accuracy of a polygenic score are derived from a quantitative genetics model as a function of the sizes of the two samples, explained genetic variance, selection thresholds for including a marker in the score, and methods for weighting effect sizes in the score. Expressions are derived for quantitative and discrete traits, the latter allowing for case/control sampling. A novel approach to estimating the variance explained by a marker panel is also proposed. It is shown that published studies with significant association of polygenic scores have been well powered, whereas those with negative results can be explained by low sample size. It is also shown that useful levels of prediction may only be approached when predictors are estimated from very large samples, up to an order of magnitude greater than currently available. Therefore, polygenic scores currently have more utility for association testing than predicting complex traits, but prediction will become more feasible as sample sizes continue to grow. Recently there has been much interest in combining multiple genetic markers into a single score for predicting disease risk. Even if many of the individual markers have no detected effect, the combined score could be a strong predictor of disease. This has allowed researchers to demonstrate that some diseases have a strong genetic basis, even if few actual genes have been identified, and it has also revealed a common genetic basis for distinct diseases. These analyses have so far been performed opportunistically, with mixed results. Here I derive formulae based on the heritability of disease and size of the study, allowing researchers to plan their analyses from a more informed position. I show that discouraging results in some previous studies were due to the low number of subjects studied, but a modest increase in study size would allow more successful analysis. However, I also show that, for genetics to become useful for predicting individual risk of disease, hundreds of thousands of subjects may be needed to estimate the gene effects. This is larger than most existing studies, but will become more common in the near future, so that gene scores will become more useful for predicting disease than has appeared to date. P-values. An independent replication sample is then analysed by constructing, for each subject, a polygenic score consisting of the weighted sum of its trait-associated alleles, for some subset of top ranking markers. Two related but distinct applications of this score are then possible. Firstly, testing for association between the score and the trait in the replication sample can determine whether associated markers reside within those contributing to the score. Secondly and perhaps more usefully, the polygenic score can be used to predict individual trait values or risks of disease Although individually significant markers in genome-wide association scans (GWAS) explain limited heritability of complex traits, evidence has been accruing that a considerable proportion of phenotypic variation can be explained by the ensemble of markers not achieving significance. Thus, while most of the specific genes underlying complex traits have yet to be identified, it is likely that many are represented on current genotyping products and specific identification is largely a matter of study size The first successful application of polygenic score analysis to GWAS data was in schizophrenia Similar results using a large mass of markers have been obtained for other complex traits including multiple sclerosis Applications of polygenic scores to individual disease prediction have so far been less successful, although proof of concept has been established through simulations Polygenic scores must be estimated from a finite training sample, and their effectiveness for association testing and risk prediction depends on the precision of this estimation as well as the proportion of variation explained by the polygenic score. The role of the sample size has not been thoroughly considered in this context. Several authors have expressed sensitivity and specificity in terms of the genetic variance of a predictor P-values, and different methods for weighting markers in the score. The power is obtained for testing a polygenic score for association in a replication sample, and the correlation, mean square error, and area under the receiver-operator characteristic curve (AUC) are obtained for a predictor estimated from a finite training sample. These results are used to assess some recent studies and to discuss prospects for the future utility of polygenic score analyses for the prediction of complex traits.In this work, statistical properties of polygenic score analyses are derived from a quantitative genetics model as a function of the explained genetic variance and sample sizes in discovery and replication samples. A range of options for constructing the score is considered, including estimation of the score from a different trait to the one predicted, selection of markers according to their In the framework considered here, a set of genetic markers is genotyped on an initial training sample and each marker is tested for association to a trait. Effect sizes are estimated for each marker and used to construct a polygenic score for each subject in an independent replication sample. The score is tested for association in the replication sample, in which the tested trait may differ from that in the training sample. The correlation and mean square error between the polygenic score and the tested trait are calculated. If the traits are binary, the AUC is obtained.More precisely, consider a pair of traits P-values.The expressions for power and accuracy are derived in terms of the parameters listed in P-value thresholds were used for including SNPs, with the most significant reported association having The ISC was the first to demonstrate the utility of testing polygenic scores Assuming a prevalence of 1%, P-value of the polygenic score decreases as the SNP inclusion threshold increases. This seems to suggest that a large number of associated markers lie within the mass of individually non-significant SNPs. In P-value of the polygenic score is shown as a function of the inclusion threshold, with the explained genetic variance set to its estimated value of 28.7% and other parameters as stated above. The figures show that this trend could be observed when as many as 90% of SNPs have no effects, and for the linear regression estimator the significance of the score continues to improve until the whole marker panel is included. Only for a very high proportion of null SNPs is there an optimal inclusion threshold less than 1. The allele count estimator has an optimum threshold less than 1 for all scenarios, but it is consistently less significant. Thus, in this dataset with high power, decreasing P-values are consistent with a range of polygenic models including those with a high proportion of null markers.In the ISC report, the P-value threshold, and the non-centrality parameter is roughly symmetrical around one-half. This suggests that given two samples of different size, it matters little which is chosen for training and which for testing. Furthermore, given an initial sample to be split into training and replication subsets, an obvious rule of thumb is to make an even split. Similar properties are seen under different genetic models (results not shown). Note that these results apply to association testing and not to individual prediction, which is discussed in the next subsection. For association testing there is a balance to be made between the precision of estimating the score in the training subset, and the power of testing the score in the replication subset. For prediction, however, the size of the replication subset does not affect the accuracy, only how precisely it is estimated; thus a larger training subset is more desirable in the prediction context.In this analysis the replication sample was smaller than the training sample, and we may ask what balance of sample sizes is optimal. Given the total sample size of 3322+2687 = 6009 cases and 3587+2656 = 6243 controls, the non-centrality parameter can be numerically maximised over the proportion of subjects allocated to the training sample. It is found that the optimal split is close to one-half regardless of the proportion of null SNPs or the The ISC further tested the schizophrenia-derived score against bipolar disorder, to test for a common genetic basis to those conditions. Their strongest result was with the Wellcome Trust Case-Control Consortium (WTCCC) sample of 1829 cases and 2935 controls, obtaining P-values for association as more SNPs were included in the score, obtaining The International Multiple Sclerosis Consortium performed a similar exercise using a training sample of 931 cases and 2431 controls, a replication sample of 876 cases and 2077 controls, and a marker panel of 59470 nearly independent SNPs In applying these ideas to breast and prostate cancers, Machiela et al did not find significant associations of polygenic scores Their prostate cancer study had a total of 2277 subjects, approximately half of which were cases, again split in a 9∶1 ratio and a marker panel of 165,508 nearly independent SNPs. Assuming a prevalence of 2.4% and sibling relative risk of 2.8 What sample size would have sufficient power to detect association of the polygenic score? For breast cancer the heritability of liability is estimated as 44% P-values <0.1 into the score, then selected SNPs with 0.1<P<0.2, then 0.2<P<0.3 and so on, giving ten analyses. Even if the trait is fully heritable and explained by these markers, this analysis has 20% power for the SNPs with P<0.1, reducing with each P-value interval. For 0.4<P<0.5, in which the authors found nominal significance of the score, the power is 6.7%. If all SNPs are included in the score, the power would be 38% if the trait is fully explained by the markers, but under a more conservative model in which the explained genetic variance is 30%, the power is just 8% and increases to 13% under an even split of training and testing samples. Again, splitting a single GWAS sample does not admit high power for testing a polygenic score.As a final example of association testing, this time with a quantitative trait, Simonson et al studied the Framingham Risk Score for cardiovascular disease risk In their study of breast and prostate cancers Machiela et al also calculated the AUC for prediction of disease from the polygenic score. Here it is more important for the training sample to be large, ensuring accurate estimation of the score, justifying the 10-fold cross-validation design. Their AUC did not exceed 53% for breast cancer and 56.4% for prostate cancer. Under the same assumptions as above, the analytic AUC is 53.6% for breast cancer if the markers explain the full genetic variance, or 51.8% if they explain half. However if the sample were infinitely large, the AUCs would be 89% and 79% respectively. For prostate cancer, the analytic AUCs are 54.1% if the markers explain the full genetic variance, and 52% if they explain half; for a large sample they would be 90% and 80%. Thus, the low AUCs observed by Machiela et al are compatible with their study design, but they could be considerably higher if a larger training sample were available.P-value thresholds from 10−5 to 0.8 were considered.Evans et al considered prediction for the seven diseases of the WTCCC P<0.8 to select SNPs into the score, as that threshold generally gave the highest AUC. At that threshold, the choice of R2 from the regression of disease on the polygenic score R2 on the liability scale is a more interpretable measure of accuracy for binary traits R2 derived from those reports are compared to analytic values assuming different levels of heritability explained by the markers. The choice of R2 do not directly reflect the degree of missing heritability; rather they reflect the effect of sampling variation on the variance explained by an estimated score. Corresponding AUC values are also shown, and it is again clear that the currently modest utility of polygenic scores for discrimination is explained by limited training sample sizes, and much better results are possible through larger samples.Several other studies have reported pseudo-sed here . The lowP-value threshold will eliminate much sampling error from the estimated score. P-value threshold is applied that leads to the highest AUC. An AUC of 0.75 is generally regarded as the minimum useful level for screening subjects already considered at risk, whereas AUC of 0.99 is sufficient for screening the population at large What sample size would permit estimation of a score with AUC at a clinical useful level, or otherwise close to its maximum value? The answer depends on The most favourable condition shown is Whole genome genotyping is now becoming feasible, under which the entire narrow-sense heritability would be represented. Assuming this is equivalent to about one million independent common SNPs h2 = 0.8) and moderate (h2 = 0.4) heritability. The prospects here appear more challenging in terms of the sample sizes needed to approach the achievable correlation. For example, height has heritability of about 0.8, and the number of associated variants is known to be at least in the hundreds Finally, To date polygenic score analyses have been performed opportunistically. The results provided here allow a more informed appraisal of these analyses, characterisation of the statistical properties of the methods, and insights into the future prospects of polygenic modelling. R code to compute the formulae in this paper is available from the author (sites.google.com/site/fdudbridge/software/).Current sample sizes are clearly adequate for testing association of a polygenic score in a replication sample, as long as full size samples are used for both training and testing. This is already apparent from the extraordinary significance levels reported in the seminal studies When a sample is to be split into two subsets, a roughly even split yields the greatest power for testing association of the score. However, for predicting individual trait values it is more important for the training set to be large, and standard procedures such as 10-fold cross-validation remain preferable. If both testing and prediction are intended from a single sample, a pragmatic approach is to ensure adequate power by allocating about 2000 cases and 2000 controls to the replication sample, providing this is less than half the total, and then to ensure high predictive accuracy by allocating the remainder to the training sample.The outlook for disease and trait prediction is more challenging. To date the severe shortfall in the accuracy of genetic predictors has generally been ascribed to incomplete coverage of marker panels or failure to identify sufficiently many associated markers. Here, however, no criteria for declaring individual significance are imposed, but neither does the calculation force the predictor to include markers that contribute no information. Under this pragmatic approach it results that tens of thousands of subjects, at least, are needed to derive predictors that are clinically useful. Furthermore, previous results on the potential accuracy of genetic prediction For some diseases, fairly high AUC has already been observed A fairly general construction of the polygenic score has been described, including weighted and unweighted methods from single marker analysis, and shrinkage methods used in multivariate analysis. There is little to choose between these estimators in terms of power, correlation or AUC, but the unweighted estimator will perform relatively worse as sample size increases since its sampling error does not reduce to zero. Shrinkage estimation leads to reduced mean square error for prediction and has some other advantages However, some ideal conditions have been assumed including independence of markers and of study subjects. In reality markers will be in linkage disequilibrium and the approximation by an effective number of independent tests is heuristic. Similarly, subjects will be related, if distantly. Results from real data may depart from those presented here if proper account is taken of relationships between subjects. In particular, shrinkage estimation is likely to improve power and correlation, as well as mean square error, by analysing all markers simultaneously rather than each one marginally P-values but not otherwise. Similarly, allowing a proportion of markers to have no effect only makes a difference when selecting markers by P-values. Thus the present results are relevant even if one does not entirely accept the polygenic model proposed. The normal distribution simplifies some calculations, but various heavy-tailed distributions have also been proposed for GWAS data The assumption that effects are normally distributed is necessary when markers are selected by their A novel approach to estimating parameters of the polygenic model has been proposed, showing promise for inferring the explained genetic variance and/or proportion of null markers. The method yields estimates that are similar to those obtained by existing approaches P-value thresholds that maximise the power and AUC are more permissive than the usual thresholds for individual markers. This means that polygenic analyses can be powerful while still including many non-significant markers, so they will continue to be useful as long as individually associated markers remain to be discovered. Although larger samples are needed for useful risk prediction, polygenic scores have an ongoing current role in assessing the variance explained by marker panels and the genetic correlation between related traits and populations.The Recall The genetic effects on A natural estimate of P-values between thresholds Now suppose markers are only selected into the polygenic score if they have two-tailed ie.Suppose further that a proportion P-values.To obtain It is well known that estimation and prediction for multivariate models can be improved, in terms of mean squared error, by assuming that their effects come from a common underlying distribution. A common approach in quantitative genetics is to fit a mixed model in which genetic markers have random effects for which best linear unbiased predictors (BLUPs) are obtained Suppose A currently common approach is to construct the polygenic score by summing the number of trait-increasing alleles across selected markers, without considering their effect sizes other than to identify the direction of association at each marker. This may be called an unweighted score, in contrast to the above approaches that estimate weights for each marker. The unweighted score may be more robust against errors in estimating the effect sizes arising from limited sample size, population heterogeneity, “winner's curse” bias, and confounding by population structure. Here a related approach is considered in which all markers are given the same absolute effect size on the standardised genotype scale. This is equivalent to the allele counting approach when all markers have the same allele frequency. When allele frequencies are heterogeneous, allele counting assumes that all markers have the same effect on the trait, whereas the present approach assumes that all markers contribute the same proportion of variance to the trait. Both models can be criticised but the present approach will allow the comparison of weighted to unweighted scores without considering the distribution of allele frequencies or their relation to the effect sizes.P-values as in The polygenic score is now calculated asThe forgoing is based on linear regression, which is the usual approach for quantitative traits. For binary traits the standard analysis is logistic regression, used both for estimating the coefficients The binary traits are now assumed to arise from a liability threshold model, under which all individuals have an underlying normally distributed trait, called the liability, and all those whose liability exceeds a fixed threshold will exhibit the trait. Although the liability is not directly observed, this model has several advantages for modelling polygenic effects, including independence of the genetic effects from the trait prevalence, and an elegant linear transformation between effects on liability to corresponding effects on the observed (0/1) trait. This model has recently been elucidated by several authors for studying the quantitative genetics of binary traits in humans, and the reader is referred to their papers for more detailed discussion Assuming the marginal liabilities Sensitivity and specificity are often of interest in the prediction of binary traits. In particular, the accuracy of a predictor can be assessed by the AUC constructed as follows. Subjects are classified such that those with a polygenic score above a fixed threshold are predicted to have the trait, those below the threshold to not have it. Sensitivity is the proportion of subjects with the trait who are correctly predicted as such, and specificity the proportion of subjects without the trait correctly predicted as such. Each possible threshold leads to a value of sensitivity and specificity, defining the receiver operator characteristic curve by plotting sensitivity against 1-specificity. The AUC can be defined as the probability that a pair of subjects, one with the trait and one without, is correctly classified by the predictor. Because the central limit theorem implies that the polygenic score is normally distributed, the expected AUC can be calculated as In case/control studies the increased ascertainment of cases leads to departure from the normal distribution of liability assumed in the previous subsection. To overcome this problem, it is again assumed that there is a linear transformation from an effect When there is no selection on To obtain the AUC, the same approach as before is used, but now usingR2 on the liability scale is more interpretable for binary traits as it is invariant to the population prevalence and sampling ratio The derived expressions involve An alternative to the liability threshold model is the log-risk model for binary traits, which is equivalent to the logistic model in the limit of low prevalence. Here the polygenic score estimates the log risk of disease, which is assumed to be normally distributed in the population with mean Given tainment . The difThe derived expressions were compared to simulations in which the major assumptions were examined under realistic scenarios. These assumptions include a large number of markers with effects, for equality in A baseline scenario was defined to reflect that seen in recent studies, as follows. Two normally distributed traits were simulated with explained genetic variances 0.4 and 0.3 and correlation of genetic effects of 0.65. Genotypes from 100,000 independent SNPs were simulated, with minor allele frequencies uniformly distributed on . This reflects current marker panels that directly explain about half the heritability P-value thresholds of 0.1 and 0.001 for π0 = 0.95 and 0.99 respectively; these thresholds yielded the highest R2 and AUC values. The score was then tested for association with the second trait in an independent sample of 4000 subjects. The correlation and mean square error between the score and the second trait were also estimated in the second sample. The association tests were used in The polygenic score was estimated using the first trait in a sample of 4000 unrelated subjects. The score was constructed using m expectation, with resulting over-dispersion in the estimating equation . Effect sizes in the two samples were drawn from the bivariate normal distribution with marginal variances 0.4, 0.3 and correlation 0.65. π(DOCX)Click here for additional data file.Table S20, proportion of SNPs having no effect on traits. P, P-value for including SNP in the polygenic score. NCP, non-centrality parameter. Power computed at α = 0.05. AUC, area under receiver-operator characteristic curve. Simulations of binary traits in prospective samples compared to analytic results. Analytic values are in parentheses. Genotypes for 100,000 SNPs were simulated in 4000 subjects in each of two samples. Minor allele frequencies were drawn from Unif. Effect sizes on liability were drawn from the bivariate normal distribution with marginal variances 0.4, 0.3 and correlation 0.65. Trait prevalence was 0.2 in both samples. π(DOCX)Click here for additional data file.Table S30, proportion of SNPs having no effect on traits. P, P-value for including SNP in the polygenic score. NCP, non-centrality parameter. Power computed at α = 0.05. AUC, area under receiver-operator characteristic curve. Simulations of binary traits in case/control samples compared to analytic results. Analytic values are in parentheses. Genotypes for 100,000 SNPs were simulated in 4000 subjects in each of two samples. Minor allele frequencies were drawn from Unif. Effect sizes on liability were drawn from a bivariate normal distribution with marginal variances 0.4, 0.3 and correlation 0.65. Trait prevalence was 0.001 in both samples, cases and controls sampled in equal proportion. π(DOCX)Click here for additional data file.Table S40, proportion of SNPs having no effect on traits. P, P-value for including SNP in the polygenic score. NCP, non-centrality parameter. Power computed at α = 0.05. MSE, mean square error. Simulations of quantitative traits compared to analytic results. Analytic values are in parentheses. Genotypes for 100,000 SNPs were simulated in 4000 subjects in each of two samples. Minor allele frequencies were drawn from Unif. Effect sizes in the two samples were drawn from Laplace distributions such that their marginal variances were 0.4, 0.3 and their correlation was 0.65. π(DOCX)Click here for additional data file.Table S50, proportion of SNPs having no effect on traits. P, P-value for including SNP in the polygenic score. NCP, non-centrality parameter. Power computed at α = 0.05. AUC, area under receiver-operator characteristic curve. Simulations of binary traits in prospective samples compared to analytic results. Analytic values are in parentheses. Genotypes for 100,000 SNPs were simulated in 4000 subjects in each of two samples. Minor allele frequencies were drawn from Unif. Effect sizes on liability were drawn from Lapace distributions such that their marginal variances were 0.4, 0.3 and their correlation was 0.65. Trait prevalence was 0.2 in both samples. π(DOCX)Click here for additional data file.Table S60, proportion of SNPs having no effect on traits. P, P-value for including SNP in the polygenic score. NCP, non-centrality parameter. Power computed at α = 0.05. AUC, area under receiver-operator characteristic curve. Simulations of binary traits in case/control samples compared to analytic results. Analytic values are in parentheses. Genotypes for 100,000 SNPs were simulated in 4000 subjects in each of two samples. Minor allele frequencies were drawn from Unif. Effect sizes on liability were drawn from Laplace distributions such that their marginal variances were 0.4, 0.3 and their correlation was 0.65. Trait prevalence was 0.001 in both samples, cases and controls sampled in equal proportion. π(DOCX)Click here for additional data file.Text S1Variance of genetic marker in a case/control sample.(DOCX)Click here for additional data file.Text S2Simulation of genotypes in a case/control study.(DOCX)Click here for additional data file.


Advances in next-generation sequencing technologies have enabled the identification of multiple rare single nucleotide polymorphisms involved in diseases or traits. Several strategies for identifying rare variants that contribute to disease susceptibility have recently been proposed. An important feature of many of these statistical methods is the pooling or collapsing of multiple rare single nucleotide variants to achieve a reasonably high frequency and effect. However, if the pooled rare variants are associated with the trait in different directions, then the pooling may weaken the signal, thereby reducing its statistical power. In the present paper, we propose a backward support vector machine (BSVM)-based variant selection procedure to identify informative disease-associated rare variants. In the selection procedure, the rare variants are weighted and collapsed according to their positive or negative associations with the disease, which may be associated with common variants and rare variants with protective, deleterious, or neutral effects. This nonparametric variant selection procedure is able to account for confounding factors and can also be adopted in other regression frameworks. The results of a simulation study and a data example show that the proposed BSVM approach is more powerful than four other approaches under the considered scenarios, while maintaining valid type I errors. Although common variants (CVs) that contribute to complex genetic diseases have been successfully identified from genome-wide association studies (GWAS), only a portion of heritability is explained by the identified loci. The “missing heritability” is widely believed to result from other genetic mechanisms, such as gene-gene interactions, epigenetics, and rare variants (RVs). It may be that much of the missing genetic component is due to gene variants that have relatively large effects but are too rare to be picked up by GWAS. In this case, rapid advances in next-generation sequencing technologies should enable substantial progress to be made in gene mapping. However, the statistical analysis of rare genetic variations is challenging. Because rare alleles are present in only a small number of patients, the traditional variant-by-variant approach is doomed to low power The combined multivariate and collapsing (CMC) method Because the effect size of the allele may depend on its frequency, Price et al. A drawback of the aforementioned methods is that they are sensitive to the presence of protective and risk variants. To account for the directions of the allele effects, Ionita-Laza et al. The two most important features of the several recently proposed statistical methods are (1) the pooling or collapsing of multiple rare single nucleotide variants together, and (2) the application of a proper weight scheme to enrich the pooled RVs. Multiple RVs, when pooled together, collectively can have a reasonably high frequency and effect. However, if the pooled RVs are associated with the trait in different directions, then the pooling weakens the signal in associated RVs and reduces the statistical power. It is helpful to classify variants according to the directions of their effects with variants that are most likely to cause disease being up-weighted, and variants that have no effect on disease being down-weighted.Machine learning methods have been widely applied in studies with small sample sizes The aim of the present study was to develop a new data-adaptive risk measure (RM) for identifying informative RVs. The proposed backward SVM (BSVM)-based approach considered the directions of the effects of the variants while weighting the individual RVs during the collapse. Specifically, to achieve adequate statistical power based on a reasonably high frequency and effect, all rare variants (RVs) were weighted and collapsed into either the “risk” or the “nonrisk” category; individual RVs with neutral effects were then removed backwardly from the two categories of collapsed variables in the proposed model selection procedure to retain informative RVs. Simulation studies under various scenarios and genetic mechanisms were conducted to compare the performances of the proposed BSVM and four other approaches. These approaches were applied to the type I diabetes mellitus (T1DM) dataset from Nejentsev et al. b is the bias. n be the total number of individuals and k. The observed affected status of individual k, k is affected; otherwise, k is unaffected. The optimal hyperplane is obtained by solving the following quadratic form:C (>0) is a penalized parameter  and major alleles for variant i, respectively, where i = 1,…, M; j = 1, 2; 1 = 1k,…, 1n; 2 = 1,…, n2k; 1+n2n = n, and defineAssuming the genotype data in the studied region for i for cases Assume that i was defined as the likelihood ratio of a mutation event in a case over a control, given the estimated mutation rate of variant i and its risk category. To obtain a similar measure for nonrisk variants, the RM for a nonrisk variant was defined as the likelihood ratio of a mutation event in a control over a case. If we assume that the mutation event follows a Poisson distribution, given the estimated mutation rate for a case 1k or a control 2k, the likelihood ratio for a mutation event of variant i occurring in cases (or controls) compared to controls (cases) is:i, and (m+2)/(m+1) is the correction factor to avoid a zero denominator, 1 = 1,…, n1k, and 2 = 1,…, n2k. The risk measure is proportional to the relative risk for a case (or control) having the mutant allele compared to a control (or case), which is approximately the odds ratio (OR) when the variant is rare A variant was classified as a “risk variant” if the number of mutations in cases was larger than the number in controls, and as a “nonrisk variant” otherwise i, denoted as RMi, was used as a weight for variant i. The features of RMi are as follows: (i) 1< RMi <∞; (ii) the larger the RMi, the higher the positive/negative association between variant i and the disease; and (iii) when there is no association between variant i and the disease, RMi is close to one.Down-weighting noncausal variants and up-weighting causal variants can improve statistical power M variants, including 1M risk and 2M nonrisk variants. Then the cumulative weighted risk minor-allele variable for individual k,1M risk variants. Similarly, the cumulative weighted protective minor-allele variable for individual k, 2M nonrisk variants. We used Assume that there are 2 be the coefficient of determination of the model, namely:t, and 2 is difficult to interpret in nonlinear models, it reportedly becomes larger with a better fit and can be used to compare nonlinear models 2 was used as an indicator of the goodness of fit for variant selection. R2 approximated to 0 under the null hypothesis; and it increased when the situation moved toward the alternative hypothesis Let Rk as 1+n2k = 1, …, n. Then we performed the following steps:i) at a time from either i) is denoted by:Remove one variant .Compute RRepeat steps 1 and 2 for all variants.i if R2(−i)>R2(−i′) for all i′i, i′ = 1,…, M−q−1. If R2(−i)≥R2, then substitute R2 by R2(−i), and Remove variant 2>R2(−i) for all i = 1,…, M-p, where p is the total number of “redundant” variants that have been removed from the model selection procedure prior to this step.Repeat steps 1–4 until RStarting with Next, the significance of the association between the disease and the informative variants remaining in the model was assessed by permutation tests. The empirical distribution under the null hypothesis was derived by randomly permuting each individual affected status in the absence of covariates, whereas each estimated affected status was randomly permuted in the presence of covariates c is a normalizing constant. Similar to Madsen and Browning U) and their population-attributable risks (PARs) The frequency of mutations for each variant A) were determined by the ORs and MAFU,To mimic a real data example, a total of 183 variants with total PARs of 0.03 and 0.05 were generated. Roughly 141 of the 183 variants were RVs (MAFs <0.01) under the simulated model The proposed RM weighting with the BSVM method had the highest power among the five weightings under scenarios with risk variants or a mixture of risk and protective variants . Table 2It is likely that the studied region, which involves multiple genes under different pathways, contains risk and protective variants. Therefore, we studied the performance of the five approaches with a mixture of risk and protective variants in the studied region . The tot−11%) for Fp, from 0.33 to 0.25 (−8%) for EREC, from 0.36 to 0.24 (−12%) for WSt, from 0.45 to 0.39 (−6%) for RBt, and from 0.53 to 0.52 (−1%) for BSVM. These results suggest that the BSVM method was more robust in the scenario with a mixture of risk and protective variants than the other four methods. The BSVM method further identified informative variants with significant effects on disease . These findings are consistent with the results from Iuliana et al. IFIH1 gene using the SVM method  and rs35337543 ; and the significant CV was rs1990760 .The p method . The BSVM method . The sigWe have proposed a novel data-adaptive BSVM-based selection procedure to identify a region with RVs associated with complex traits and individual variants in the disease-associated gene/region. Likelihood ratios of the Poisson distributions for individual variants between cases and controls were used to weight the variants, which were collapsed into two variables according to the effect directions. The selection procedure was applied to the two collapsed variables to select informative variants associated with disease. Permutation tests were used to assess the significance of the gene/region with selected variants and to identify possible functional individual variants in the significance region.This approach has several useful features. As an SVM approach, it does not rely on asymptotic statistical theory and is applicable to studies with limited sample sizes. By starting with collapsed high-frequency variants, it eases the concern of low power due to the sparseness of RVs. The data-adaptive weighting scheme accounts for the directions of effects of risk and nonrisk variants. This RM-based weighting and model selection procedure could be adopted in other approaches for identification of RV. The categorized, collapsed variables are nearly orthogonal to each other, which improves the power for identifying informative variants in the presence of mixed effects. This nonparametric approach does not require any prespecified model assumptions, can be applied to scenarios with CVs and RVs by including CVs as additional covariates, and allows for covariate adjustments. Finally, the approach can be used to identify significant individual variants associated with disease for further study, diagnostics, and predication.In the simulation study and data example, the proposed method outperformed other current methods in terms of power, while maintaining valid type I errors. The choice of C  in equation (2) is a trade-off between precision and variation. Previous studies have shown that the performance for RV prediction is similar when C is set at 1, 10, or 100 http://sb.nhri.org.tw/BSVM/.In the data example, BSVM appeared to be the most powerful of the five methods for RV analysis; but it also took the longest time to run Appendix S1Technical details of the SVM Method.(DOC)Click here for additional data file.