The direct estimation of heritability from genome-wide common variant data as implemented in the program Genome-wide Complex Trait Analysis (GCTA) has provided a means to quantify heritability attributable to all interrogated variants. We have quantified the variance in liability to disease explained by all SNPs for two phenotypically-related neurobehavioral disorders, obsessive-compulsive disorder (OCD) and Tourette Syndrome (TS), using GCTA. Our analysis yielded a heritability point estimate of 0.58  for TS, and 0.37  for OCD. In addition, we conducted multiple genomic partitioning analyses to identify genomic elements that concentrate this heritability. We examined genomic architectures of TS and OCD by chromosome, MAF bin, and functional annotations. In addition, we assessed heritability for early onset and adult onset OCD. Among other notable results, we found that SNPs with a minor allele frequency of less than 5% accounted for 21% of the TS heritability and 0% of the OCD heritability. Additionally, we identified a significant contribution to TS and OCD heritability by variants significantly associated with gene expression in two regions of the brain  for which we had available expression quantitative trait loci (eQTLs). Finally we analyzed the genetic correlation between TS and OCD, revealing a genetic correlation of 0.41 . These results are very close to previous heritability estimates for TS and OCD based on twin and family studies, suggesting that very little, if any, heritability is truly missing  from TS and OCD GWAS studies of common variation. The results also indicate that there is some genetic overlap between these two phenotypically-related neuropsychiatric disorders, but suggest that the two disorders have distinct genetic architectures. Family and twin studies have shown that genetic risk factors are important in the development of Tourette Syndrome (TS) and obsessive compulsive disorder (OCD). However, efforts to identify the individual genetic risk factors involved in these two neuropsychiatric disorders have been largely unsuccessful. One possible explanation for this is that many genetic variations scattered throughout the genome each contribute a small amount to the overall risk. For TS and OCD, the genetic architecture  is presently unknown. This study examined the genetic architecture of TS and OCD in a variety of ways. We found that rare genetic changes account for more genetic risk in TS than in OCD; certain chromosomes contribute to OCD risk more than others; and variants that influence the level of genes expressed in two regions of the brain can account for a significant amount of risk for both TS and OCD. Results from this study might help in determining where, and what kind of variants are individual risk factors for TS and OCD and where they might be located in the human genome. The limited heritability explained by significant GWAS findings has led to the so-called “missing heritability” dilemma and subsequent hypotheses have been generated for how to capture the heritable factors contributing to human trait variation For most complex traits, DNA sequence variants that meet the genome-wide significance threshold do not explain the majority of the heritability as estimated by twin and family studies The application of genome-wide estimation of heritability using restricted maximum likelihood (REML) methods has provided a new means to quantify narrow sense heritability attributable to all interrogated variants in GWAS 2 = 27%–45% adult onset OCD; 65% for childhood onset OCD, h2 = 60% for TS) and likely to be genetically related Tourette Syndrome (TS) and obsessive-compulsive disorder (OCD) are neurodevelopmental disorders with overlapping neural circuitries and similarities in phenotypic expression This study sought to quantify the heritability of both TS and OCD using genome wide genotype data and the REML approach implemented in GCTA All participants 18 years of age and older gave informed consent. Individuals under 18 years of age gave assent after a parent signed a consent form on their behalf. The Ethics Committees of each participating site approved this research and the research was conducted in accordance with the Declaration of Helsinki.The datasets used in this study are described in depth elsewhere  or “heritability” between cross-platform controls   . Additiowww.complextraitgenomics.com) was used to create a genetic relationship matrix (GRM) file containing IBD relationship calculations for all pair-wise sets of individuals. Principal components were determined within GCTA, using all genotype data, and the top 20 principal components were applied to each analysis. The REML analysis was then performed using the respective GRMs and principal component quantitative covariates. As this analysis was performed with dichotomous case/control traits, it was necessary to convert the phenotypic variance to an underlying liability scale. This conversion uses population prevalence to adjust for case/control ascertainment in the sample and to modify the phenotypic variance estimate accordingly . We conducted three primary analyses  and five exploratory analyses . For each primary analysis, ten permutations of the phenotype were performed and GCTA was run on each permutation to observe the stability of the heritability estimate.For each analysis presented, GCTA v1.2  to assess the effect of co-morbidity on the cross-disorder genetic correlation. We then applied a likelihood ratio test (LRT) to determine the statistical significance of each genetic correlation.Imputation was performed using IMPUTE v2.1.2 and the 1000 Genomes Project data as a reference panel. Only imputed SNPs that were in strong linkage disequilibrium (LD) (info>0.6) with genotyped SNPs and had a high certainty (>90%) of the predicted genotypes were retained. Imputed SNPs that showed significant genotyping platform effects were excluded. Imputed results were converted to MaCH format  using an in-house script. MaCH dosage data was used to create GRMs for each chromosome. Chromosome specific GRMs were then merged as needed for additional analyses. The total number of imputed SNPs after QC included 7,657,106 SNPs in both the TS and OCD samples.A separate GRM was generated for each chromosome. Each GRM was then run in separate REML analysis. An additional analysis was conducted in which all chromosomes were modeled jointly in a single REML analysis.We chose not to employ a minor allele frequency (MAF) cutoff in any of the heritability analyses. This decision was based on the observation that minor allele frequency cutoffs did not alter estimates of heritability for the control-control analysis after establishment of stringent differential missingness rates and call rate. We partitioned the directly genotyped and imputed variants according to MAF bin. For the directly genotyped variants we created six bins representing MAFs from 0.001–.05, >0.05–0.1, >.1–.2, >.2–.3, >.3–.4, and >.4–.5 and generated GRMs for each bin. For the imputed genotypes we created two bins representing MAF 0.001–0.05 and >0.05 to 0.5 and generated GRMs for each bin. For each set of variants (directly genotyped and imputed respectively) we then combined binned GRMs in a single joint REML analysis, allowing the effects of LD to be partitioned by the REML analytic approach.We annotated variants for genic and intergenic classification using ANNOVAR  Multiple studies have reported significantly higher heritability for early-onset OCD than for adult onset OCD 2 = 0.000001; se = 0.11, p = 0.5) . The overall narrow-sense heritability for TS calculated using the directly genotyped data of 617 TS cases and 4,116 controls was 0.58  and for OCD  was 0.37 . In order to test for possible inflation in the TS heritability point estimate due to small sample size, the OCD analysis was repeated using a random set of 617 OCD cases that matched the TS sample size. This experiment yielded a near-identical heritability point estimate for OCD with an expected increase in the standard error . For each primary analysis, ten permutations of the phenotype were conducted as an additional control, yielding on average no significant heritability . Analyses were also conducted on imputed data, resulting in similar estimates of heritability for TS  and OCD .Analysis of the control datasets split by platform demonstrated no artifactual “cross-platform” heritability  and OCD . The genetic correlation between the two disorders was 0.41 (se = 0.15), which was significantly different from zero . We conducted an exploratory bivariate analysis which limited the included SNPs to eQTLs identified in parietal cortex or cerebellum and found a genetic correlation of 0.31 (se = 0.17) which was also significantly different from zero . Our assessment of the impact of overlapping phenotypic co-morbidity on the estimate of genetic correlation resulted in a smaller, yet purer set of samples (after removing 316 samples with known TS/tic and OCD co-morbidity) and yielded a genetic correlation of 0.50 .2TS = 0.61, h2OCD = 0.35) were not different than the global univariate heritability estimates   and S6. These results suggest that population stratification was appropriately controlled in these analyses.For both the TS and OCD phenotypes, the summed total of individual “by chromosome” heritability estimates  or between number of genes and heritability  for OCD did not reach statistical significance .In addition, there was a significant correlation between both chromosome length and heritability , and number of genes per chromosome and heritability  in the TS data . The cor and S6. When chromosome 15 was removed, a significant correlation between chromosome length and heritability was recovered . Greater than expected heritability per chromosome was discovered in the TS data for chromosomes 2, 5, 11, 16 and 20 and S8. In addition, some chromosomes contributed less heritability to OCD than expected due to chromosome length alone. Notably chromosome 6, which houses the HLA locus, did not contribute to overall heritability estimates in OCD or TS.To test individual chromosomes for any significant concentration of heritability beyond that expected by chromosome length, SNP number, or gene number, we calculated the expected proportion of heritability for each chromosome based on the number of SNPs (in our data) as well as the number of genes (from SangerVega) on each chromosome, assuming a polygenic model with a uniform distribution of heritability across the genome. A comparative plot of observed “by chromosome” heritability relative to the expected heritability under the uniform distribution model demonstrated that chromosome 15 harbored a larger proportion of heritability for OCD than expected based on either the number of SNPs or number of genes represented on the chromosome . This result was observed in both the directly genotyped data and imputed data. Using the directly genotyped data, TS SNPs with MAF<0.05  represented 21%  of the total calculated heritability, while OCD SNPs with MAF<0.05  represented 0%  of the total calculated heritability. Similar results were observed using the imputed data, with approximately 30% of the total heritability of TS captured by variants with MAF<0.05  and 0% of the total heritability of OCD captured by variants with MAF<0.05 .We identified a significant difference between TS and OCD in the proportion of heritability accounted for by variants with MAF<0.05 2 = 0.15, se = 0.06, p = 0.003) of the total OCD heritability . In the analysis of imputed data, parietal lobe eQTLs accounted for 28%  of the total TS heritability and 29%  of the total OCD heritability. Cerebellar eQTLs accounted for 35%  of the total OCD heritability but only 19%  of the total TS heritability . When the brain eQTLs were further subdivided into parietal “only”, cerebellum “only” and those present in parietal lobe and cerebellum we found that ∼25% of both TS and OCD heritability was accounted for by parietal eQTLs, ∼10% of both TS and OCD heritability was accounted for by eQTLs found in both tissues, and that cerebellar eQTLs again accounted for more heritability (20%) in OCD than in TS (9%) . We then tested a final model in which brain eQTLs from cerebellum and parietal tissues were combined into a single “brain-only” partition, and included in the same joint analysis with muscle eQTLs, eQTL found in both brain and muscle, and a non-eQTL partition. In this model, brain eQTLs accounted for 33%  of the total TS heritability and 59%  of the total heritability for OCD. Skeletal muscle eQTLs accounted for 25%  of the total TS heritability and 25%  of the total heritability for OCD. The overlapping set of eQTLs identified in both muscle and brain accounted for 8% heritability in TS  and 0%  of total OCD heritability. Finally, the remaining non-eQTL portion of SNPs accounted for only 34%  of TS heritability and 16%  of OCD heritability .In the analysis of directly genotyped data, we found that genic variants accounted for 53%  of the total TS heritability and 40% (h2 = 45–65%) than adult-onset OCD (h2 = 27–47%) .It has been observed that early-onset OCD is more heritable  correspond well with previously reported heritability estimates from family and twin studies GCTA has now been applied to a number of complex traits, including TS and OCD 2 thresholds, the dosage format of imputed data prevented it from being subjected to the same strict Hardy-Weinberg thresholds as the directly genotyped data. Therefore this small decrease in measured heritability may reflect additional noise in the imputed data contributed by lower quality SNPs. Alternatively, the decrease may reflect the possibility that even with very stringent QC some minor residual technical artifacts may have remained in the directly genotyped data. Perhaps most interesting though, is the observation that the imputed data did not show a significant increase in heritability, even with a substantial increase in the number of interrogated variants, suggesting that the directly genotyped data alone sufficiently captured the narrow-sense heritability present in SNP level data.The difference between the heritability estimates calculated from imputed and directly genotyped data was not significant. However, the imputed heritability estimates were slightly but consistently lower compared to the estimates generated from the directly genotyped data. While we employed strict rWe identified a significant genetic correlation between TS and OCD of 0.41 (se = 0.15). This estimate of genetic overlap is smaller than that observed for schizophrenia/bipolar disorder (0.68±0.04), but similar to that of bipolar disorder/major depressive disorder (0.47±0.06) and schizophrenia/major depressive disorder (0.43±0.06) We went on to examine the genomic distribution of liability by partitioning the heritability by chromosome. We found that the additive heritability estimated by chromosome for either OCD or TS was not significantly different from the cumulative univariate heritability calculated by using all data together. This served as an additional quality control check and confirmed the absence of residual LD between chromosomes, which can arise in a sample with cryptic relatedness or population substructure  and S6. This increase in correlation is quite similar to the increase in the correlation between chromosome length and heritability reported for multiple sclerosis (MS) The initial correlation between OCD heritability and chromosome length increased substantially after removal of chromosome 15 Of note, essentially no heritability for either OCD or TS was observed on chromosome 6, which encodes both the HLA and histone gene clusters. This absence of heritability within the MHC region is relevant to these two phenotypes, since an autoimmune etiology for both OCD and TS has been proposed, based on similarities between these two disorders and the acute neuropsychiatric presentation of patients with Sydenham chorea in the setting of acute rheumatic fever and triggered by Group A streptococcal infection no heritability was captured by SNPs with MAF<5%, while the majority of the heritability detected was due to those SNPs with MAF>30%. In contrast, for TS, 21% of the total heritability was captured by SNPs with MAF less than 5% with the remaining bulk of the heritability shared approximately equally among alleles with MAF between 0.10–0.50. Analysis of imputed data confirmed these findings and showed that SNPs with MAF<0.05 accounted for 30% of the total TS heritability and 0% of the total OCD heritability. To ensure that the difference between TS and OCD rare SNP heritability estimates were not due to subtle population substructure in the TS sample, we conducted an additional analysis which further partitioned the MAF<5% bin by chromosome. We then compared the estimate of heritability calculated by summing each chromosome  to the estimate of heritability based on all MAF<5% SNPs in a single analysis  and found no significant difference. If population substructure was present in the TS sample and was a source of bias contributing to the increased heritability identified in the rare bin, we would have expected to see inflation of the heritability estimate due to LD between chromosomes when partitioned by chromosome and then summed In an effort to further understand the genomic architecture of OCD and TS, we performed exploratory analyses of heritability across the MAF spectrum. By running all MAF bins together in a single REML analysis, we partitioned the effects of LD across each bin, as Lee et al (2012) previously demonstrated through simulation that this approach restricts the effects of LD between bins and reflects expected heritability per bin based on simulated risk allele distributions. For OCD, The observation that TS and OCD have such different patterns for heritability estimated across the MAF spectrum points to the value that such analyses may provide for illuminating genetic architecture. There is clearly support for analysis of rare variants and follow-up sequencing in TS given the contribution to heritability observed for SNPs with MAF<0.05. The observations in OCD are also intriguing with respect to questions on the set of genetic models that would be consistent with heritability being concentrated among variants with high MAF. Are such patterns consistent with particular models for the age of a disorder, or perhaps with aspects of the evolutionary history of contributing risk alleles? It will also be important to investigate whether such analyses applied to other disorders will reveal a full continuum with respect to the proportion of phenotypic variance attributable to variants across the MAF spectrum or something more discrete with overall patterns more similar to OCD at one end and TS at the other. Replication analysis with larger samples and additional phenotypes will undoubtedly shed more light on the analysis presented here.2 = 0.19, se = 0.08, p = 0.009) in a joint analysis with an additional non-brain tissue (muscle), although the TS “brain-only” partition approaches significance   and muscle eQTLs in an effort to concentrate heritability within smaller putatively functional classes of testable variants  = 0.06) . The resOur results examining the heritability of childhood-onset OCD are in line with previous studies that suggest a higher heritability for childhood-onset OCD than for adult onset OCD. However, because of the smaller sample sizes due to splitting the OCD sample into two groups based on age of onset, the 95% confidence intervals for childhood-onset and adult-onset OCD overlap, and are not significantly different from each other. With increased sample sizes it may be possible to confirm these observed heritability differences and to obtain more precise estimates of the relative heritability of child and adult onset OCD.Our results explain essentially all of the heritability of TS and a majority of the heritability of OCD established by twin and family studies. One factor that may have contributed to the significant proportion of heritability explained by our results is the ascertainment strategy employed to collect the samples. As Klei and colleagues (2012) elegantly demonstrated, heritability estimated from samples belonging to multiplex families can be greater than those generated by samples belonging to simplex families. This phenomenon is most likely a matter of increased polygenic load reflected in the multiplex samples, as opposed to differing allelic architectures In conclusion, this study provides substantial evidence that both TS and OCD are highly heritable, polygenic, and that a significant majority of the heritability of both disorders is captured by GWAS SNP variants. Using both directly genotyped and imputed data, we also provide evidence of allelic architecture differences between TS and OCD. Specifically, we identified a significant contribution from rare variants in the genomic architecture of TS that appears to be absent from the architecture of OCD. Our results also provide additional evidence of a prominent role for chromosome 15 in OCD liability and possible concentration of TS liability on chromosomes 2, 5, 11, 12, 16 and 20. We also find that brain eQTLs concentrate a significant proportion of the heritability present in TS and OCD. It is unlikely that the differences in genetic architecture between TS and OCD are due to incomplete matching during QC or other, unknown, technical biases, as all cases were genotyped with identical technology, shared the same control set, and were imputed together. Taken together, these results advance our understanding of the overlapping and non-overlapping genomic architectures of TS and OCD and suggest that non-overlapping elements of the architecture of each phenotype may be a limiting factor in the genetic relationship between them. Moreover, these results may be used to inform priorities for future studies of both disorders. For example, given the apparent contribution of rare variants to the heritability of TS, DNA sequencing may be a particularly informative analysis, whereas larger sample sizes and additional GWAS is likely to identify the majority of susceptibility variants for both disorders. Future studies aimed at understanding the genetic control of shared neurocircuitry in TS and OCD may be most well powered by testing the association of shared genetic risk  with a well-defined quantitative neurobiological endophenotype. Studies such as the one presented here continue to highlight the value of “big picture” analyses, which provide insight into the genetic landscape of a phenotype, as a necessary and intelligent complement to the mapping of specific risk variants.Figure S1Q-Q plot of the distribution of p-values for all directly genotyped SNPs in the “control-control” logistic regression analysis in which platform was substituted for phenotype. The top 5 principal components were used as covariates in the analysis. We observed no deviation from the expected distribution under the null hypothesis of no association.(JPG)Click here for additional data file.Figure S2The distribution of pi-hat  among TS cases. A pi-hat threshold of 0.05 was implemented for all analyses.(JPG)Click here for additional data file.Figure S3The distribution of pi-hat  among OCD cases. A pi-hat threshold of 0.05 was implemented for all analyses.(JPG)Click here for additional data file.Figure S4The distribution of pi-hat  among controls. A pi-hat threshold of 0.05 was implemented for all analyses.(JPG)Click here for additional data file.Figure S5The x-axis of Figure 5 shows the difference between the actual OCD heritability calculated per chromosome and the expected heritability calculated per chromosome based on the proportion of genes represented by the given chromosome. Each grey bar represents a chromosome and the error bars shown represent the error in the actual heritability estimate. The only chromosome showing significant deviation from expectation is chromosome 15.(PDF)Click here for additional data file.Figure S6The x-axis of Figure 6 shows the difference between the actual OCD heritability calculated per chromosome and the expected heritability calculated per chromosome based on the proportion of SNPs represented by the given chromosome. Each grey bar represents a chromosome and the error bars shown represent the error in the actual heritability estimate. The only chromosome showing significant deviation from expectation is chromosome 15.(PDF)Click here for additional data file.Figure S7The x-axis of Figure 7 shows the difference between the actual TS heritability calculated per chromosome and the expected heritability calculated per chromosome based on the proportion of genes represented by the given chromosome.(PDF)Click here for additional data file.Figure S8The x-axis of Figure 8 shows the difference between the actual TS heritability calculated per chromosome and the expected heritability calculated per chromosome based on the proportion of SNPs represented by the given chromosome. Each grey bar represents a chromosome and the error bars shown represent the error in the actual heritability estimate. Chromosomes 2, 5, 16 and 20 show increased heritability compared to expectation based on both proportion of genes and proportion of SNPs.(PDF)Click here for additional data file.Figure S9Figure displays the eQTL annotation based bins including 1) a “parietal-only” bin consisting of eQTLs identified in parietal cortex and not in cerebellum, 2) a “cerebellum-only” bin consisting of eQTLs identified in cerebellum and not in parietal cortex, and a “parietal and cerebellum” bin consisting of eQTLs identified in both cerebellum and parietal cortex. Finally, a non-eQTL partition was included.(PDF)Click here for additional data file.Figure S10Figure displays the eQTL annotation-based bins including 1) a “brain-only” bin consisting of eQTLs identified in parietal cortex or cerebellum and not in muscle, 2) a “muscle-only” bin consisting of eQTLs identified in muscle and not in parietal cortex or cerebellum, and a “brain and muscle” bin consisting of eQTLs identified in muscle and either cerebellum, parietal cortex, or both. Finally, a non-eQTL partition was included. The asterisk represents a significant p-value of p = 0.009.(PDF)Click here for additional data file.Methods S1Description of additional methods used in the quality control of samples and SNPs for GCTA analysis. Additionally, a brief description of the identification of eQTL. Finally we provide analytic details of the calculation of heritability on the sibling recurrence risk scale.(DOC)Click here for additional data file.Table S1Effects of differing pi-hat thresholds on Tourette Syndrome and OCD heritability estimates. Pi-hat refers to the proportion of alleles shared IBD and thus represents a relatedness threshold required for each analysis.(DOC)Click here for additional data file.Table S2Control-control analysis with differing QC thresholds. Table showing changes to the control-control heritability estimate based on differing filtering approaches to the data. Numbers in each cell represent the number of SNPs filtered based on each threshold. MAF = minor allele frequency. Diff SNP Missing = genotypic differential missingness rate. HWD = SNPs with significant deviation (p<0.05) from Hardy Weinberg Equilibrium. SNP Call Rate = Genotyping call rate per sample. Platform Effect SNP = SNPs with significant platform effects. Total # SNPs = Total number of SNPs surviving QC and used in heritability analysis. Total # Sample = Total number of subjects surviving QC and used in heritability analysis. Heritability (se) = Heritability point estimate and standard error of the estimate. P-value = likelihood ration test generated p-value for significance of heritability estimate.(DOC)Click here for additional data file.Table S3Heritability for Tourette syndrome, obsessive-compulsive disorder, and early onset obsessive-compulsive disorder at a range of reported population prevalence rates.(DOC)Click here for additional data file.Table S41st-GCTA refers to the risk to first degree relatives calculated from the given population prevalence and GCTA based heritability estimate. The title λ1st-lit refers to the risk to first degree relatives calculated from the given population prevalence and the heritability estimates from the literature cited in the main text of the paper.Heritability in terms of sibling recurrence risk (λ) for Tourette syndrome, obsessive-compulsive disorder, and early onset obsessive-compulsive disorder at a range of population prevalences. The title λ(DOC)Click here for additional data file.Table S5Tourette Syndrome heritability partitioned by chromosome. Heritability estimates given for each chromosome for both directly genotyped and imputed data. P-values calculated with a likelihood ratio test are also included; * indicates p-values significant after Bonferroni correction.(DOC)Click here for additional data file.Table S6Obsessive-compulsive disorder heritability partitioned by chromosome. Heritability estimates given for each chromosome for both directly genotyped and imputed data. P-values calculated with a likelihood ratio test are also included; * indicates p-values significant after Bonferroni correction.(DOC)Click here for additional data file.Table S7GWAS estimated heritability partitioned by genic regions. Heritability estimates for TS and OCD partitioned based on genic annotation. “Genic” includes all coding, intronic, 3′UTR and 5′UTR SNPs. Intergenic is defined as not otherwise genic. The number of SNPs , heritability, and proportion of total heritability is given for TS and OCD.(DOC)Click here for additional data file.Table S8Partitioning analysis of heritability based on brain eQTL annotations. Partitions include eQTLs identified in cerebellum only, in parietal cortex only, in both parietal cortex and cerebellum, and non-eQTL SNPs.(DOC)Click here for additional data file.Table S9Partitioning analysis of heritability based on brain and skeletal muscle eQTL annotations. Partitions include eQTLs identified in brain only, in muscle only, in both brain and muscle, and non-eQTL SNPs.(DOC)Click here for additional data file.Table S10Proportion heritability and correlation with chromosome length for all phenotypes analyzed with GCTA. Table includes data from representative account of GCTA publications with respective reference, phenotype studied, proportion of total twin/family study heritability estimated by GCTA analysis, correlations reported for heritability by chromosome and chromosome length, adjusted correlation reported for heritability by chromosome and chromosome length .(DOC)Click here for additional data file.


In the present study we attempt to clarify why three such ‘environmental’ measures  are consistently found to be heritable. Through multivariate genetic analysis of a sample of adolescent twins from the UK we show that the heritability of these putative environmental measures can be explained via their association with five behavioural phenotypes: oppositionality, delinquency, physical aggression, depression and anxiety. This is consistent with the notion that being genetically susceptible to certain behavioural difficulties could lead to exposure to certain life events, and this may account for the reported heritability of ‘environmental’ measures. Results are discussed in the context of possible active, evocative and passive gene–environment correlations.An increasing body of evidence shows that many ‘environmental’ measures are heritable, indicating genetic involvement in environmental exposure (or  Genes play an important role in explaining the appearance, behaviour and personality characteristics of people  elements of the family environment are genetically correlated with both antisocial behaviour and depression , paternal negativity and negative life events.We focus on these putative environmental measures because they are frequently reported to be heritable .Data were collected via postal questionnaire. The first wave of data was weighted (at the family level) to match the distribution of educational qualifications observed in a nationally representative sample . Resultant models allow for intragroup correlation and relax the requirement that observations be independent of one another. They are therefore suitable for the analysis of samples of related individuals.Phenotypic relationships between variables were explored using the survey models of Stata 10  were employed to assess whether the heritability of each of our environmental measures was accounted for via their association with the behavioural phenotypes see Fig. . Environχ2 fit statistic to test for significant change in model fit. Akaike’s Information Criterion (AIC) was also used in tandem with the −2LL. Broadly speaking, when comparing models a smaller AIC value suggests a better (or more parsimonious) fit. The AIC can be particularly useful when comparing models that are not nested (e.g. ACE models vs. saturated models). Prior to genetic analyses square-root transformations were applied to all variables to normalise their distributions. Residuals were taken to account for the effects of sex and age on all variables.Models were fitted using −2log likelihood simultaneously in 5 groups; MZ male, DZ male, MZ female, DZ female, and DZ mixed-sex pairs. Nested models were tested using the Means and standard deviations, and the results of regression analyses examining the effects of age and sex on each of the study variables, are presented in Table Pair-wise correlations between phenotypes are presented in Table Univariate genetic analyses for all of the variables included in the current study have been presented elsewhere , we note that our reliance on self-report measures is a limitation. Specifically, shared method variance and perceptual bias may have inflated the phenotypic correlations between measures and using other/multiple informants may have resulted in different patterns of findings. It is unclear how this may have affected the heritability estimates and pattern of genetic correlations between our variables. However, if issues of reporter bias, shared method variance and perceptual bias affect MZ and DZ twins in similar ways then it seems unlikely that they would affect heritability estimates or estimates of genetic correlation between variables.We hypothesised that the heritability of parental negativity and negative life events would be explained via their association with oppositionality, delinquency, physical aggression, depression and anxiety. All of these behavioural phenotypes were positively associated with the environmental measures, consistent with the hypothesis that adolescents with emotional and behavioural difficulties tend to be subject to and/or provoke elevated levels of parental negativity and experience an increased number of negative life events.For maternal negativity, oppositionality, delinquency, depression and anxiety were the phenotypes with which genetic correlations were significant. That is, genetic factors influencing these behaviours were also involved in the experience of maternal negativity. These gene–environment correlations could be active in nature, whereby the adolescent’s genetically influenced behaviour leads them to seek out conflict with their parents, they could be evocative in nature, whereby the adolescent’s genetically influenced behaviour provokes negativity and/or they could be passive, whereby genetic factors that result in negativity on the part of the mother are shared with the adolescent, in whom they lead to oppositional, delinquent, depressive and anxious behaviour. In our Cholesky decomposition no residual genetic variance remained in maternal negativity once that shared with the behavioural phenotypes was accounted for.For paternal negativity the Cholesky decomposition indicated that 9 % of genetic variance remained after accounting for that shared with the 5 behavioural phenotypes. Confidence intervals included zero, indicating that this was not significant; however this was true for many of the estimates. This could reflect low power and/or may be a result of the small phenotypic correlations between variables. Paternal negativity had significant genetic correlations with oppositionality and delinquency, indicating that these 2 variables were of most importance in explaining the heritability of paternal negativity.The heritability of negative life events was entirely accounted for in our Cholesky decomposition and genetic correlations in the correlated factors solution were significant for oppositionality, delinquency, physical aggression and depression. This would indicate that genetic factors involved in each of these behavioural phenotypes are also involved in the experience of negative life events. It is noteworthy also that genetic factors involved in the experience of negative life events were almost perfectly correlated with those involved in oppositionality and delinquency.Oppositionality and delinquency seemed to be the most important behavioural phenotypes in explaining the heritability of all our environmental variables—displaying genetic correlations with each . Depression was related to maternal negativity and negative life events, with anxiety and physical aggression being genetically related to one environmental variable each. It is intriguing that physical aggression, being a serious problem behaviour, was only weakly related to maternal/paternal negativity and not genetically correlated at all. This could be attributed to the artefactual effects of using a sample displaying only low levels of physical aggression. However aggression was genetically correlated with negative life events, thus physical aggression may in fact not be genetically related to parental negativity at all.In the present article we have shown that genetic factors play a role in explaining why some adolescents report experiencing environments high in stressors while some report experiencing environments low in stressors. Further, we have shown that this heritability can be explained via the association between these environmental measures and behavioural and emotional problems. There are several ways in which we can interpret this finding. The first explanation is derived from the concepts of active and evocative rGE: whereby genetic factors operate in such a way as to make a person create or seek out an environment that ‘matches’ their genotype. In this interpretation our models would show that genetic factors involved in oppositionality, delinquency, physical aggression, and depression lead a person to increase their likelihood of experiencing negative life events, perhaps through excessive risk taking or an interpersonal style characterised by instability and conflict. This interpretation would also mean that genes involved in oppositionality, delinquency, depression and anxiety in children evoke negativity in their mother. Interestingly this would mean that only genes involved in oppositionality and delinquency evoke negativity in their father, perhaps indicating greater responsiveness to child internalising in mothers than fathers.The notion that an individual would be genetically predisposed to create for themselves an environment comprising multiple ‘stressors’ may at first glance seem counterintuitive. How could such genes evolve? To take antisocial behaviour as an example, we know that antisocial behaviour is under genetic influence. An individual predisposed to such behaviour will be more successful in some environments than others. Most probably, they will achieve the greatest success in settings in which rule-breaking or aggressive behaviour is (A) accepted (i.e. is unlikely to lead to rejection or other negative consequences) and is (B) associated with positive outcomes. Research has shown that in deviant peer environments antisocial behaviour is associated with popularity  passive rGE is actually more likely to load onto C than A (Neiderhiser et al. Parental negativity is associated with a variety of negative outcomes (Rutter et al.


The extent of LD depends on the genetic structure of the population and the density of markers. The aim of this study was to calculate accuracy of direct genomic estimated breeding values (DGEBV) using best linear unbiased genomic prediction (GBLUP) for different marker densities, heritabilities and sizes of the TS in simulated populations that mimicked previously reported extent and pattern of LD in beef cattle.The success of genomic selection depends mainly on the extent of linkage disequilibrium (LD) between markers and quantitative trait loci (QTL), the number of animals in the training set (TS) and the heritability  and marker densities (40 k or 800 k). Increasing the number of animals in the TS by 4-fold and using their phenotypes to estimate marker effects was not sufficient to maintain or increase the accuracy of DGEBV obtained using estimated breeding values (EBVs) when the trait h2 was lower than 0.40 for both marker densities. Comparing to expected accuracies of parent average (PA), the gains by using DGEBV would be of 27%, 13% and 10% for trait h2 equal to 0.10, 0.25 and 0.40, respectively, considering the scenario with 40 k markers and 1920 bulls in TS.The accuracy of DGEBV increased significantly (p < 0.05) with the increase in the number of bulls in the TS , trait hAs reported in dairy cattle, the size of the TS and the extent of LD have major impact on the accuracy of DGEBV. Based on the findings of this simulation study, large TS, as well as dense marker panels, aiming to increase the level of LD between markers and QTL, will likely be needed in beef cattle for successful implementation of genomic selection. Genomic selection is a method of marker-assisted selection based on LD that potentially explores all QTL in the genome . The breThe BV calculated from the estimated effects of markers is often called DGEBV and the blended value between DGEBV and traditional EBV is often called Genomic Estimated Breeding Value (GEBV). The accuracy of DGEBV and GEBV depends on: 1) the level of LD between markers and QTL; 2) the number of animals in the TS; 3) the heritability of the trait and 4) the distribution of QTL effects 13]] for -5 for both markers and QTLs was considered to establish mutation-drift equilibrium in historical generations. The same mutation rate was also applied in all subsequent generations after the historical ones. The parameters used for simulating the genome are given in Table The simulated genome consisted of 29 pairs of autosomes with length identical to the real bovine genome based on Btau_3.1 assembling  totalingThe training set was composed of bulls from generations three to eight for both POP1 and POP2. The reason for excluding the first two generations was to use data from a population undergoing selection, which would be mostly the case in beef cattle. In order to estimate the effects of the 40 k segregating markers, all the bulls (n = 1920) that had more than 50 offspring (average progeny size = 73) were selected from POP1 for the three levels of heritability . Of these, 960 and 480 bulls were randomly sampled so that the average accuracy of EBVs was kept the same across the TS sizes within each level of heritability. Therefore, the average progeny size was approximately the same (73) for the three TSs with an average accuracy of EBVs equal to 0.79, 0.90 or 0.94 for heritability of 0.10, 0.25 or 0.40, respectively. For the purpose of estimating the effects of 800 k markers in POP2, only 480 bulls had more than 50 offspring (average progeny size = 73) because of the smaller population size and, therefore, these were selected from POP2 for the three levels of heritabilities . However, considering that this number of bulls with highly accurate EBV (n = 480) is realistic for most beef cattle breeding programs, this scenario would be useful for assessing the accuracy of genomic selection using a high density marker panel.Two other additional TS were created by randomly selecting 7680 and 1920 animals from POP1 and POP2, respectively. In this case, the phenotypes were used to estimate the marker effects, what represented a 4-fold increase in the TS. Figure th generation of POP1 and POP2, respectively.The prediction sets were composed of 8000 and 2000 individuals randomly chosen from the 10The EBVs of animals were calculated by the standard animal model:y is the vector of trait phenotypes, μ is the overall mean, Z is an incidence matrix and a is the vector of animals' additive genetic effects and e is a vector of random errors. The variance of y was assumed to be A is the additive genetic relationship matrix and where A ridge regression model was used to estimate SNP effects for using in computing DGEBV.The model can be written asy is the vector of either trait phenotypes or EBVs calculated from trait phenotypes and pedigree data by BLUP, μ is the overall mean, X is the matrix of marker genotypes for each animal and β is the vector of marker effects, and e is a vector of random errors.where i.e., 0, 1 or 2. The ridge regression factor used assuming a common variance for the marker effects, i.e The marker genotypes of an individual were re-coded as the number of copies of one of the SNP alleles, VanRaden .The DGEBV was computed for the animals in the prediction set asX is the matrix of marker genotypes for each animal in the prediction set and where The gebv software  was usedThe accuracy of DGEBV was calculated as the correlation between the DGEBV and the true breeding value and standard errors were computed as the standard deviation of the accuracies across the 10 replicates, divided by The differences between the average accuracies of DGEBV across scenarios were tested by t-test.The accuracies of DGEBV were regressed on number of animals in the TS, using a quadratic regression, to assess the effect of increasing the TS size.2r, which is the squared correlation of the alleles at 2 loci [Linkage Disequilibrium was measured by t 2 loci :where D = f(AB)-f(A)f(B), and f(AB), f(A), f(a), f(B), f(b) are observed frequencies of haplotypes AB and of alleles A, a, B, b, respectively.2 ris a more suitable measure to estimate LD for biallelic markers, such as SNPs, because 2 ris less sensitive to allelic frequency and sample size than D' [It was demonstrated that  than D' -20.Due to the computing time required to calculate all possible pair-wise LD, the LD statistics for all pair-wise LD were calculated only for BTA 1 and for one replicate. However, the statistics should illustrate well the decay of simulated LD for the entire genome. The statistics for LD between all adjacent SNP were calculated, however, for all 29 BTA.The average levels of LD between adjacent SNP in the recent generations of POP1 and POP2 are given in Table 2 rbetween adjacent SNP across all autosomes for moderate heritability (0.25) in the recent generations was 0.25 and 0.32 for POP1 (40 k) and POP2 (800 k), respectively , using bulls genotyped with the Illumina BovineSNP50 chip and similar to the 2 rreported by [2 r= 0.21 between markers 30-35 kb apart).The overall orted by  for Gyr orted by  for a mu2 rbetween all SNP pairs for different distance ranges up to 1 Mb for BTA1. The highest average estimated 2 rwas in the range of 0.22-0.24 for a distance of 0-0.10 Mb. The 2 rvalues decreased with increasing distance between SNP, but not as sharply as the decrease reported for Holstein cattle [Table n cattle -23.2 r> 0.30 for ranges 0-0.1 Mb, 0-0.2 Mb, 0-0.5 Mb and 0-1 Mb was 28%, 25%, 15% and 9%, respectively. These results are similar to findings of [2 r> 0.30 of 23%, 20%, 14% and 10% for the same ranges, respectively.In the current simulation study, for moderate heritability (0.25) and POP1 (40 k), the % of dings of  for Gyr 2 rof 0.31, 0.22 and 0.15 for Angus and crossbred cattle for distance ranges between 0-0.03 Mb, 0.03-0.06 Mb and 0.06-0.10 Mb, respectively. The simulated results in the present study for the distance range 0-0.10 Mb seem in line with those results reported by [Using the Illumina BovineSNP50 chip,  reportedorted by .2 rfor eight breeds of cattle varying from 0.15 to 0.20 for a distance range from 0-0.1 Mb, which is similar to the r2 observed in the simulated data for the same distance range  between adjacent SNPs and distribution of SNP pairs across different LD ranges on chromosome 1 in the recent generations for three heritability levels and POP1 and POP2. The % of SNP pairs with 2 r> 0.30 did not differ across the heritabilities, probably because the number of generations under selection was small (10).Table 2 r> 0.30) in POP2 (800 k) while 33% of the SNP pairs showed high LD in POP1 (40 k) for moderate heritability (0.25). This difference of ten points seems not very high, but when it is translated to number of SNP pairs in high LD in each marker density, it becomes quite significant and has an impact on the accuracy of genomic selection, as shown later in the results.When comparing the marker density, 43% of SNP pairs showed high LD  with the increase in the number of bulls in the TS, heritability of the trait and density of markers , y = 0.220 + 0.00036x - 8.2e-8x2  and y = 0.228 + 0.00037x - 8.3e-8x2  for heritability = 0.10, 0.25 and 0.40, respectively. Figure The DGEBV accuracies were regressed on the number of bulls in the TS, using a quadratic regression. The estimated regressions were y = 0.256 + 0.00026x - 5.2eThe highest accuracy (0.64) was observed for heritability of 0.40 and 1920 bulls in the TS Table . This vaThe effect of heritability was not as evident for 480 bulls in the TS, as it was for 960 and 1920 bulls Table , reflectThe response variable used for calculating the marker effects also affected the accuracy of DGEBV. Table Table When the number of bulls genotyped with 800 k SNP markers was 1920 and their phenotypes were used for estimating marker effects, the accuracy of DGEBV increased only for heritability 0.40 (p < 0.10), while for the other two levels of heritability the accuracy decreased (p < 0.05) compared to accuracies from 480 bulls in the TS and using EBV for estimating marker effects.One of the main advantages of using genomic information is for traits difficult or expensive to measure for which traditional evaluations are not usually available or to obtain accurate EBV early in the animal's life, when the own phenotypic information has not been measured yet. For the latter situation, if we consider that the average EBV of the parents is the only available information early in the animal's life, one could compare the accuracies provided by PA and the accuracies of DGEBV. Since the reliability of PA is a quarter of the sum of reliabilities of the EBV of parents, considering the average reliability of EBV of bulls in the TS reported in this study and the average reliability of the EBVs of the dams in the simulated data, the expected accuracies for PA would be 0.44, 0.53 and 0.58 for heritability = 0.10, 0.25 and 0.40, respectively. These accuracies are smaller than those accuracies of DGEBV considering 1920 bulls in the TS for POP1 (40 k) for all heritability levels. Therefore, the gains in accuracy by using DGEBV would be of 27%, 13% and 10% compared to accuracy of PA for these conditions. If PA is unavailable, then the use of DGEBV could potentially be even more valuable.Schenkel et al.  reportedThe main issue that has been discussed in most studies involving genomic selection is whether it will bring additional benefits, considering the cost of genotyping. An alternative to reduce the cost of genotyping and, thus, increase the number of genotyped animals, is the imputation of genotypes, which would allow genotyped animals with a less dense SNP panels  to be imputed to a denser SNP panels , using a reference population genotyped with the denser SNP panel . This alAs reported in dairy cattle, the size of the training set and the extent of linkage disequilibrium have major impact on the accuracy of direct genomic EBV. Based on the findings of this simulation study, large training sets, as well as dense marker panels, aiming to increase the level of linkage disequilibrium between markers and QTL, will likely be needed in beef cattle for successful implementation of genomic selection.Gains in accuracy by using direct genomic EBV and, therefore, before the animal having an accurate EBV, showed more advantage for traits with a moderate to low heritability.Increasing the number of animals in the TS by 4-fold and using their phenotypes to estimate marker effects was not sufficient to maintain or increase the accuracy of direct genomic EBV obtained using estimated breeding values when the trait heritability was lower than 40% for both marker densities, i.e. 40 k and 800 k SNPs.This investigation provides preliminary insights on expected gains in accuracy by using direct genomic EBV in beef cattle. Additional simulation studies are warranted.The authors declare that they have no competing interests.FVB carried out the simulations, performed the simulated data analysis and drafted the manuscript. MS participated in the design of the simulations process and wrote the code of the main software used in the study. JBN and JAC critically revised the manuscript. FSS contributed to the design of the simulations and analysis of simulated data. In addition, FSS revised the manuscript. All authors read and approved the final manuscript.


To detect the difference between two groups, conventional methods would fail to apply due to the instability in estimating variances in t-test and a high proportion of tied values in AUC (area under the receiver operating characteristic curve) estimates. The significance analysis of microarrays (SAM) may also not be satisfactory, since its performance is sensitive to the tuning parameter, and its selection is not straightforward. In this work, we propose a robust rerank approach to overcome the above-mentioned diffculties. In particular, we obtain a rank-based statistic for each feature based on the concept of “rank-over-variable.” Techniques of “random subset” and “rerank” are then iteratively applied to rank features, and the leading features will be selected for further studies. The proposed re-rank approach is especially applicable for large-p-small-n datasets. Moreover, it is insensitive to the selection of tuning parameters, which is an appealing property for practical implementation. Simulation studies and real data analysis of pooling-based genome wide association (GWA) studies demonstrate the usefulness of our method.Large- Recently, many researches encounter the problem where the data objects have an extremely large number of features while the available sample size is relatively small. In view of the number of features, unless there is a large sample size, conventional statistical methods that based on asymptotic theory are not applicable. This is so-called the curse of dimensionality. To improve the accuracy and efficiency of data analysis, it is helpful to reduce the number of features before fitting statistical models. Various dimension reduction methods have been proposed, which can be categorized into two categories: feature extraction and feature selection . The fort-test takes into account the sample variances to detect mean change between two groups, and it is very powerful when the normality assumption holds. However, the data is not always normally distributed especially for the case of small sample size. The instability in estimating variances in this situation would also make type-I error inflated and fail to apply. The Significance Analysis of Microarrays (SAM) [s0 to the denominator of the t-test statistic. However, it is still difficult to apply since its detection power is sensitive to s0 value and, to the best of our knowledge, there is no optimal data-driven approach to select s0.To detect the difference between two groups, one approach is fold change . It is cys (SAM)  is propop-small-n datasets. This can be seen by considering a case-control study with n1 cases and n0 controls, where there are at most n0n1 distinct AUC values which can be much smaller than the number of features. In this case, the high proportion of tied values would make it hard to construct a ranking list. To improve the detection power while keeping the robustness, methods based on the idea of “rank-over-variable” were proposed including Rank Product [t-test, rank-over-variable methods do not involve the estimation of variance but it has been reported to be able to detect both changes in mean and correlation between two groups [p-small-n datasets and is not sensitive to the selection of tuning parameters. Nonparametric methods are distribution-free and robust to the presence of outliers. To achieve robustness, these methods consider the ranks of data instead of the original measurements. Unfortunately, traditional “rank-over-sample” methods such as Wilcoxon rank sum test or area under the receiver operating characteristic curve (AUC) would fail to deal with the large- Product  and Rank Product . In theso groups . Motivatt-test, and SAM. The paper is ended with conclusions in The rest of this paper is organized as follows. In p markers with n1 cases and n0 controls. Let Xij and Yij be the continuous measurement for marker j, j = 1,…, p, of subject i in the case and control groups, respectively. The goal is to identify those markers which are truly associated with disease. To construct a ranking list of markers, we consider a rank-based statistic by modifying the method of Alvo et al. [jth marker. Let RX* be the rank of Xij* among {Xij*, j = 1,…, p} for subject i in decreasing order, and RY* is similarly defined. The rank-based statistic Sj of marker j is then calculated to be the absolute value of the mean difference between {RX*,…, RX*} and {RY*,…, RY*}; that is,j then should possess a large value of Sj. Note that the concept of “rank-over-variable” we adopt here to construct RX* and RY* is more appropriate than the traditional rank-over-sample methods to analyze large-p-small-n datasets as described in  Consider a case-control study that examines o et al. . Define μj before ranking over variables within a subject. We note that this centering is critical. In the construction of , all theH0: The orders of centered markers within two groups are identical.  Violation of the null hypothesis then indicates the existence of some relevant features, and those features can be reasonably identified by the ranking score .Sj may not be satisfactory. To enhance the detection power of the rank-based statistic Sj, we further apply the techniques of “random subset” and “rerank” [I(·) to denote an indicator function.If there are fewer irrelevant markers, the relevant markers might be more likely to be ranked in the top list. In most cases, however, the proportion of relevant markers is much lower than that of irrelevant markers, and the performance of the ranking list directly based on “rerank” , 10 as dℓ1b) Randomly select a marker index subset {Sjb)( : j ∈ {ℓ1b)(}} in ((2) Calculate {(b)}} in  based onb = 1,…, B, and output the adjusted rank-based statistic(3) Repeat Steps  1-2 for Sj with fewer irrelevant variables should be more efficient. Following the strategy of Chang and Chen [B times.The idea of random subset is intuitive: calculation of and Chen , the sizSj*, however, is still calculated with the all markers being involved. Considering a ranking list of markers constructed by ( : j ∈ It} defined in (pt is the number of markers in It. (1) Calculate {fined in  and(5)wSj*t) Based on {pT+1 < M1, and output(3) Repeat Steps  1-2 until Sj*t) under consideration. To make statistics from different iteration comparable, we use Sj*t)(/pt instead of Sj*t) are commonly used indices for feature selection. However, when the sample size is extremely small , these methods may not be ready to be applied. In this study, we alternatively propose a method to directly estimate the number of truly relevant markers based on the constructed ranking list. Given a ranking list, researchers can select P value for each marker, we compute a modified P-value νm to determine whether all of the higher-ranked markers are relevant. The algorithm is described later.Consider a ranking list constructed by the rerank approach. If a marker is relevant, it implies that all of the higher-ranked markers in this ranking list are also relevant. Based on the idea of Cook and Yin , insteadSj**(0) : j = 1,…, p} defined in ((1) Calculate {fined in  and S-(0Sj**(0) : j = 1,…, p}. Let ℓm)( be the index such that Sℓm)(∗∗(0) is the mth largest. (2) Construct a ranking list based on {m = 1,2,…, p, (i)ℓm+1)Sj**b), calculate {fined in  and S-m((iii)b = 1,…, B, and outputrepeat Step  3(i)-(ii) for (3) For νm values to determine M1. Assume m* is the number of truly relevant markers and we are given a correct ranking list. Firstly, in the population level, it is obvious that νm is an increasing function of m provided the ranking list is correct. When m = m*, the algorithm actually permutes all irrelevant markers to form the permuted data, while the relevant markers are not permuted. In this case, the permuted data should behave very similarly to the original one and, hence, the distribution of νm* is close to 0.5. Moreover, when m > m*, νm is expected to be increasing uniformly in m, since we are including markers without separation abilities, and finally to reach unity when m = p. On the other hand, when m < m*, the relevant markers are permuted and the value of νm value should be lower than 0.5, and the pattern of {νm : m < m*} should be far away from that of {νm : m > m*}. Based on the previous properties, we thus suggest to chooseWe now describe the rationale of this algorithm and how to use the m* = 10 markers in the case group that are distributed as N. With 100 cases and 100 controls, νm curve rises rapidly before reaching 0.5. After passing νm = 0.5, the curve increases uniformly with increasing m. An obvious change point at m = 10 with ν10 ≈ 0.5 suggests that M1 = 10 is a suitable choice. m = 10. When the sample size is merely 10  study dataset. Instead of individual genotyping which is more expensive, using pooled DNA samples is an effective strategy to reduce the costs of GWA studies. In a pooling-based GWA study, the sample is genotyped in pools of individuals instead of individually genotyping. In particular, the data points Xij (Yij) from a pooling-based GWA study are the estimated allele frequencies for SNP j of pool i in the case (control) group. However, it will generate an ultrahigh dimensional dataset with extremely small sample size. For example, there are 249,473 markers but only 8 case and 8 control pools available in our bipolar dataset. Moreover, the additional measurement error from the pooling process and the existence of outliers have the potential to decrease detection power. In this situation, the proposed rerank approach is more suitable to deal with the large-p-small-n datasets and is more robust to the pooling error and outliers. These facts will be confirmed by the following numerical studies.The proposed rerank approach is applicable to analyze large-n1 case pools and n0 control pools are constructed by randomly selecting n1 × s cases and n0 × s controls from GAIN-MDD dataset, where s is the pooling size. Let j of pool i in the case and control groups, respectively. To mimic the existence of pooling error and outliers, the observed MAF is generated byYij is similarly defined. Collect {Xij : j = 1,…, 416170}i=1n1 and {Yij : j = 1,…, 416170}i=1n0 to form a simulated DNA pooling dataset. The anticipated aim of this simulation study is to recover the 100 truly relevant SNPs by analyzing the simulated DNA pooling dataset. We repeat simulation studies 100 times and report the averaged number of truly relevant SNPs identified in the top ranking list of each method. We use M0 = 5000, B = 100, and q = 87.5 for rerank approach. The SAM is implemented by the samr R package (from http://www-stat.stanford.edu/~tibs/SAM/) [σ, there are three situations considered: (A) without pooling error and outliers (σ = 0); (B) with pooling error (σ = 0.05); and (C) 1% data points are outliers with σ = 5, and σ = 0.05 otherwise.We simulate DNA pooling datasets from a real individual genotype dataset called GAIN-MDD dataset, which was accessed through the Genetic Association Information Network (GAIN) studies database of Genotypes and Phenotypes (dbGaP) for major depressive disorder (MDD) , 13. Theσ = 0, under the case of n0 = n1 = 16 (each with size s = 100), M1 and is better than t-test except for large M1. Note that the 100 truly relevant SNPs are selected based on chi-square test, which is similar to t-test, and it is reasonable for t-test to obtain similar ranking list of susceptible SNPs, even when data was aggregated. For the case of n0 = n1 = 8 (each with size s = 200), t-test and AUC have worse performances due to the instability in estimating variances and high proportion of tied values, respectively. In contrast, the proposed rerank approach does outperform these two methods for any given M1. In the presence of pooling errors . Unfortunately, s0* is unknown in advance and there is no guarantee that the suggested algorithm by [s0 is critical to the performance of SAM, especially for small sample size and in the presence of outliers. On the other hand, the performance of the rerank approach is similar to that of SAM with optimal s0* for small M1 and is better than SAM with the estimated M1.In Figures  package . Observirithm by  can chooM0 (the number of prescreened SNPs) and q% (the percentage of rerank) values under equal numbers of case and control pools and σ = 0.05. M0  especially for small sample size (n0 = n1 = 8), although there is no obvious difference for larger sample size (n0 = n1 = 16). q except for the case of q = 50. These simulation results then suggest to use a conservative value of M0 and q, and the performance of rerank approach is guaranteed. In summary, the rerank approach is more robust to small sample size, pooling error, and outliers and is insensitive to the selection of tuning parameters.Another advantage of our rerank approach is its insensitivity to the selection of tuning parameters. To see this, we further report the simulation results for various In this subsection, we demonstrate a real data analysis using the proposed rerank approach. The dataset is from a two-stage GWA study to identify common variants for the association with bipolar disorder . The bipM1 = 100, B = 100 and q = 87.5. Among those SNPs, 52 SNPs do not map to any gene while the remaining SNPs can map to 43 genes totally. According to previous studies, etiology of bipolar disorder involves neurotransmitter, neuronal system, immune function, and brain development. Among the 43 genes, we only focus on 8 genes that are associated with brain or neuron. They can be categorized into different biological functions, such as brain-specific chemokines or neurokines and receptor or ligand that regulates neuronal positioning or axon guidance. We next select 81 tag SNPs for the 8 genes based on Tagger [Recall the aim of Stage 1 is to design a panel with 96 SNPs for that validation by individually genotyping in Stage 2. The selection process is shown in n Tagger . In addin Tagger .P-value in Stage 2 are based on the genetic model with the most significant result. Among the 16 SNPs, 13 of them attain 5% significant level in Stage 2 wherein 6 markers are positively relevant to bipolar disorder (OR = 1.4∼1.5) and 7 markers are negatively relevant (OR = 0.5∼0.7). One can see that the analysis results from Stage 1 and Stage 2 are consistent. It implies that the susceptible markers identified by our rerank approach have high reproducibility even using the pooled DNA data. Those relevant markers , however, are listed in the much lower rank of t-test. The poor performance of t-test can be improved by SAM, but it still could not perform as efficient as the rerank approach did. For example, the SNP 3, SNP 6, and SNP 8 have very small P-values , but not in the top list of SAM.To evaluate the reproducibility of the findings from Stage 1, To validate the findings from Stage 1, we further conduct a set-based analysis for the 8 selected genes under different genetic models of association test by PLINK  using inBased on the previously mentioned replication and validation steps by analyzing individual genotype data, our rerank approach indeed has the ability to efficiently detect associations using pooled DNA data. Researchers can focus on these candidate SNPs or genes for further biological studies.p-small-n datasets with continuous measurements to select differential features between two groups, such as gene expression datasets and biomarker datasets. It provides researchers a sizeable number of differential features for further studies. In this study, we propose a robust rerank approach to create a ranking list for feature selection, which comprises three components: (1) rank-based statistic (rank-over-variable), (2) random subset, and (3) rerank. The rank-based statistic is the main scoring function for quantifying association strength, which is motivated by the Rank Test of Alvo et al. . We alsop-small-n situation, but the information of correlations among features can also be taken into account during the ranking process. In other words, although the rank-based statistic is defined as the mean difference of rank values, it is likely to have the ability to detect both mean and correlation changes between two groups [In the rerank approach, it involves an important concept: rank-over-variable. The advantage is not only to avoid tied values for ranking in the large-o groups . It is i


P<0.05) proportion of variance explained by all SNPs on the Affymetrix 5.0 genotyping array . Longer genomic segments tend to explain more phenotypic variation, with a correlation of 0.78 between the estimate of variance explained by individual chromosomes and their physical length, and 1% of the genome explains approximately 1% of the genetic variance. Despite the fact that there are a few SNPs with large effects for some traits, these results suggest that polygenicity is ubiquitous for most human complex traits and that a substantial proportion of the “missing heritability” is captured by common SNPs.The estimate of  The “missing heritability” problem has been intensely debated for the last few years. Possible explanations include the existence of many genetic variants each with a small effect, rare variants with large effects, and heritability being over-estimated. Previous studies using whole-genome estimation have demonstrated that for human complex traits such as height, body mass index, and intelligence, a large portion of the heritability can be captured by all the common SNPs on the current genotyping arrays. These studies, however, were all concentrated only on a few traits. In this study, we analysed 49 quantitative traits in a sample of ∼7,000 unrelated Korean individuals. We found that, on average over all the traits, common SNPs on the Affymetrix 5.0 genotyping array explain approximately a third of the heritability, that genetic variants are widely distributed across the whole genome with longer chromosomes explaining more phenotypic variation, and that approximately any 1% of the genome explains 1% of the heritability. Despite examples where a few variants explain a substantial amount of variation, all these results are consistent with polygenicity being ubiquitous for most complex traits. The five years wave of genome-wide association studies (GWAS) has uncovered thousands of single nucleotide polymorphisms (SNPs) to be associated with hundreds of human complex traits including common diseases We used the data from the Korea Association Resource (KARE) project P<0.05) and 26 of which reached experimental-wise significance level after Bonferroni correction for multiple traits (likelihood ratio test P<0.001) h2) estimated from pedigree analyses in the literature (P = 0.017) that traits with a higher estimate of h2 were more likely to have a larger estimate of h2 were from various different studies, usually with large standard errors and mostly in samples of European ancestry. In contrast, when we performed a genome-wide association (GWA) analysis in the same sample, we identified genome-wide significant (P<5×10−8) SNPs for 25 of the 49 traits. On average across the 25 traits, the top associated SNPs from GWA analyses explained only 1.5% (range of 0.5% to 3.8%) of phenotypic variance . In general, there was a substantial amount of variance explained by all SNPs on the Affymetrix 5.0 genotyping array  for each trait. We calculated θP for a range of threshold p-values and plotted them against the expected values under the null hypothesis of no association   but their effect sizes are too small to be genome-wide significant (P<5×10−8).We calculated the proportion of SNPs with p-values that passed a threshold p-value in a GWA analysis  . This plme small  and suchme small . The queof 0.031 , meaningLC) for each trait. We did not observe a linear correlation between LC for any particular traits  (P = 0.413), and the intercept was 0.008 (SE = 0.007) which was not significantly different from zero (P = 0.289), suggesting that on average 1% of the genome approximately explains 1% of the genetic variance. Despite that there are SNPs with large effects for some traits , we then partitioned 9 traits  except Here zero , and plor traits  as stron of 0.78 . We showw traits  and by rw traits . We alsoomosomes . We furt genome) . The rege traits , all theIn addition, we partitioned  regions . We furtPrevious studies using the whole-genome estimation approach The estimates of P = 0.161), and was significantly (P = 0.015) smaller than the estimate from another study in European Americans (P = 0.741). We estimated the narrow-sense heritability for 11 traits by from a family study in Koreans  or for BMI  in Koreans was comparable to that estimated in Europeans. We then estimated the variance explained by all SNPs on Affymetrix 5.0 array in the sample of 11,586 unrelated European Americans as used in P = 0.118). Therefore, the difference between the estimate of The estimate of  Koreans . The estR2 is approximately 4ρ2(1−ρ2)/N where E(R2) = ρ2 and N is number of observations (number of chromosomes in this case). Given ρ2 = 0.5 and N = 22, the SE of the regression R2 is ∼0.2. Therefore, the difference between the correlation (between the variance explained and DNA length) in genic regions and that in intergenic regions is unlikely to be significant. In addition, in the partitioning analysis of intergenic regions, chromosome 2 seems to be an outlier (P = 0.118).It is demonstrated by the genome partitioning analysis that there was a strong linear relationship between the estimates of variance explained by individual chromosomes and chromosome length . The cor outlier . For exaMoreover, we attempted to investigate the enrichment of genetic variants in genes involved in biological pathways. For any particular trait, there are a number of biological pathways that are important to the trait development. We chose the well-known insulin signal transduction pathway as an example to demonstrate the use of GCTA to partition the genetic variance based on functional annotations. We took SNPs that are ±20 kb away from 103 genes that are involved in insulin signaling pathway. There were 955 SNPs which covered ∼0.45% of the genome. We then performed the genome partitioning analysis to decompose In conclusion, we showed by whole genome estimation and partitioning analyses that, most human complex traits, if not all, appear to be highly polygenic, i.e. there are a large number of genetic variants segregating in the population with a small effect widely distributed across the whole genome. All the common SNPs on the Affymetrix 5.0 array explain approximately a third of heritability on average over all the 49 traits analysed in this study. The remaining unexplained two thirds of heritability could be due to causal variants including the common and rare ones that are not well tagged by SNPs on the array or possibly due to the heritability was over-estimated in the family/twin studies. The conclusion drawn from previous studies that heritability is not missing but due to many variants with small effects is not specific for human height in European populations but likely to be in common for most human complex traits and populations. Taken all together, it implies that although whole genome sequencing data will provide much denser genomic coverage than the current genotyping array and will therefore identify more associated variants and explain more genetic variance, large sample size is still essential.z-scores, in each of the two cohorts (Ansung and Ansan) and in each gender group separately.This study used the data from the Korea Association Resource (KARE) project, which has been described elsewhere P value<10−6 using PLINK The genomic DNAs were isolated from peripheral blood drawn from the participants and were genotyped with 500,568 SNPs on the Affymetrix 5.0 genotyping array y is a vector of phenotypes, b is a vector of fixed effects with its incidence matrix X, AG being the SNP-derived GRM and We estimated the genetic relationship matrix (GRM) between all pairs of individuals from all the genotyped SNPs and excluded one of each pair of individuals with estimated relationship >0.025 retaining 7,170 unrelated individuals. For each trait, we then estimated the variance that can be captured by all SNPs using the restricted maximum likelihood (REML) approach in mixed linear model Figure S1Principal component analysis (PCA). The genotype data of the KARE cohort  was combined with the data from the HapMap3 project (PDF)Click here for additional data file.Figure S2Pairwise phenotypic correlations between the 49 traits. The traits are classified into 10 groups: obesity, blood pressure & pulse, BMD, lipids, diabetes index, blood cell count, blood ions, liver function, lung function, and kidney function. The phenotypic correlations between traits in the same groups are stronger than those in different groups. From a principal component analysis of the phenotypic correlation matrix, the first 33 eigenvectors explain >95% of variance.(PDF)Click here for additional data file.Figure S3P = 0.017) and the regression R2 is 0.131. Detailed information can be found in Variance explained by all SNPs estimated in the present study against the heritability estimates from pedigree analyses in literatures for the 49 traits. The regression slope is 0.137 ((PDF)Click here for additional data file.Figure S4θP) value averaged across 47 traits  are plotted. B) −log10(θP) of all the 47 traits are plotted.The observed proportion of SNPs with p-values passed a threshold p-value from genome-wide association analysis vs. the expected value . Shown on both axes are on the −log10 scale. A) −log10((PDF)Click here for additional data file.Figure S5Estimate of variance explained by each chromosome against chromosome length for each of the 47 traits .(PDF)Click here for additional data file.Figure S6Proportion of variance attributed to each chromosome averaged across traits against chromosome length when the number of SNPs on each chromosome is equal. There are 3500 SNPs randomly sampled from each chromosome. The estimate of variance explained by each chromosome is an average across all traits.(PDF)Click here for additional data file.Figure S7The estimates of variance explained by individual chromosomes against chromosome length for the 47 traits .(PDF)Click here for additional data file.Figure S8Manhattan plot of GWAS results for the traits with single variants of large effects. Panels A), B), C) and D) are for traits GLU60, HBA1C, RBC and RGTP, respectively.(PDF)Click here for additional data file.Table S1Summary description of the 49 traits in the KARE cohort.(PDF)Click here for additional data file.Table S2Estimates of variance explained by all SNPs for the 49 traits.(PDF)Click here for additional data file.Table S3Variance explained by all the SNPs on individual chromosomes for the 49 traits but HOMA and INS0.(PDF)Click here for additional data file.Table S4Estimates of the variance explained by all the genic and intergenic SNPs averaged across the 47 traits . A genic region is defined as ±0 kb, ±20 kb and ±50 kb of the 3′ and 5′ UTRs of a gene.(PDF)Click here for additional data file.Table S5Numbers of genic and intergenic SNPs on each chromosome.(PDF)Click here for additional data file.Table S6Estimate of heritability from a pedigree analysis for 11 traits. Data and analysis are described in (PDF)Click here for additional data file.Table S7Estimates of variance explained by SNPs at the gene regions that are involved in insulin signaling pathway for 11 lipids and diabetes related traits.(PDF)Click here for additional data file.Text S1Difference between the estimates of variance explained by all SNPs in Europeans and in Koreans.(PDF)Click here for additional data file.Text S2Difference in number of SNPs and MAF distribution between genic and intergenic SNPs.(PDF)Click here for additional data file.


FLT1. In stage 1, collapsing rare variants decreased false positives but increased false negatives. In stage 2, we developed a good-fitting SEM model that included all nine genes simulated to affect Q1  and found that FLT1 had the largest effect on Q1 (βstd = 0.33 ± 0.05). Using replicate 137 estimates as population values, we found that the mean relative bias in the parameters  and their standard errors across 100 replicates was on average, less than 5%. Our latent variable SEM approach provides a viable framework for modeling aggregate effects of rare and common variants in multiple genes, but more elegant methods are needed in stage 1 to minimize type I and type II error.Methods that can evaluate aggregate effects of rare and common variants are limited. Therefore, we applied a two-stage approach to evaluate aggregate gene effects in the 1000 Genomes Project data, which contain 24,487 single-nucleotide polymorphisms (SNPs) in 697 unrelated individuals from 7 populations. In stage 1, we identified potentially interesting genes (PIGs) as those having at least one SNP meeting Bonferroni correction using univariate, multiple regression models. In stage 2, we evaluate aggregate PIG effects on trait, Q1, by modeling each gene as a latent construct, which is defined by multiple common and rare variants, using the multivariate statistical framework of structural equation modeling (SEM). In stage 1, we found that PIGs varied markedly between a randomly selected replicate (replicate 137) and 100 other replicates, with the exception of  The 1000 Genomes Project is an international public-private consortium aiming to build the most detailed map of human genetic variation with the overarching goal to improve our understanding of the genetic contribution to common human diseases. Initially launched in 2008, three pilot studies have been completed to test multiple sequencing methods. Pilot Project 3 involved sequencing the coding regions (exons) of 3,205 genes in 697 individuals from 7 populations, which revealed 24,487 rare and common genetic variants. The sequencing data from Pilot Project 3 were used for Genetic Analysis Workshop 17 (GAW17), and details of this data set, including how the phenotypes were simulated, can be found in Almasy et al. [ post hoc analyses, we used knowledge that 39 SNPs in 9 genes, primarily in the vascular endothelial growth factor (VEGF) pathway, were simulated to be associated with Q1.Although strategies have been developed to evaluate the contribution of rare variants to disease susceptibility in nonfamilial data, including collapsing methods, which are reviewed by Dering et al. , approacWe first examined the distribution of Q1, which we arbitrarily chose from the three simulated quantitative phenotypes available  and Q1 using linear regression models adjusted for all the covariates provided in the GAW17 data set  using PLINK, v. 1.07. In addition, we collapsed rare variants  in each gene using the indicator coding method ,5 in MATFLT1) represent the overall variation in a gene, which we formally describe by multiple SNPs y is the p × 1 vector of observed variables, η is the m × 1 vector of latent random variables, ε is the p × 1 vector of measurement errors for y, and Λy is the p × n matrix of coefficients relating y to η.where The general form of the structural model imposes constraints such that:η = Βη + ζ, (2)Β is the m × m matrix of path coefficients and ζ is the m × 1 vector of errors or disturbances in the endogenous (dependent) latent variables.where q-dimensional vector of covariates (x), an m × q matrix of regression coefficients (Γ), and an m-dimensional vector of intercepts (α):The structural model can be modified by adding a η = α + Βη + Γx + ζ. (3)Similar to our prior work using common variants to describe overall variation in a gene ,7, we usp-values are from two-sided tests.The chi-square test evaluates whether the covariance matrix is equal to the model-implied covariance matrix predicted by the parameters, but it is sensitive to sample size and complexity. Thus, other fit indexes, including the CFI, RMSEA, and SRMR, have been used to evaluate model fit . The CFIp ≤ 8.33 × 10−6) and without (p ≤ 2.04 × 10−6) collapsing rare variants (MAF < 0.05) (Table FLT1 (Table Without knowledge of the underlying simulated model and using a randomly selected replicate (replicate 137), we evaluated potential associations between each SNP and trait Q1 in stage 1. We found that several genes had a least one SNP meeting or exceeding the Bonferroni-corrected level with  vs. 0.53 (B)), and increased the variance explained in Q1 (R2: 0.30 ± 0.04 (A) vs. 0.36 ± 0.04 (B)). In a larger SEM  was slightly lower than that in the reduced model , but FLT1 remained the gene most strongly associated with Q1, followed by SPHKAP, LRRN2, C5ORF25, and FADS3. Genes AKAP13 and OR2T34 were not associated with Q1. Population structure was not significantly associated with Q1 or with genes where paths are not shown.In stage 2, when building the FLT1, which had at least one SNP in all 100 replicates exceeding the Bonferroni-corrected p-value in models adjusted for 10 or 12 PCs, and with and without rare variants collapsed. KDR was the next most consistent PIG, which was identified in 12 and 20 of the 100 replicates when rare variants were and were not collapsed, respectively; the results were the same when adjusting for 10 and 12 PCs.In post hoc analyses, we found that the list of PIGs varied markedly across replicates (99–136 and 138–200), with the exception of FLT1, FLT4, KDR, ARNT, ELAVL4, HIF1A, HIF3A, VEGFA, VEGFC), primarily in the VEGF pathway, were simulated to be associated with Q1.We obtained the answers to the GAW17 simulation model to better understand the performance of our stage 1 approach and to develop a stage 2 model that would more closely reflect the simulated model. The answers revealed that 39 SNPs in 9 genes  versus not collapsed . The number of true-positive and false-negative genes was similar for models adjusted for 10 and 12 PCs and when rare variants were and were not collapsed  did not materially improve the number of true-positive genes when rare variants were collapsed (not shown). Although we were most interested in identifying causal genes in stage 1, we note that the number of false-positive SNPs over the 100 replicates decreased with adjustment for increasing numbers of PCs . The numbers of false-negative SNPs were similar when adjusting for 10 PCs  and 12 PCs  with most replicates correctly identifying FLT1 SNPs C13S522 and C13S523 (not shown).With regard to stage 1 performance, we found that the number of false-positive genes decreased with adjustment for increasing numbers of PCs. As shown in Table http://www.genome.jp/kegg/pathway.html; VEGF Signaling, Cytokine-Cytokine Receptor Interaction, Pathways in Cancer) to better understand the biological relationships between the nine genes. We developed a good-fitting model  that included all nine genes simulated to affect Q1  was greater than in prior models. FLT1 remained the gene most strongly associated with Q1, followed by ARNT, VEGFA, KDR, VEGFC, FLT4, and HIF3A. Smoking was simulated to be associated with KDR, but we observed only a marginal association  and found that Smoking was more highly associated with HIF3A and ELAVL4. Modeling all nine genes simultaneously revealed that HIF1A was associated with VEGFC but that ELAVL4 and HIF1A were not associated with Q1. Removing paths designated by a dashed line   were 0.32% for Λ, 0.98% for ε, and 2.19% for ζ. The MRB was generally similar between common and rare variants. For example, in the FLT1 common SNP C13S523 (MAF = 0.07) and the FLT1 rare SNP C13S524 (MAF = 0.004), the MRB in Λ and the SE of Λ were 0.35% in C13S523, 0.62% in C13S524, and 0.33% in C13S523 vs. 0.98% in C13S524. The MRB of ε was 0.31% in C13S523 and 0.22% in C13S524, and the MRB of the SE of ε was 0.63% in C13S523 and 0.20% in C13S534. The largest bias was observed in the path coefficients , which was quite severe in some cases, such as the HIF1A path coefficient, where the bias reached 67.94%. Interestingly, the post hoc analysis revealed that genes represented by private variants, such as HIF1A, that were associated with Q1 in replicate 137 were not significantly associated with Q1 in most replicates. Also, the effects of covariates  varied markedly across replicates. Model fit, however, was generally consistent across replicates, with the average CFI, RMSEA, and RMSR being 0.91, 0.04, and 0.02, respectively.To evaluate the performance of the stage 2 SEM model, we used estimates from a randomly selected replicate (replicate 137) to represent population values (because the GAW17 answers did not contain standardized estimates for aggregate gene effects that we could directly compare to) and compared these population values to estimates from 100 replicates (replicates 99–136 and 138–200) available in the GAW17 data [FLT1) over all 100 replicates (replicates 99–136 and 138–200). Our stage 2 SEM results were able to confirm the importance of FLT1, because irrespective of the other genes included in the model . We found that the MRB in the answer-driven stage 2 SEM model’s parameters and standard errors across 100 replicates was less than 5%. In addition, our stage 2 SEM model  and between covariates and genes  that were not discussed in the GAW17 answers. Thus, we believe that modeling all nine genes simultaneously together with the relevant environmental factors and population structure in a hierarchical manner that better reflects the underlying biology using latent variable SEM provides an improved understanding of each gene’s relevance in the disease pathophysiology compared to standard multiple regression methods.In stage 1, adjusting for 10 or 12 PCs  and colOur latent gene construct approach provides a viable framework for evaluating the aggregate effects of rare and common variants in multiple genes on a trait while adjusting for population substructure; however, more elegant methods are needed in stage 1 to minimize false positives and concomitantly improve identification of true-positive genes.The authors declare that they have no competing interests.NLN conceived of the study, managed design and coordination, performed stage 2 analyses, and drafted the manuscript. LXZ performed data cleaning and conducted stage 1 analyses. Both authors read and approved the final manuscript.


Currently there is a great deal of interest in developing methods for testing the role that rare variation plays in disease development. Here we propose a weighted association test that accumulates genetic variation across a signaling pathway. We evaluate our approach by analyzing simulated phenotype data from an exome sequencing study of 697 unrelated individuals from the Genetic Analysis Workshop 17 (GAW17) data set. Although our weighted approach identifies several interesting pathways associated with phenotype Q1, so does an alternative unweighted accumulation approach. Such a result is not unexpected because there is no systematic relationship between the allele frequency of a variant and its effect on phenotype in the GAW17 simulation model. Next-generation sequencing technology allows for the characterization of virtually all of an individual’s genetic variation. Genome-wide association studies (GWAS) have successfully detected hundreds of disease-susceptible loci that harbor common variants. However, the common variants identified so far have explained only a small portion of the genetic risk of most of the diseases studied. Some researchers have argued that this is due in part to rare variants having a larger role in disease etiology than previously suspected. Some recent studies support this reasoning -11.T. Morris and Zeggini [z-score across all possible values for threshold T, assuming that the variants having minor allele frequency under this threshold are more likely to be functional. Madsen and Browning [Several approaches have been proposed to analyze rare variants for association with disease. The cohort allelic sums test (CAST) is a simple grouping method that compares the number of affected and unaffected individuals who have variants ,12,13. L Zeggini  proposed Zeggini  proposedHere, we propose a weighted group-wise association test that accumulates genetic variation across a signaling pathway. We extend the basic idea behind the Madsen and Browning  weightinP. Let iY, i = 1, 2, …, N, be the phenotype for individual i. We define ijI for individual i to be the number of minor alleles at SNP j. Let iX be a genetic summary score, which we define as:Suppose that the number of SNPs in a genetic unit  is jw is a weight that is applied to the jth SNP.where jw is taken to be 1 for all j. Thus rare and common SNPs are treated in the same way, and iX is the simple sum of the number of minor alleles in the gene or pathway. This approach is similar to that of Morris and Zeggini’s method [We evaluate two weighting schemes. In the first scheme, s method ; they dej as:In the second scheme, we calculate the frequency of nonreference mutations among nonextreme individuals at position δ(iY) = 1 when iY is within one standard deviation of the mean and δ(iY) = 0 otherwise. Adding a 1 to the numerator and a 2 to the denominator ensures that the frequency jp is nonzero, so that the weight used in the second scheme,where iX. We refer to this scheme simply as weighted.remains finite . Note thiX, we assume that it is related to iY through the linear model:For both approaches, once we have defined the genetic score ε is an unknown error term. A Wald statistic, where stimator . BecauseWe evaluate our approach using the simulated GAW17 data set. These data are described in detail elsewhere . Althoughttps://www.pharmgkb.org/) [http://www.geneontology.org). Although not defining a signaling pathway, the GO biological process domain classifies genes by their involvement in biological processes and therefore presents an interesting unit over which to accumulate genetic variation. This approach allows us to classify 2,304 out of 3,205 genes into 3,009 biological processes. The GO data are contained in two files: a human genetic association file, dated September 15, 2010, revision 1.1433; and a genetic ontology file, dated September 6, 2010, revision 1.160. We note that in both of these classification schemes (PharmGKB and GO) one gene may be mapped to several pathways or biological processes. A pathway or biological process is taken to be significantly associated with the phenotype if its permutation p-value does not exceed the Bonferroni corrected significance threshold 0.05(821 + 3009) ~ 1.3055 × 10–5. The entire analysis is repeated using both the weighted and unweighted schemes. Only nonsynonymous SNPs are considered throughout.We characterize gene sets using information from two databases. The first, PharmGKB (kb.org/) , provideThe results of these analyses, applied to replicate 1, can be found in Tables Table VEGFA, FLT1, KDR, HIF1A, and ARNT are consistently represented both in the significant PharmGKB pathways and the significant GO processes. A comparison of the results in Table We informally explored which genes were important in these significant pathways and processes by enumerating the number of times a given gene was present in a significant pathway or process. The genes occurring in the biological processes from the GO data set are compared with the ones in the signaling pathways from the PharmGKB data set. Table We presented two tests (weighted and unweighted) that accumulate genetic variation across a signaling pathway or biological process. In the analyses presented here, we found that the unweighted approach worked as well as, or better than, the weighted approach. We believe that this is strictly due to the structure of this particular simulation, in which the effect sizes of causal SNPs show no trend with the frequency of the causal variant. In situations where rarer SNPs are, in fact, more highly penetrant, we would expect a weighted approach to be more powerful.In the analyses presented here, an accumulation approach seemed to work well. However, we must offer two important caveats. First, when moving from a gene-based to a pathway-based approach, the power of the approach becomes increasingly dependent on the state of existing biological knowledge and its representation in databases such as PharmGKB and GO. Even though we constructed pathways and biological processes without considering the true simulation model, our results are bound to be an overly optimistic representation of the power of a pathway-based approach. After all, the GAW17 simulation was constructed by accessing the same biological knowledge  that we used to construct our pathways. Second, we computed a genetic score by simply summing the number of mutations in a gene or pathway and ignoring the directionality of the effect. This approach will be powerful when mutations lead to a shift in the phenotype in only one direction (as in the GAW17 simulation). However, it is likely that some mutations could lead to higher values of a phenotype and that other mutations could lead to lower values. This is possible even within a gene and becomes even more likely when considering a collection of genes, such as in a signaling pathway.The authors declare that there are no competing interests.CX, GAS, and ASA designed the study. CX implemented the methods and conducted the analyses. CX, GAS, and ASA wrote the manuscript.