The human genome encodes a limited number of genes yet contributes to individual differences in a vast array of heritable traits. A possible explanation for the capacity our genome to generate this virtually unlimited range of phenotypic variation in complex traits is to assume functional interactions between genes. Therefore we searched two mammalian genomes to identify potential epistatic interactions by looking for co-adapted genes marked by excess two-locus genetic differentiation between populations/lineages using publicly available SNP genotype data. The practical motivation for this effort is to reduce the number of pair-wise tests that need to be performed in genome-wide association studies aimed at detecting G×G interactions, by focusing on pairs predicted to be more likely to jointly affect variation in complex traits. Hence, this approach generates a list of candidate interactions that can be empirically tested. In both the mouse and human data we observed two-locus genetic differentiation in excess of what can be expected from chance alone based on simulations. In an attempt to validate our hypothesis that pairs of genes showing excess genetic divergence represent potential functional interactions, we selected a small set of gene combinations postulated to be interacting based on our analyses and looked for a combined effect of the selected genes on variation in complex traits in both mice and man. In both cases the individual effect of the genes were not significant, instead we observed marginally significant interaction effects. These results show that genome wide searches for gene-gene interactions based on population genetic data are feasible and can generate interesting candidate gene pairs to be further tested for their contribution to phenotypic variation in complex traits. The presence of epistatic interactions between genes has fundamental consequences for the course and outcome of evolution by natural selection We explored two mammalian genomes for functional gene-gene interactions and followed up a selection of candidate gene pairs to detect a possible joint effect on phenotypic variation in a complex trait in both mice using a well characterized set of mouse lines (BxD) and in humans using a Dutch twin cohort.Recombinant inbred lines (RILs) are generated by inbreeding the progeny of two parental lines that are themselves inbred. As a result an individual line can have only one of a possible four two-locus genotypes: aabb, aaBB, AAbb or AABB and all are expected to occur in equal frequencies in a large collection of RILs. However, if these four genotypes do not equally persist through the many generations of inbreeding, i.e. if there is a selective advantage of a specific combination of alleles, than not all two-locus genotypes will be observed in equal frequencies. In other words, in a large set of RILs we might observe significant Linkage Disequilibrium (LD) between physically unlinked genes if these genes jointly affect an adaptive phenotype st was calculated which is a measure of genetic distance between populations originally introduced by Sewall Wright. When considering natural populations a known complication of this approach is the confounding effects of selection and demography In contrast to the mouse data, the available human genotypes were derived from outbred, ethnically distinct populations. In this case pairs of functionally interacting genes can be detected following a slightly different approach. Considering only bi-allelic loci such as SNPs, two-locus genotypes are transmitted from one generation to another in one out of four possible combinations: for the AaBb genotype the gamets can be Ab, AB, ab, aB. If selection favors one of these configurations  above the others, than excess genetic differentiation between three major human populations at the level of trans-haplotype frequencies may indicate epistatic interaction between genes for the reasons outlined above. In contrast to the recombinant inbred lines, where phase is evident, in outbred human populations trans-haplotype frequencies had to be estimated. From these frequencies Fhttp://www.genenetwork.org/dbdoc/BXDGeno.html) we calculated LD and corresponding p-values for 6,659,288 pairs of physically unlinked, autosomal SNPs  of the phenotypic variation (p = 6.5×10−5) in the amount of 3% ethanol consumed per 24 hours when given ad libitum access  interacting with Paraoxonase 2 (rs13478608) and LOC665113 (similar to Traf2 and NCK-interacting kinase) (rs13459183) interacting with Ptpre (rs13479546). The biological functions of the latter two are not yet known. In contrast, paraoxonase 2 is an antioxidant protein and Nrf2 is a known regulator of gene expression of antioxidant proteins and phase II detoxification enzymes st) (2) within populations among the NSCS and NS were identical indicating that the two samples are well matched with respect to potential sources of bias due to genomic localization, allele frequency spectrum and also ascertainment (−13) , but the difference between NS and NSCS based haplotypes remained highly significant as well (p<10−13). This result is underlined by simple visual inspection of the distributions, which reveals a much “thicker” right tail of the NSCS distribution. Although high levels of genetic differentiation were also observed among the NS, starting from approximately Fst>0.35, two third of the data were NSCS. Hence, in this dataset the prediction that a SNP pair is NSCS rather than NS based on high levels of Fst alone yields a False Discovery Rate of ∼0.33. In other words, the potentially functional NSCS pairs are 2 fold overrepresented at high levels of genetic differentiation.Based on publicly available genotype data from Perlegen/HapMap we estimated trans-haplotype frequencies for 12,875,275 combinations of 5075 autosomal NSCS and compared the distribution of the genetic distances (Wright's Fst)  and S4 ttainment . NSCS trnt (−13) . The anast values. The observed variability between replicates is very low and the combinations randomly declared NSCS vs. NS show no significant difference in the pattern of genetic differentiation , identified GPR156, a GABA(B) related G-protein coupled receptor. We examined all interactors of GPR156 detected here and found GABRR3 (represented by rs832032), neuregulin 3 (rs17101193), DNAI2 (rs1979370) and DEF6 (rs2395617) all of which are related to GABA receptor functioning. GABRR3 is a GABA receptor. Family members of neuregulin 3, are known to affect GABA receptor expressionGiven our interpretation that NSCS trans-haplotypes that show excess genetic differentiation between populations represent functional interactions between genes again we scrutinized our results to see whether genes known to have functional interactions from molecular studies had been identified. We prioritized the NSCS based on the number of pairs each individual SNP was involved in at Fst>0.35. This rather arbitrary cutoff was chosen because at this level of genetic differentiation the NSCS were 2 fold overrepresented compared to the NS in this dataset. Indeed, one of the NSCS (rs902790) with the highest number of reasonably strong interactions  or among the NS (humans). However, the aim of the present approach is rather to first ascertain candidate “co-adapted” genes to be tested for association with complex traits, thus strongly reducing the number of tests in the analysis of specific phenotypes. Indeed, in both the mouse and the human analysis we selected a limited subset of combinations that were likely to be involved in epistatic interactions. In both cases no main effects of these candidate “co-adapted” genes were found on the complex traits analysed. However, we observed marginally significant interaction effects of these “co-adapted” genes on ethanol consumption in mice and on anxiety/depression in humans. Replication of these associations are necessary to ascertain that they are not false positives, but the results are consistent with the prediction that the interaction between these genes rather than their individual effects should be associated with phenotypic variation.A profound difficulty in a phenotype based assessment of epistasis on a genome wide scale is the need to correct for a huge number of tests with obvious consequences for statistical power. Recently strategies have been proposed to tackle this problem all combinations involving the gene/SNP with the strong main effect to yield a high signal. Clearly this is not the case demonstrated by the fact that the 707 Bonferroni significant combinations in the mouse data involved 315 SNPs. The SNP involved in the highest number of interactions was only present in 15 pairs and 40% of the 315 SNPs was involved in not more than 2 combinations. Real interactions rather than strong individual effects must clearly be involved in the majority of the cases. An obvious inference from these results is that standard genetic analyses of complex traits are bound to miss the vast majority of relevant genes. In contrast, here we show that first ascertaining candidate co-adapted genes from population genomic data followed up by an association study is a feasible way to simultaneously detect multiple susceptibility genes for complex (disease) phenotypes even if these lack any individual effect on their own.Estimating the genome wide preference of functional interactions from these results remains difficult because divergence taking two genes into account does not necessarily have to be caused by the interaction among the genes. A strong individual effect of either of them might explain the observed pattern. While we can not exclude that strong main effects contribute to the observed patters we would argue that this can not explain the majority of the cases. If that were the case we should expect http://www.genenetwork.org/dbdoc/BXDGeno.html). Linkage disequilibrium was calculated as the square of the correlation coefficient between two loci across the 89 lines and corresponding p-values were derived from a chi-squared test. Heterozygous RIL genotypes were treated as missing data. SNPs were considered unlinked if they were on different chromosomes or were more than 50 cM apart. Extreme values of allele frequencies may bias LD estimates but in RILs, allele frequencies at all loci should be by definition 0.5. In this dataset the average allele frequency was 0.4996+/−0.079 (SD). QTLCartographer was used to simulate genotyes for 89 recombinant inbred lines with 200 neutral loci per chromosome. Pairwise r2 values were calculated for unlinked SNPs from 1000 replicates.The genotype data on the BXD mouse recombinant inbred lines were downloaded from The GeneNetwork (http://www.nervenet.org/main/databases.html). For the association analysis a multiple linear regression model was implemented in R with the RIL phenotypes as dependent variables and the interaction terms of the SNP pairs as predictors. The number of BxD lines with phenotype data is much lower than the number of lines that have been genotyped, around the 20 depending on the phenotype. Because of this, in the initial screen of the 626 phenotypes only the interaction terms were considered to avoid fitting an over-parameterized model. However, the main effects were included in the analysis of the best fitting model to assess the significance of the interaction terms per se. None of the four main effects were significant in the full model which explained 66% of the phenotypic variation between the RILs. Bonferroni correction was applied to correct for the number of phenotypes tested for determining the significance of the best fitting model.The phenotype data on the BXD mouse recombinant inbred lines were downloaded from Nervenet  as predicting variables. Although all included predictors had a significant effect, the total amount of variance explained was small and the difference between NS and NSCS remained highly significant .Genotype data for a large number of SNPs is available based on 24, 23 and 24 individuals from respectively an Asian, African-American and Caucasian population from Perlegen/HapMap. Out of the approximately 1.5 million SNPs with available genotypes, 5075 were found to be non-synonymous coding variants, polymorphic in all three populations. Unlike in mouse RILs, phase is not evident in outbred genotype data, thus trans-haplotype frequencies were estimated in each population separately with the Expectation-Maximization algorithm implemented in the LDmax software 2) from the simulations was very similar to the real data. This could be expected as 1.5 Mb is a large enough distance for most polymorphisms to be in low LD in the general populations simulated here. Once the average distance between loci is large enough not to be in strong LD a further decrease in marker spacing is not necessary for the simulation results to be representative. The distribution of “NS” vs. “NSCS” Fst values were compared from this data, using 100 replicates and a total of approximately 2.5 billion genetic distances.Using the cosi software for coalescent simulations we generated genotype data for 48, 46 and 48 chromosomes respectively from the three human populations. We implemented parameters as described in a recent calibration of the method Details of the Dutch twin cohort and the phenotypic measures used have been described by previously Table S1(46.60 MB ZIP)Click here for additional data file.Table S2(0.02 MB ZIP)Click here for additional data file.Table S3(78.31 MB ZIP)Click here for additional data file.Table S4(0.04 MB ZIP)Click here for additional data file.Figure S1(0.73 MB TIF)Click here for additional data file.


The question of a genetic contribution to the higher prevalence and incidence of end stage kidney disease (ESKD) among African Americans (AA) remained unresolved, until recent findings using admixture mapping pointed to the association of a genomic locus on chromosome 22 with this disease phenotype. In the current study we utilize this example to demonstrate the utility of applying a multi-step admixture mapping approach.A multi-step case only admixture mapping study, consisted of the following steps was designed: 1) Assembly of the sample dataset (ESKD AA); 2) Design of the estimated mutual information ancestry informative markers (n = 2016) screening panel 3); Genotyping the sample set whose size was determined by a power analysis (n = 576) appropriate for the initial screening panel; 4) Inference of local ancestry for each individual and identification of regions with increased AA ancestry using two different ancestry inference statistical approaches; 5) Enrichment of the initial screening panel; 6) Power analysis of the enriched panel 7) Genotyping of additional samples. 8) Re-analysis of the genotyping results to identify a genetic risk locus.The initial screening phase yielded a significant peak using the ADMIXMAP ancestry inference program applying case only statistics. Subgroup analysis of 299 ESKD patients with no history of diabetes yielded peaks using both the ANCESTRYMAP and ADMIXMAP ancestry inference programs. The significant peak was found on chromosome 22. Genotyping of additional ancestry informative markers on chromosome 22 that took into account linkage disequilibrium in the ancestral populations, and the addition of samples increased the statistical significance of the finding.A multi-step admixture mapping analysis of AA ESKD patients replicated the finding of a candidate risk locus on chromosome 22, contributing to the heightened susceptibility of African Americans to develop non-diabetic ESKD, and underscores the importance of using mutual information and multiple ancestry inference approaches to achieve a robust analysis, using relatively small datasets of "affected" only individuals. The current study suggests solutions to some limitations of existing admixture mapping methodologies, such as considerations regarding the distribution of ancestry information along the genome and its effects on power calculations and sample size. Even in those constituencies where such renal replacement modalities are available, quality of life and lifespan are dramatically reduced, and in many regions of the world where renal replacement therapy is not available, ESKD is fatal [Chronic kidney disease (CKD) encompasses a spectrum of different pathophysiologic processes associated with abnormal kidney function, and a progressive decline in glomerular filtration rate (GFR), culminating in a degree of irreversible loss of GFR , as the population-based genome wide mapping tool. AM makes use of the relatively recent admixture in the Americas of individuals of African and European ancestry ,16, and Despite the reproducibility of the locus on chromosome 22 as a candidate region for the increased risk of African Americans , and Hispanic Americans  to develop ESKD, the causative mutation accounting for the AM signal was not identified within the MYH9 gene . In the current study we utilize an information-theory based measure which we have recently developed , designaA multi-step case only AM study was designed, suitable to the available sample set and genomic association question. Study design consisted of the following steps: 1) Assembly of the sample dataset; 2) Design of the AIMs screening panel 3); Genotyping a sample set whose size is determined by a power analysis appropriate for the initial screening panel of genome wide ancestry informative SNP markers; 4) Inference of local ancestry for each individual and identification of regions with increased AA ancestry using two different ancestry inference statistical approaches; 5) Enrichment of the initial screening panel with additional AIMs markers located on the chromosome of interest identified in step 4; 6) Power analysis of the directed enriched panel 7) Genotyping of additional samples using the enriched panel. 8) Re-analysis of the genotyping results to identify a genetic risk locus.The patient group included all consenting ESKD patients recruited from DaVita Cabrini and Fresenius dialysis facilities in New York (NY) City. Informed consent was obtained from all patients and a questionnaire completed. The entire clinical research protocol was approved by the IRB of the participating institutions, Ancestry was designated by self identification, the birthplaces of each subject and both parents were also recorded. Some of the samples in the current study, were also included as part of a comparative analysis in a study which reported the role of MYH9 alleles in the risk for ESKD among Hispanic Americans . Self idAs a platform for the AIMs screening panel we used a panel of 2000 AIMs validated by Tian et al  Tian Pa. All phyIn order to determine the sample size needed for the case only AM screening step we conducted a set of simulations using the EMI based screening panel, using ANCESTRYMAP, and compared its performance to the Tian panel.A multiplicative risk model parameterized by several ethnicity relative risk values (ERR) was used. We generated samples of admixed-individual genotypes for a case only analysis using ANCESTRYMAP. For each run, a single marker location on chromosome 4 and 22 was designated as the disease-predisposition locus. In order to evaluate the performance of the EMI based screening panel across the entire chromosome, a set of disease-predisposition loci were chosen using a resolution of four markers per Cm; consequently, 627 and 186 uniformly selected locations across chromosome 4 and 22 (respectively) were used in the power experiments. A range of ethnicity relative risk (ERR) ratios, between 0.4 and .0.8, were set as the disease model parameters, all assuming that the African population exhibits the higher disease risk. Power was measured as the proportion of runs which identified the putative disease loci. We have tested the power to detect a disease loci with genome log-factor >2 using ANCESTRYMAP. The power of the current screening panel was compared to the 2000 AIMs panel which appeared in Tian et.al [According to the power simulations for an ethnicity risk ratio of 0.6 only 576 AA ESKD patients were needed in order to reach a power of 80%, using the EMI based screening panel, and assuming a homogeneous phenotype in terms of the risk locus. Accordingly 576 self declared AA ESKD patients were genotyped for the 2016 AIMs screening panel using the GoldenGate assay. Only SNPs with genotype call rates of 85% or more were included in the analysis phase.Both ANCESTRYMAP  and ADMIU is evaluated as the posterior expectation of the realized score, and the observed information V is calculated by subtracting the missing information  from the complete information . The models from ADMIXMAP calculate results in terms of standard normal Z statistics and p values. In this study we report the minus log base 10 of the affected only p values from ADMIXMAP final report.ADMIXMAP: 500 iterations were used for burn-in of the Markov chain. The tests for linkage provided in ADMIXMAP  are scor-3 for at least 2 consecutive AIMs within a range of 4 Cm.The Results of step 5 were reviewed, and regions for further investigation were chosen according the following criteria: 1) LGS Local ≥ 2: The log likelihood of the LGS score obtained by averaging over all the markers on a chromosome as computed by ANCESTRYMAP. 2) In ADMIXMAP, p value ≤ 10Chromosomes with screening AM loci which met the foregoing criteria were further genotyped using an enriched AIMs panel, selected using the EMI algorithm. As indicated in the Results section - the chromosome of interest to which the AIMs enrichment markers were added is chromosome 22, based on the analysis of the genome wide screening marker panel. The enrichment process excluded AIMs that had already been genotyped in the non-enriched EMI panel. A total of an additional 39 AIMs were available using this approach for chromosome 22 to generate the enriched AIMs marker panel  together with the AIMs of chromosome 1 in order to evaluate individual ancestry more accurately. Accordingly for an ethnicity risk ratio of 0.6 an additional 240 AA ESKD patients were needed in order to reach a power of 80%, using the EMI based enriched panel for chromosome 22. It should be noted that at the time of the second step power analysis, the heterogeneity of the sample set into two disease categories (diabetic and non-diabetic) was not yet known and therefore was not included in the power analysis.An additional 257 Self identified AAs with ESKD (155 with diabetes and 102 without diabetes) were genotyped using the directed enriched panel together with the 576 samples, which had undergone genome wide genotyping.The results were reanalyzed using both ADMIXMAP and ANCESTRYMAP, exactly as described for Step 5 above. A statistically significant locus was considered as a locus with LGS >5 using ANCESTRYMAP, and a - LOG (P) > 5 using ADMIXMAP for at least two consecutive SNPs. In order to take into consideration the effect of LD among the ancestral populations on the results, AIMs which were 50 kB or less close to each other were omitted  panel , using mAn ANOVA analysis of the Fisher information content (FIC), as provided in Tian et al  for the Since previous studies ,22,27 ha-3 for at least 2 consecutive AIMs in a range of 4 centimorgans (Cm) using ADMIXMAP - namely chromosomes 5 and 22  using ANCESTRYMAP. No candidate loci were observed according to the stepwise criteria for proceeding to peak choice, as outlined in Methods, namely a locus genome statistic (LGS) local ≥ 2  on chroAs shown in Figure The excess of African ancestry associated with the genomic region on chromosome 22 noted above, is also presented in Table The AM analysis in the current study confirms the results of previous studies ,14 whichsine qua non for proceeding with further mechanistic research for such a locus, and certainly for genetic counseling and clinical applications. In the case of AM in particular, it has been recommended that data should be analyzed using at least two of the several different available ancestry inference programs [In contrast to the two previously reported AM studies, our results were obtained using a different and independent marker panel, a different and independent patient sample set, and two different analytic approaches. The importance of replicating identification of genetic risk loci for common complex disease susceptibility has been highlighted as a programs . Failureprograms . In the programs ,33. Furtprograms . The curprograms ). Thoughprograms ,14.Each of the three studies used a different sample set, but all of the samples were of African American heritage. The current study also utilized a different AIMs panel and two different analytical methods, confirming the utility of AM as an effective mapping approach using relevant populations and disease phenotypes. The use of two different analytic approaches also reduces the risk of false positive results inherent in the methodology of AM and emanating from the complex patterns of LD among panel SNPs in ancestral populations. Future research will be needed in order to validate the genetic risk conferred by the chromosome 22 loci in other populations, other stages of CKD, and possibly other modifier loci, taking into the account the complex heritability and multi-factorial nature of ESKD,36The current study also highlights additional points of more general interest pertaining to AM which might be of interest and utility in application to other sample sets and disease states - especially when only small sample sets or weaker ERRs are involved. Examples could include the increased susceptibility to systemic lupus erythematosus (SLE)  and the The results of the power analysis of the non-enriched screening panel in the current study, demonstrated a non-homogenous distribution of ancestry information across the genome , which would then not make it to the step of scrutiny by an enriched panel on the chromosome or region of interest. It is reassuring that in the current study - an initial screening panel of only 2,016 SNPs and what turned out to be an initial sample set of only 277 relevant (non-diabetic ESKD) samples, led to the appropriate next steps, using ANCESTRYMAP and ADMIXMAP as the initial ancestry inference programs, which converged on one shared risk locus.An additional important lesson from the current study is the inferential power achieved by combining two different analytic and computational platforms, once genotype information is available. Although previous guidelines for AM methodology recommended the use of at least 2 analytical approaches , most puANCESTRYMAP was used because of its unique LGS local score, which can point to a possible association for a given chromosome, unlike ADMIXMAP software which instead provides statistics for individual markers only. Indeed, in the current study, ANCESTRYMAP yielded no peaks across all chromosomes for the entire sample set, but did yield a candidate peak in the non-diabetic subset of samples Figure , 3, consThe goals of the enrichment process were to validate and fine tune the screening panel results, and to narrow the region. The results of ANCESTRYMAP with its LGS local parameter yielded two candidate peaks on chromosome 22 Figure . Based oIn the current study it may be observed that the p values obtained from ADMIXMAP, were more significant in comparison to those obtained using the ANCESTRYMAP LOD scores  ancestry informative markers screening panel. The AIMs were chosen according to EMI enrichment algorithm. 2016 markers were chosen.Click here for fileDirected enriched panel chromosome 22. Enrichment of the screening panel was applied to chromosome 22. All additional AIMs were chosen according to EMI algorithm. 39 additional AIMs were added. For the sub-analysis of the effect of ancestral LD markers which were 50 kB apart from each other or less were omitted from the analysis. In the status column 1 = AIMs from screening panel 2 = AIMs from directed enriched panel. 3 = AIMs from directed enriched panel which were omiited due to a distance of less than 50 kB from other markers.Click here for fileDistribution of Fisher Information Content (FIC) along the genome for the 2016 markers of the screening panel. For each chromosome the mean FIC (2 red circles), two standard deviations of the FIC value (dashed line) and outliers of AIMs with high FIC (red plus) are presented.Click here for fileDistribution of expected mutual information (EMI) score along the genome for the 2016 markers of the screening panel. The Y axis for each chromosome represents the EMI score  and the range of FIC  are displayed. P values represent differences in the distribution of FIC as was calculated by pairwise Kolmogorov-Smirnov test.Click here for fileChromosome 15 LGS and - LOG (P) scores of the screening panel by ANCESTRYMAP and ADMIXMAP respectively. LGS and - LOG (P) are provided by ANCESTRYMAP and ADMIXMAP respectivly for AIMs along chromosome 15. Using the screening panel a total of 576 ESKD AA patients (Red line) were genotyped of whom 299 ESKD patients did not have diabetes mellitus (NonDM) (Blue line).Click here for file


P = 0.02) of maternal effect. We conducted a genome-wide association analysis for height, testing both the direct effect of the focal individual's genotype and the indirect effect of the maternal genotype. Offspring height showed suggestive evidence of association with maternal genotype for two single-nucleotide polymorphisms in the trafficking protein particle complex 9 gene TRAPPC9 (NIBP), which plays a role in neuronal NF-κB signalling. This work establishes a methodological framework for identifying genetic variants that may influence the contribution of the maternal environment to offspring phenotypes.Many phenotypes may be influenced by the prenatal environment of the mother and/or maternal care, and these maternal effects may have a heritable component. We have implemented in the computer program SOLAR a variance components-based method for detecting indirect effects of maternal genotype on offspring phenotype. Of six phenotypes measured in three generations of the Framingham Heart Study, height showed the strongest evidence ( Much research has focused on the impact of measurable properties of the mother  on subsequent phenotypes in their children  16 Framingham Heart Study (FHS) data release (Problem 2). All authors of this study are 'approved users' of these data per the NHLBI Data Use Certification of April 2008. Analysis of these data was approved by the Institutional Review Board of the University of Texas Health Science Center, San Antonio.Outlying phenotype measurements (more than four standard deviations from the mean) were removed from the lipid measures , 43 for triglyceride (TG)) on the assumption that these represented assay errors. The data were normal-quantile-transformed before analysis using the SOLAR "inormal" option to meet the distributional assumptions of the variance components and regression methods. The normal quantile  transformation is robust to a range of departures from normality and also removed scale effects by standardizing the data. Transformations of this type are convenient for batch processing of multiple phenotypes .all SNPs for the non-genotyped implicit mothers of genotyped and phenotyped founders. These maternal genotypes entered the association analysis as properties of their offspring ; the 'virtual' mothers did not enter the analysis otherwise.Individuals with incomplete genotype data were given imputed genotype scores for the missing markers using the -- infer option in the computer program Merlin ,10 Merlii, j may be decomposed into additive genetic and environmental components in the usual way:We have implemented in SOLAR a general model for incorporating polygenic maternal effects -14. BrieI is an identity term , ϕ is a coefficient of coancestry, σz is the phenotypic covariance, and σ2e and σ2a are, respectively, environmental and additive genetic variances. The additive genetic covariance can be further decomposed to include maternal effects:where ϕ is the coancestry coefficient for i and the mother of j, and 2ϕ is the coancestry of the mothers. ρa, am is the additive genetic correlation between direct and maternal effects. Decomposition of the environmental component of Eq. 1 is modified from Eq. 14 of Bijma  if i, j are siblings or half-siblings, ρmo ∈  if i, j are mother and offspring, or 0 otherwise. Our modification from Bijma [σ2mito; the mitochondrial variance component is structured by a matrix whose elements are 1 if i, j belong to the same matriline or 0 otherwise, as described by Czerwinski et al. [with om Bijma  was thati et al. .Measured genotype analysis was conducted for each polymorphic SNP by including its genotype score  as a covariate in the mixed model . Unlike 2, and their interactions were included as covariates in all models, and use of antihypertensive medication was a covariate for SBP and DBP. The use of an indicator variable-type covariate for medication has been questioned, especially with regard to BP [We tested our maternal random effects model on quantitative phenotypes , systolic blood pressure (SBP) and diastolic blood pressure (DBP), fasting total and HDL cholesterol and triglycerides) in individuals measured at exams when they were as similar as possible in mean age Table . Sex, agrd to BP ,18. In rrd to BP ; this diP = 0.02 at 4 degrees of freedom; 4 df is probably over-conservative [P = 0.008, 1 df), evidently capturing some of the maternal effects when these were not explicitly modeled.Table ervative ). IntereWe performed measured genotype (MG) tests of association for own genotype (OMG), maternal measured genotype (MMG), and conditional maternal measured genotype (CMMG), for 476,987 autosomal SNPs from the Affymetrix 500k panel. The saturated maternal effects model was used as the null for all analyses. No SNP gave significant evidence of own- or maternal-genotype association with height when corrected for multiple testing using a Bonferroni test . We did not attempt to account for any linkage disequilibrium among the SNPs in our sample. The SNPs with strongest evidence for OMG, MMG, and CMMG are listed in Table MPZL1 (OMIM #604376), a protein tyrosine phosphatase involved in cell proliferation and differentiation. Our next four highest 'hits' were in the mucolipin2 gene MCOLN2 on 1p22.Several recent studies have undertaken genome-wide association analysis of human height -22. ThesTRAPPC9 gene on chromosome 8 and an intergenic region on chromosome 18. The trafficking protein particle complex 9 gene TRAPPC9 (NIBP) plays a role in neuronal NF-κB signalling [Because the published genome-wide association study on height used unrelated individuals, none reported maternal effects. Interestingly, among our strongest maternal associations are repeated hits in two regions: the gnalling  but has We have implemented combined random-effects, measured-genotype fixed effects approach for discovery of genetic variants contributing to the indirect effect of maternal genotype on offspring phenotype. We have identified two regions on chromosomes 2 and 8 - with suggestive association at two SNPs in each region - that may contribute to maternal effects on human height. The tools developed here should be of use for a variety of phenotypes and diseases for which an effect of maternal environment is known or suspected, including height, hypertension, birthweight, and the metabolic syndrome.BMI: Body mass index; CMMG: Conditional maternal measured genotype; DBP: Diastolic blood pressure; FHS: Framingham Heart Study; GAW16: Genetic Analysis Workshop 16; HDL: High-density lipoprotein; MG: Measured genotype; MMG: Maternal measured genotype; OMG: Own measured genotype; PG: Polygenic SBP: Systolic blood pressure; SNP: Single-nucleotide polymorphism; TG: Triglyceride.The authors declare that they have no competing interests.JB, LA, TDD, and JWK participated in the design of the study. TDD prepared the phenotype and genotype data for analysis. JWK and CPP implemented the maternal-effects analysis in SOLAR. JWK performed the analyses and drafted the manuscript.


We applied a penalized regression approach to single-nucleotide polymorphisms in regions on chromosomes 1, 6, and 9 of the North American Rheumatoid Arthritis Consortium data. Results were compared with a standard single-locus association test. Overall, the penalized regression approach did not appear to offer any advantage with respect to either detection or localization of disease-associated polymorphisms, compared with the single-locus approach. Penalized regression approaches are an attractive option for the analysis of large numbers of predictor variables (such as genotypes at many genetic loci) that may influence a response variable (such as disease status). Most genome-wide studies use single-locus association tests such as the Cochran-Armitage trend test, or, equivalently, logistic regression with a single predictor variable (encoding the effect of a particular locus) included in the regression equation at any given time. Theoretically, regression methods allow the simultaneous inclusion of several different variables in the regression equation, e.g., variables coding for genotype rather than allele effects (thus modeling "dominance"), or variables that encode effects at several different loci. However, standard regression methods fail when the sample size (the number of people) is small compared to the number of predictors.β of parameter estimates (regression coefficients) βj  at p predictors that minimizes the sum of squared differences Standard linear regression can be formulated as finding the vector i, yi is a quantitative outcome variable and xij is a predictor variable . In penalized regression, one minimizes this function subject to a constraint on the coefficients such as where, for person gcorresponds to the original sum of squared differences, his a penalty term, and λ is a tuning parameter (or vector of parameters) that controls the strength of penalization. Ridge regression [2 penaltywhere gression  uses a sproducing coefficients that are scaled down or "shrunk" towards zero and prediction models that often perform better that least-squares owing to a bias-variance trade-off . All pre1 penalty, resulting in both shrinkage and variable selection, in that many of the coefficients become set to zero. Zou and Hastie [hthat is a convex combination of the lasso and ridge penaltiesuses an Ld Hastie  proposedλ1 or λ2 is close to 0. Zou and Hastie [λ2).which they termed the naïve elastic net. However, this method can over-shrink the coefficients and performs poorly unless either f = g + h withThe naïve and modified elastic net approaches enjoy a grouping property whereby predictors that are highly correlated tend to have similar coefficient estimates . An alte and penalty termG groups  and fg and lgindicate the first and last predictor in group g. The penalty term in the group lasso is intermediate between the L1 penalty of the lasso and the L2 penalty used in ridge regression and, as pointed out by Wu and Lange [f = g + h, with g equal to either half the sum of squared differences as above (denoted l2 regression) or to l1 regression), with the penalty term taking the formHere, the predictors are divided into nd Lange , providend Lange  actuallyβg||2 instead of λ2.This is similar in form to the naïve elastic net penalty, except that, like the group lasso, it uses ||f = g + h with the penalization term h taking one of the forms above, and gequalling minus one [Penalization is an attractive option in genetic studies because it allows the grouping of predictors that relate to the same genetic variant or region, and also because we genuinely expect the vast majority of loci to have regression coefficient 0. Although originally developed for quantitative outcomes, penalization methods have been extended to deal with binary outcomes (such as disease). Penalization is achieved by minimizing an objective function inus one  or two [inus one  times thHLA and PTPN22, and also reporting a new locus on chromosome 9. We therefore focused on these regions for application of our penalized regression approach.We analyzed the North American Rheumatoid Arthritis Consortium (NARAC) data, consisting of 868 rheumatoid arthritis (RA) cases and 1194 controls genotyped at 545,080 single-nucleotide polymorphisms (SNPs) across 22 autosomal chromosomes. These data were recently used in combination with additional samples [p-value < 10-7. We also removed individuals with >5% missing genotypes. We used multidimensional scaling of the Genetic Analysis Workshop (GAW) 16 data, together with publicly available HapMap data on 210 unrelated individuals from four populations, to confirm that the individuals from the GAW data had European ancestry and were not related.We used the software PLINK  to perfoWe used PLINK to perform a Cochran-Armitage trend test at each SNP. Unlike Plenge et al. , we madeWe applied the group lasso procedure proposed by Meier et al.  implemenConsideration of groups of predictors simultaneously could be useful if one wished to include more than one predictor per SNP  or to impose some other grouping based on (for example) biological function. However, in our analyses, we used only a single predictor variable per locus , and thus each SNP formed a group by itself.β of the convex functionThe group lasso estimator  is definl is the logistic regression log-likelihood function and the function g (not relevant here). The choice of the tuning parameter λ controls the amount of penalization. A natural way to estimate λ is to use cross-validation [λ equal to log(G), where G is the number of groups, in our case the number of SNPs to be fitted in the model. Thus, λ varied from log(1000) = 6.9 to log(7000) = 8.85 in the results described below.where lidation , howeverlidation  to take z-score at each locus by dividing the observed regression coefficient by its estimated standard error, and converted this to a p-value, assuming the z-score to be normally distributed. This procedure is not, strictly speaking, correct, because penalized regression does not enjoy the asymptotic properties of standard regression procedures: shrinkage of the regression coefficients means their distribution cannot be assumed to be asymptotically normal. However, we hoped that this procedure would provide us with a ballpark estimate of the relative significance of the regression coefficients (relative to one another), even if the exact significance levels could not be considered reliable.The output from a penalized regression procedure consists of an estimated regression coefficient for each predictor in the model: model selection is performed by estimation rather than hypothesis testing . Becauseλ) took between 10 and 12 hours; this increased significantly with the number of markers . The penalized regression procedure did not appear to offer any great advantage over the single-locus analysis with respect to either detection or localization of the putatively associated polymorphisms. We also examined the value of the estimated penalized regression coefficient at each SNP (for which no bootstrapping was required) when using windows of either 1000, 2000, 5000, or 7000 SNPs (data not shown). Again, no clear advantage over single-locus analysis, with respect to either detection or localization of putative causal variants, was observed.Figure detection of disease-associated polymorphisms. A more promising application is the fine-mapping problem, in which one is interested in determining from a smaller  set of strongly correlated predictors in a region, which ones drive the association and are thus potentially causal or lie close to causal variant(s). Simulations suggest that penalized regression may offer some improvement over single-locus methods in this regard [p-values, across the regions investigated. Further investigation (data not shown) suggests that use of a higher penalty may produce better results: ideally one might wish to use cross-validation to choose the best value of λ from a range of possible values; however, this is likely to be prohibitively time-consuming on a genome-wide scale. Further investigation of alternative penalization algorithms and of methods for choosing penalization parameters and assessing significance is warranted.Penalization approaches are an appealing alternative to standard regression techniques for analysis of large numbers of predictor variables in the context of genome-wide association studies. Use of such techniques is just beginning to emerge: ridge regression  has beens regard ,13, althGAW: Genetic Analysis Workshop; WE: Hardy-Weinberg equilibrium; LD: Linkage disequilibrium; NARAC: North American Rheumatoid Arthritis Consortium; RA: Rheumatoid arthritis; SNPs: Single-nucleotide polymorphisms.The authors declare that they have no competing interests.PC participated in the design of the study, carried out the statistical analysis, and helped draft the manuscript. HJC conceived of the study, participated in its design, and drafted the final manuscript. Both authors read and approved the final manuscript.


As genome-wide association studies grow in popularity for the identification of genetic factors for common and rare diseases, analytical methods to comb through large numbers of genetic variants efficiently to identify disease association are increasingly in demand. We have developed a pattern-based data-mining approach to discover unlinked multilocus genetic effects for complex disease and to detect genotype × phenotype/genotype × environment interactions. On a densely mapped chromosome 18 data set for rheumatoid arthritis that was made available by Genetic Analysis Workshop 15, this method detected two potential two-locus associations as well as a putative two-locus gene × gender interaction. Long considered to hold promise for dissecting the genetic etiology of complex diseases , genome-2-based test statistics. For the work described in this report, we applied the pattern-based method on the chromosome 18 data set on rheumatoid arthritis (RA) ascertained by the North American Rheumatoid Arthritis Consortium (NARAC) that was made available for the Genetic Analysis Workshop 15 (GAW15). Ten patterns were found to be significantly associated with the RA phenotype after multiple testing correction. The significance of those ten patterns was confirmed using Monte Carlo simulation. Furthermore, we identified a potentially significant multi-gene/gender interaction involving two loci: SNP0177 and the LD region containing markers SNP0603–SNP0615.We have developed a pattern-based mining strategy (manuscript in preparation) to detect local  and global (unlinked markers) multilocus genetic associations as well as gene × gene/gene × environment interactions. The pattern-based method exhaustively yet efficiently identifies all patterns satisfying pre-defined pattern search criteria and evaluates the association of patterns to disease state through a χData are organized in a two-dimensional data matrix with markers as columns, individuals as rows, and individuals' alleles or genotypes as cell values. Each marker is represented by five columns: one column for each of the two alleles of the marker and one column for each of the three possible genotypes for the marker. A pattern is defined as a maximal sub-matrix of the data matrix in which the value of each marker across all individuals in the sub-matrix satisfies a predefined equivalence criterion such as same genotype value. A sub-matrix is maximal if 1) no more rows can be added while keeping the columns fixed and, 2) no more columns can be added when keeping the rows fixed. Under this formulation patterns can be used to model both multilocus allelic and multilocus genotypic contributions to disease state.support threshold, which specifies the minimum number of rows a pattern must have; and the locus threshold, which specifies the extent of locus interaction. For example, with the support and locus thresholds set to 20 and 2 respectively, all reported patterns will have 20 or more case supports and mostly one or two markers. In the significance evaluation step, a 2 × 2 contingency table is constructed for each pattern to tally its support in the case and control populations . The two categorical variables tabulated are population type ("cases" vs. "controls") and pattern match status ("matches" vs. "does not match"). Partially missing data are excluded. The p-value is obtained from a χ2 test of independence and then adjusted for multiple testing. A modified Bonferroni correction for multiple testing is applied to each pattern, using as the correction factor the total number of patterns that contain equal or greater case support than the target pattern under significance evaluation, rather than the total number of patterns identified. As a result, the adjusted significance is robust against the arbitrary selection of values for parameters in the pattern discovery step. The odds ratio with confidence interval is also calculated for each pattern.Pattern Examiner is a nonparametric data mining-based method for the detection of multilocus associations and gene × gene/gene × environment interactions on data collected in population-based case/control studies. This method has two steps: 1) pattern discovery and 2) significance evaluation. In the pattern discovery step, patterns are identified using as input data from the case population only. The extensiveness (and execution time) of the pattern discovery step is controlled by two parameters: the N contingency tables were constructed with the observed N genotypes of a significant pattern as rows and genders as columns. Three chi-square values, χ2case, χ2control, and χ2pooled, were then obtained for cases only, controls only, and cases and controls pooled, respectively. The p-value was obtained using χ2 = χ2case + χ2control - χ2pooled with N - 1 degree of freedom.To test for the null hypothesis that there is no difference on genotype × gender interaction between cases and controls, three 2 × p-values ≤ 0.01 before multiple testing correction. After Bonferroni correction, ten patterns remained significant, as shown in Table p-value"). Interestingly, all significant patterns share the following characteristics: 1) they all contain marker SNP0177 with allele 1, suggesting a dominant effect for marker SNP0177; 2) they all have odds ratio around two, suggesting a modest relative risk; 3) they all have large number of case support , suggesting a rather common inheritance; and 4) they are all mapped to intergenic regions on chromosome 18. Furthermore, except for markers SNP672 and SNP0177, all other markers in those ten patterns are mapped to two LD blocks as identified by the HapBlock program [We identified 2.6 million patterns, mostly containing two markers, from the NARAC chromosome 18 data set, for a support threshold of 20 and a locus threshold of 2. From this set, 65,689 patterns were found to have  program  . In 20 out of 400 (5%) simulated data sets we observed five or more false-positive patterns. These results suggest that the ten significant patterns discovered in the real data set are unlikely to be an artifact of chance alone. Furthermore, if we consider the fact that these ten patterns share the same marker, SNP0177, then the significance gets even stronger: out of the 400 simulated data sets there was only 1 case (0.25%) where sharing of a common marker was observed in ten or more patterns.To further evaluate the significance of those ten patterns, we performed a Monte Carlo simulation using 400 simulated data sets generated by randomizing the case-control assignment of the 920 individuals in the study while maintaining the female/male ratio in both cases and controls. The pattern-based method was applied to each simulated data set. On average, 2.7 million patterns were identified from each data set, which were then subject to test statistics and multiple testing correction. In 8 out of 400 (2%) simulated data sets we observed ten or more patterns that had N contingency tables for each marker in the significant patterns and for each significant pattern with observed genotypes for marker or pattern as rows. Four variations of the contingency tables were constructed as detailed in the legend of Table p = 0.00118) as in females (p = 0.00109) despite the much smaller sample size. When both female and male populations were considered together ("With gender partition"), an even stronger association between the pair of markers and the disease was observed. For individuals with the 1/1–1/2 genotype for markers SNP0177 and SNP0615, an odds ratio of 11.7  was observed in females over males. For individuals with the 2/2–1/2 genotype for markers SNP0177 and SNP0615, an odds ratio of 7.51  was observed in males over females. Logistic regression analysis on the interaction between the pattern and gender also yielded a significant p-value of 0.0021 (data not shown). Furthermore, a test for differential interaction in cases and controls yielded a p-value of 0.0016, suggesting that there is significant interaction between the SNP0177–SNP0615 pattern and gender in the affected individuals vs. unaffected individuals. Similar results were obtained for all patterns containing markers in the SNP0603–0615 LD block (data not shown). On the other hand, no differential interaction in cases and controls was observed for the three remaining significant patterns (data not shown).It is known that the incidence rate of RA is higher in females. Indeed, there is a matching 3.82:1 female/male ratio in both the case sample and control sample of this data set. However, as shown in Table Several lines of evidence suggest that the significant multilocus associations we detected with Pattern Examiner on the NARAC chromosome 18 data set provided by GAW15 might be true associations: 1) except for marker SNP0177 and SNP0672, multiple markers from the same LD region  were found to be in different significant patterns; 2) all markers in the same LD region displayed consistent dominant  or recessive (a homozygote genotype in a pattern) effect; 3) a Monte Carlo simulation with randomized cases and controls produced a type I error probability of 0.02 for the observed results. The singleton SNP0177 does raise a flag because it is in a strong LD region with adjacent markers. Further investigation is necessary to confirm the role SNP0177 plays in the association. The ultimate proof for true association will have to come from replication studies. Taking advantage of our method's ability to detect multilocus association, we performed a novel multilocus gene × gender interaction analysis and detected a two-locus gene × gender interaction that was supported by three independent assays. Detailed analysis revealed large odds ratios for certain genotype combinations. However, a wide confidence interval  dampens our enthusiasm. Again, further investigation with larger sample sizes is necessary to confirm this observation.2 test (p = 0.0002 for most markers in this region), the significance disappeared after Bonferroni correction with 2300 markers. After applying a less stringent Bonferroni correction using the number of LD blocks (233 LD blocks were identified by the HapBlock program) in this 10-Mb region, those markers resurfaced as significant. Because none of the significant patterns identified by the pattern-based method included markers SNP1097–1107, this locus might act alone as a risk factor for RA.Several reports in the "Association – Problem 2" group of GAW15 have identified the LD region including markers SNP1097–1107 to be significantly associated with RA [[By focusing on detecting multilocus association and interactions, the pattern-based method complements the traditional single marker association test. A preliminary power analysis (data not shown) suggested that this method has more power than the traditional single marker-based analysis under a couple of two-locus disease models. Additional power analysis is needed to further validate its utility.We have identified two potential multilocus associations (SNP0177/SNP1130–1131 and SNP0177/SNP0603–0615) with RA as well as evidence of interaction between gender and loci SNP0177/SNP0603–0615.Dr. Zhong Li is currently employed by High Throughput Biology Inc. (HTB) and serves as its President. He owns stocks of HTB and has the potential to gain commercially from this publication. No patent was filed at this time on the methods discussed in the manuscript. Dr. Andrea Califano is currently consulting and on the Advisory Board of High Throughput Biology Inc.(HTB), for whichhe receives a very small monthly compensation. He has no stock nor holds any position in any other company that stands to commercially gain from this publication. He has no further conflict of interest. No patent was filed at this time on the methods discussed in the manuscript. Dr. Aris Floratos has received consulting fees from High Throughput Biology Inc. He has no stock nor holds any position in any other company that stands to commercially gain from this publication. He has no further conflict of interest. No patent was filed at this time on the methods discussed in the manuscript. Dr. Tian Zheng has no competing interests.


Human genome resequencing technologies are becoming ever more affordable and provide a valuable source of data about rare genetic variants in the human genome. Such rare variation may play an important role in explaining the missing heritability of complex human traits. We implement an existing method for analyzing rare variants by testing for association with the mutational load across genes. In this study, we make use of simulated data from the Genetic Analysis Workshop 17 to assess the power of this approach to detect association with simulated quantitative and dichotomous phenotypes and to evaluate the impact of missing genotypes on the power of the analysis. According to our results, the mutational load based rare variant analysis method is relatively robust to call-rate and is adequately powered for genome-wide association analysis. IFIH1 gene and type 1 diabetes [The success of genome-wide association studies (GWAS) to identify novel loci that contribute to complex human traits has been well publicized . Howeverdiabetes .Until recently, the availability of data appropriate for rare variant association analysis has been extremely limited. However, with improvements in the efficiency of deep resequencing technologies, discovery and analysis of rare variants is becoming increasingly cost-effective and financially feasible in large disease- or population-based cohorts at the level of specific genes or even exome-wide. Furthermore, large-scale whole-genome resequencing efforts, such as the 1000 Genomes Project , continuOne common approach to the joint analysis of rare variants within the same gene is to focus on their mutational load, searching for accumulations of minor alleles across individuals with the same or similar phenotype ,7. Simulin denote the number of rare variants for which the ith individual has been successfully genotyped, and let ir denote the number of these variants for which the individual carries at least one copy of the minor allele. We can model the phenotype iy of the ith individual in a generalized linear modeling (GLM) framework, given by:Consider a sample of unrelated individuals typed for rare variants within the same gene. Let g is the link function, xi denotes a vector of covariate measurements for the ith individual with corresponding regression coefficients β, and parameter λ is the expected increase in the phenotype for an individual carrying a full complement of minor alleles at rare variants compared to an individual carrying none. Thus we construct a likelihood ratio test of association of the mutational load of rare variants with disease by comparing the maximized likelihoods of two models by means of analysis of deviance: (1) the null model where λ = 0 and (2) the alternative model where λ is unconstrained. The contribution of the ith individual to the likelihood is weighted by in to allow for differential call rates between samples.where http://www.well.ox.ac.uk/GRANVIL. The software can be applied to quantitative traits and dichotomous phenotypes and can adjust for potential confounders as covariates. Users must provide a list of genes, with start and stop positions, together with a map file for variant locations.The described method has been implemented using the GRANVIL software, which is freely available for download from The data provided by GAW17 contain genotype data for 697 individuals from the 1000 Genomes Project . Individλ, implemented in the GWAMA software [We make use of the simulated GAW17 data to investigate the type I error rate and power of GRANVIL to detect association with quantitative traits Q1, Q2, and Q4 and the dichotomous disease (CC) phenotype. We consider rare variants to have MAF < 5%. GRANVIL gives equal weight to all these rare variants in the gene, irrespective of their potential functional role. We therefore performed two analyses of each replicate of phenotype data: (1) including all rare variants, irrespective of function; and (2) restricting rare variants to those that are nonsynonymous. We used GRANVIL to test for association with the mutational load in each gene containing at least two rare variants. Phenotype data for individual NA07347 was excluded because of extreme deviation from the mean in most replicates . For eacsoftware .To assess the effect of genotype call rate on type I error rates and power, we randomly removed rare variant genotypes from individuals to simulate missing data. We considered a range of missing data rates: 0.1%, 0.5%, 1%, 5%, and 10% of all available genotypes. To take account of the possibility of allele-specific failure rates, we also considered a more complex model in which heterozygous and rare homozygous genotypes were more difficult to call. Specifically, we randomly removed 1% of common homozygous genotypes, 5% of heterozygous genotypes, and 10% of rare homozygous genotypes. For each model of missing genotype data, we generated 1,000 replicates of data, each from a randomly selected phenotype file from GAW17.p ≤ 3.86 × 10−5 . We assessed power by considering all genes known to be causal for the respective phenotype and calculated type I error rate by considering all noncausal genes [The power (type I error rate) was assessed at a nominal Bonferroni-corrected threshold of Analysis of all rare variants and analysis of only nonsynonymous rare variants generated qualitatively similar results. We thus present here the results for the analysis of nonsynonymous variants.FLT1 gene with Q1 in 100% of the runs  and HIF1A . Interestingly, the power of HIF1A was lower in our models with higher random call rates, although this is likely to reflect stochastic variation in our simulations. The type I error rate for the detection of association with Q1 was higher than expected in several noncausal genes, including OR2T34, OR2T3, NOMO1, and HLA-B. The high type I error rates remained, irrespective of the call rate; for example, association with OR2T34 was detected in 78.4% of replicates for a 90% random call rate and increased to 85.9% of replicates when there were no missing data. Thus these type I errors have not occurred as a result of missing genotypes but because of extended linkage disequilibrium between rare variants across chromosomes.Despite the simulated rate of missing genotype data, we were able to detect the association of the causal BCHE, LPL, SIRT1, SREBF1, and VLDRL, but only in a small percentage of replicates   Figure .FLT1 gene locus in 5% of replicates with no missing genotype data, 5.3% of replicates with a 99.9% call rate and the allele-specific model, and only 1.6% of replicates with a 90% random call rate. The second-ranked causal gene was PIK3C3, identified in just 1.7% of replicates with no missing genotype data  phenotype, we were able to detect the causal a Figure . In addiOne of the key advantages of testing for association of the mutational load within a gene is that we can take account of multiple rare variants simultaneously . Our resWe considered two models of missing genotype data: random failure and an allele-specific model that gives greater probability to uncalled heterozygous and rare homozygous genotypes. Our results were consistent across these two models. This is presumably because for rare variants most of the genotypes are common homozygotes and are thus more robust to call rates determined by the presence of a minor allele.In this paper, we considered the effect of missing genotype data on the power and type I error rates of a method that tests for association of the mutational load of rare variants within genes. However, sequence and genotyping errors also play an important role in the performance of any association approach for common or rare variants. Analysis of the pilot data from the 1000 Genomes Project suggests greater concordance with HapMap for common homozygous genotypes (more than 99%) than for heterozygous or rare homozygous genotypes (95–98%). The simulated GAW17 data could also be used to assess the effect of a range of sequencing and genotyping error models on the performance of rare variant mutational load analyses.The results of our analysis of the simulated GAW17 data suggest that the GRANVIL approach for testing association with the mutational load of rare variants within a gene is relatively robust to missing genotype data, occurring either at random or with differential allele-specific failures. Our power to detect association with causal genes was not dramatically affected by call rate. Similarly, the type I error rate for noncausal genes is relatively unaffected by the rate of missing genotypes but is somewhat inflated by the extent of long-range linkage disequilibrium between noncausal genes.The authors declare that there are no competing interests.RM participated in the design of the study, performed the statistical analysis and drafted the manuscript. AK participated in the statistical analysis and helped to draft the manuscript. AM conceived of the study, and participated in its design and coordination and helped to draft the manuscript. All authors read and approved the final manuscript.


Association studies using tag SNPs have been successful in detecting disease-associated common variants. However, common variants, with rare exceptions, explain only at most 5–10% of the heritability resulting from genetic factors, which leads to the common disease/rare variants assumption. Indeed, recent studies using sequencing technologies have demonstrated that common diseases can be due to rare variants that could not be systematically studied earlier. Unfortunately, methods for common variants are not optimal if applied to rare variants. To identify rare variants that affect disease risk, several investigators have designed new approaches based on the idea of collapsing different rare variants inside the same genomic block  to enrich the signal. Here, we consider three different collapsing methods in the multimarker regression model and compared their performance on the Genetic Analysis Workshop 17 data using the consistency of results across different simulations and the cross-validation prediction error rate. The comparison shows that the proportion collapsing method seems to outperform the other two methods and can find both truly associated rare and common variants. Moreover, we explore one way of incorporating the functional annotations for the variants in the data that collapses nonsynonymous and synonymous variants separately to allow for different penalties on them. The incorporation of functional annotations led to higher sensitivity and specificity levels when the detection results were compared with the answer sheet. The initial analysis was performed without knowledge of the simulating model. Genome-wide association studies (GWAS) have successfully identified thousands of common variants associated with the risk of common diseases ,2. To daTypical GWAS detect disease-associated variants using indirect linkage disequilibrium (LD) mapping, which captures the information of correlated single-nucleotide polymorphisms (SNPs) using a set of tag SNPs to reduce the number of testing. However, this strategy is not efficient when applied to rare variants because the correlation between the rare variants and the tag SNPs is often weak as a result of the low MAF of the rare variants. Alternative LD measures for fine mapping have been developed and offer some advantages over the traditional LD mapping . In addiTo analyze the sequencing data, many investigators have developed association tests to detect disease-associated rare variants. These tests fall into three main types: (1) multiple univariate single-marker tests, (2) multiple-marker tests, and (3) collapsing methods. The univariate single-marker tests assess the significance of association for every rare variant independently. The multiple-marker tests instead test for the association of a set of variants simultaneously . Both siHere, we consider three different collapsing methods for rare variants in the same gene. Regression with a LASSO (least absolute shrinkage and selection operator) penalty is then used to choose the significant collapsed rare variants or common variants. The three collapsing methods are compared based on the consistency across replicates, the cross-validation error rate of the fitted model, and the list of true causal variants. The most significant common variants and collapsed rare variants are shown. We also explore the incorporation of the functional annotation information of all the variants in the regression model. By comparing the results with the list of true causal variants, we find that incorporation of the functional annotation leads to higher sensitivity and specificity levels.All the variants are divided into two groups. Variants with MAF > 5% fall into the common variants group, and all the other variants form the rare variants group. Note that this definition of rare variants is specific to this paper. We also considered a more common definition of rare variants with MAF ≤ 1% and came to the same conclusions (results not shown). The rare variants in the same gene are collapsed using the proportion coding (PROP), the data-adaptive sum (DAS), and the weighted-sum (WS) methods. Details and assumptions of these collapsing methods can be found in Dering et al. .i the collapsed genetic score is l and jv. Note that for the weighted sum collapsing method, G =  denote the set of all the genes and CV =  denote the set of all common variants. If iY is the disease status or the trait value of individual i, then the multiple regression model is:We used a multiple regression model to assess the association of variants with the phenotype after the collapsing. Suppose that in individual iE is the vector of the environmental variables for individual i, Eβ is the vector of coefficients for these variables, g(·) is the link function, and iμ is the mean of iY. For binary disease status we use the logit link function, and for the other three quantitative trait models we use the identity link function. For parameter estimation, we use a least absolute shrinkage and selection operator (LASSO) [where  (LASSO) , which pi, ijs = 1 if gene j has a nonzero coefficient and 0 otherwise. Then the consistency of the method across different replicates is measured by:The Genetic Analysis Workshop 17 (GAW17) data contain 200 simulations, and we treat them as replicates. We use each of the replicates to fit the regression model using a LASSO. Genes with nonzero estimated coefficients are taken to be identified. The consistency of the identified genes across replicates by each method is measured in the following way. Suppose that in the fitted model for replicate F contains all the genes identified by the model fitted in at least one replicate data set and |F| is the size of F. The three collapsing methods are compared based on this consistency score. The ability of the consistency score to evaluate the performance of the collapsing methods is debatable because a method can be consistently bad but have a good consistency score. Therefore we further compare the three collapsing methods using the cross-validation error rate of the fitted model. We fit one model for each of the 200 replicates and use the fitted model to predict the trait values in the other 199 replicates. The prediction is then compared with the true values to calculate the error rate. For the disease trait, an area under curve (AUC) score is calculated for each of the 199 validation replicates and the average AUC score is returned, whereas for quantitative traits the mean-square error is used as the measure of prediction error.where Mutations in the coding region that change the function of the encoded proteins or that fall into highly conserved regions tend to affect the biological function significantly. For each SNP in the data, the functional annotation describes whether the SNP is nonsynonymous or synonymous. We try to incorporate this functional annotation information by collapsing the nonsynonymous and synonymous SNPs separately and shrinking their parameters to different extents to allow different probabilities of association. The modified model can be formulated as:lg, respectively. To shrink the parameters for the synonymous and nonsynonymous variants to different extents, the penalized log-likelihood function is set as:where l(β) is the log-likelihood function, ja = ns indicates that the corresponding variant is nonsynonymous, and ja = s indicates that the variant is synonymous. The two penalty parameters nsλ and sλ are chosen based on the cross-validation error rate within each replicate data set.where Two hundred simulations in the GAW17 data set [Alternatively, we fit one model for each replicate and use the fitted model to predict the trait values of the other 199 replicates. The improvement in the prediction accuracy resulting from the genetic features is thus obtained and is shown in Table In addition, we rank genes and variants based on the number of replicates that provide nonzero parameter estimates for them. For a given threshold, the set of significant genes or variants can be defined. By comparing this list of genes with the true causal variants and genes for disease, Q1, and Q2, we calculate the sensitivity and specificity to draw the receiver operating characteristic (ROC) curves, which are shown in Figure Intuitively, mutations in a gene that change the function of the corresponding encoded protein tend to be more deleterious. Therefore we collapse the nonsynonymous and synonymous rare variants into two different terms and allow different shrinkage for them in the LASSO model. We use the proportion collapsing method to do the collapsing because of its consistently good performance for most of the criteria and trait models. Results before and after incorporating the functional annotation information are compared with the list of truly associated SNPs to generate the ROC curves and their AUC scores, which are shown in Figure In Table We compared three different collapsing methods using the GAW17 data and explored one way to incorporate the functional annotation information. The analysis shows that for the GAW17 data, the proportion collapsing method tends to have the best performance in terms of consistency across different simulations and cross-validation error rate. Furthermore, incorporation of the functional information leads to higher specificity and sensitivity levels. Finally, by comparing the identified genes with the true causal genes, we show that the LASSO method in combination with the rare-variants collapsing method is able to detect most of the true causal variants and genes for the three quantitative traits.However, several issues need to be addressed with regard to the analysis. First, note that, based on both the consistency score and the cross-validation error rate, the performance of the proportion collapsing method drops when applied to Q2 and disease trait compared to Q1. In fact, Q1 is affected by the covariates Age and Smoke, which can be consistently detected easily and which cause the consistency score to be the best. For disease and Q2, this effect of the covariates is much weaker and thus leads to worse consistency. These results suggest that the consistency score may not be optimal to evaluate the performance of the collapsing methods.Second, the improvement in the AUC score achieved by incorporating the functional annotation was not impressive for disease and Q1, given that all the functional variants in the simulation model are nonsynonymous. This again can be related to the higher residual heritability of Q1 resulting from variants not included in the data set. It also suggests that our current way of incorporating the functional annotation is not optimal.Third, many important questions are not answered in this analysis. They include how to detect the interactions between genes and environmental variables, alternative ways to incorporate the functional annotation such as Bayesian methods with different prior probabilities for the synonymous and nonsynonymous variants, adding the quantitative traits in the disease models as predictors, and applying the generalized additive model.The authors declare that they have no competing interests.XY conceived of the study, performed the data analysis and wrote the manuscript. LL, JSL and WZ participated in the data preprocessing and analysis. JF helped to draft the manuscript. All authors participated in design of the study. HZ conceived of the study, coordinated the analysis and wrote the manuscript. All authors read and approved the final manuscript.


Current models of schizophrenia and bipolar disorder implicate multiple genes,however their biological relationships remain elusive. To test the genetic roleof glutamate receptors and their interacting scaffold proteins, the exons of tenglutamatergic ‘hub’ genes in 1304 individuals were re-sequenced incase and control samples. No significant difference in the overall number ofnon-synonymous single nucleotide polymorphisms (nsSNPs) was observed betweencases and controls. However, cluster analysis of nsSNPs identified two exonsencoding the cysteine-rich domain and first transmembrane helix of GRM1 as arisk locus with five mutations highly enriched within these domains. A newsplice variant lacking the transmembrane GPCR domain of GRM1 was discovered inthe human brain and the GRM1 mutation cluster could perturb the regulation ofthis variant. The predicted effect on individuals harbouring multiple mutationsdistributed in their ten hub genes was also examined. Diseased individualspossessed an increased load of deleteriousness from multiple concurrent rare andcommon coding variants. Together, these data suggest a disease model in whichthe interplay of compound genetic coding variants, distributed among glutamatereceptors and their interacting proteins, contribute to the pathogenesis ofschizophrenia and bipolar disorders. N-methyl-D-aspartate) receptorantagonists produce schizophrenia-like psychotic symptoms Schizophrenia and bipolar disorder are common heritable disorders showingconsiderable clinical and genetic overlap de novo copy number variation (CNV) Recent genome-wide association studies (GWAS) of schizophrenia identified rareGRIN1, GRIN2A, GRIN2B),AMPA (α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid) receptor, metabotropic(GRM1) glutamate receptor, and their MAGUK primary bindingpartners DLG1, DLG2, DLG3, andDLG4, which encode SAP97, PSD93, SAP102 and PSD95,respectively.The function of both ion-channel forming (ionotropic) To address the possibility that glutamate receptors together with their associatedsignalling proteins, acting alone or in combination, contribute to geneticsusceptibility in schizophrenia and bipolar disorder, a study of rare and commoncoding polymorphisms was performed. Variants that alter the amino acid sequence, theprotein structure and may be functionally important were identified by deepsequencing exons in the 10 hub genes of 1344 individuals . These iIn a parallel study, we genotyped tag-SNPs within a wider set of 169 MASC genes and96 other candidate genes. Consistent with other genome wide association studies ofschizophrenia and bipolar disorder DNA sequencing of the 10 hub genes from 503 schizophrenic, 263 bipolar and 538ancestrally matched controls identified 62 different coding variants . Of these 62 mutations, 24 were foundsolely in either the schizophrenia or bipolar disorder cohort and 16 were foundsolely in the control group . Since the frequency of these disease only nsSNPs orany single coding polymorphism did not predict disease risk , we askeGRM1, the metabotropic glutamate receptorsubtype 1 (mGluR1)  .mGluR1 (mGluR1) . TheGRM cluster . All but cluster .In order to gain further insight into the potential effect of these polymorphisms onthe GRM1 receptor, the nsSNP cluster was mapped onto available protein models  and the GRM1. Therefore we examined if there was evidence ofalternative splicing at this junction in human brain total RNA using cerebral cortexsudden-death autopsy samples. RT-PCR across the exon-exon boundary revealed the fulllength GRM1 mRNA and the presence of an exon skipped RNA thatencoded an mGluR1 completely lacking the GPCR domain and a short c-terminal domain. This allele frequency in caseswas similar to that of recurrent large deletions on chromosomes 22, 15 and 1, whichwere associated with schizophrenia at frequencies of 0.4%, 0.3%, and0.3%, respectively GRM1 suggest these mutations are ‘functionallyrecurrent’ and may be amenable to therapeutic intervention The total proportion of patients carrying one of these nsSNPs within this region ofGRM1 cluster alsocontained other nsSNPs distributed in the other hub genes, which prompted thequestion if individual variants alone were sufficient, or could act in concert withother molecular determinants. Such interactions have already been demonstrated bygenetic studies in mice with compound mutations in MAGUK proteins Several patients containing a mutation from the The predicted deleterious effect of each nsSNP was measured taking into accountmultiple independent parameters including sequence conservation, effect onstructural stability, proximity to phosphorylation sites, glycosylation sites anddisulphide bonds see . The meaoutermost subset of concentricVenn diagram). In contrast, individuals with at least two concurrentnsSNPs the net increase in deleteriousness increased to 15%, . For three or more concurrent nsSNPsthe net increase in deleteriousness was also 15%, but with a diminishingnumber of individuals in this subset significance is less. Overall, these data are consistent with theconcurrence of multiple nsSNPs having greater adverse effects in schizophrenia andbipolar disorder than in controls. Importantly, the genetic load detected here isdistributed among components of a receptor-signaling complex that is fundamental tocognition and provides a plausible genetic revision of the long-standing glutamatehypothesis of psychosis disorders Combinations of two or more nsSNPs, referred to as concurrent nsSNPs  were fouGRM1 identified in this association study has not previously beenlinked genetically with schizophrenia and bipolar disorder, although other evidencesupports its involvement in these and other neurological disorders GRM1 has a well-established role in the commonest form ofmental retardation, Fragile X syndrome DLG4 mRNA is mediated by the fragile X mental retardationprotein (FMRP) and is enhanced by GRM1 activation DLG3 translation, and DLG3 mutations alsoproduce X-linked mental retardation CYFIP1, containing a rare micro-deletion was found in a recentstudy of copy number variants in schizophrenia GRM1 and other genes encoding synapticcomponents are important for cognitive health generally Schizophrenia and bipolar have been described in psychiatry as a spectrum of manydisorders with heterogeneous presentation, from which it has been proposed thatgenetics may lead to a sub-classification of these diseases into subtypes Whilst categorizing disease subtypes is of immense importance, it is likelygenome-wide studies that rely on the homogeneity of the disease cohort and measurethe frequency distribution of tag-SNPs alone The patient DNA samples (from blood) comprised Caucasian individuals contactedthrough the inpatient and outpatient services of hospitals in South EastScotland. A diagnosis of schizophrenia or bipolar disorder was based oninformation from an interview with the patient using the Schedule for AffectiveDisorders and Schizophrenia–Life time version (SADS-L) supplemented bycase note review and frequently by information from medical staff, relatives andcare givers. Final diagnoses, based on DSM-IV criteria (American PsychiatricAssociation 2000) were reached by consensus between two trained psychiatrists.The control group was composed of individuals that have undergone longitudinalassessment for cognitive ability and did not suffer from psychiatric disease[Lothian Birth Cohort 1921 (LBC 1921), Exons and the flanking sequence of the ten candidate genes were extracted fromthe Vega database The density of nsSNPs was calculated as the number of nsSNPs within a genomicregion divided by the length of that region (defined by the nsSNP positions onthe outer edges of the cluster). The minimum cluster length was limited to 40codons representing the approximate minimum size of a protein domain All possible groupings of nsSNPs within the 11  proteins were considered as a potentialcluster. For each potential cluster, the significance of the deviation from theaverage density was tested using a Poisson model with an average 0.6 nsSNPs per100 codons and the cluster with the most significant density increase wasselected. It is of note that taking all the nsSNPs in our dataset, the averagedensity (0.6 nsSNPs per 100 codons) is similar to that predicted for the humanpopulation (0.55 nsSNPs per 100 codons) The experiment-wide significance level of the best cluster within each gene wasevaluated for each potential cluster by comparing its p-value from a Poissondistribution to the p-values from a Poisson distribution of randomly placednsSNPs in each gene. This ‘extreme Poisson p-value distribution’ wasconstructed for each protein isoform in the following way:100,000 randomizations of positions of affected residues wereperformed.In each randomization replicate, all contiguous subsets of nsSNPs werecompared to the mean SNP density in that protein isoform and the Poissonp-value of the densest subset was recorded for each replicate.One hundred thousand randomizations on each isoform allowed us toconstruct a distribution of extreme Poisson p-values for each proteinisoform.Finally, each protein's most dense cluster Poisson p-value was compared tothe distribution of Poisson P-values obtained by randomization. The computedsignificance of each protein's best cluster was corrected using theBenjamini-Hochberg false discovery rate.column J)greater than or equal to the observed value (column I). These permutation tests were alsoperformed on restricted subsets of individuals who carried at least one, two ormore and three or more non-synonymous variants. Restricting the sample furtherinto groups with four or more was not investigated due to the restricted samplesizes that would result in low statistical power to significantly detect anydifference. P-values are shown in supplementary column L.Multiple parameters see  were useTotal RNA was extracted from sudden-death autopsy brain samples . GRM1 splice variants were amplified, sequenced and cloned byPCR see .2 of 0.8 and minimum minor allele frequency of0.05. SNPs were submitted to Illumina for GoldenGate assay design and thosejudged to be viable assay targets (design score > = 0.4)were ordered as 3 Oligo Pool Assays. 12 assays were repeated in all 3 pools as aquality control measure. Consistent with other genome wide association studiesof schizophrenia and bipolar disorder Tag-SNPs within a wider set of 169 MASC genes and 96 other candidates see  and S7 wSupporting Information S1Document contains detailed methods for the detection and analysis of codingvariants, investigations into the GRM1 nsSNP cluster, tag-SNPs, and thecontrol cohort (LBC).(DOC)Click here for additional data file.Datasheet S1Exon re-sequencing genotypes from schizophrenia, bipolar disorder and control(LBC). First and second columns indicate patient code and their cohort,respectively. The remaining columns are headed by nsSNP names, under whichare the genotypes for each individual.(XLS)Click here for additional data file.Datasheet S21 and dbSNP2.nsSNP name, chromosomal locus, frequency in each cohort, functionalannotation, and scoring for each nsSNP. All nsSNPs have also been depositedin G2Cdb(XLS)Click here for additional data file.Datasheet S3details of the statistics for identifying nsSNP clusters and estimation oftheir significance by randomization analysis.(XLS)Click here for additional data file.Datasheet S4Identities and scores of individuals with concurrent nsSNPs.(XLS)Click here for additional data file.Datasheet S5tag-SNP genotypes of schizophrenia and LBC individuals.(TXT)Click here for additional data file.Datasheet S6List of genes tagged for genotyping with permutation test p-value for eachgene and rank.(XLS)Click here for additional data file.Datasheet S7Fisher's exact test of association for each tag-SNP.(XLS)Click here for additional data file.Datasheet S8Table 1: List of protein-protein interactions used in linear regressionanalysis (see section 3.8 of the supplementary information). Table 2: Listsfor each gene the number  of interactions theprotein (encoded by the gene) makes with the 10 hub proteins.(XLS)Click here for additional data file.Datasheet S9Statistics for concurrent nsSNPs analysis showing an increasing netdeleteriousness correlated with increasing nsSNP count.(XLS)Click here for additional data file.