Autism spectrum disorder (ASD) is well recognized to be genetically heterogeneous. It is assumed that the genetic risk factors give rise to a broad spectrum of indistinguishable behavioral presentations.We tested this assumption by analyzing the Autism Diagnostic Interview-Revised (ADI-R) symptom profiles in samples comprising six genetic disorders that carry an increased risk for ASD . We mined the data to test the existence and specificity of ADI-R profiles using a multiclass extension of support vector machine (SVM) learning. We subsequently applied the SVM genetic disorder algorithm on idiopathic ASD profiles from the Autism Genetics Resource Exchange (AGRE).Genetic disorders were associated with behavioral specificity, indicated by the accuracy and certainty of SVM predictions; one-by-one genetic disorder stratifications were highly accurate leading to 63% accuracy of correct genotype prediction when all six genetic disorder groups were analyzed simultaneously. Application of the SVM algorithm to AGRE cases indicated that the algorithm could detect similarity of genetic behavioral signatures in idiopathic ASD subjects. Also, affected sib pairs in the AGRE were behaviorally more similar when they had been allocated to the same genetic disorder group.Our findings provide evidence for genotype-phenotype correlations in relation to autistic symptomatology. SVM algorithms may be used to stratify idiopathic cases of ASD according to behavioral signature patterns associated with genetic disorders. Together, the results suggest a new approach for disentangling the heterogeneity of ASD. Autism spectrum disorder (ASD) is a behaviorally defined syndrome characterized by variable abnormalities in social interactions and communication, in association with restricted interest patterns and unusual stereotyped behaviors. There has been a concerted effort over the last 20 years to identify causal genetic risk factors and as a result, an increasing number of rare, highly penetrant genetic variants are being implicated . When prThe variability in phenotypic expression of autism observed in monozygotic twin pairs, coupled with the evidence from molecular genetic studies supporting a polygenic multi-factorial liability model has led to the recognition that the many genetic risk factors for autism give rise to a broad spectrum of behavioral presentations and hence the concept of autism as a spectrum disorder. The adoption of this model has led to an implicit assumption that specific genotype-phenotype correlations are unlikely to exist. However, there is evidence that ASD symptoms may be dissociable at the genetic level. Different genetic linkage regions have been obtained for social interaction and repetitive behavioral domains in ASD patients , and disIn the present study, we have undertaken a proof of concept study to determine if these genotype-phenotype correlations exist and whether they could be useful to disentangle the heterogeneity of ASD and complement future genetic studies. Support vector machine (SVM) learning was used to analyze ‘signatures’ of autistic symptomatology in six genetic developmental disorders associated with an increased risk for ASD -20. BaseThe six genetic disorders we included in the study were: 22q11.2 deletion syndrome (22q11DS), Down’s syndrome (DS) , Prader-http://www.agre.org) [The AGRE database was used for the selection of idiopathic subjects (gre.org) ,34. AGREAutism symptom variables were extracted from the ADI-R which was used to interview the parents of each subject . The ADIStandard principal component analysis (PCA) of ADI-R item scores was used to investigate the extent of overlap between the symptom profiles of the different genetic groups.The SVM method was used as a supervised learning method (incorporating the knowledge of the genotype) to classify genotype membership on the basis of ADI-R item scores. SVM is currently one of the most popular machine learning methods used in data mining, due to its firm theoretical foundation and proven superiority in applications. With regards to SVM, a radial basis kernel function was used, with optimal gamma and cost parameter values determined in a nested n-fold or, equivalently, leave-one-out cross-validation (LOOCV) procedure, n being the number of observations in the sample. Each observation in turn was left out of the sample, and an SVM classifier was optimized and built on the remaining n - 1 observations. In this way, an independent assessment of correctness of the predicted class can be achieved for each observation in the sample, resulting in an independent estimate of the accuracy of SVM on the whole sample. In each one of the remaining samples, the optimization with respect to the gamma and cost parameter was achieved by applying a second LOOCV procedure, in which each of these n - 1 observations in turn was left out of the sample and SVM models were fitted to the remaining n - 2 observations, using a grid of combinations of gamma and cost parameter values. In a similar fashion as described above, accuracy was determined for every combination of gamma and cost parameter values on the grid, and the optimal value of gamma and cost parameter was determined as the one giving the highest accuracy. Finally, an SVM model was fitted to the n - 1 observations remaining in the outer loop using these optimal values. SVM by nature is a method for binary (two group) classification, so a multiclass (k classes) extension was used, based on the ‘one-against-one’ approach, in which k(k - 1)/2 binary classifiers are trained; the appropriate ‘predicted’ class is found by a voting scheme, choosing the most frequently assigned class by the binary classifiers.post hoc, be used to obtain a predicted probability for each class, which can be used as outcome parameters to evaluate the confidence of SVM predictions.Thus, the class assigned by SVM is the one with the maximum votes from all one-versus-one (2-group) classifications, based on the decision values of the 2-group classifiers. These decision values can also, The software used was the libSVM program, implemented through the SVM function in the e1071 library in R .As a starting point, we explored the distribution of autism symptom profiles in the genetic disorder sample by PCA. The PCA plot showed that, on average, some genetic disorder profiles were overlapping where others were more clearly separable Figure . This piTo perform a more sophisticated pattern analysis, we turned to machine learning analysis. We used SVM as a supervised learning method to investigate genotype-phenotype relationships between the six genetic disorders and the item scores from the ADI-R algorithm. The essential difference with the unsupervised PCA or clustering analysis used above is that the SVM approach incorporates the knowledge of the genotype in the analysis. The SVM allocations to genetic disorder groups occurred in two steps. First, the SVM analyzed 2-group, ‘one-against-one’ comparisons. Subsequently, the multiclass extension was used to select the most appropriate ‘predicted’ genetic disorder class for each subject on the basis of the most frequently assigned class by the binary classifiers. The binary one-by-one comparisons showed high accuracies of up to 97% of correct genetic group allocations Table . As a reP = 0.002) between the predicted probabilities and the likelihood of correct classification, which provides support for the robustness of the model and encouraged us to test the classifier in further samples.To further evaluate the validity of the prediction model, we investigated the correlation between the predicted probabilities and the proportion of cases correctly assigned to each genetic group, based on LOOCV output. This tests the expectation of the model that higher probabilities reflect greater confidence in prediction, as shown by increasing ‘correctness’ in classification. We observed a significant correlation  of each of the ADI-R items to the SVM classifier was extracted. The result of this analysis showed that four of the top five most influential items pertained to ASD symptoms that related to the quality of social interaction Table . By contIt was notable that the predicted probabilities in SMC15 cases were also relatively high for prediction to the PWS group. This seemed plausible, as both disorders are associated with differences in the ‘dosage’ of genes located in chromosome 15q11-13. By contrast, SMC15 could be clearly discriminated from 22q11DS by SVM, which corresponded with a lack of overlap in the PCA between these two groups . This resulted in similar assignment accuracies and predicted probabilities (data not shown). In subsequent analyses we used the algorithm derived from all patients from our genetic disorder samples, irrespective of whether they met formal criteria for ASD diagnosis, since from a clinical perspective, we also wanted to include the profiles of subjects who scored below ADI-R thresholds for ASD.P = 0.0024), between the genetic groups and random data (P <0.001) and between AGRE0 and random data . This indicated that the algorithm derived from the genetic disorders detected non-random pattern information.Next, we considered whether the genetic disorder algorithm could detect a degree of similarity in patterns of autistic behavior in a sample of ‘idiopathic’ cases. To test this hypothesis, we applied the algorithm to ADI-R data obtained from the AGRE dataset in order. It should be noted that the AGRE sample functioned as a ‘blind’ sample in this context, as we could not validate the outcome with genetic labels. Therefore, we performed analyses to indicate if the algorithm would detect meaningful associations or if these would not differ from random associations, for example not informed by genetic disorder labels. Thus, we generated randomly permuted ADI-R item data from the AGRE0 dataset and compared the distribution of predicted probabilities in the real (AGRE0 and genetic disorder sample) compared to the randomly generated data. The probabilities differed significantly between these groups. As expected, the highest predicted probabilities were observed among the genetic disorder cases. Indeed, the lowest probabilities were observed in the randomly generated AGRE subsample. There was also a significant difference between the genetic groups and AGRE0  would be significantly more often assigned to the same genetic disorder class and be relatively more similar in their behavioral profile than non-related subjects. To test this, we examined the concurrence in class assignment (X-square) and correlation between affected sib pairs in the SVM assigned class and predicted probabilities.P = 0.015). Furthermore, the predicted probabilities for the assigned class in AGRE1 (sib1) were significantly correlated with the predicted probabilities of their affected sibling AGRE2 (sib2)  .Significant dependence between the class assignment of siblings in AGRE1 and the other sibling in AGRE2 was indicated . To confirm the notion of enhanced behavioral similarity between siblings allocated to the same genetic disorder class, we examined the ADI-R scores directly. We used the first principle component (PC1) of the ADI-R scores as a summary measure. Overall (disregarding genetic disorder class), the PC1s of sibs were not significantly correlated , but when split out for concordance of genetic disorder prediction, the correlations were 0.71 and -0.16 for concordant sibs and discordant sibs, respectively, with P <0.001 for ‘concordant’ versus ‘discordant’ sibs. Overall, the sibling analysis indicated that the familial liability to ASD may be partitioned according to the relative likelihood of disturbance related to certain genetic disorders.Interestingly, the correlation in prediction probabilities was driven by a correlation (r = 0.35) between sib pairs assigned to the same class compared with ‘discordant’ sibs (r = -0.18), that is sibling pairs that had not been assigned to the same class. In addition, we found that the covariance in probabilities between sibs was greater when both sibs were assigned to the same genetic disorder class  was substantial given the fact that five groups were compared. Indeed, this result was derived from one-by-one genetic disorder comparisons, in which strong contrast were evident. It was notable, however, that the SVM algorithm derived from the current sample differentiated between some classes better than others. This variability might be explained by the variation in sample sizes; thus, in future larger samples will need to be investigated. It was also notable that the ratings of the pattern of social dysfunction were among the best contributors to class prediction, raising the possibility that particular styles of social impairment may be related to particular genetic risk factors. Although differences in the typology of social impairments have been noted in ASD , differeThe subjects of this study were included because they were ascertained for the presence of a genetic disorder and were assessed regardless of the presence or absence of behavioral concerns. Although this approach is likely to have minimized ascertainment biases, some bias cannot be ruled out. However, any enrichment of behavioral abnormalities in these cohorts is unlikely to give rise to the specific patterns of associations identified here. It was reassuring in this respect that the algorithm derived from all cases in the genetic disorder samples gave comparable results to the analyses that included only the subjects who scored above the ADI-R threshold for ASD. Analysis confirmed that IQ did not seem to act as a confounding factor in the SVM predictions. Also, the influence of age and medication as cofounds could be ruled out, as the ADI-R algorithm codes behaviors between 4 and 5 years old .The application of the genetic disorder algorithm to AGRE samples indicated that the behavioral patterns observed in cases of idiopathic autism were not random. Therefore, these results could be used to estimate relative similarity to behavioral profiles designated from the genetic disorders. In addition, the sibling analysis showed correlation of SVM predictions between affected sib pairs. These findings indicate the feasibility to partition familiality into components according to patterns of autistic symptomatology, for example concordance in relative similarity to behavioral profiles related to the genetic disorders. This notion should be followed up by studies that incorporate genetic or pathway information to ascertain the behavior-based stratification in idiopathic samples. For instance, our allocation in idiopathic ASD to TSC-derived patterns may be supported by molecular data showing mammalian target of rapamycin (mTOR) pathway deregulation. Such a result would support the view that perturbation of the mTOR signaling cascade is a common pathophysiological feature of human neurological disorders, including mental retardation syndromes and ASDs . If confOur proof of concept study indicates the existence of ‘signature’ autistic behavioral profiles that index underlying genetic risk processes. These signatures may be helpful in disentangling the etiological and phenotypic heterogeneity evident in ASD, but warrant replication in larger and independent samples. The approach presented in this study could hold promise as a means of stratifying patients who may benefit from treatments targeted at specific pathways and as a way of identifying those patients in whom interventions may have unwanted effects.22q11DS: 22q11.2 deletion syndrome; ADI-R: Autism Diagnostic Interview-Revised; AGRE: Autism Genetics Resource Exchange; ASD: Autism spectrum disorder; CNV: Copy number variant; CREC: College Research Ethics Committee; DS: Down’s syndrome; IQ: Intelligence quotient; LOOCV: Leave-one-out cross-validation; METC: Medical Research Ethics Committee; mTOR: Mammalian target of rapamycin; PCA: Principal component analysis; PWS: Prader-Willi syndrome; SMC15: Supernumerary marker chromosome 15; SVM: Support vector machine; TSC: Tuberous sclerosis complex; XXY: Klinefelter syndrome.The authors declare no conflicts of interest.HB designed the study, analyzed and interpreted the data, and drafted and revised the manuscript. ME designed the study, analyzed and interpreted the data, and drafted and revised the manuscript. MK undertook data interpretation, and drafted and revised the manuscript. SC analyzed and interpreted the data, and drafted and revised the manuscript. JV designed the study, analyzed and interpreted the data, and drafted and revised the manuscript. PB designed the study, analyzed and interpreted the data, and drafted and revised the manuscript. All authors read and approved the final manuscript.


One of the limiting factors of current genome-wide association studies (GWAS) is the inability of current methods to comprehensively examine SNP interactions for a reasonable sized dataset. It is hypothesised that this limitation is one of the reasons that GWAS studies have not been able to have a greater impact ,2. Many In this presentation, we validate the robustness of a novel algorithm known as Optimal Pairwise Epistasis (OPE) for exhaustively examining all pairwise interactions in GWAS data. This method is based on the systematic evaluation of “binary genotype pairs” (BG-pairs), i.e. the pairs of complementary binary classification of genotype calls for an individual SNP, or a pair of SNPs. We can quantify the discrimination potential of BG-pairs using a family of statistics based on odds ratios.The approach is computationally efficient: the dataset reported here as Study 1 (consisting of ~310K SNPs and 2200 samples ). The meWe have tested our approach over 2 independent GWAS studies of Celiac disease: the first  with 77


The genome-wide association study (GWAS) is a useful approach to identify genes affecting economically important traits in dairy cattle. Here, we report the results from a GWAS based on high-density SNP genotype data and estimated breeding values for nine production, fertility, body conformation, udder health and workability traits in the Brown Swiss cattle population that is part of the international genomic evaluation program.GWASs were performed using 50 k SNP chip data and deregressed estimated breeding values (DEBVs) for nine traits from between 2061 and 5043 bulls that were part of the international genomic evaluation program coordinated by Interbull Center. The nine traits were milk yield (MY), fat yield (FY), protein yield (PY), lactating cow’s ability to recycle after calving (CRC), angularity (ANG), body depth (BDE), stature (STA), milk somatic cell score (SCS) and milk speed (MSP). Analyses were performed using a linear mixed model correcting for population confounding. A total of 74 SNPs were detected to be genome-wide significantly associated with one or several of the nine analyzed traits. The strongest signal was identified on chromosome 25 for milk production traits, stature and body depth. Other signals were on chromosome 11 for angularity, chromosome 24 for somatic cell score, and chromosome 6 for milking speed. Some signals overlapped with earlier reported QTL for similar traits in other cattle populations and were located close to interesting candidate genes worthy of further investigations.Our study shows that international genetic evaluation data is a useful resource for identifying genetic factors influencing complex traits in livestock. Several genome wide significant association signals could be identified in the Brown Swiss population, including a major signal on BTA25. Our findings report several associations and plausible candidate genes that deserve further exploration in other populations and molecular dissection to explore the potential economic impact and the genetic mechanisms underlying these production traits in cattle. Genome wide association studies (GWAS) have for a number of years been a useful tool for detecting genetic variants associated with complex traits in human genetics,2. With Since the seminal QTL mapping work in cattle by Georges et al., a largeA distinct feature of dairy cattle populations is the recent small effective population size that results from a widespread use of artificial insemination. Furthermore, dairy cattle have been subjected to long-term, intensive directional artificial selection and assortative mating scheme for milk production traits in general, and milk yield in particular. This population history has largely influenced the pattern of linkage disequilibrium (LD) in the dairy cattle breeds. For instance, the Bovine Hapmap Consortium reportedA major challenge in the statistical analysis of GWAS data is the sensitivity to systematic confounding factors that might lead to false positive associations, and the primary causes of such confounding result from either population stratification or family structure. So far,The Brown Swiss cattle is best known for their high milk yield and ability to produce well under challenging conditions in terms of temperature and feed. It is important in dairy production in Western Europe and North America. Since 1996, the Interbull Centre has routinely received data from Brown Swiss bulls from many countries and carried out an international breeding evaluation resulting in comparable estimated breeding values (EBVs) for these bulls across countries. In this study, we make use of the international EBVs of Brown Swiss bulls from several countries and genotypes from the Illumina Bovine SNP50 Beadchip  that were collected for use in the national and international genomic prediction effort, to perform a GWAS to identify loci contributing to several for economically important traits in Brown Swiss cattle.The nine traits selected for this GWAS analysis were milk yield (MY), fat yield (FY), protein yield (PY), lactating cow’s ability to recycle after calving (CRC), angularity (ANG), body depth (BDE), stature (STA), milk somatic cell (SCS) and milking speed (MSP). The descriptive statistics of these traits are provided in Table The pairwise Pearson correlation coefficients for all pairs of traits are given in Table To examine the possible population structure in the analyzed population, principal component analysis (PCA) was performed for all 7038 individuals based on the kinship matrix estimated from SNPs. Two sub-groups were identified of 6784 and 254 bulls, respectively , hydroxyacylglutathione hydrolase (HAGH), and heparan sulfate (glucosamine) 3-O-sulfotransferase 6 (HS3ST6)  , fibrinogen C domain containing 1 (FIBCD1), laminin gamma 3 (LAMC3) were close to the signal. Other SNPs associated with angularity were also detected on BTA1, 8, 12 and 29.A peak consisting of five SNPs with genome-wide significant effects on angularity was detected at the distal region of BTA11. Four of these five SNPs were located between 87.3 Mb and 88.0 Mb. The closest gene mapping to this peak is the  Figure , but othbta-mir-2380) was located close to the peak at 31.1 Mb  reached genome wide significance. An interesting candidate microRNA (afamin (AFM or ALB2), alpha-fetoprotein (AFP or FETA_Bovine), albumin (ALB) as well as the Interleukin-8 (IL8) genes were located in the close vicinity of the peak  in Holstein and Finnish Ayrshire-32. Thislization. Courtlalization have earin human, which fd traits. Based oTo date, a total of 16 QTL affecting angularity have been identified on 11 aubta-mir-2380; Additional fileSchulman et al. reportedIL8  for a large number of Brown Swiss bulls are routinely delivered to Interbull Centre as part of the international breeding evaluation program for dairy cattle. The natAs a bull’s breeding value  includes pedigree information, there is a risk that SNP could be significantly associated with the trait due to the pedigree information rather than phenotype. Thus, deregressed solutions removing the contribution of information from relatives were calculated for each bull. The equation for de-regression is as foDEBV is de-regressed EBV, PA represents parent average, EBV is estimated breeding value, and RELdau is reliability from daughters. This conversion analysis was done using the R package[Where  package. The bulp < 0.01. Individuals were also excluded from the analysis if they had more than 10% missing genotypes. There were slight differences in the outcome of the quality control between the traits as the sample of individuals for the traits differed slightly for the reason described above.Genotype information was initially available for 44,826 SNPs on the Illumina Bovine SNP50K Beadchip. We applied the following quality control of these SNPs before conducting statistical analysis: SNPs were discarded if i) its call rate was less than 90%, ii) if its minor allele frequency (MAF) was less than 2% or iii) it departed from Hardy-Weinberg equilibrium at a threshold of To examine whether population stratification was a problem in our data, principle component analysis (PCA) was carried out using the GCTA software, which iTo analyze this data, where familial confounding existed, a linear mixed model implemented in the program EMMAX was usedY denotes the vector of deregressed EBVs (DEBVs), X is the vector of genotypes at the locus being tested, β is the additive fixed effect attributed to the locus, and ε is the vector of residual error with ε ~ N , and u is the vector of the background polygenic effects with u ~ N .Where G, describes the genome-wide relatedness between the individuals and is estimated once based on the identity-in-state (IBS) of the genotyped markers. The parameters of the model σ2u and σ2e are estimated using restricted maximum likelihood (REML) for each SNP. Generalized least squares (GLS) is employed to estimate the effect β and an F-test test to test the null hypothesis H0: β =0.The kinship matrix, Significance testing was based on Bonferroni corrected significance thresholds correcting for the number of SNP loci tested. Genomic control was alsoLocations of SNPs and gene clusters were identified based on the Bovine genome NCBI build 6.1 and ENSEMBL,35.Bos taurus chromosome N; EBVs: Estimated breeding values; DEBVs: Deregressed estimated breeding values; MY: Milk yield; FY: Fat yield; PY: Protein yield; CRC: Lactating cow’s ability to recycle after calving; ANG: Angularity; BDE: Body depth; STA: Stature; SCS: Milk somatic cell; MSP: Milking speed.GWAS: Genome-wide association study; PCA: Principle component analysis; LD: Linkage disequilibrium; SNP: Single nucleotide polymorphism; Bp: Base pairs; Kb: Kilo base pairs; Mb: Mega base pairs; MAF: Minor allele frequency; cM: CentiMorgan; QTL: Quantitative trait locus; BTAN: The authors declare no competing interests.ÖC and HJ initiated and planned the study. JG implemented the data analysis. JG drafted the manuscript and all authors together wrote the final paper. All authors read and approved the final manuscript.Figure S1. Principal component analysis of the total sample of 7038 bulls. Plot of the first two principal components (PC1 and PC2) of each individual based on SNP information to evaluate the extent of population structure.Click here for fileFigureS2. Manhattan plots for eight traits based on a linear mixed model and genomic control. Manhattan plot showing the association of the traits to BTA1-29. The chromosomes are plotted separately by color. The P-values of the association were after genomic control transformed to –log10 . The horizontal dashed line indicates the genome-wide Bonferroni-corrected significance level. Included traits are MY (milk yield), FY (fat yield), PY (protein yield), CRC , ANG (angularity), BDE (body depth), SCS (milk somatic cell count) and MSP (milking speed).Click here for fileFigureS3. Quantile-quantile (Q-Q) plots of P-values of SNPs from EMMAX for the nine analyzed traits The blue dots represent the association P-values. The dark line denotes the expected pattern under the null hypothesis, whereas the red line is the observed pattern. Deviations between the two lines indicate how the test statistics of loci deviate from the null hypothesis. MY: milk yield, FY: fat yield, PY: protein yield, CRC: lactating cow’s ability to recycle after calving, ANG: angularity, BDE: body depth, STA: stature, SCS: milk somatic cell count, MSP: milking speed.Click here for fileTable S1. Genome-wide significant SNP effects for each of the nine analyzed traits.Click here for fileFigure S4. 1 Mb gene clusters surrounding the association signals for somatic cell score on BTA24 and milking speed on BTA6. Gene clusters in 1 Mb regions surrounding the main association signals for A) somatic cell score on BTA24 and B) milking speed on BTA6.Click here for fileFigure S5. The association of milk yield to BTA25 with and without stature as a covariate. The p-values for the association of milk yield to BTA25 was obtained using a linear mixed model and genomic control and then transformed to –log10 . The horizontal dashed line indicates the genome-wide significance level . Additional fileClick here for fileFigure S6. The association of fat yield to BTA25 with and without stature as a covariate. The p-values for the association of fat yield to BTA25 was obtained using a linear mixed model and genomic control and then transformed to –log10 . The horizontal dashed line indicates the genome-wide significance level . Additional fileClick here for file


Common, complex diseases are hypothesized to result from a combination of common and rare genetic variants. We developed a unified framework for the joint association testing of both types of variants. Within the framework, we developed a union-intersection test suitable for genome-wide analysis of single nucleotide polymorphisms (SNPs), candidate gene data, as well as medical sequencing data. The union-intersection test is a composite test of association of genotype frequencies and differential correlation among markers.We demonstrated by computer simulation that the false positive error rate was controlled at the expected level. We also demonstrated scenarios in which the multi-locus test was more powerful than traditional single marker analysis. To illustrate use of the union-intersection test with real data, we analyzed a publically available data set of 319,813 autosomal SNPs genotyped for 938 cases of Parkinson disease and 863 neurologically normal controls for which no genome-wide significant results were found by traditional single marker analysis. We also analyzed an independent follow-up sample of 183 cases and 248 controls for replication.GAK, which is involved in clathrin-mediated membrane trafficking. We also found suggestive evidence that directionally inconsistent marginal effects from single marker analysis appeared to result from risk being driven by different haplotypes in the two samples for the genes SYN3 and NGLY1, which are involved in neurotransmitter release and proteasomal degradation, respectively. These results illustrate the utility of our unified framework for genome-wide association analysis of common, complex diseases.We identified a single risk haplotype with a directionally consistent effect in both samples in the gene  The resulting set of p-values is then adjusted for multiple comparisons, usually a Bonferroni correction for the number of tests performed.Mapping disease susceptibility loci for complex diseases has proven to be challenging. The etiology of a complex disease is multifactorial, with both genetic and environmental risk factors and interactions among these risk factors. Genome-wide association (GWA) studies are an alternative to traditional family-based linkage studies for mapping disease susceptibility loci for complex diseases. The most common design to date for GWA studies is to genotype a dense panel  of single-nucleotide polymorphisms (SNPs) for a large collection of unrelated cases and controls. SNPs are then tested one marker at a time for association most often using contingency table analysis, Single marker analysis involves the marginalization of effects over all genetic and environmental backgrounds. Consequently, effect sizes for single markers tend to be small , necessitating sample sizes of thousands to obtain reasonable levels of power at genome-wide significance levels [Alternatively, consider a biochemical pathway consisting of many genes, which may be located on different chromosomes and hence may segregate independently. This motivation raises the general question of how to test a set of markers that may be biologically related but not correlated via linkage disequilibrium. Possibilities include multivariate techniques such as the F test or multiple regression. However, these techniques can also lose power due to large degrees of freedom.r2 and D', are biased upwards when allele frequencies are low or sample sizes are small [A third issue for association analysis is low power for rare variants that medical sequencing is expected to uncover. To overcome low power for variants with frequencies < 5%, specialized methods for grouping variants have been described ,4, but sre small .In response to all of these motivations, we propose a flexible multi-locus method based on unions of multiple SNPs that yields a test that always has only one degree of freedom. The method implicitly accounts for linkage disequilibrium and is appropriate for simultaneous analysis of common and rare variants. We demonstrate by simulation that our method has valid control of the false positive error rate while yielding more power than traditional single marker analysis. We also demonstrate by simulation that our method is sensitive to any source of differential correlation among markers. We then analyze two publicly available data sets for Parkinson disease (PD) for which no significant associations were detected by single marker analysis -9. Usinghttp://www.ncbi.nlm.nih.gov/omim) is the second most common neurodegenerative disorder after Alzheimer disease. For the discovery sample, we obtained publicly available data from the PROGENI and GenePD studies of familial PD [Parkinson disease  be the probability of event X and P(Y) be the probability of event Y. The probability of the union of events X and Y, p (X ∪ Y), is P (X ∪ Y) = P (X) + P (Y) - P (X ∩ Y). To estimate the probability of the intersection P (X ∩ Y), we need a measure of correlation. One commonly used measure of correlation is the pairwise correlation coefficient, given by To illustrate the construction of a union based on classical (binary) logic, consider two events. Let A represent the major allele and B represent the minor allele at a SNP. With respect to the minor allele, dominant coding of the three genotypes  is given by  and recessive coding is given by . Additive coding of the number of copies of the minor allele, i.e.,, can be achieved by summing over dominant and recessive variables since  +  =  and thus need not be separately considered [r2 is a commonly used measure of linkage disequilibrium. Thus, unions implicitly account for correlation between markers, including coupling (r > 0) or repulsion (r < 0) phase. It is critical to note that this use of the correlation coefficient encompasses gametic phase disequilibrium as well as other sources of correlation such as epistasis and natural selection. Also note that, by definition, P (X ∪ X) = P(X), demonstrating the equivalence of analysis of a union of one marker with traditional single marker analysis.In the genetic context, let nsidered . r2 is ak markers. The choice of non-overlapping sets was made to facilitate calculating the genome-wide testing burden. Let ij xbe a binary indicator variable for the ith individual and the jth union. With two markers (loci denoted by subscripts) under dominant coding for the minor allele,There are many possible coding schemes one could implement within this framework. In this study, we construct unions over consecutive, non-overlapping sets of B allele (the null hypothesis is the intersection) and a value of 1 indicates the presence of at least one B allele . Similarly, with two markers under recessive coding for the minor allele,in which ? represents missing data. Under dominant coding, a value of 0 indicates the absence of at least one BB genotype (the null hypothesis is the intersection) and a value of 1 indicates the presence of at least one BB genotype . Any individual for which ij x= ? is removed from analysis of the jth union. Note that this choice of implementation relies solely on counting individuals with pre-specified multi-locus genotypes, does not require estimation of ip, jp, or r, and does not assume Hardy-Weinberg equilibrium.Under recessive coding, a value of 0 indicates the absence of at least one jth union, the 2 × 2 contingency table is constructed by counting the numbers of individuals for which ij xis 0 or 1 among cases and controls. The test has only one degree of freedom, regardless of k. We control for multiple comparisons using a Bonferroni correction for the number of unions tested. The number of unions tested is given by x. This implementation of multiplicity control preserves more power as k increases and as the testing burden is consequently reduced. Given 319,813 SNPs in the discovery sample and accounting for both dominant and recessive coding over unions of size one to five, the genome-wide significance level was For case-control data, we test for association using Fisher's exact test. For the med in R .http://www.sph.umich.edu/csg/abecasis/MACH/download/. For the reference panel, we retrieved the combined HapMap phase II+III raw genotype files for the CEU sample http://hapmap.ncbi.nlm.nih.gov/downloads/genotypes/latest_phaseII+III_ncbi_b36/forward/non-redundant/. We filtered the 3,907,239 autosomal CEU SNPs based on the inclusion of unrelated individuals only, a minor allele frequency ≥ 0.01, a SNP missingness rate ≤ 5%, and an individual missingness rate ≤ 5%. We inferred haplotype phases for the reference data using the settings --rounds 50 --states 200. We conditioned imputation on the maximum-likelihood estimates of the crossover map and the error rate map. We retained all imputed genotype calls for which the posterior probability ≥ 0.9.Imputation was performed using MACH, version 1.0.16 http://pngu.mgh.harvard.edu/purcell/plink/[We performed haplotype analysis using PLINK version 1.06 ll/plink/. Brieflyvs. marginal effects  [We also compared the union test to the collapsing method , a set-bherwise" . Thus, t(r2 = 0) . The colData processing for quality control for both samples is depicted in Figure -8  unions, and haplotype structure, with no requirement for the estimation of haplotypes or phase. Union testing can be viewed as a generalization of grouping schemes for analysis of independent rare variants ,4 that ailibrium ) in a muilibrium .The union test is a composite test of association of genotype frequencies and differential correlation among markers. Union tests are also haplotype tests and are sensitive to processes such as natural selection and population structure that may lead to differential correlation among markers. Previous analyses did not detect substantial population structure in either PD data set . HoweverNOD2 associated with Crohn's disease [Our proposed method is very flexible. The choice of which SNPs to combine into unions belongs to the investigator. We chose to combine consecutive SNPs in non-overlapping sets in order to take advantage of linkage disequilibrium, so that union testing may be viewed as a generalization of haplotype testing, while minimizing the correlation between tests. With an appropriate grouping scheme, unions may be used to address allelic heterogeneity, which occurs when the phenotype of interest is caused by different mutations within the same gene . The rol disease . Alterna disease , as has  disease  and chol disease . Unions e.g., non-overlapping windows), union testing can also reduce the testing burden compared to single marker analysis. However, instead of non-overlapping windows as we used herein, a sliding window approach could be employed, at the cost of a higher testing burden.Although we tested unions using contingency table analysis, it is straightforward to adapt our coding for use with generalized linear models and thus to incorporate covariates into the analysis. Our method is also flexible with respect to genetic models, such that coding for SNPs may be any combination of dominant, additive, or recessive . DependiThere are two main disadvantages of unions. One disadvantage is that the SNP(s) and/or haplotype(s) within a union driving association cannot be inferred. If genome-wide analysis is intended as exploratory and hypothesis-generating, then this disadvantage is not a concern. The second disadvantage is that there are scenarios under which statistical power may be lost, depending on how collapsing is achieved. As with other collapsing methods, the power of union testing decreases if the size of the union is too large, whether or not the included variants are causal . This liNGLY1 (GeneID 55768), which encodes an enzyme thought to participate in proteasomal degradation of misfolded glycoproteins [GAK (GeneID 2580), which regulates clathrin-mediated membrane trafficking [GAK was found to be associated under an additive model [GAK as well as five other genes, leading to poor resolution at this locus. SNPs rs1159220 and rs5998577 are intronic in the gene SYN3 (GeneID 8224). Synapsins are essential for assembly of synaptic vesicles and modulate neurotransmitter release, with expression of SYN3 being neuron-specific [We illustrated union testing by reanalyzing genome-wide genotype data for Parkinson disease. As expected, our findings represent a superset of those originally described . SNP rs9proteins . SNP rs1K GeneID 80, whichspecific . As withGAK gene on chromosome 4 and identified two other regions with suggestive evidence of multiple low-frequency risk haplotypes.We have developed a unified framework using unions of multi-locus genotypes to powerfully, flexibly, and efficiently analyze genome-wide genotype data, candidate gene data, or medical sequencing data. Implementation with standard statistical packages (we used R) is straightforward. We replicated as significantly affecting PD risk a single, low-frequency haplotype in the region of the Recent attempts at elucidating the genetic architecture of complex traits have been hampered by the use of methods that do not account for correlation in the data, are overly stringent, and are underpowered in the presence of allelic or locus heterogeneity and rare variants. To address these issues, we developed a powerful and efficient multivariable method based on unions of variants. Our method produces multivariable test statistics with reduced degrees of freedom compared to haplotype-based methods, implicitly accounts for linkage disequilibrium, and reduces the testing burden. Our method also generalizes collapsing methods as previously described for analysis of rare variants. Thus, we provide a unified framework for the analysis of one or more variants with any pattern of linkage disequilibrium and with any minor genotype frequency. Our method is suitable for genome-wide genotype data, candidate gene data, exome sequencing data, and whole genome sequencing data. Using our new method, we found evidence supporting susceptibility to PD at three loci.DS designed the study, analyzed the data, and drafted the manuscript. LKV conceived of the study and contributed to the interpretation of the results and to the writing of the manuscript. All authors read and approved the final manuscript.Table comparing the validity of the union test and the kernel machine-based test. See the legend for Figure Click here for fileTable comparing the power of the union test and the kernel machine-based test for multiple independent markers with moderate effects. See the legend for Figure Click here for fileTable comparing the power of the union test and the kernel machine-based test for multiple independent markers with larger effects. See the legend for Figure Click here for fileTable comparing the power of the union test and the kernel machine-based test for markers with opposing effects. See the legend for Figure Click here for fileTable comparing the power of the union test and the kernel machine-based test for dilute signal. See the legend for Figure Click here for fileTable comparing the power of the union test and the kernel machine-based test for correlated predictors.See the legend for Figure Click here for fileTable comparing the power of the union test and the kernel machine-based test for epistasis. See the legend for Figure Click here for fileTable comparing the power of the union test and the kernel machine-based test for differential correlation between markers. See the legend for Figure Click here for fileQuantile-quantile plots for genomic control. A) The discovery sample. B) The replication sample. The red lines indicate the expected distribution. The inflation factors are shown, indicated by λGC.Click here for file


Multifactor Dimensionality Reduction (MDR) is a popular and successful data mining method developed to characterize and detect nonlinear complex gene-gene interactions (epistasis) that are associated with disease susceptibility. Because MDR uses a combinatorial search strategy to detect interaction, several filtration techniques have been developed to remove genes (SNPs) that have no interactive effects prior to analysis. However, the cutoff values implemented for these filtration methods are arbitrary, therefore different choices of cutoff values will lead to different selections of genes (SNPs).We suggest incorporating a global test of p-values to filtration procedures to identify the optimal number of genes/SNPs for further MDR analysis and demonstrate this approach using a ReliefF filter technique. We compare the performance of different global testing procedures in this context, including the Kolmogorov-Smirnov test, the inverse chi-square test, the inverse normal test, the logit test, the Wilcoxon test and Tippett’s test. Additionally we demonstrate the approach on a real data application with a candidate gene study of drug response in Juvenile Idiopathic Arthritis.Extensive simulation of correlated p-values show that the inverse chi-square test is the most appropriate approach to be incorporated with the screening approach to determine the optimal number of SNPs for the final MDR analysis. The Kolmogorov-Smirnov test has high inflation of Type I errors when p-values are highly correlated or when p-values peak near the center of histogram. Tippett’s test has very low power when the effect size of GxG interactions is small.The proposed global tests can serve as a screening approach prior to individual tests to prevent false discovery. Strong power in small sample sizes and well controlled Type I error in absence of GxG interactions make global tests highly recommended in epistasis studies. Recent advances in genotyping technology have allowed for the rapid and easy interrogation of large numbers of genetic variants for association with common, complex disease. While there have been a number of successes in association mapping studies, the associations found typically explain very little of the overall heritability of the traits being studied. There are several potential reasons for this “missing heritability”, and one of those potential explanations is epistatic interactions (gene-gene interactions). It is hypothesized that such interactions play an important role in the etiology of complex (non-Mendelian) traits, but detecting such interactions presents a number of statistical and computation challenges . In respMultifactor Dimensionality Reduction (MDR) is a popular and highly successful statistical method developed to detect and characterize nonlinear complex gene-gene or gene-environment interactions (epistasis) that could be associated with disease susceptibility. The method was first proposed by Ritchie et al.  to deteck = 2, 3, 4 …) interactions. For each multi-locus combination, the ratio of cases to controls within each contingency table cell is calculated, and then each cell is assigned a status of high-risk or low-risk by comparing this ratio to the ratio of cases: controls in the overall dataset. Cells with a ratio greater than the overall ratio are assigned “high-risk” status, and those with a ratio lower than the overall ratio are assigned “low-risk” status. Subsequently, a balanced classification accuracy is calculated for each multi-locus combination, and the optimal model is selected based on the highest balanced accuracy. This model selection approach is performed in concert with a cross-validation procedure, usually 10-fold, which randomly divides the whole data set into a training set and a validation set. The testing accuracy is the balanced accuracy when the classification rule developed from the training data set is applied to the testing data set. The cross validation count (CVC) summarizes the number of times a model is the top model in each of the cross-validation splits of the data. The optimal k-way  interaction model with the highest training accuracy and the highest CVC is then selected as the winner model. Finally, the significance of the selected optimal model is assessed by permutation testing . MDR can be performed by an open source software mdr2.0 and model goodness-of-fit and significance can be assessed using software mdrpt1.0 [While the MDR approach is widely used, to make this paper self-contained, we give a brief description of the method. MDR is often applied to genotypic data to detect gene-gene (GxG) interactions among single nucleotide polymorphism (SNP) and the original implementation of this method can be extended to detect the interactions in other types of data when the explanatory variables are categorical variables and the outcome variable is binary. As the scale of association studies has expanded (with larger numbers of SNPs), a filtration step is often implemented in the first step of MDR analysis to remove noisy SNPs. In this step, a subset of genes that are unlikely to interact with others is removed by filtration methods such as SURF , TuRF 66 etc. Remdrpt1.0  or in thmdrpt1.0 .In this work, we seek to address two existing issues in the current MDR analysis. First, current filtration approaches do not evaluate the significance of the SNPs considered  and there is no clear guideline for the cutoff point of such filtration measures. This leads inconsistency in the optimal number of SNPs remaining for the final MDR analysis.k-way interaction, as the number of partitions for k-way interaction over m loci is Second, as there is a growing appreciation that the etiology of human diseases is extremely complex, many investigators are using MDR to evaluate many potential interactive effects, and not just a single final best model . In thisFalse discoveries and losing power to detect the signal after the multiplicity adjustment are two concurrent issues in analyzing high dimensional data. Instead of replacing all the existing methods to control the false discovery, we propose to add the global tests to the current MDR framework as an ad-hoc screening process to prevent false discoveries. We will explain the rationale and utility of global tests in Section Global tests.Incorporating global tests within the filtration procedures can reveal a trend of gene interactive patterns when noisy genes (SNPs) are removed step by step using ReliefF or other filtration techniques. In the current study, we demonstrate this approach in a candidate gene study of drug response in Juvenile Idiopathic Arthritis, using the ReleifF filter. Additionally, we perform a simulation study comparing several different global testing approaches for a range of genetic etiologies to compare the power of different approaches.k way interactions among m loci (T be the test statistic with the cumulative distribution function (CDF) F0(t) and the inverse CDF H0. Let P be the p-value corresponding to the test statistic T. Under H0, we have The idea of global testing is to assess the patterns of p-values from multiple testing of iform 0, . To see m loci have k-way interactions (Hα), it is expected to observe the p-values shifting towards 0. To see this, let F(t) be the CDF under Hα and k-way interactions among m loci.When a proportion of H0) might even shift toward 1 or peak near the center (Patterns 3 and 4). The goals are to rule out Patterns 1, 3 and 4 and only move forward to the final MDR analysis when p-values are in Pattern 2.The rationale of global testing is to ensure p-values are not randomly and uniformly distributed (Pattern 1) before we investigate each single p-value. Correlated p-values without significant effects  and remove noisy genes (SNPs) with little interactive effects to determine the optimal number of SNPs for the final MDR analysis. The ReliefF algorithm estimates weights to measure the potential accuracy of attributes in prediction of phenotype. The redundant attribute will be assigned a lower score. When applied in gene-gene interactions, a higher ReliefF score indicates a stronger interactive effect for the corresponding gene (SNP). ReliefF algorithm first uses x- nearest neighborhood approach x subjects in neighborhood  from the control group and from test group respectively. An attribute (SNP) will be assigned score 1 (−1) if the attribute from the selected subject matches (mismatches) one of x nearest subjects from the same phenotype group. Similarly, an attribute will be assigned score −1 (1) if the attribute from the selected subject matches (mismatches) one of the nearest subjects from the different phenotype group. The score will be aggregated for all subjects and normalized (divided) by the total number of subjects and neighbors. Detailed description of ReliefF algorithm for filtering genotyping data can be found in Section 3 of [We propose incorporating global testing of p-values with ReliefF  gene filion 3 of .m candidate SNPs, perform the ReliefF algorithm on m SNPs and sort SNPs by ReliefF scores in an ascending order. Generate p-values for the exhaustive search of k-way interactions among a total of m SNPs using the original or extended MDR methods. For each k-way interaction, one p-value of MDR analysis is generated by permutation test. Let m1 be the number of remaining SNPs. Perform the global testing on k-way interactions of the remaining SNPs. Continue to remove SNPs with the lowest ReliefF score one by one and perform global testing after each removal of a SNP. One can stop the process when the remaining SNPs reach a predetermined minimum number. Choose the optimal number of SNPs for the final MDR analysis as the largest number of SNPs with global testing p-value < α. Often we set The flow chart of the testing procedure is presented in Figure Here we introduce 6 global tests that can be applied to test hypothesis (1). These six tests are based on different approaches to detect deviation from uniformity. We will survey these methods and compare their power using a case study and Monte-Carlo simulations.KS test is a non-parametric test that can be applied to compare the distance between an empirical distribution of i.i.d. p-values and Uniform. For hypothesis test (1), define the one-sided KS statistic as rding to , the p-vn degrees of freedom. For a one sided test (1), reject H0 if Fisher  shows thH0, H0 if Z < Zα where Zα is Transform p-value to normal z score by letting H0, the distribution of L can be closely approximated by Student’s t-distribution with H0 if Logit transform p-value by letting (1−pi)).  shows thn p-values from MDR testing along with n2 observations randomly drawn from Uniform from least to greatest and denote them by W be the sum of the ranks corresponding to n p-values from MDR testing. For one-sided test (1), we can reject H0 if ωα is chosen to make the Type I error probability equal α. Values of ωα are given in Table A6 by [n,n2) going to infinity, one can apply normal approximation on the standardized W.Order le A6 by . For larUniform distribution, Tippett’s test will reject H0 if Tippett’s Test  is basedrth smallest p-values where Cγ,α of obtaining r significant statistics by chance in a group of n tests. Suppose there are r tests with p-values less than α, Wilkinson’s test rejects H0 if P(r) has been distributed with parameters r and n-r + 1, tables of the incomplete beta function can be used to obtain critical values of P(r) directly. In our work, we will not include Wilkinson’s test in case study and power simulation because this method does not provide p-value for the testing results.Wilkinson  extendedif cr,α<α. Because3-5) have been associated with improved response to the drug in adults with rheumatoid arthritis [We used a real dataset to illustrate how to apply our proposed global testing to prevent false discovery and to determine the optimal number of SNPs for the final MDR analysis. Juvenile Idiopathic Arthritis (JIA) is one of the most common chronic diseases of childhood, affecting an estimated 300,000 children in the U.S. alone, and is an important cause of morbidity and disability in children . Althougrthritis . Studiesrthritis . Due to n%). Hierarchical clustering was performed to identify patterns of MTXglun%, and two clusters were determined based on the hierarchical clustering of normalized MTXglu1-5%. Subjects in cluster 1 had lower concentration of short chain polyglutamates (MTXglu1-2%) and higher concentration of long chain polyglutamates (MTXglu3-5%) as compared to subjects in cluster 2 (p < 0.05). These clusters reflected distinct patterns in the proportion of MTXglu concentrations.In this case study, we analyzed 25 SNPs from 17 candidate genes in the folate pathway  and ITPA (rs2295553) with testing balance accuracy = 0.7374 (p = 0.0045). The MDR analysis was performed by an open source software mdr2.0 and model goodness-of-fit and significance was assessed by permutation using software mdrpt1.0 [After the filtration and global testing, we removed 4 SNPs as suggested by Inverse chi test with FDR correction Table  and perfDHFR rs737 and ITPDHFR) enzyme is a well known important target of MTX action. When DHFR is inhibited by MTX the subsequent production of reduced folates such as tetrahydrofolate (THF) 5,10 methenyl-THF and 5-methyl-THF are altered, affecting not only total cellular folate concentrations but also the downstream effects from one carbon donation including homocysteine remethylation and pyrimidine and purine synthesis thought to result in an anti-proliferative effect [DHFR also results in a buildup of the precursor dihydrofolate (DHF) which in its polyglutamated state has inhibitory effects upon enzymes within the pathway as well [ITPA) plays a role in de novo purine synthesis, and is closely related to adenosine metabolism, which is thought to contribute to MTX response via its anti-inflammatory effect [ITPA interestingly have been shown by other authors to contribute to MTX response as part of a candidate gene study in JIA [The dihydrofolate reductase  and with Beta. Beta distribution is very flexible to characterize the patterns of p-values . We generated p-values from· Independent Uniform,· Correlated · Correlated · Correlated · Correlated · Correlated These six scenarios cover Patterns 1, 3 and 4 with no signs of GxG interactions in Figure In addition to Uniform distributions, we also simulated correlated Beta mixtures in formula 4.1)-(4.4) regarding p-values shifting to 1 or peaking near the center Patterns 3 and 4). We conservatively set correlation coefficient  and 4. W.1-(4.4) π was set to be 0.1 and 0.4, indicating different proportions of tests with significant GxG interactions. In most cases, parameters In the second simulation study, we are interested in the power of each of the approaches to detect the GxG interactions by performing the hypothesis testing (1) to detect · Correlated · Correlated · Correlated · Correlated · Correlated · Correlated As in the Type I error simulation, in the power simulation, we used sample sizes ranging from 20 to 500 and perform simulation 1000 times. The power is the percentage of results across the 1000 replicates where the null hypothesis was rejected. We present the power comparison results under week correlation  1 Table . These rhttp://www.childrensmercy.org/Content/view.aspx?id=22812.The global tests have been implemented in R. The R code is available at Multifactor Dimensionality Reduction (MDR) is a novel statistical method developed to characterize and detect nonlinear complex gene-gene interactions (epistasis) that could be associated with disease susceptibility. We suggest incorporating global test to filtration procedures to reveal a trend of gene interactive patterns when noisy genes are removed step by step using ReliefF or other filtration techniques. The optimal number of genes for further MDR analysis can be identified by p-values of global testing. A real data applications and empirical assessment of our proposed methods reveal strong trends in global testing of p-values and clear patterns of distribution of p-values in three scenarios: 1) presence of GxG interactions, 2) absence of GxG interactions, 3) weak GxG interactions that needs filtration to remove noisy genes. The proposed global tests can serve as a screening approach before individual tests to prevent false discovery. Strong power in small sample sizes and well controlled Type I error in absence of GxG interactions makes these tests highly recommended in epistasis studies.Global testing has not been implemented in MDR analyses in the literature we have reviewed. Currently, researchers rely on adjustment of individual p-values such as false discovery rate (FDR) as suggested by . Due to Through extensive simulation on correlated p-values, our study shows that the Inverse chi test is the most powerful approach to be incorporated with the filtration techniques to determine the optimal number of SNPs for the final MDR analysis. The KS test might have high inflation of Type I errors when p-values are highly correlated or when p-values peak near the center of histogram (Pattern 4). The Tippett’s test has very low power when the effect size of Pattern 2 is small.We observe mild inflation of Type I error (<0.07) when p-values are Uniform with a random correlation matrix. Our global tests are implemented for screening SNPs and investigators can continue to use multiplicity adjustment algorithms such as FDR to adjust individual p-values in the final MDR analysis to prevent false discoveries. As a result, slight inflation in Type I error (<0.07) is acceptable in practice. Moreover, in our case study, we show that one can utilize the decreasing trend of global test results Figure  to facilIt is worthwhile to point out the proposed global tests can effectively prevent false discovery without losing the power to detect significant GxG interactions. To prevent the false discovery, current MDR applications typically choose one optimal model for each k-way interaction. This method has two major drawbacks: firstly, the false positive discovery is not reduced by choosing one optimal model; secondly, choosing one optimal models may overlook other potential GxG interactions that also contributes to the disease susceptibility.The major contribution of our manuscript is to incorporate global testing procedures to MDR framework. Our proposed global tests will provide p-values to help practitioners determine the appropriate number of SNPs to be remained in the final analysis. The current filtration process does not provide p-values. Therefore, using arbitrary cutoff value in the current process might lead to over-filtering or under-filtering of SNPs.All 6 global tests are based on statistical inference instead of permutation. These 6 tests run very fast in a single computer. The major computational challenges are in the generation of p-values for MDR through permutation tests but this is not the major focus of our work. Several works have been devoted to improve the efficiency and shorten the computing time in MDR analysis in high-throughput data. We will defer interested readers to the corresponding citations for computing issues in high-throughput MDR analysis. These computational limitations make our strategy appropriate in large scale candidate gene studies, but may be limited in application to genome-wide association studies until further improvements in computing speed are realized or very large-scale computing resources are available.http://www.epistasis.org). In this work, we utilize ReliefF for filtration. There have been other filtration techniques proposed in literature. For instance, [MDR permutation computing time is largely dependent on the dimension of data sets. In other words, the computing time increases as the number of SNPs and/or the number of subjects increases. Interestingly, the dimension of data does little impact on the computing time of global tests. The computing time for global tests of 1000 p-values is very close to tests of 10 p-values. Several filtration approaches have been proposed and some  have been implemented in the MDR software . Let σij be the component in Σ0. We can convert the covariance matrix, Σ0 to correlation matrix Σ with components X0. Let U are correlated uniform variables with correlation matrix Σ.In the above method, There are no competing interests to this work.HD and MB conceived of the study. AMR aided in study design and MDR method. HD and AMR performed the simulations and data analysis. MB, RG, and SL performed the clinical data collection, genotyping and interpretation of case study findings. All authors contributed to the manuscript writing. All authors read and approved the final manuscript.


Predisposition to complex diseases is explained in part by genetic variation, and complex diseases are frequently comorbid, consistent with pleiotropic genetic variation influencing comorbidity. Genome Wide Association (GWA) studies typically assess association between SNPs and a single-disease phenotype. Fisher meta-analysis combines evidence of association from single-disease GWA studies, assuming that each study is an independent test of the same hypothesis. The Rank Product (RP) method overcomes limitations posed by Fisher assumptions, though RP was not designed for GWA data.We modified RP to accommodate GWA data, and we call it modRP. Using p-values output from GWA studies, we aggregate evidence for association between SNPs and related phenotypes. To assess significance, RP randomly samples the observed ranks to develop the null distribution of the RP statistic, and then places the observed RPs into the null distribution. ModRP eliminates the effect of linkage disequilibrium and controls for differences in power at tested SNPs, to meet RP assumptions in application to GWA data.After validating modRP based on both positive and negative control studies, we searched for pleiotropic influences on comorbid substance use disorders in a novel study, and found two SNPs to be significantly associated with comorbid cocaine, opium, and nicotine dependence. Placing these SNPs into biological context, we developed a protein network modeling the interaction of cocaine, nicotine, and opium with these variants.ModRP is a novel approach to identifying pleiotropic genetic influences on comorbid complex diseases. It can be used to assess association for related phenotypes where raw data is unavailable or inappropriate for analysis using other approaches. The method is conceptually simple and produces statistically significant, biologically relevant results. N) for each phenotype tested based on the fold-change values. The product of the ranks is calculated (RP statistic) for each row. To assess significance, the null distribution of the RP statistic is derived by randomly sampling from the ranks in each column, and forming many RP statistics. Each observed RP statistic is placed into the null distribution, and non-parametric p-values are calculated. We report here a modified RP method (modRP) that ensures that we meet the assumptions of RP in application to GWA by explicitly disrupting linkage disequilibrium (LD) and by grouping SNPs based on minor allele frequency (MAF) (see supplement for RP assumptions). In this work, we validated modRP based on available control studies, then found a novel, statistically significant, biologically relevant association between two SNPs and comorbid substance dependence phenotypes, providing a model for this gene-environment interaction and demonstrating the usefulness of the approach.Genome Wide Association (GWA) studies typically assess evidence of association between individual variants (e.g. SNPs) and a single-disease phenotype. Extending GWA to assess pleiotropic influences on comorbidity is a reasonable next-step in complex disease analysis. Approaches to GWA for comorbid phenotypes that combine raw data may not be possible if the raw data are unavailable or are inappropriate to combine . Fisher meta-analysis  combinesFor each analysis, we merged the datasets from individual studies by SNP identifier, ranked each column by p-value, calculated the observed RP for each SNP, and sorted SNPs by increasing RP. For each SNP, we downloaded chromosome position and MAF annotation from HapMart , or used9 valid iterations (meeting both LD and MAF requirements) in permutation testing, performed tests in pairs, and ensured that each pair of tests yielded essentially the same results. If not, we increased the number of iterations until the criterion was met. We report the higher p-value for each pair of results. We applied a Bonferroni correction to adjust for multiple hypothesis testing, based on the number of SNPs. For comparison among methods, for each test we also performed traditional Fisher meta-analysis, modified Fisher , and RP. See supplement for effectiveness of modRP and run time.We used 10We first tested modRP using datasets from Lind, et al. , who comADAMTSL3 gene . In the EA population, we found rs1476880 to be significantly associated with cocaine/nicotine comorbidity, with a p-value of 5.38E-06. This SNP tags the SOD3 gene . In addition, evidence for association of rs1476880 with the three-way comorbidity of cocaine/opium/nicotine dependence is even more significant , consistent with an amplified signal in the three-way comorbidity, and in the combined population. A systems biology interpretation of these results is provided in the supplement, using GeneGo's MetaCore software .In a novel study Table  we assesSOD3 has not been previously associated with drug abuse, though there are documented connections between oxidative stress and nicotine [ADAMTSL3, although the ADAM gene family has been associated with multiple diseases induced by oxidative stress [In this work, we introduce modRP, a method to identify pleiotropic influences on comorbid phenotypes, and compare modRP to four related methods. ModRP combines summary data from related GWA studies, while controlling for minor allele frequency and linkage disequilibrium. Comparison of modRP performance to studies by Lind, et al.,  and Yu, nicotine , heroin nicotine , and cocnicotine  dependennicotine ,10 and te stress ,12.ModRP combines prior evidence of association with related phenotypes to identify novel variants which may influence comorbid phenotypes through common underlying mechanisms. The algorithm uses p-values for association with single-disease phenotypes as input, combines this evidence to form a test statistic for each SNP, and assesses the significance of each test statistic. Raw data, which may be unavailable or inappropriate for combining, is not required by modRP. The algorithm provides significant insight into genetic variation influencing pleiotropy. This work opens the door to analysis of comorbid or single-disease phenotypes, assessed in a single population or in independent populations.The authors declare that they have no competing interests.RCM, MAS, JDC, and KSS conceived the approach, developed and tested modRP, and drafted the paper. AK and JMV interpreted biological significance.Details of the algorithm, control studies and systems biology. A Word document providing additional details on assumptions, studies used as controls, and systems biology interpretation.Click here for file


Arabidopsis thaliana dataset MOT1 and flowering-time regulation by the FRI-FLC expression network, and a novel association for Leaf serration are used to illustrate the contribution of major individual loci, expression pathways, and gene-by-environment interactions to the genetic variance heterogeneity.The phenotypic effect of a gene is normally described by the mean-difference between alternative genotypes. A gene may, however, also influence the phenotype by causing a difference in variance between genotypes. Here, we reanalyze a publicly available  Arabidopsis thaliana GWAS dataset to detect genetic effects on the variance heterogeneity, and our results indicate that the environmental variance is under extensive genetic control by a large number of variance-controlling loci across the genome. A straightforward extension of current quantitative genetics theory was derived to estimate the contribution of genetic variance heterogeneity to the phenotypic variance for loci detected in the vGWAS. This showed that some variance-controlling loci explained more than 20% of the phenotypic variance. Genetic variance heterogeneity was detected in various biological processes, including cellular control of ion levels in the plant and regulation of flowering. Our findings indicate that further studies of genetically determined variance heterogeneity are important to further understand the extent of its biological importance. Accounting for variance-controlling loci in complex trait genetic studies is a useful way to identify previously unexplained genetic variance, dissect the genetic control of environmental variance, and gain biological insight into the genetic regulation of complex traits.The most well-studied effects of genes are those leading to different phenotypic means for alternative genotypes. A less well-explored type of genetic control is that resulting in a heterogeneity in variance between genotypes. Here, we reanalyze a publicly available  Complex traits are determined both by genes and environmental factors. For these phenotypes, the genetic effects of allelic variability are most often described as shifts in the mean phenotype between individuals with different single- or multi-locus genotypes. These mean effects will result in both additive and non-additive genetic variance, but the main focus in most GWAS studies to date has been to detect additive effects of loci and consequently explain the contribution of individual genes to the narrow-sense heritability . It also allows mapping of loci where incomplete LD between the causal polymorphism and the tested marker, multiple functional alleles, gene-gene or gene-by-environment interactions leads to a heterogeneity in variance, rather than a mean difference, between the genotypes In this study, we perform a Arabidopsis thaliana dataset http://arabidopsis.usc.edu). The original GWAS a-priori candidates and the detected association signals was argued to be a useful validation of the GWAS strategy in Arabidopsis thaliana.We re-analyzed a publicly available Here, we performed a vGWAS for the 83, of the 107, measured traits that were quantitative using a Brown-Forsythe test  and by the low-variance allele frequency (LAF). Figure A2 in Text S1). Given this, it is not surprising that the most significant variance-controlling loci in the vGWAS have high LAF , which supports the theoretical expectation of a low false positive rate for the Brown-Forsythe test in a vGWAS Our proposed vGWAS strategy is based on the Brown-Forsythe test and we show empirically, and through simulations, that it is powerful while still controlling the false-positive rate: The power of the vGWAS is influenced by large  , Table 1et al.et al.et al.Table 1–83 in Text S1). The vGWAS signals are thus more frequent in regions of known candidate genes and the two most significant signals in our vGWAS both map to candidate genes listed by Atwell et al.AtwellMOT1 were in the vGWAS found to be associated with the molybdenum concentration . The level of molybdenum in Arabidopsis is known to be regulated by the mitochondrial molybdenum transporter encoded by this gene MOT1 explains i.e. 57% rather than 10% of the earlier reported broad sense heritability for this trait Several SNPs covering the only exon of the gene ntration Figure 3MOT1 affects the variance heterogeneity in this population might initially seem surprising, as the original studies only report an effect on the mean. However, a closer inspection of the results by Baxter et al. , we re-estimated the differences in the mean (1.35 v.s. 0.22) and the standard deviation (0.59 v.s. 0.10) between Col-0 , however, shows that the signal is very low in the coding region of ANAC13 and also that the coding region is in low LD with the SNPs that display the strongest association signals. This makes it less likely that the causative mutation leading to the observed effect on the phenotype is located in the coding region of this gene. Further studies of this Variation in Serration (VS) locus, including e.g. the regulatory regions of ANAC13, are needed to identify the biological explanation for the observed effect.A novel locus affecting MOT1 and VS, primarily affect the variance heterogeneity between genotypes in this dataset and only have small effects on the mean. When looking beyond these two loci to explore the total contribution of the sub-vGWAS significant loci to the phenotypic variance, many of these were found to also have effects on the mean (FRI (Frigida) that had the highest significance in the standard GWAS FRI-genotypes , which in turn delays flowering  FRI allele has appeared and remained multiple times in natural populations Here we observe a variance heterogeneity between FRI plays a central role in the vernalization response in Arabidopsis thaliana, where dominant alleles at this locus acts to confer late flowering, which is reverted to earliness by vernalization. Here, we find a gene-by-environment interaction effect between FRI and vernalization on both the mean and variance in flowering-time . Several alternative quantitative genetics models have been proposed for modeling the genetic effect on the environmental variance (see e.g. Text S1), and it is worth noting that both the narrow sense heritability e.g.For testing variance-controlling SNPs in the vGWAS, we use the Brown-Forsythe (Levene) test. The Brown-Forsythe is a statistical test for the equality of group variances and is based on an ANOVA of the absolute deviation from the median. It has earlier been shown to be robust to deviations from normality of the phenotypic distribution in GWAS applications i.e. the inflation factor estimated by comparing the distribution of the sample In an ordinary GWAS, genomic control (GC) is used to shrink any existing inflation of the test scores . Figure A3: Power of the Brown-Forsythe test with respect to the level of variance heterogeneity. Figure A4: A simulation study comparing the genome-wide p-values of vGWAS before and after genomic control (GC). Figure B1–B83: Summary of vGWAS results for the 83 analyzed quantitative traits. Table 1–83: GWAS and vGWAS scores and ranks of the 83 analyzed quantitative traits. Tutorial of the R package vGWAS together with its documentation.(PDF)Click here for additional data file.