While sequencing can still be prohibitive for large studies, commercially available genotyping arrays targeting rare variants prove to be a reasonable alternative. A technical challenge of array based methods is the task of deriving genotype classes (homozygous or heterozygous) by clustering intensity data points. The performance of clustering tools for common polymorphisms is well established, while their performance when conducted with a large proportion of rare variants  is less known. We have compared the performance of four clustering tools  for the genotyping of over 10,000 samples using the Illumina’s HumanExome BeadChip, which includes 247,870 variants, 90% of which have a minor allele frequency below 5% in a population of European ancestry. Different reference parameters for GenCall and different initial parameters for GenoSNP were tested. Genotyping accuracy was assessed using data from the 1000 Genomes Project as a gold standard, and agreement between tools was measured.Along with the improvement of high throughput sequencing technologies, the genetics community is showing marked interest for the GenoSNP’s calls with the gold standard was below expectations and was increased by changing the tool’s initial parameters. While the four tools provided concordance with the gold standard above 99% for common alleles, some of them performed poorly for rare alleles. The reproducibility of genotype calls for each tool was assessed using experimental duplicates which provided concordance rates above 99%. The inter-tool agreement of genotype calls was high for approximately 95% of variants. Most tools yielded similar error rates (approximately 0.02), except for zCall which performed better with a 0.00164 mean error rate.Concordance of GenoSNP clustering tool could not be run straight “out of the box” with the HumanExome BeadChip, as modification of hard coded parameters was necessary to achieve optimal performance. Overall, GenCall marginally outperformed the other tools for the HumanExome BeadChip. The use of experimental replicates provided a valuable quality control tool for genotyping projects with rare variants.The  More than 13,500 genome-wide association studies (GWAS) of complex human diseases have been performed since 2008. These sSNP arrays offer the possibility of rapid genotyping of thousands of samples with highly reliable results at low cost. Several commercial arrays now include a large fraction of rare single nucleotide variants (SNV) discovered by high-throughput sequencing technologies. The latter, while still expensive compared to SNP arrays, allows for the discovery of all variants, rare and common, located in the genome of sequenced individuals. The Illumina HumanExome BeadChip provides a compromise between genotyping SNP arrays and next generation sequencing by enabling the genotyping of rare SNVs in thousands of samples at relatively low cost. The HumanExome BeadChip is enriched for rare and low frequency coding variations previously identified from the sequenced exomes of approximately 12,000 individuals of diverse populations for variations seen in more than two individuals and in more than two sequencing projects. Compareet al.[e.g.within-sample information) to genotype rare variants could theoretically outperform reference-based methods, as these would suffer from the limited information available in the training sets for the homozygous and heterozygous clusters of rare alleles. Such within-sample methods are implemented in GenoSNP[M3[optiCall[between- and within-sample approaches. Other tools, such as GenCall (available in the GenomeStudio software)[zCall tool exclusively genotypes markers that have been previously “missed” by a another tool, and was also recently described[A recent review of clustering tools for widely used Illumina BeadChip arrays was presented by Ritchie et al.. They ren GenoSNP. Some toenoSNP[M3 and opti[optiCall, use a moftware), rely onescribed.GenCall, GenoSNP, optiCall and zCall for clustering markers from the HumanExome BeadChip have been analysed and compared. With the growing interest of the community for studies with rare variants[For this project, the performance of variants,6,15,16,GenCall, part of the GenomeStudio software version V2011.1[GenoSNP version 1.3[optiCall version 0.3.3[zCall version 3.2[Four clustering tools were compared:  V2011.1, GenoSNPsion 1.3, optiCalon 0.3.3 and zCalsion 3.2. All fouGenCall is Illumina’s proprietary tool and is available through the GenomeStudio software. For a complete description of this tool, refer to Ritchie et al.[X and Y) to compute the associated polar coordinates (r and θ) for each marker/sample pair. Next, using a between-sample model, meaning that it calls one marker by looking at the population of samples, it assigns genotypes by determining the nearest cluster using a reference containing the expected position of each genotype cluster for every marker as determined from the HapMap data. If required, the user may modify the position of each of the expected clusters to be more representative of the data at hand. By pre-assigning the expected position of each cluster, this method can readily provide a genotyping assignation of rare variants for studies having only a small number of samples. However, due to experimental variabilities and genomic variations in different populations, the position of the observed cluster’s centroid might shift when compared with the expected one. A considerable amount of manual cluster adjustments might be needed to achieve good genotype calls.ie et al.. In briea, (7) mitochondrial markers, (8) markers on sex chromosomes, (9) markers that fail reproducibility tests, (10) markers with a small cluster separation or (11) markers with low quality score. To compare the efficiency of this modified cluster file, the results from GenCall with the original cluster file were also included in the analysis.For this project, a custom cluster file was created by modifying the expected position of the genotype cluster’s centroid for a subset of markers by using all samples from the dataset. The markers selected for manual inspection were: (1) markers with a high heterozygous frequency, (2) markers with a low mean intensity, (3) markers with a low call frequency, (4) markers with a low minor allele frequency with no heterozygous calls, (5) markers showing an excess of heterozygous calls, (6) markers with low AA T means or low BB T meansGenoSNP uses a within-sample model, meaning that it assigns genotypes to all markers of a single sample at once[X and Y allele intensities extracted using the GenomeStudio software and calls genotypes by fitting a four-components mixture of Student’s t-distributions on different subsets of markers (separated by Bead Pools) by the mean of a Variational Bayes Expectation Maximization algorithm (VB-EM). The use of this method improves robustness by allowing uncertainty in the statistical model, in contrast to standard expectation maximisation methods. GenoSNP computes the posterior probability of the marker genotype calls. As this tool calls one sample at a time, it offers the flexibility of providing final sample genotyping results before the whole study dataset is ready to be processed. It can also be parallelized by running the tool on multiple samples at a time, and it does not require a reference panel. It is generally expected that this tool would perform well with rare variants, as their genotypes will be clustered with higher frequency variants according to measured X and Y allele intensities . at once. It usesGenoSNP as soon as they were released from the genotyping center. A posterior probability cutoff of 0.8 was used to achieve higher quality calls. To ascertain the quality of the results once all samples were genotyped, the mean and the median intensities of all calls for each sample were plotted.To speed up the genotyping process, samples were called using optiCall tool uses a mixture of between- and within-sample models. It uses a subset of  intensities from random samples at a random marker to find a prior distribution to the statistical model used to call genotypes across markers. This distribution is inferred by using an EM algorithm to fit a four-class mixture of Student’s t-distributions. The initial values used by the EM algorithm are obtained by using the kmeans++ algorithm[a priori probabilities are assumed to be uniform . Then, a second mixture of t-distributions is used for the between-sample clustering, where the previously estimated priors are used in a Maximum-A-Posteriori (MAP) estimate of its parameters.The lgorithm and the optiCall relies on deviation from the Hardy-Weinberg Equilibrium (HWE). The tool will try to improve the genotype calls when the HWE test fails (p<5×10-15) by fitting the previously described model without a prior.To measure the quality of genotype calls, zCall tool separates the clusters for rare variants by partitioning the  intensity space using horizontal and vertical thresholds. Their positions are derived from the mean and variance of the homozygote clusters for common variants that were previously called and are scaled according to a z-score factor to optimize concordance with the default tool. Genotypes are then assigned with respect to their position relative to the z-score scaled coordinates. Accordingly, rare variants are called by defining a distance threshold. The homozygote threshold for the major allele is estimated from the first calling tool’s genotypes, and the rare allele’s threshold is estimated by linear regression from the means and standard deviations of X and Y intensities of common markers.This tool functions as a post-processing tool (after a default one has been used). The zCazCall was used as a post-processing step after GenCall (GenomeStudio). Version 3.2 was used, where all z thresholds were derived from GenomeStudio’s final report, from which samples were filtered out based on call rate and global heterozygosity. A z threshold of 8 was used after comparing the concordance with the original calls (maximum of 99.27%). Only missing genotypes from the original GenomeStudio report were recalled by zCall.As recommended by the authors, NA17281, 15 replicates of NA17251 and 3 replicates of NA12763 from the Coriell Institute  Cohort. We also included 95 experimental replicates of s Project). Finalls Project, and 93%s Project. The resκ) and Fleiss’ pi (π), two widely used statistics, to compute the extent of agreement between raters[κ computes the extent of agreement between two tools by first computing the overall agreement probability (Equation 1), using a two-way contingency table  and genotype category, where nkl indicates the number of samples that tool 1 and 2 classified into genotypes k and l, respectively. We used Cohen’s kappa  and pe|κ is the proportion of agreement expected by chance.where i and genotype k, rik represents the total number of tools that called genotype k for sample i. Fleiss’ π is then defined by Equation 3[The data can be summarized in a frequency table  due to quality issues (e.g. low intensity).The possible set of genotypes included the ϵ) with pedigree data have been proposed and reviewed by Liu et al. for their use with unrelated samples[Several methods for error rate estimation  with the HumanExome BeadChip data where a majority of markers are rare. This can be explained by the proportion of the minor allele in the population, p1, which is almost null. For these cases, ϵ was approximated using ϵ≃(C1-C3+1)/3  for each evaluated genotype. The maximal probability is used to define the genotype to be called. We observed a majority of samples with a high proportion of low quality calls . Cluster plots were created for some of the poorly performing samples which raised concern about the calling quality  greatly improved the quality of the clustering tool , the two tools  were used for comparison with the other tools in this study.The y FigureA and1D.et al.[z threshold should be determined by trying different values of z to find the one with the most concordance to the original GenCall calls. Here, the optimal value of z was determined to be 8, having a concordance of 99.27% with the original data.According to Goldstein et al., the opti.e. the calling rate, or inversely, the missing rate). The sample and marker missing rates of the six tools were compared . The optimized version of GenoSNP increased both the mean sample and marker calling rates by 18.5% (from 80.6% to 99.1%). These rates were inferior to those of the other tools: 99.6%, 99.8%, 99.6% and 99.9% for GenCall , optiCall and zCall, respectively. It is important to note that the missing rate of zCall is bound to be less than or equal to that of GenCall, as zCall will only call missing genotypes from the results produced by GenCall. Also, the missing rates of GenCall were slightly better when using the optimized cluster file when compared to the original one. A non-parametric Friedman Rank Sum test comparing tools showed a statistically significant difference in both sample and marker missing rates , even though the rates seemed similar . More specifically, 0.55- and 0.83-fold decreases, on average, were observed for sample and marker missing rates, respectively, when comparing the original and the optimized cluster file for GenCall.One important property of a calling tool is its capacity to assign a genotype to the majority of samples and markers . Even though zCall reduced the missing rate from a mean of 0.4% to 0.09%, it added variability in the newly called genotypes, slightly decreasing the concordance between replicated samples when compared with the original results . Overall, the call concordance between replicates was similar (> 99% concordance). GenCall had the highest concordance rate with a mean of 99.997% between replicated sample pairs. Optimizing GenCall’s cluster file had only a minor effect on the mean concordance, with a difference of 1.5×10-3%.The dataset contained a high number of technical replicates. The concordance of genotype calls between replicates was computed for the five tools Figure. The opt1000 Genomes Project was included three times to the original dataset to assess the concordance with next-generation sequencing. The genotypes called from the different tools were compared to the third release of the 1000 Genomes Project, comprised of low coverage whole genome and high coverage exome sequencing data. The comparison with this gold standard was performed using the pyGenClean tool[NA12763. Apart from the original GenoSNP, all the tools had concordance rates greater than 99%. GenCall (optimized cluster file) had the highest concordance rate (mean of 99.897%), closely followed by zCall (mean of 99.879%). GenCall  also performed well, with a mean concordance of 99.855%. Then, calls were categorized according to their allele content: either (1) homozygous calls for the common allele or (2) involving the rare allele . The frequencies were computed using the corresponding dataset (i.e. tool). TableNA12763 for genotypes called as homozygous for the common allele. Apart from the original GenoSNP on one replicate, all had concordance rates greater than 99%. GenCall  had the highest concordance rate (mean of 99.948%), closely followed by GenCall (optimized cluster file) and zCall (mean of 99.939% and 99.928% respectively). TableGenCall (optimized cluster file) had the highest concordance rate (mean of 99.493%), closely followed by zCall (mean of 99.405%). The other tool had a lower concordance rate (i.e. between 95% and 97%).One sample sequenced by the ean tool. Since tκ and percent agreement  provided the best result set, its agreement with the other three tools  was considered , Fleiss’ κ was computed  and 5% were markers that were zeroed out while optimizing GenCall’s cluster file. The proportion of rare variants (when compared to common or zeroed out ones) was significantly higher in the outlier group . Out of the approximately three thousands outlier markers that were comparable with the 1000 Genomes Project data, GenCall had the highest concordance for the three replicates of NA12763 (average of 98.925%), followed by zCall (average of 98.448%) . The zCall tool provided the lowest estimated error rate with a mean of 0.164%, followed by GenCall (optimized cluster file) with a mean of 0.166%. A non-parametric Friedman Rank Sum test comparing tools showed a significant difference in the error rate distributions . Pairwise dependent-samples non-parametric sign tests comparing pairwise tools were also significant .Error rates were estimated by using the genotypic model , where This study compares the performance of widely used clustering tools when applied to genotyping data from Illumina’s HumanExome BeadChip. This genotyping array includes a large proportion of rare variants that were previously identified by sequencing technologies. The dataset used here included 10,520 unique samples along with a high number of technical replicates for quality assessment.GenoSNP, which relies on a within-sample model, did not perform well when used straight “out of the box”. This might be explained by the high density of markers in each BeadPool, which is higher than for Illumina’s Human 1M BeadChip . The latter was successfully tested by GenoSNP’s authors. This problem was mostly obvious with cluster plots . The optimized tool  increased the concordance to a mean of 99.61%. The quality threshold of 0.8 provided a better separation of the three clusters, but increased the missing rate of both sample and marker (mean of 0.87%).Contrary to our original expectations, s Figure. The conGenCall relies on a between-sample model that requires reference parameters to perform its clustering. As such, it is common practice to manually modify the reference cluster parameters to ensure the best quality of results when the population analyzed is different from the one used to generate the reference parameters. This task requires a significant amount of manual labor which increases with the number of samples and markers. Loading the raw data, normalizing and modifying the original cluster file took one person 5 work days, compared to only a few days to generate the intensity files for the other tools. When we compared the genotype results from GenCall using the original cluster file with the ones generated with the optimized cluster file, we saw only limited improvement in the overall concordance of genotype calls with those of the gold standard. When partitioning calls according to their allele content, we saw a limited decrease in the concordance of homozygous calls involving the common allele when compared with the gold standard, while the concordance of calls involving the rare allele improved by approximately 0.5%. A limited improvement in the concordance between technical replicates was observed. However, the optimization of the cluster file had a greater impact on the missing rate per sample and per loci (0.19% improvement in both cases). According to normal quality control procedures, a filter to remove samples and markers with a missing rate greater than 2% is typically imposed prior to genetic analysis[analysis. By optiGenCall’s  concordance with the 1000 Genomes Project might be overestimated due to the nature of its reference parameters. Indeed, the reference cluster file was created by using estimated cluster position for each of the markers in the HapMap population. Hence, the sample NA12763 is expected to have a higher concordance value than samples from the Montreal Heart Institute Cohort owing to the CEU HapMap population. One possible way to overcome this limitation would be to sequence a few of our own cohort samples, however, it could be argued that the sequencing technology itself would not provide an adequate gold standard in this situation.It should be noted that this study was limited by the lack of an independent gold standard for concordance analysis. GenCall  provided the highest concordance rate between experimental replicates (99.997%) when compared to other tools. The other tools  performed relatively well, all providing a mean concordance greater than 99%.Many study designs will plan to include experimental replicates chosen from the genotyped cohort to assess the reproducibility of the genotyping pipeline and the precision of the results. Including a reference sample to the study design offers the additional possibility of assessing the accuracy of the results. High precision is particularly important as it provides optimal power for statistical analysis and can GenoSNP at only one of the three replicates of NA12763). Other metrics have shown that all the tools (once optimized) performed almost at the same efficiency level on the HumanExome BeadChip. The major difference arose when in the presence of rare markers, where the accuracy of all the tools decreased below 99.5% (as low as 96% for some) for genotypes involving the rare allele. Within-sample tools like GenoSNP can process samples in an efficient manner by running single samples and smaller batches of samples in parallel instead of having to wait for a large amount of samples to be genotyped and normalized. Unfortunately, even with the proper optimization of initial parameters, GenoSNP could not outperform the other tools. However, GenCall, Illumina’s proprietary tool, performed better than the other tested tools with respect to concordance with the gold standard for genotypes involving the rare allele (accuracy) and slightly better for the concordance in between technical replicates (precision). The fact that zCall has been run as a post-process of GenCall without the use of the reference cluster file optimization (since it is not mandatory) might explain why it’s accuracy was not as high as the optimized GenCall for calls involving the rare allele. Since the third version of zCall derives its thresholds from GenomeStudio’s report, the call rate will increase and better accuracy might be possible if the original cluster file is optimized beforehand.All clustering tools had a high accuracy (>99.8%) when calling common markers  outperformed the other tools in terms of precision and accuracy . Its accuracy was also higher for the markers with low inter-tool agreement. However, when using the optimized cluster file, GenCall’s accuracy for the homozygous calls  was lower than when using the default cluster file. When considering missing and estimated error rates, zCall outperformed the other tools, closely followed by GenCall (optimized cluster file). It is important to mention that the task of optimizing the cluster file is time consuming. Furthermore, all the other tools presented here require intensity data provided by the GenomeStudio software and possible file conversion, which increase the total execution time.Recommending a single clustering tool according to the metrics shown in this report is not straightforward. In general, GenCall’s cluster file at those loci and the visual inspection of the cluster plots should provide high quality datasets for downstream analysis.The parallel use of multiple clustering tools offers the possibility of identifying discordant markers which can be further investigated. But notably, the manual optimization of aθ values of the center of the AA and BB clusters in normalized polar coordinates, respectively.b Outliers are observations that fall below Q1-1.5(IQR) or above Q3+1.5(IQR), where Q1 and Q3 are respectively the first and third quartiles and IQR=Q3-Q1 is the interquartile range.The authors declare that they have no competing interests.GenoSNP’s initial parameters, performed analyses, compared the tools, implemented the statistical tests and drafted the manuscript. MAL contributed to the analysis and to the manuscript. AB contributed to the statistical analyses and the manuscript. SP contributed to the experimental design, analysis and the manuscript. VN contributed to the manual optimization of GenCall and the manuscript. JCT leads the Montreal Heart Institute Cohort and directs the genomic project with the HumanExome BeadChip. MPD supervised the project, participated in the design and coordination of the study, supervised the laboratory and revised the manuscript. All authors read and approved the final manuscript.LPLP worked on the experimental design, optimized Additional materials. Supplemental Equation S1: The genotypic model for error rate estimation was tested by Liu et al. for common variants only. However, we found that the possible values of ϵ were out of bound (i.e. negative or above one) for a majority of rare markers. For those cases, ϵ was approximated using ϵ≃(C1-C3+1)/3. Supplemental Table S1: Distribution of n samples by calling tool in q categories. The set of possible categories are all possible genotypes . This table is computed for each marker and for each pair of calling tools. The overall agreement probability and Cohen’s κ are shown in Equation 1 and 2 of the main text, respectively. Supplemental Table S2: Distribution of r calling tools by n samples and q response categories. The set of possible categories are all possible genotypes . This table is computed for each marker and for each calling tool. Fleiss’ π is explained in Equation 3 of the main text. Supplemental Table S3: Call concordance and number of compared markers for the three control replicates when compared to the 1000 Genomes Project for the markers that were outliers for their Fleiss’ π values. The following four tools were compared: GenCall (optimized cluster file), GenoSNP (optimized), optiCall (without excluding markers failing Hardy-Weinberg) and zCall.Click here for file


Current studies of phenotype diversity by genome-wide association studies (GWAS) are mainly focused on identifying genetic variants that influence level changes of individual traits without considering additional alterations at the system-level. However, in addition to level alterations of single phenotypes, differences in association between phenotype levels are observed across different physiological states. Such differences in molecular correlations between states can potentially reveal information about the system state beyond that reported by changes in mean levels alone. In this study, we describe a novel methodological approach, which we refer to as genome metabolome integrated network analysis (GEMINi) consisting of a combination of correlation network analysis and genome-wide correlation study. The proposed methodology exploits differences in molecular associations to uncover genetic variants involved in phenotype variation. We test the performance of the GEMINi approach in a simulation study and illustrate its use in the context of obesity and detailed quantitative metabolomics data on systemic metabolism. Application of GEMINi revealed a set of metabolic associations which differ between normal and obese individuals. While no significant associations were found between genetic variants and body mass index using a standard GWAS approach, further investigation of the identified differences in metabolic association revealed a number of loci, several of which have been previously implicated with obesity-related processes. This study highlights the advantage of using molecular associations as an alternative phenotype when studying the genetic basis of complex traits and diseases. These studies have substantially increased our knowledge of genes that influence phenotypic variations. For instance, in obesity genetics, substantial progress has been made with the discovery of at least 50 common and rare variants influencing obesity-related traits –6. Yet, In an earlier work , we highIn this study, we hypothesize that some of the undetected variants might be associated not with changes in mean levels of a phenotype, as studied by conventional GWAS, but with alterations that occur at a higher system-level. To investigate the potential use of differences in molecular dependencies to uncover genetic variants associated with phenotype variation, we propose a novel analytical approach to integrate metabolic and genetic information, which we refer to as genome metabolome integrated network analysis (GEMINi). A simulation study is initially presented to assess the performance of the proposed methodology. We then demonstrate the use of our approach by investigating metabolic changes in relation to obesity using two independent population-based cohorts, totalling to over 5000 individuals. A recently established serum NMR metabolomic platform  was applThe proposed GEMINi approach identifies potentially new genetic components of obesity. Differences in association between serum metabolites were identified, comprising several metabolites linked by previous studies to the development of obesity-related disorders. Metabolites involved in such differential connections included all sizes of very-low-density lipoprotein particles (VLDL) as well as several low-molecular-weight metabolites. Further investigation of these phenotypic differences revealed a set of genetic variants significantly associated with these differential metabolic dependencies. Several of the associated genes have been previously implicated in obesity-related traits. Besides the GEMINi approach, we also performed two standard analyses. First, we looked for associations between genetic variants and body mass index (BMI) by a conventional GWAS approach. Second, we looked for associations between mean levels of the metabolites and BMI. Using the conventional GWAS approach, we found no associations at a genome-wide significance level between single nucleotide polymorphisms (SNPs) and BMI. These results highlight the advantage of using differences in statistical association between different molecules as an additional phenotype in the study of common trait variation and demonstrate the applicability of our approach to uncover further molecular factors potentially involved in the pathogenesis of complex traits.2.2.1.We used data from two large population-based cohorts, the Northern Finland Birth Cohort 1966 (NFBC1966) and the Northern Finland Birth Cohort 1986 (NFBC1986). The methods and aims of these studies have been published previously . In brie2.2.−2. Individuals were classified as non-obese if their BMI was equal or lower than 25 kg m−2 and equal or greater than 18.5 kg m−2. For the NFBC1986, individuals were classified as obese and non-obese by calculating the age- and sex-specific BMI percentiles. The non-obese group includes females with measures of BMI equal or lower than 24.05 kg m−2 and equal or greater than 17.4 kg m−2 and males with BMI equal or lower than 24.2 kg m−2 and equal greater than 17 kg m−2 (fifth percentile to less than the 85th percentile). The obese group includes female with BMI greater than 27.5 kg m−2 and males with BMI greater than 28.2 kg m−2 (greater than the 95th percentile). Individuals were excluded from analysis based on the following criteria: non-fasting, diagnosed type I or II diabetes, pregnancy, lipid-lowering medication, missing data on glucose and/or weight measures and/or height. The sample size for NFBC1966 is 3464 subjects (Nnon-obese = 3023 and Nobese = 441) and for NFBC1986 it is 3791 subjects (Nnon-obese = 3565 and Nobese = 226). The clinical characteristics of the study groups are presented in the electronic supplementary material, tables S1 and S2.For the differential network analysis, individuals were classified into two groups: obese and non-obese according to their BMI values. For the NFBC1966, individuals were classified as obese if their BMI exceeded 30 kg m2.3.The metabolic data for the two cohorts were acquired using the same high-throughput serum NMR metabolomics platform the details of which have been described previously ,14. Meta2.4.p-value from a Hardy–Weinberg equilibrium test was p < 1 × 10−4. The final genetic dataset included 4815 individuals and 318 443 SNPsOnly the NFBC1966 were used for the genetic analysis, because genome-wide data for the NFBC1986 were not available. Details for the genotyping procedure and quality control are presented in reference . In brie2.5.In this study, we perform and compare two statistical procedures. First, we perform a standard analysis of the associations between metabolic levels and BMI using univariate linear regression and between genetic variants and BMI following a conventional GWAS approach. The second approach, which we refer to as GEMINi, is a combination of (i) differential network analysis of metabolic associations, and (ii) genome-wide correlation (GWC) study. We assess the performance of the proposed GEMINi methodology by performing a simulation study . All analyses were adjusted for sex differences in serum metabolite levels.2.5.1.p < 5 × 10−8 [A conventional GWAS approach is used to test for associations between genetic variants and BMI. The analysis is performed following the standard single-SNP approach where SNPs are tested one at a time. Associations were investigated using linear regression assuming an additive effect on the trait and including sex as a covariate. Significant associations between genetic variants and BMI measures were assessed by setting genome-wide significance to 5 × 10−8 .p < 0.01/M, where M = 38 denotes the total number of serum metabolite measures.We use linear regression to test the effect of serum metabolites on BMI. The analyses are performed following a univariate approach where metabolites are tested one at a time. We included sex as a covariate to correct for sex differences in serum metabolic profiles. To identify significant associations between serum metabolites and BMI, we use a conservative Bonferroni-corrected significance level, N = 4346).The above analyses were conducted including all the individuals for which genetic, metabolic and BMI data were available  identified in step one. To assess the biological significance of our findings, identified SNPs are assigned to the nearest gene (maximum distance 1 Mb).In the second step, we perform a GWCA to identify genetic variants associated with differences in metabolic associations. As for the standard GWAS study, all individuals for whom genetic data are available were included in the analysis. To find the desired associations, we first classify individuals according to the number of copies of the less frequent allele carried, giving genotype groups A (0 copies) and B (one or two copies). SNPs are tested one at a time. Subsequently, the correlation between metabolites eference . To corrAll analyses were conducted in R v. 2.14.1, apart from the conventional GWAS that was carried out in SNPtest v. 2.0. Computation of the partial correlation matrix was performed using the R package GeneNet. The differential networks were built and visualized using the R package igraph. The package psych in R was used to test for differences between correlation coefficients.3.3.1.3.1.1.p-values obtained from the GWAS analysis is presented in the electronic supplementary material, figure S1. Although no SNPs showed association at the genome-wide significance threshold (p < 5 × 10−8), several notable associations were found, of which the most significant was a variant within a gene encoding for a transcriptional factor-activating enhancer-binding protein two-beta (TFAP2B)  expressed in adipose tissue. The TFAP2B-rs987237 genetic variant has been previously associated with a number of metabolic disorders, including development of T2DM [p < 0.001. The results for a list of loci localized within known obesity genes are presented in the electronic supplementary material, table S3.We performed a standard GWAS analysis where associations between genetic variants and BMI (as a continuous variable) were tested. A Manhattan plot of the  of T2DM , BMI [22 of T2DM . In addip < 5 × 10−8), application of the GWAS approach to a single population frequently fails to identify statistically significant associations. Despite the low p-values for some of the previously reported obesity-related genes, we did not reach the genome-wide significance threshold (p < 5 × 10−8) which might indicate the lack of power in this cohort to identify loci with key roles in determining variations in BMI.Owing to the stringent genome-wide significance threshold (3.1.2.p < 0.01/M) with BMI. Very large, large HDL and mean diameter for LDL and HDL particles are inversely associated with BMI in both cohorts. No association was found between BMI and apolipoprotein A in either of the cohorts. In NFBC1966, medium HDL is inversely associated with BMI, but shows no association in NFBC1986, which is potentially owing to the age difference between cohorts [We performed an inspection of the data using linear regression to explore associations between serum metabolites and BMI. Results for the two cohorts are presented in  cohorts . Tests oThe large number of significant associations between BMI and the metabolite concentrations reflects the close relationship between obesity and systemic metabolism. However, it is not only the concentration levels of serum metabolites that can change owing to variations in total body mass, but also the dependencies between metabolites can be affected. To investigate how metabolic associations differ between non-obese and obese individuals and to what extent these differences can serve as an indicator of important molecular alteration between these physiological states, we use the GEMINi approach.3.2.3.2.1.DiffNet and AUCGWCA). Results are presented in the electronic supplementary material, figures S3 and S4.We carried out a simulation study to assess the performance of the GEMINi approach . Four different scenarios were simulated by combining different values of (i) minor allele frequency, and (ii) differences in associations between variables across groups. These scenarios were created to cover the range of variation observed in the data. To illustrate the predictive power of GEMINi, the receiver operating characteristic (ROC) curve analysis was used for each of the two steps of the GEMINi approach  and the area under the curves determined (AUCDiffNet = 1.0 and AUCGWCA = 1). With small differences in associations between variables across groups (simulation 3 and simulation 4), the accuracy of GEMINi drops, showing moderate prediction values. The area under the ROC curves for simulation 3, for the two steps of the GEMINi approach are AUCDiffNet 0.7748 and AUCGWCA 0.7793. For simulation 4, the area under the ROC curves are AUCDiffNe = 0.6885 and AUCGWCA = 0.7377.We observe that for large differences in associations between variables across groups (simulation 1 and 2), the GEMINi approach shows perfect prediction value , and use estimates of partial correlation as measures of metabolic dependency. Metabolic associations that are consistently different across the two physiological conditions (obese and non-obese) in the two study cohorts are interpreted as obesity-related molecular characteristics and are further investigated in the GWCA.c). The differential network for NFBC1966 (figure 2a) consists of a set of 29 connected variables, which are organized in 36 pairwise differential interactions. The differential network for NFBC1986 (figure 2b) comprises a group of 25 differentially connected variables, which are organized in 19 pairwise differential interactions. We observe similar patterns of differences in the metabolic associations in these two differential networks. For both networks, the majority of the connected variables represent measures of VLDL (dark green nodes), LDL (light blue nodes), HDL (dark orange nodes) and amino acids (pink nodes). Five metabolites—pyruvate, histidine, lactate, tyrosine, total lipids in small HDL—show no connections in either of the two networks. Five overlapping connections are observed between the two networks (figure 2c). This overlap is significantly higher than expected at random with p-value = 1.97 × 10−4 from a hypergeometric test with N = 703 pairs, M = 36, K = 19, x = 5). The overlapping connections highlight differences in the pairwise associations between VLDL measures which occur throughout all size ranges, one measure of HDL (M-HDL-L) and two low-molecular-weight metabolites (urea and 3-hydroxybutyrate). Moreover, not only are a number of connected components overlapping between the two networks, but also the signs of the difference in partial correlations are identical (represented as connection colours). We observe that the correlation is significantly higher in the obese group for small VLDL and large VLDL, ApoB and mean diameter for VLDL, large VLDL and small VLDL, very large and medium VLDL and extremely large VLDL and medium HDL (red edges). On the other hand, we observe that partial correlation between the pair urea and 3-hydroxybutyrate is significantly lowered (blue edges) in the obese group.The differential analysis for BMI is presented in figure 2A number of obesity-related differences in metabolic associations identified here are in line with prior studies on obesity-related traits. For instance, the central position and abundance of VLDL-related measures in the differential networks may reflect disregulation in VLDL metabolism. These alterations may result from the shift from small VLDL particles to enlarged VLDL . There iThe relatively large number of independently replicated results and the known relevance of the identified metabolites to obesity provide strong support for differential association analysis in improving our understanding of the biological mechanisms of disease. Assuming that these metabolic differences are related to obesity, we hypothesized that these measures could be used as an additional phenotype to identify genetic variants associated with obesity-related traits. To test this hypothesis, we performed a GWCA.3.2.3.p < 5 × 10−8/D; D = 5). The identified SNPs are localized in 18 genetic regions across 14 chromosomes. A brief description of the identified genetic variants, including their accession numbers, chromosomal positions, obtained p-values, along with candidate genes associated with the genetic marker is presented in p-values obtained from the GWCA is presented in the electronic supplementary material, figure S5. In addition, we report the levels of association between differences in metabolic association and SNPs localized in genes previously reported for BMI [The associations of 318 443 SNPs with the differences in metabolite–metabolite partial correlations were individually tested. Our analysis revealed 24 loci significantly associated with differences in associations between one pair of metabolites, namely total lipids in medium VLDL and very-large VLDL . Variations in this genetic region have been previously found to be implicated in the control of lipid levels ,29. Anotp < 5 × 10−8/D; see the electronic supplementary material, table S4), we observe a relatively high association (p < 1 × 10−4) between a number of these SNPs and differences in association between total lipids in medium VLDL and very-large VLDL. These SNPs are localized in five obesity-related genetic regions, namely fat mass and obesity-associated protein (rs4784351 with p = 3.62 × 10−5); transmembrane protein 18 (rs2049480 with p = 8.13 × 10−7); neurexin-3-alpha ; cell adhesion molecule 2 gene (rs9812103 with p = 1.70 × 10−5); LDL receptor-related protein 1B (rs2049480 with p = 8.13 × 10−7). In addition, two SNPs localized within genes previously reported to influence human serum metabolite levels [p < 1 × 10−4 with differences in correlation between total lipids in medium VLDL and very-large VLDL . These two genetic variants correspond to SNP rs560887 (p = 8.95 × 10−5), which is localized within a gene encoding for glucose-6-phosphatase, catalytic, 2 and SNP rs261336 (p = 9.31 × 10−5), which is localized within hepatic lipase gene.While none of the SNPs localized within genes previously associated with BMI  reach the levels  show ass4.While GWASs have greatly contributed to the identification of genetic variants associated with complex traits, these variants typically appear to explain only a small proportion of the observed variability in phenotypes. In this study, we have proposed the analysis of additional phenotypic variations such as differences in associations between metabolic measures to aid the discovery of genetic factors involved in complex traits. To this end, we have introduced a novel analytical approach for the combined analysis of metabolic and genetic information.p-values for some of the previously reported obesity-related gene lend weight to our assertion that the GEMINi method can retrieve useful and biologically meaningful relationships between genetic variants and differences in molecular association. This study therefore highlights the importance of investigating differences in association between metabolites or other phenotypic indicators as an additional phenotype to identify novel loci with key roles in the pathogenesis of complex traits.Initially, we examined the relationship between obesity and serum metabolites by performing a differential analysis of metabolic associations. Here, we investigated how metabolic associations differ between non-obese and obese individuals and to what extent these differences in metabolic associations can reveal key features of obesity condition. These findings were therefore interpreted as strong evidence of a relationship between these metabolic associations and obesity. We performed a GWCA where genetic variants were tested for association with metabolic correlations. Unlike standard GWAS, which did not reveal any significant associations, this approach yielded many significant genetic loci. A clear limitation of our study is the lack of a replication cohort for our genetic findings. However, the fact that we found no associations following standard GWAS, but did find a large number of associations using our GWC approach, many of which are implicated in obesity-related processes, is very promising. Moreover, the relatively low


Using either the population-based or family-based subset alone predictably limited resolution to detect DN SNPs. For 384,197 SNPs passing quality control (QC), none achieved strict genome-wide significance (1.4 × 10−7) using 1171 singletons (577/594 cases/controls) or 1738 pooled singletons and offspring probands (841/897). Similarly, none of the 352,004 SNPs passing QC in 567 family trios (264/303 case/control proband trios) reached genome-wide significance. Testing the top 10 SNPs ranked using aggregated conditional power resulted in two SNPs reaching genome-wide significance, rs11645147 on chromosome 16 (p = 1.74 × 10−4 < 0.05/10 = 0.005) and rs7866522 on chromosome 9 (p = 0.0033). Efficient usage of mixed designs incorporating both unrelated and family-based data may help to uncover associations otherwise difficult to detect in the presence of massive multiple testing corrections. Capitalizing on the strengths of both types while using screening approaches may be useful especially in light of large-scale, next-generation sequencing and rare variant studies.Genome-wide association studies (GWAS) explore the relationship between genome variability and disease susceptibility with either population- or family-based data. Here, we have evaluated the utility of combining population- and family-based statistical association tests and have proposed a method for reducing the burden of multiple testing. Unrelated singleton and parent-offspring trio cases and controls from the Genetics of Kidneys in Diabetes (GoKinD) study were analyzed for genetic association with diabetic nephropathy (DN) in type 1 diabetics (T1D). The Cochran-Armitage test for trend and the family-based association test were employed using either unrelated cases and controls or trios, respectively. In addition to combining single nucleotide polymorphism (SNP)  The successes and failures of genome-wide association studies (GWAS) have made for both interesting scientific dialog and the development of innovative statistical methodologies. While debate continues around reasons for the so-called missing heritability of GWAS, the sheer number of replicable genetic associations discovered using this approach is unarguable . This strategy of combining the offspring from trios, or, more generally, a randomly selected non-founder from a pedigree, with the unrelated cases and controls has been common practice  in type 1 diabetics (T1D). T1D patient probands were screened to identify cases with kidney disease and controls with normal renal status despite long-term diabetes. When possible, both parents of the proband were enrolled to form family trios and DNA was collected for all T1D patients and participating parents  and family-based subjects (trios), against adding the trio offspring into a pooled unrelated subset, to analyze using common case-control statistics as in the initial analysis of Pezzolesi et al. . We thenGenetic association using the subset of unrelateds was examined using the Cochran-Armitage test for trend assuming an additive genetic mode of inheritance. The trend test was adjusted for sex and stratified by center using a Cochran-Mantel-Haenszel test as in the original GoKinD GWAS. These tests were conducted with and without the addition of offspring cases and controls in order to replicate the original findings and to use within the proposed framework, respectively Figure  and R R.Along with adding resolution for QC, the addition of parents makes possible traditional family-based association testing (FBAT). FBATs were calculated using the FBAT package  will be ranked highly by virtue of providing more likelihood of finding an association that is present. More formally, the Van Steen algorithm  and described by Sharma et al. .Note that our selection approach results in rankings equivalent to those from multiplying the rankings from both subsets. Importantly, this method is subjectively chosen and can likely be optimized in future research.p-values is converted into a Z-score and then weighted by the square root of the subset sample size to comprise a meta-analytic Z-score. In addition to meta-analytic methodologies, we also compared to an approach the aggregates data across the subsamples rather than the p-values . Areas of suggestive association noted in the pooled population-based analysis  were similar to results from Pezzolesi et al.  is contained in the protein tyrosine phosphatase, receptor, D gene (PTPRD). Members of the protein tyrosine phosphatase family are known to be signaling molecules which regulate processes such as cell growth, differentiation, mitotic cycle, and oncogenic transformation  is located in proximity to the glutamate receptor, ionotropic, N-methyl D-aspartate 2A gene (GRIN2A).Selection of the top 10 ranked SNPs from screening approaches combined across the unrelated and trio subsets and testing with Fisher's test resulted in two SNPs achieving genome-wide significance  study , statistically independent assessments of each SNP's power to detect an association allows for more efficient genome-wide testing. Here we aggregated the independently obtained marker rankings using parental information in the family-based data and data partitioning in the population-based data. By limiting testing to the conventionally-used top 10 highest ranked markers (Herbert et al., Applying screening methods due to Van Steen et al.  and McQuWith the growing availability of GWAS and now sequencing data, association studies have increasingly reported positive results. Multiple-hypothesis testing, low power, study design variability, phenotypic definition, and population structure continue to pose investigational difficulties (Laird and Lange, The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


F-statistic and sliced inverse regression. The procedure is tested on the data set provided by the Genetic Analysis Workshop 17 (GAW17). After preliminary data reduction, we ranked markers according to their F-statistic values. Top-ranked markers were then subjected to sliced inverse regression, and those with higher absolute coefficients in the most significant sliced inverse regression direction were selected. The procedure yields good false discovery rates for the GAW17 data and thus is a promising method for future study on rare variants.The advance of high-throughput next-generation sequencing technology makes possible the analysis of rare variants. However, the investigation of rare variants in unrelated-individuals data sets faces the challenge of low power, and most methods circumvent the difficulty by using various collapsing procedures based on genes, pathways, or gene clusters. We suggest a new way to identify causal rare variants using the  There is a growing interest in the role of rare variants in disease etiology—rare in the sense that the minor allele frequency (MAF) is less than 1%. Earlier genome-wide association studies identified risk loci that accounted for only 5–10% of disease heritability . HoweverF-statistic for all the markers. We show that the F-statistic does not down-weight a rare variant despite its low allele frequency and thus is effective in capturing the effect of the rare variant. Next, we apply sliced inverse regression (SIR) to top-ranked markers selected by the F-statistic. When the number of selected top markers is not too large, we find that SIR performs well in identifying the SNPs used to simulate the Genetic Analysis Workshop 17 (GAW17) phenotypes from the top markers (hereafter these SNPs are referred to as the answers).In this paper, we propose a three-step method that does not use collapsing. After removing the SNPs that are identical in value across all subjects in the data, we calculate the The data set  from GAWBecause most of the SNPs are rare variants, many of them take identical values across all individuals in the data set; that is, statistically they are indistinguishable. In the preliminary data reduction step, we remove the identical-valued SNPs and keep track of them for later reference. By doing so, we reduce the 24,487 SNPs to 15,124 distinguishable markers. The benefit of this procedure is twofold. First, the dimension is reduced for subsequent statistical analysis, and, second, removing identical-valued SNPs prevents the numerical problems caused by degenerate matrices in regression and principal component types of analyses.F-statistic, as defined in the simple linear regression model, takes the form:The where:iY=0β+ 1X1iβ+Iεith observation i= 1,…,n using standard notations. In particular, iε are independent normally distributed random variables with mean 0 and variance σ2. Let Y’s. SSR and SSE are the regression sum of squares and the error sum of squares, respectively. The estimated model is:is the simple regression model for F-statistic for each of the 15,124 markers by fitting a simple linear regression model, one marker at a time. The response variable Y is the average value of Q1 over 10 replications. The markers are then ranked by F values. A number of top markers are selected for further analysis in the next step.We calculate the X, we estimate an inverse regression of X on sliced Y. The inverse regression, that is, the computation of E(X|Y), converts a high-dimensional regression problem of Y on X to many simple regressions of X on Y. In estimating E(X|Y), the range of Y is divided into small intervals (sliced) to increase computational efficiency. Next, we perform a principal components analysis on E(X|Y), and the principal components (PCs) are returned. These are the SIR effective dimension reduction directions discussed by Li [SIR  is a noned by Li . We simpF-statistic. Because the first SIR direction (DIR1) contains the most important information of the data, it is the most significant, and we use only this SIR direction in our method. Next, we perform a two-mean clustering analysis on the absolute DIR1 coefficients. The markers in the cluster with higher mean are our final candidates for causal SNPs.Top markers selected from the previous step are subjected to SIR, and the response variable of SIR is the same as the one used in the previous step of determining the Our method is first applied to data from replicates 1 to 10 (group 1). To assess the false discovery rate (FDR) of our method, we divided the 200 replications of the GAW17 data set into 20 groups with 10 replicates per group . We average the ratios of the number of identified answers to the number of final candidate SNPs over 20 groups to obtain the FDR.F-statistic (Table β (influence level) of the answers were all relatively high. This result shows that the answers found by the F-statistic have strong main risk effects.For the group 1 data, there are eight answers in the top 100 markers ranked by the p-value of DIR1 reported by the SIR provides us with a clue regarding an upper bound for the number of markers to be selected. In the group 1 data, with 70 markers or less, the p-value of DIR1 are all well below 0.1%, but with 80 markers the p-value rises by more than 20 times, to 2%. This suggests that the number of markers that needs to be used should be at most 70. Second, the histograms of the F-statistic show a clear gap at about the top 30th position for most of the 20 groups. Thus we use the top 30th marker as the cutoff position. The results of the other cutoff positions are also calculated . When the explanatory variables  are binary, the F-statistic in Eq. (1) is the same as the F-statistic for comparing multiple group means. We decompose the numerator into two parts: In the first part x1 is the minor allele, and in the second part ix,i=2, …, n, are all major alleles. The decomposition in the following equation shows the weights given to the two parts and provides an insight into the power of the F-statistic for a rare variant:We explain why the where:The first part on the right-hand side of Eq. (3) can be written:The second part of Eq. (3) can be written:n − 1) times that for the major allele. This helps to manifest the effects of rare variants on the response.Thus the weight given to the regression sum of squares (SSR) for the minor allele is  to the previously identified SNPs when applying the F-statistic to all markers. This suggests that a separate treatment of common and rare variants is a promising strategy for further investigation.In the preceding analysis, we calculated the F-statistics on all markers and select those with the top F values. Finally, we perform SIR on the top markers and perform two-mean clustering on the absolute coefficients of the first SIR direction. Markers in the cluster with a higher mean are the final candidates for causal SNPs. Using the top 30 markers from the F-statistic, we find that the FDR is 20.8% and that the average number of answers is 4.3. We show that the proposed method is an effective and easy-to-use feature selection approach in the context of rare variants.We use traditional statistical methods for new applications in the context of rare variant research. A three-step method is introduced. First, we perform a simple data reduction by removing identical-valued SNPs. Second, we calculate The authors declare that there are no competing interests.HW carried out the statistical analysis and drafted the manuscript. CHH provided technical support for data management. SHL and TZ participated in the design of statistical analysis and presentation of results. IH conceived of the study, designed the statistical analysis, and helped to draft the manuscript.


Multiple sclerosis (MS) is the most common cause of chronic neurologic disability beginning in early to middle adult life. Results from recent genome-wide association studies (GWAS) have substantially lengthened the list of disease loci and provide convincing evidence supporting a multifactorial and polygenic model of inheritance. Nevertheless, the knowledge of MS genetics remains incomplete, with many risk alleles still to be revealed.We used a discovery GWAS dataset  and a multi-step logistic regression protocol to identify novel genetic associations. The emerging genetic profile included 350 independent markers and was used to calculate and estimate the cumulative genetic risk in an independent validation dataset . Analysis of covariance (ANCOVA) was implemented to compare clinical characteristics of individuals with various degrees of genetic risk. Gene ontology and pathway enrichment analysis was done using the DAVID functional annotation tool, the GO Tree Machine, and the Pathway-Express profiling tool.P = 0.04) was detected for age of disease onset between the affected misclassified as controls (mean = 36 years) and the other three groups .In the discovery dataset, the median cumulative genetic risk (P-Hat) was 0.903 and 0.007 in the case and control groups, respectively, together with 79.9% classification sensitivity and 95.8% specificity. The identified profile shows a significant enrichment of genes involved in the immune response, cell adhesion, cell communication/signaling, nervous system development, and neuronal signaling, including ionotropic glutamate receptors, which have been implicated in the pathological mechanism driving neurodegeneration. In the validation dataset, the median cumulative genetic risk was 0.59 and 0.32 in the case and control groups, respectively, with classification sensitivity 62.3% and specificity 75.9%. No differences in disease progression or T2-lesion volumes were observed among four levels of predicted genetic risk groups . On the other hand, a significant difference (F = 2.75, The results are consistent with the polygenic model of inheritance. The cumulative genetic risk established using currently available genome-wide association data provides important insights into disease heterogeneity and completeness of current knowledge in MS genetics. On the other hand, some authors suggest that both of these risks are difficult to assess and the denominator is generally underestimated while the numerator is overestimated [s may be less than 10 [Multiple sclerosis (MS) is a common cause of non-traumatic neurological disability in young adults. Extensive epidemiological and laboratory data indicate that genetic susceptibility is an important determinant of MS risk ,2; this pulation . In nortstimated ; a more  than 10 . In addi than 10 ,9; howevHLA) gene cluster in chromosome 6p21.3 represents by far the strongest MS susceptibility locus genome-wide. The primary signal maps to the HLA-DRB1 gene in the class II segment of the locus, but complex hierarchical allelic and/or haplotypic effects and protective signals in the class I region between HLA-A and HLA-C have been reported as well [IL2RA, IL7R, EVI5, CD58, CLEC16A, CD226, GPC5, and TYK2 [TNFRSF1A, ICSBP1/IRF8 and CD6 [MS behaves as a prototypic complex genetic disorder, and although a single-gene etiology cannot be ruled out for a subset of pedigrees, data from recent genome-wide association studies (GWAS) provide convincing evidence that support a multifactorial and polygenic model of inheritance -14. It i as well -21. Otheand TYK2 ,14,22-25 and CD6 . In addi and CD6 , the resA genome-wide meta-analysis of MS was recently completed and reported . Since eP < 0.001) of the meta-analysis in the discovery dataset by individual chromosomes and implement a logistic regression analysis using alternation between the type I and type III sums of squares tests to remove markers that are in linkage disequilibrium (LD). The top ranked SNPs  are forced into the model first. We then calculate the residual effect of each of the other SNPs after accounting for the effect of the top ranked SNPs. We used gender and sample country of origin  as covariates in the model to account for possible population heterogeneity. Furthermore, conditional logistic regression was implemented conditioning on DRB1*15:01 status (Yes versus No) in order to control the effect of genetic heterogeneity. This method is preferred to the conventional logistic regression model in estimating the gene risk effect after 'conditioning out' the baseline risk in DRB1*15:01 carriers and non-carriers, and it is thus efficient in eliminating the redundancy of markers that are in LD with DRB1*15:01. HLA-DRB1*15:01 status was determined using a tagging marker (rs3135388).All statistical analyses were performed using SAS v.9.1.3 and JMP Genomics v. 4.0 . Principle component analysis was implemented prior to data analysis to assess population substructure. Although no significant population substructure was observed when compared to the HapMap CEU data, a few outliers were removed. We organize the top association analysis results  = ln(P-Hat/1 - P-Hat) = 0+β1X1+β2X2+···+BiXiβ; and thus, P-Hat = 1/1+ expβ0 + β1X1 + β2X2 + ···+BiXi)-), where Ŷi = intercept + βcenter × Xcenter + βgender × Xgender + ∑βj×Xij; βj is the estimated regression coefficient of genetic marker j, and j = 1 to 350; Xij is the fractional genotype of marker j of individual i. The values of intercept, βcenter, βgender, and βj are the maximum likelihood estimates obtained from the logistic regression model. The regression coefficient reflects the differential contribution of each SNP, and the odds ratio is estimated by exponentiating the corresponding regression coefficient. In order to assess how well the genetic profile can differentiate MS cases from the controls, the cumulative genetic risk classification is performed. If Ŷi of an individual is >0, then the individual is classified as a MS case, and if Ŷi is <0, then they are classified as a control. When Ŷi = 0, the estimated probability of being an MS patient is 0.5.Logistic regression stepwise selection was applied to select a set of genes from the identified independent markers and establish a genetic profile to assess the cumulative genetic risk of individuals (P-Hat). Logistic regression is used for prediction of the probability of occurrence of an event by fitting data to a logit function. It is a generalized linear model used for binomial regression. The logit of the unknown binomial probabilities (P-Hat) is modeled as a linear function of the P-value <0.05 indicates a lack of fit of the fitted logistic regression model [Classification sensitivity and specificity are assessed. Classification sensitivity is defined as the percentage of affected individuals that are classified as an MS case, and specificity as the percentage of controls that are classified as a control. Analysis of covariance (ANCOVA) was implemented to compare clinical characteristics of individuals with various degrees of genetic risk , with gender as covariate in the model. The Hosmer-Lemeshow goodness-of-fit test was implemented to test if the observed probability is equal to the expected probability based on the fitted model; a on model .Gene ontology enrichment analysis was done using the DAVID functional annotation tool  and GO THLA-DRB1*15:01 was similar across the disease groups. As expected, gender ratios were different between cases and controls in all datasets. Gender was fit into the model for all subsequent analyses to minimize the effect of this difference. Using the top 12 validated disease variants for MS including HLA-DRB1  and validation datasets  are shown in Table DRB1*15:01 status as covariates. A relatively lax threshold of significance was chosen to compensate for the lack of statistical power to detect minor effects. Markers with P-value <0.001  from both analyses were selected for further study. Altogether, 11,334 markers (0.44% of the 2.56 million markers) were included in the stage II analysis.Case-control logistic regression analysis was implemented on the discovery dataset with 8,844 samples . Two regression models were applied. The first model included center and gender as covariates, whereas the second model included center, gender and DRB1*15:01 [P-value from the type I test indicated that the marker showed an independent effect in addition to the preceding markers that were already placed in the model. The second test sought to examine multicollinearity in between markers due to LD (type III sums of squares test). The P-value from the type III test indicated if the marker of interest remained significant after all other markers were placed in the model. Thus, if any two markers in the model were in LD, one or both of the marker's P-value would not be significant. Markers that did not reach P < 0.01 from both type I and type III tests were removed. The flow chart of analysis procedures is shown in Additional file P < 10-5 (the most significant markers per gene), then placed this set of markers into a logistic regression analysis in the sequence of significance to examine independence of markers (type I test). This first set of independent markers was then placed in a logistic regression model (type III test) to search for markers with remaining effect at P < 0.001. The second set of markers was then selected and combined with the first set of markers, and was examined using both type I and type III analyses in a logistic regression model again to examine independent effect and multicollinearity. Markers that did not show additional independent effects were removed. This expanded set of independent markers was then placed into a regression model (type III test) to search for additional independent markers. These steps were repeated until all markers with an independent effect at P < 0.001 were identified. The analysis identified 713 independent markers across all autosomal chromosomes, and included the original GWAS and meta-analysis associated markers . Markers with significance at -Log10 (p) > 6.0 are shown in Table The main objective of the stage II analysis was to trim redundancy among the 11,334 markers identified in the stage I analysis. Conditional logistic regression was used to remove markers in LD with P = 0.01, P = 0.05, P = 0.1) was implemented. The stepwise-selection process included an alternation between forward selection of a set of significant markers and backward elimination of markers that did not retain significance at the selected threshold after additional markers were placed in the model. The stepwise selection process terminated when additional significant markers could not be fitted into the model. The covariates included in the logistic regression analysis were center and gender. This analysis identified 350 genes using P = 0.05 as the cutoff selecting criteria, including CD58, EVI5, IRF8, RGS1, CD226, TNFRSF1a, CD6, and IL7R. However, IL2Ra, CLEC16a, IRF8, and HLA-C did not survive the stepwise regression analysis.Using the identified 713 independent markers, we performed a model fitting analysis to select the optimal set of variants that gave the best estimation of the cumulative genetic risk mediated by common alleles for an individual and that differentiated MS cases from controls. Logistic regression analysis using stepwise-selection with different selection entrance and remaining cutoff values . Classification sensitivity only increased from 79.9% to 80.3%, and the adjusted R2 only improved from 0.75  to 0.76 (391 markers). Therefore, we tested the predictive power of the selected 350 variants  explained disease status in this dataset. The explanatory potential of these variables can be expressed as a summary estimate of the predicted probability of an individual being a MS case (P-Hat). The median of the cumulative genetic risk in the case group is 0.90, and in the control group 0.01. Quantiles of the estimated cumulative genetic risk (P-Hat) using different genetic models is summarized in Table el Table .The genetic profile established in the stage III analysis was tested on an independent dataset including 1,618 MS cases and 1,988 controls . We usedDRB1*15:01 status showed the strong effect of the allele or haplotype (high P-Hat: 63.2% in DRB1*15:01+ versus 36.8% in DRB1*15:01-), along with the decrease in the proportion of DRB1*15:01 carriers from the highest P-Hat group to the lowest P-Hat group: . Similar association was observed with gender    were grouped into four clusters using their predicted probability of being a MS patient (P-Hat): high ; medium ; low ; misclassified . Not surprisingly, Chi-square testing for the association of genetic load with 3), and age of disease onset (years) were analyzed using ANCOVA tests, with gender as covariate in the model. MSSS was transformed using square-root transformation for normality assumption. T2-lesion volumes (mm3) were transformed using cube-root transformation for normality assumption. The global test results did not show statistically significant difference between the four groups on MSSS  and T2-lesion volumes , whether age of disease onset was placed in the model as a covariate or not . However, there was a significant difference in age of disease onset between the MS affected misclassified as controls (mean = 36 years) and the other three groups  (Table Multiple Sclerosis Severity Score (MSSS), T2-lesion volumes  and MHC class I and class II genes.To gain insights into the biological significance of the 350 variants identified in our analysis and assess how these may relate to the etiology of MS, we interrogated the gene list for enrichment of known biological labels such as gene ontologies and protein pathways. DAVID  identifiPartially powered GWAS and ensuing meta-analysis have identified a number of non-HLA candidate genes associated with MS susceptibility -14. Each2 (Nagelkerke's R2) of different models using the discovery and validation datasets were compared  in the genetic profile, we used logistic regression condition on DRB1*15:01 (+/-) to assess R2 of the six MHC variants. The total variance accounted for these non-DRB1 MHC genes is 2.1% in the discovery dataset, and 2.6% in the replication dataset.In order to better understand the magnitude of variance explained by different sets of genes in the logistic regression models, adjusted R2 of the logistic regression model is 0.75 and the r-square attributable to genetic factors in this model accounted for only 56.5%, suggesting that without fitting environmental triggers into the model, predictive accuracy will remain limited. A large number of environmental exposures have been investigated in MS, but recent epidemiologic and laboratory studies have provided support primarily for vitamin D and Epstein-Barr virus exposure [Several factors could have contributed to the relatively low sensitivity of the selected genes. First, the power of the discovery dataset is more likely inadequate to detect all susceptibility genes. Even though we have used the largest MS genetic dataset available to date, it has been suggested that a dataset with 10,000 cases and 10,000 controls might be able to reach a desirable level of power for GWAS analysis in order to effectively control both type I and type II errors. This is especially valid for less frequent alleles  and effect size (odds ratio) in the range 1.1 to 1.3 ,36. Secoexposure ,38. A reexposure . Fifth, All these confounders are reflected in the fact that some individuals in the control group carry a high cumulative genetic risk (P-Hat >0.8). Thus, in this experiment utilizing the most updated MS genetic dataset, a high cumulative genetic risk is not sufficient to predict with high confidence affectation status even in the discovery dataset Table . AdditioCDH2, CADM1, CNTN1, NCAM2, NRXN1, and NRXN3) and several neuronal receptors, such as the G-protein coupled receptors , as well as the metabotropic glutamate receptor (GRM8) and ionotropic glutamate receptors (GRIK4 and GRIN2B). Interestingly, members of the glutamate receptor pathway have been previously identified by our group in both the network-based study of one of the GWAS datasets included in the meta-analysis utilized here  [GRIA1, GRID2, SLC1A2) [GRIA3) associated with interferon response in MS [Most validated MS susceptibility loci have well-defined roles in immunologic functions, consistent with the hypothesis that MS etiology has its primary roots in early immune system dysregulation, precipitating secondary neuronal degeneration. On the other hand, a network-based pathway analysis of two GWAS in MS, where evidence for genetic association was combined with evidence for protein-protein interaction, demonstrated the role of neural pathway genes (axon guidance and long-term potentiation) in conferring susceptibility . The gen, GRIK4)  and an i SLC1A2) . A more se in MS . These ose in MS ,43. The In summary, the cumulative genetic risk estimation using a genetic profile composed of 350 genes provides a useful index of the genetic risk leading to MS. The incomplete classification accuracy reflects most likely the limited power of available genetic datasets and the difficulties in incorporating gene-gene interactions and gene-environment interactions. The imminent publication of larger high-resolution GWAS and transcriptomic studies together with recent progress in identifying true environmental variables will refine this and other modeling approaches for a greater understanding of MS genetics and assessment of translational applications.ANCOVA: analysis of covariance; AUC: area under curve; FDR: false discovery rate; GWAS: genome-wide association study; HLA: human leukocyte antigen; LD: linkage disequilibrium; MS: multiple sclerosis; MSSS: Multiple Sclerosis Severity Score; ROC: receiver operating characteristic; SNP: single-nucleotide polymorphism.The authors declare that they have no competing interests.JW and JRO conceived and designed the experiments. JW, PIWdB and PLdJ performed the experiments. JW completed the statistical analysis. SEB, DP, DP, LBC, PIWdB, LK, CHP, DAH and PLdJ contributed reagents/materials/analysis tools. JW, JRO, DP and PMM wrote the paper.Table S1. Marker information of the 12 validated genes.Click here for fileTable S2. Flow chart of analysis procedures to identify independent MS susceptibility markers.Click here for fileTable S3. Independent markers significant at FDR P ≤ 0.05 in the discovery dataset .Click here for fileTable S4. Genetic profile used for assessing the cumulative genetic risk (350 genes).Click here for file


Genetic imprinting is the most well-known cause for parent-of-origin effect (POE) whereby a gene is differentially expressed depending on the parental origin of the same alleles. Genetic imprinting is related to several human disorders, including diabetes, breast cancer, alcoholism, and obesity. This phenomenon has been shown to be important for normal embryonic development in mammals. Traditional association approaches ignore this important genetic phenomenon. In this study, we generalize the natural and orthogonal interactions (NOIA) framework to allow for estimation of both main allelic effects and POEs. We develop a statistical (Stat-POE) model that has the orthogonal estimates of parameters including the POEs. We conducted simulation studies for both quantitative and qualitative traits to evaluate the performance of the statistical and functional models with different levels of POEs. Our results showed that the newly proposed Stat-POE model, which ensures orthogonality of variance components if Hardy-Weinberg Equilibrium (HWE) or equal minor and major allele frequencies is satisfied, had greater power for detecting the main allelic additive effect than a Func-POE model, which codes according to allelic substitutions, for both quantitative and qualitative traits. The power for detecting the POE was the same for the Stat-POE and Func-POE models under HWE for quantitative traits. Imprinted genes have been implicated in several complex human disorders, including diabetes, breast cancer, alcoholism, and obesity Genetic imprinting frequently affects genes during embryogenesis and is the most well-known parent-of-origin effect (POE). Imprinting causes the differential expression of genes based on the parental origin of the chromosome Several statistical approaches have been developed for modeling POEs and imprinting effects. Shete et al. implemented a variance-components method for testing genetic linkage by incorporating an imprinting parameter Most traditional association approaches assume that the two alleles from the parents contribute equally to the trait, thereby ignoring the potentially important genetic phenomenon, POEs. These approaches estimate the main allelic effect, which could also be considered as the overall genetic effect, without considering POEs. Thus, it is important to develop new methods applicable to genome-wide scans that model the differential contribution of paternal and maternal alleles. It is desired that a method that allows for POE also maintain the power to detect the main allelic effect after adding one or more parameters to the model. Therefore, the proper and orthogonal decomposition of genetic variance renders this framework meaningful and useful to estimate main allelic effects along with the POE.The natural and orthogonal interactions (NOIA) model was originally developed as a framework for estimating genetic effects for a quantitative trait and gene-gene (GxG) interactions Genome-wide association studies (GWASs) have achieved great success in identifying genetic susceptibility loci associated with human disorders and traits in the past decade, such as cancer, diabetes, hypertension and heart diseases In this study, we generalize the NOIA framework to incorporate POEs. We show that more disease-associated genes could be detected by incorporating POEs with orthogonal models than by using traditional models, and that the NOIA POE model would fulfill the requirement of maintaining the power to detect the main allelic effect for complex diseases when multiple loci contribute to disease risk. The orthogonality of the statistical formulation of NOIA framework is important, especially when multiple loci are contributing to the outcome. Using Kronecker product rule, our one-locus NOIA POE formulation can be easily extended to the general case of multiple loci  to model general GxG/GxE interactions in the presence of imprinting effect, making NOIA a unified framework for detecting GxG/GxE interactions along with imprinting effect. Here we focus on one-locus association analysis for quantitative trait, implementing NOIA into a POE integrated framework by re-parameterization.From the NOIA statistical model without POE  and the traditional functional model without POE , we derived the formulas of several different quantitative trait association models, including a statistical POE (Stat-POE) model and a functional POE (Func-POE) model. Then, we evaluated the performance of the Stat-POE and Func-POE models. We also compared the performance of the POE models (Stat-POE and Func-POE) with that of the models without POE incorporated . These studies were all performed for both a simulated quantitative trait dataset and a qualitative trait dataset. We found that the incorporation of POE into the statistical model did not affect the estimation of the main allelic effect. Moreover, the power of the statistical models with POE incorporated was higher in the presence of imprinting than that of the usual models without POE for detecting the main allelic effect for both the quantitative trait and qualitative trait. Although our methods were developed and evaluated for single locus association study, we show that they can be straightforwardly extended to gene-gene interaction or gene-environment interaction models.We first briefly review the NOIA model without POE detecting. Using the usual approach for genotype-phenotype mapping of a quantitative trait locus (QTL), if the trait is influenced by a single diallelic locus, with alleles Several methods have been proposed for mapping a quantitative trait controlled by one locus with two alleles. The vector of genotypic values The vector of genetic effects  interactions The genetic effects, We notice the Stat-Usual and Func-Usual models have same estimators for the dominant effect and different estimators for the additive effect as timation .In this section, we extend the models described above by incorporating the POE and evaluate the performance of these extended models in detecting both the overall genetic effect and POE. For a gene with POE, the vector of genotypic values Similar to We have two different ways to construct a functional and a statistical model with POE. First, we can do so by decomposing the additive effects into two paternal and maternal additive effects, resulting in Model 1 for the functional model and Model 2 for the statistical model see . In thisLet Let Therefore, according to The POE functional model (Func-POE) and statistical model (Stat-POE) are related byWe have previously showed that the Stat-Usual model was orthogonal in the sense that the estimates of the four parameters were uncorrelated Note thatAlso, To show that the additive variance, And The two additive variance components ormation . On the thogonal . Howeverthogonal .We performed simulation studies for both a quantitative trait and a qualitative trait (case-control) using an approach similar to that used in To simulate samples of independent individuals with a quantitative trait controlled by a diallelic locus, we assumed that the gene is under HWE. The case that a gene is not under HWE was not considered in our study, and will be investigated in our future work. For a given value of the minor allelic frequency  for both quantitative traits and qualitative traits.First we performed a simulation study for a quantitative trait in three scenarios with strong, moderate, or weak imprinting effect while the main allelic additive effect remained the same . The truTo evaluate the performance of these models in detecting main allelic additive effect and POE, we calculated the statistical power of four models under different critical values of P values obtained using a Wald test . Figure To evaluate whether the MAF influences the estimation of the genetic effects by these models, we also performed analyses for quantitative traits when the MAF was 0.03 and 0.48, respectively –S2. FiguSimilarly, we also performed analyses for simulated case-control data. The simulating values for each of the two scenarios are shown in Another simulation was performed with a moderate POE for case-control data . InteresSimulations were also performed when MAF was set as 0.03 and 0.48 for case-control design, respectively –S4. For We summarized the detailed power comparison of the Stat-POE and Func-POE models in Type I error was evaluated for both the quantitative trait and the qualitative trait by simulating a null scenario where there was no main genetic effect or POE. We estimated the type I error for the main additive effect, POE and dominant effect for both quantitative traits and case-control traits when the MAF was set as 0.03, 0.28 or 0.48 . The falIn this study, we extended the NOIA framework, which was initially developed for epistatic analysis of quantitative traits, by incorporating POE for genetic association analysis. Herein, we propose a unified framework for one-locus association study that allows for main allelic additive effect, the dominant effect and POE estimation via linear regression or logistic regression. Using simulation, we illustrated the statistical properties of this extended framework on one-locus association study. Although the Func-POE model sometimes presented slightly greater power than the Stat-POE model for estimation of POE for qualitative trait. The Stat-POE model are always preferred than the Func-POE model in detecting overall additive effect for quantitative traits and qualitative traits, because of its much greater power.We conducted genetic variance decomposition to show that the Stat-POE model was orthogonal when either HWE or equal minor and major allele frequencies is satisfied for quantitative traits –25. Thusion (D3)  is ratheUsing simulation, we demonstrated that the statistical models, including the Stat-POE and Stat-Usual models, had better performance for detecting the main allelic additive effect than the functional models, Func-POE model and Func-Usual for both quantitative traits and qualitative traits. These two POE models on detecting the POE had the same power when OE model –2. The pHowever, the performance of these two models for detecting the main allelic effect and dominance effect had a different pattern in qualitative traits  and 5. IWe also illustrate why the proposed model can detect more disease-associated genes than the traditional models in model setting as follows. First, the orthogonal  model proposed by Alvarez-Castro et al. orthogonalizes the estimation of the additive and dominant effects but the usual model  does not. We constructed the test statistics of the Stat-Usual and Func-Usual models for quantitative traits with and without dominance components effects . The tesSeveral recent studies have incorporated POEs in association analyses for quantitative traits. Genome-wide rapid association using mixed model and regression (GRAMMAR) and its extension are a recently developed approach that is based on a measured genotype approach and has been shown to have greater power than the transmission disequilibrium test (TDT)-based tests Although our extension of the NOIA is expected to provide new insights into disease gene mapping, pedigree data are needed for our framework to be used to estimate transmitting information of each heterozygotes or homozygotes locus. Obtaining the transmitting status of one locus is possible for non-informative pedigrees determined by nearby linked loci or haplotype phasing. Or we could use weighted analysis in which the probabilities of each genotype are used. A future direction of our next step will be to extend our formulations to incorporate non-deterministic genotypes due to insufficient parental information or missing data. Alvarez-Castro and Carlborg handled internal mapping by implementing the Haley-Knott Regression with NOIA The motivation of our implemented framework was based on the orthogonality property of NOIA which allows for easy model selection and variance component analysis. A next step is to extend the formulation proposed here to multi-locus and/or environmental factor cases, including gene-gene interaction and gene-environment interaction analyses when POE is incorporated. Conceptually, this generalization should be fairly straightforward using the Kronecker product rule as in Figure S1Power under different critical values of the P values obtained using the Wald test for the quantitative simulation data influence by a genetic factor with strong POE (scenario 1). The minor allele frequency was 0.03. Power for detecting (a) the main allelic additive effect, (b) the POE and (c) the dominant effect.(TIFF)Click here for additional data file.Figure S2Power under different critical values of the P values obtained using the Wald test for the quantitative simulation data influence by a genetic factor with strong POE (scenario 1). The minor allele frequency was 0.48. Power for detecting (a) the main allelic additive effect, (b) the POE and (c) the dominant effect.(TIFF)Click here for additional data file.Figure S3Power under different critical values of the P values obtained using the Wald test for the case-control simulation data influence by a genetic factor with POE (scenario 2). The minor allele frequency was 0.03. Power for detecting (a) the main allelic additive effect, (b) the POE and (c) the dominant effect.(TIF)Click here for additional data file.Figure S4Power under different critical values of the P values obtained using the Wald test for the case-control simulation data influence by a genetic factor with POE (scenario 2). The minor allele frequency was 0.48. Power for detecting (a) the main allelic additive effect, (b) the POE and (c) the dominant effect.(TIF)Click here for additional data file.Text S1POE models before transformation.(DOCX)Click here for additional data file.Text S2Orthogonality of the Stat-POE model before transformation.(DOCX)Click here for additional data file.Text S3Orthogonality of the Stat-POE model after transformation.(DOCX)Click here for additional data file.Text S4Orthogonality of the Func-POE models.(DOCX)Click here for additional data file.Text S5Test Statistics for Full and Reduced One-Locus Models.(DOCX)Click here for additional data file.Text S6R coding of Stat-POE and Func-POE models.(DOCX)Click here for additional data file.