Comprehensive evaluation of common genetic variations through association of single nucleotide polymorphisms (SNPs) with complex human diseases on the genome-wide scale is an active area in human genome research. One of the fundamental questions in a SNP-disease association study is to find an optimal subset of SNPs with predicting power for disease status. To find that subset while reducing study burden in terms of time and costs, one can potentially reconcile information redundancy from associations between SNP markers.We have developed a feature selection method named Supervised Recursive Feature Addition (SRFA). This method combines supervised learning and statistical measures for the chosen candidate features/SNPs to reconcile the redundancy information and, in doing so, improve the classification performance in association studies. Additionally, we have proposed a Support Vector based Recursive Feature Addition (SVRFA) scheme in SNP-disease association analysis.We have proposed using SRFA with different statistical learning classifiers and SVRFA for both SNP selection and disease classification and then applying them to two complex disease data sets. In general, our approaches outperform the well-known feature selection method of Support Vector Machine Recursive Feature Elimination and logic regression-based SNP selection for disease classification in genetic association studies. Our study further indicates that both genetic and environmental variables should be taken into account when doing disease predictions and classifications for the most complex human diseases that have gene-environment interactions. Correlating DNA sequence variations with phenotypic differences has challenged biomedical research community for decades. Substantial efforts have been made to identify all common genetic variations in humans, including single nucleotide polymorphisms (SNPs), deletions and insertions . The IntTo date the efficiency of searching for optimal set of SNPs has not been efficient. To counter this trend, we propose reconciling information redundancy from associations between SNP markers. This method not only successfully identifies the approximate optimal set of SNPs but also potentially reduces the burden involved with genetic association studies such as time and cost .One primary cause for the lack of success in searching for optimal sets of SNPs is that the high dimensionality and highly correlated features of SNPs hinder the power of identifying small to moderate genetic effects connectable to complex diseases. The need to incorporate covariates of other environmental risk factors as effect modifiers or confounders further worsens “the curse of dimensionality problem” in mapping genes associated with complex diseases .r2 measure for case control association studies. Anderson and Novembre [et al. [et al. [et al. [et al. [et al. investigated the connection between “bidirectional gene pair” and cancer [How do we evaluate the searching for optimal SNPs? It must be predetermined prior to searching how SNPs are needed to provide enough predicting power of disease status. This is not a new question; it comes out of the overall recent statistical and computational endeavors that focus on feature selection from massive and highly dimensional genomic data. Specifically, in genome-wide disease association studies, various models and algorithms have been proposed for selecting an optimal subset of SNPs -13. LinkNovembre  and Mann [et al.  proposed [et al.  showcase [et al.  proposed [et al. ; score s [et al. , and wei [et al.  were prod cancer .Recently, Schwender and Ickstadt  demonstrIn this paper, we developed a feature selection method named Supervised Recursive Feature Addition (SRFA). It not only allows for the selection of genomic information but helps to identify the optimal subset of SNPs necessary for finding the variations associated with disease. This method combines supervised learning and statistical measures for the chosen candidate SNPs and/or environmental variables to reconcile redundancy information for improving the classification and prediction performance. We implemented SRFA with different statistical learning classifiers for both SNP selection and disease classification and then compared their performances with popular classification models, such as logic regression and Support Vector Machine Recursive Feature Elimination (SVMRFE). Additionally, we proposed a Support Vector based Recursive Feature Addition (SVRFA) scheme for SNP-disease association analysis. To evaluate and to demonstrate the proposed methods, we applied them to two complex SNP-disease data sets, the Myocardial Infarction Case & Control (MICC) data set and a subset of The North American Rheumatoid Arthritis Consortium (NARAC) data, for both SNP selection and disease classification.Fig. Fig. Overall, regarding the testing accuracies, the feature selection method NMSC-MSC performed the best, followed by NBC-MSC, MMW-MSC, MSW-MSC and SVMRFE; TTEST and RANKSUM performed the worst. Comparing NBC to NMSC, the performance of NMSC is, on average, superior to NBC. Figs. Tables Since it is still too expensive to genotype all available SNPs across the human genome, we need advanced approaches to mine the minimum SNPs with the highest prediction accuracy for complex diseases. Our method of exploiting information redundancy from associations among SNP markers provides an efficient and relatively inexpensive method of searching for the optimal or approximate optimal subset of SNPs in genetic association studies. In this paper we specifically propose supervised learning-based strategies, SRFA and SVRFA, to reconcile the redundancy in the highly correlated SNP data to identify the subset of SNPs that enables the most efficient classification of individuals at risk for disease. We evaluated SRA and SVRFA against some popular methods for SNP-disease association studies, and were able to evidence the improvement made by our proposed methods.Compared with the well-known feature selection methods SVMRFE and LOGICFS, our methods evidenced a higher testing accuracy. When SRFA is associated with two learning classifiers, we have two feature selection methods, NMSC-MSC and NBC-MSC. On average, NMSC-MSC performed better. Among the support vector based feature selection methods, MSW-MSC, MMW-MSC, and SVMRFE, in general, MMW-MSC is the best performer. In comparison SRFA with SVRFA, SRFA performed better than the latter. Our study shows that supervised-learning based MSC feature selection not only reduces the redundancy, but also improves the classification accuracy.An important factor in the evaluation of testing accuracy worth expounding upon is the training model. In our experiments, training with the use of DENFIS and other neural network classifiers always achieved high training accuracy but the testing accuracy was comparatively not good and over-fitting often happened. Since complex evolutionary learning and classification models, such as DENFIS, almost always require large sample size to elicit their effects, the over-fitting problem is probably related to the relatively small sample sizes. While the complexity of the model increases to achieve higher training accuracy, the requirement for more training samples also increases. If the sample size is not large enough, the relation and model mined from the training samples are not suitable for testing and, as a result, over-fitting happens. This is the reason that complex models fit training samples but not necessarily testing samples very well.Another point worthy of mentioning is that the learning classifier and feature selection are strictly paired. For instance, NMSC-MSC with the use of NMSC performed the best in the experiments on NARAC CHR18SNP, but NMSC-MSC with the use of NBC was not as good.The issue of environmental variables also requires discussion. For the MICC data set, with the inclusion of environmental variables, we greatly improved prediction and classification performances. Without the environmental variables, LOGICFS only achieved a 54.4%+/-1.5% correct classification rate. Also, SRFA provided a low (<60%) correct classification rate on the testing data when only using the SNPs, but a higher (>73%) correct classification rate after including the environmental variables as well. These results confirm that complex diseases usually involve both genetic factors and environmental cues. Therefore, both genetic and environmental variables should be taken into account when doing disease predictions and classifications for the most complex human diseases that have gene-environment interactions.In our experiments, when SVM was applied to the feature sets extracted from the NARAC CHR18SNP genotype data, the classification performance was pretty poor. However, SVM worked well on the feature sets extracted from the MICC data. In our view, the difference might be caused by the following two reasons. First, NARAC CHR18SNP consists of categorical SNP data only, while the MICC data set consists of many environmental variables of which most follow continuous distributions and have major impact on the classification. Second, it might be caused by the failure of optimizing the parameters for the SVM in testing NARAC CHR 18SNP.Our study shows that, with the use of our methods, even small SNPs and/or environmental variables can obtain good predictive capacity. In the analyses of MICC data, it was evident that, after applying our method with 3-5 variables, we can achieve up to 75% classification accuracy after applying our methods Fig. . On the We proposed SRFA with different statistical learning classifiers and SVRFA for both SNP selections and disease classifications, and then applied them to two complex disease data sets. In general, our approaches outperform the well-known feature selection method of Support Vector Machine Recursive Feature Elimination and logic regression based SNP selection for disease classification involved in genetic association studies. Our study further indicates that both genetic and environmental variables should be taken into account when doing disease predictions and classifications for the most complex human diseases that have gene-environment interactions.Application 1: Genes and the environment are links between important health conditions: Periodontal Disease (PD) and Cardiovascular Disease (CVD). Cardiovascular disease is the number one cause of death and disability in the Western world. Almost 1 million Americans die of CVD each year, which accounts for 42% of all US deaths. Numerous clinical and epidemiological studies have shown a consistent association between PD and CVD [ and CVD , and theetc. Selection of genetic variables was based on the well-known Seattle web site  by using the candidate approach that included 31 SNPs. This study evaluates the SNP-environment and variable-disease associations especially the effects of SNPs and environmental variables to disease. The original MICC data set contained some missing values. In our experiments, we filtered out the missing values and their associated observations.The studied Myocardial Infarction Case & Control (MICC) data set is a result of a population based study. The sample included residents of Erie and Niagara counties in New York State, and all were in age group 35 to 69 years. There were 614 white male patients with Myocardial Infarction matched with 614 control males (without CVD) by age (+/- 5 year) and smoking habits; 206 white pre- and post-menopausal females with MI matched with 412 control females (without CVD) by age (+/- 5 year), menopausal status, years since menopause (+/- 2 year), and smoking habits. Diabetics were excluded. The features in the data set included 29 environmental variables, such as two protein variables (ACHMN and CALMEA), which were known to be related to periodontal disease, and smoking status, menopausal status, blood pressure, blood cholesterol, body mass index, drinking status, Application 2: Rheumatoid arthritis (RA) is an autoimmune disease that causes chronic inflammation of joints, tissues around joints, or other organs in body. RA affects more than two million people in the United States. Women account for 70% of patients with RA. While women are two to three times more likely to get RA, men who have RA tend to have more severe symptoms. It afflicts people of all races equally. Onset usually occurs between 30 and 50 years old. Data for this analysis was provided as part of Genetics Analysis Workshop (GAW) 15. The North American Rheumatoid Arthritis Consortium (NARAC), led by Peter Gregersen, has provided microsatellite and SNP scans, quantitative phenotypes, and clinical measures, with additional genotype data provided by Robert Plenge and Ann Begovich. We studied the SNP case-control data named “CHR18SNP.dat” offered by NARAC. In the data file, a dense panel of 2300 SNPs was genotyped by Illumina for an approximately 10 kb region of chromosome 18q. These markers were individually genotyped on 460 cases and 460 controls. Controls were recruited from a New York City population. The objective of this study is to identify SNPs of chromosome 18 that are significantly associated with rheumatoid arthritis. The significant SNPs identified here could be used as a starting point for biologists developing genetic tests that indicate increased risk of developing rheumatoid arthritis.SRFA combines supervised learning and statistical similarity measures among the chosen features and the candidates and is presented as follows:Step 1: Each individual feature is ranked from the highest classification accuracy to the lowest classification accuracy with the use of a supervised learning classifier.p-value measured by score test-statistics is chosen as the first element. At this point the chosen feature set, 1G, consists of the first feature, 1g, which corresponds to feature dimension one.Step 2: The feature with the highest classification accuracy is chosen as the first feature. If multiple features achieved the same highest classification accuracy, the one with the lowest N+1)-dimensional feature set, N+1G = {1g, 2g, …, Ng, N+1g}, is produced by adding N+1g to the current N-dimensional feature set NG = {1g, 2g,…, Ng}. N+1g is chosen as follows: Temporarily add each feature ig  outside of NG to NG; the classification accuracy of each feature set NG + {ig} is then recorded; that cg which gives the highest classification accuracy is included into the set of candidates, C. Generally C includes many features, but only one−the feature that is least statistically similar to the already chosen features−will be selected as N+1g to form the next feature set N+1G. We call this step Candidate Feature Addition. The goal is to obtain the most informative and least redundant feature set. The statistical similarity measure is based on the Spearman Correlation Coefficient  or the Pearson Correlation Coefficient  between the chosen features ng  and the candidate cg . The Sum of the square of the Correlation (SC) is calculated to measure the similarity and is defined as follows:Step 3: The  is the minimum:The selection of This strategy is called Minimum SC (MSC).Step 4: A feature is recursively added to the chosen feature set from steps 1-3 with supervised learning and the similarity measures until classification accuracy stops to increase.Our SRFA based MSC is denoted as classifier-MSC. For example, if the classifier is Naive Bayes Classifier (NBC), we call the feature selection NBC-MSC.et al. [Support Vector Machines (SVMs) -16 have et al.  proposedet al. . Based o1. Train an SVM on each individual feature in the data set to reach an SVM with a weighted vector c for feature i: i =c (iw)2. The features corresponding to the lowest c are selected as candidates. The candidate with the highest statistical significance is the first element of the feature set. At this point the chosen feature set, 1G, consists of the first feature, 1g, which corresponds to feature dimension one.2. Rank features according to criterion N+1)st dimensional feature set, N+1 =G {1g, 2g, …, Ng, N+1g} is produced by adding N+1g to the N dimensional feature set NG = {1g, 2g,…,Ng}. The choice of N+1g is described as follows:3. The  outside of NG to NG, train an SVM on feature set NG + {ig}, update c, and calculate the measures after introducing ig as follows:Temporarily add each feature N+1g, corresponding to measures SW and MW, respectively. The candidate set is denoted as C. The first strategy is to pick up the feature with the minimum SW into C; and the second one is based on the minimum MW.Here we have two strategies to choose candidates as N+1g, despite whether set C contains multiple candidates or a single one. We chose N+1g from C based on the calculation of SC(jg), shown in (1), and Minimum SC (MSC) standard, listed in (2).Only one feature will be chosen as SW, calculated in (5), combining with Minimum SC standard, presented in (2) as MSW-MSC. Similarly we call the support vector based Minimum MW in (6) that is combined with Minimum SC in (2) as MMW-MSC. Both MSW-MSC and MMW-MSC are Support Vector based Recursive Feature Addition (SVRFA) algorithms.We call the support vector based Minimum We implemented SRFA with various statistical learning classifiers (with different complexity) proposed in section 2.1. The learning classifiers for feature selections were Naive Bayes Classifier (NBC) , NearestWe implemented and tested our SVRFA (MSW-MSC and MMW-MSC) methods proposed in section 2.2. For comparison purposes, other popular methods, such as Support Vector Machine Recursive Feature Elimination (SVMRFE), logistic regression based Wald t-test and Logic regression (LOGICFS) for SNP selection and disease classification were compared. In addition, we also applied SVM and other traditional neural network classifiers, such as Levenberg-Marquardt trained feed-forward neural network classifier and back-propagation trained feed-forward neural network classifier , for difCross-validation has been widely used for selecting tuning parameters and optimizing the number of selected genes in the context of building classifiers to avoid over-fitting. We split the data into training and testing samples in each run and built the model based on training samples only and evaluated the performance on the testing samples by using cross-validation. We performed and then tested the accuracy of 20 runs.The authors declare that they have no competing interests.QL performed the study and drafted the manuscript; JY conceived the project and designed the experiments; ZC assisted the study and the manuscript preparation; MQY designed the project and helped to design the algorithms; AHS and XH supervised the study and obtained the supports. All authors have read and approved the final manuscript.


With the development of high-throughput single-nucleotide polymorphism (SNP) technologies, the vast number of SNPs in smaller samples poses a challenge to the application of classical statistical procedures. A possible solution is to use a two-stage approach for case-control data in which, in the first stage, a screening test selects a small number of SNPs for further analysis. The second stage then estimates the effects of the selected variables using logistic regression (logReg). Here, we introduce a novel approach in which the selection of SNPs is based on the permutation importance estimated by random forests (RFs). For this, we used the simulated data provided for the Genetic Analysis Workshop 15 without knowledge of the true model.The data set was randomly split into a first and a second data set. In the first stage, RFs were grown to pre-select the 37 most important variables, and these were reduced to 32 variables by haplotype tagging. In the second stage, we estimated parameters using logReg.The highest effect estimates were obtained for five simulated loci. We detected smoking, gender, and the parental DR alleles as covariates. After correction for multiple testing, we identified two out of four genes simulated with a direct effect on rheumatoid arthritis risk and all covariates without any false positive.We showed that a two-staged approach with a screening of SNPs by RFs is suitable to detect candidate SNPs in genome-wide association studies for complex diseases. To identify genetic polymorphisms predisposing for a complex disease, genome-wide association studies have become more promising with the advances in technological possibilities. The use of 10 k, 100 k, 300 k or 500 k single-nucleotide polymorphisms (SNP) chips increases the chance of detecting associations between the investigated disease and its causative mutations, while at the same time posing challenges for statistical analyses. Specifically, the availability of a vast number of variables with uncertain dependency structures in comparatively small samples makes the application of classical statistical procedures difficult. A possible approach to dealing with huge numbers of SNPs is to use a two-stage approach. Here, typically, the first stage selects a small number of SNPs for further analysis, whereas the second validates the findings in an independent sample.The aim of our work is to introduce a novel two-stage approach for large-scale association analysis. Specifically, interesting SNPs are identified in the first stage based on random forests (RFs) ,2. The sThe first replicate of the genome-wide SNP data set and, as phenotype data, RA affection status, gender, lifetime smoking, age at ascertainment, as well as DR alleles from father and mother, were utilized. To mimic a case-control study, we randomly selected one affected sibling per affected pair for the cases and one unaffected sibling per control family for the controls, thus obtaining 1500 cases and 2000 unrelated controls. For the two-stage approach, we randomly split the data into two sets with 750 cases and 1000 controls each.The first stage of our approach was designed to screen for variables most likely to differentiate between cases and controls. Using the phenotype and genotype information for first of the two data sets, RFs with classification trees (CART) were grown to pre-select the most important variables .The importance of the variables was estimated as the permutation importance in a RF. To this end, the number of correct classifications of the out-of-bag (OOB) cases is calculated in every single tree grown in the forest. Then, the values of the specific variable are randomly permuted in the OOB individuals, and these are then re-classified using these new values. Finally, the number of correct classifications with the permuted values was compared with the number of correct classifications in the original data. The difference between these fractions, averaged over all trees in the RF, gives the permutation importance for the respective variable.To grow RFs and estimate permutation importance values, we used the software R  with theDíaz-Uriarte et al.  proposed1. Compute global importance score for every variable as described above.2. Sort variables according to their score.3. Grow a RF with the most important variable as single predictor.4. Compute OOB error for this RF.5. Add next important variable to the set of predictors and grow a RF.6. Repeat steps 4 and 5.On the basis of the resulting OOB prediction error estimates, we chose the smallest set of variables leading to a small prediction error (see below for more information).R2 ≥ 0.5 as criterion for SNP selection.To avoid multicollinearity of the variables in the second stage, we applied the haplotype tagging approach by Chapman et al.  using thp-values were adjusted according to the Bonferroni-Holm procedure [The aim of the second step was to obtain valid parameter estimates for the selected variables in a logReg. To reduce the amount of overfitting because of data-dependent variable selection in the first stage, we used an independent data set. Lacking a specific biological hypothesis, an additive genetic effect for each SNP was assumed as recommended , and therocedure . BecauseFigure For further analyses, the OOB prediction errors were estimated in RFs with different numbers of variables Figure . It can In the second stage, consideration of all variables in the logReg model Table  shows thTo summarize, our results show that RFs can be applied as a pre-screening tool in genome-wide association studies. Our two-staged approach with a selection of SNPs by RFs is suitable to detect promising candidate SNPs in large-scale association studies for complex diseases.The author(s) declare that they have no competing interests.


Many phenotypes of public health importance  involve complex pathways of action. Interactions between genetic variants or between genetic variants and environmental factors likely play important roles in the functioning of these pathways. Unfortunately, complex interacting systems are likely to have important interacting factors that may not readily reveal themselves to univariate analyses. Instead, detecting the role of some of these factors may require analyses that are sensitive to interaction effects.In this study, we evaluate the sensitivity and specificity of the restricted partition method (RPM) to detect signals related to coronary artery disease in the Genetic Analysis Workshop 16 Problem 3 data using the 50,000 k candidate gene single-nucleotide polymorphism set. Power and false-positive rates were evaluated using the first 100 replicate datasets. This included an exploration of the utility of using of all genotyped family members compared with selecting one member per family. Coronary artery calcification (CAC) is a quantitative trait that is a consistently found in areas of coronary artery narrowing. In the Genetic Analysis Workshop (GAW) 16 simulation, CAC was used as a surrogate for plaque build-up as a risk factor for a heart attack. Coronary event (CE), e.g., myocardial infarction, was a binary trait included in the data. Because the Framingham Heart Study sample was not ascertained as a case-control study and CEs were relatively rare in the data, we expected the data would have less power to detect factors contributing CE independently from CAC than it would to detect factors contributing directly to CAC. We note that lipids  are well known factors associated with coronary artery disease.The restricted partition method (RPM) uses multiple comparisons to evaluate whether the phenotypes associated with each (multilocus) genotype in a particular model  come from the same distribution. If the answer is "no", the method proposes a partition of the genotypes. The test statistic is the proportion of the trait variation explained by the partition. The statistic's significance is determined by permutation testing. Because the RPM is appropriate for either quantitative or binary phenotypes ,2, we chThe RPM was developed as a method for analyzing datasets consisting of unrelated subjects. Since the Framingham Heart Study data is family-based, one goal of this study was to compare the utility of naively including all subjects in an RPM analysis to that of analyzing a subset of the data consisting of only one subject per family. A second question addressed by these analyses is whether true signals could be distinguished from noise in pairwise analyses of a large set of candidate SNPs.We knew the true model before starting our analyses.The true model for CAC involved the lipids , age, and five SNPs from the 50,000 candidate gene SNP set that directly affected CAC. One of these SNPs, Het, acted independently of the others and displayed over-dominance (heterosis). SNPs PE1 and PE2 interacted with each other to affect CAC, but theoretically would not display any effects when analyzed separately. SNPs ME1 and ME2 acted primarily through an interaction, but ME2 displayed a measurable effect when analyzed alone, while ME1 did not. Perhaps unrealistically, the dependence of CAC on lipids was modeled in such a way that exercise and lipid-lowering medication could decrease CAC.The primary risk factor for CE was CAC. Thinking of CAC as a surrogate for plaque build-up, the constricting effect of smoking on arteries can be viewed as if smoking effectively increased CAC. This was how the effect of smoking was incorporated in the generating model. The model included two additional polymorphisms that modified risk: SLoc modified of risk only in smokers; EventLoc had a small direct effect on risk for all subjects.For a complete description of the simulation model including a diagram illustrating the relationships between predictors and phenotypes, see Kraja et al. .Because CAC only develops in middle age, but is affected by lipid-lowering medication, we restricted our analyses on data from the second examination of each subject in the hope of maximizing the variance in CAC due to genetic effects. Because of the computational complexity of analyzing all pairwise interactions, we used only the first 100 data replicates and the 50,000 candidate gene SNP set for our analysis.N = 1130). We will refer to these two datasets as the "full data" and the "unrelateds data," respectively. The goal of this dual analysis approach was to evaluate the benefits of increased sample size versus the potential increase of false positives when including related individuals in an analysis intended for unrelated (or very distantly related) individuals. The two datasets had similar distributions of the sexes  and smoking . Because of the ascertainment strategy, the average age in the "Unrelateds" dataset was greater than that in the full dataset (63.1 vs. 52.6) and the CE rate was higher (11.8% vs. 7.7%). If this difference has an effect, it would be expected to increase to power of the "Unrelateds" data to detect factors related to CE.Analyses were first run on the full dataset of 6479 subjects, ignoring family structure. Next, analyses were run on a subset consisting of just one member of each family, the oldest subject  from this portion of the analysis. This left 42,461 SNPs for the analysis of false positives in the "All Subjects" dataset, and 41,101 SNPs in the "Unrelateds" dataset. Univariate RPM analyses were run on all these SNPs for each of the two traits in each of the 100 replicate datasets. p-Values were estimated from 1,000,000 permutations per SNP. To save computation time, the false-positive distribution for pairwise analyses was not estimated by exhaustively evaluating all of the nearly 1 billion pairs of null SNPs in each replicate. Instead, the distribution was estimated from a random sampling of 1,000,000 null pairs chosen independently from each of the 100 replicates .To estimate the false-positive rates, we began by cleaning the data as we would for any analysis: removing all monomorphic SNPs (defined by fewer than 0.1% heterozygous subjects) and SNPs with a high proportion of missing genotypes . Because signals associated with SNPs in linkage disequilibrium (LD) with the true causative factors for CAC and CE should not be considered "false" positives, we removed the few SNPs displaying LD with any causative SNP , the increased power gained by including related subjects can be worth the loss of an accurate estimate of effect-size.In the GAW16 simulated data, based on the true Framingham Heart Study genotypes and family structure, analysis using the RPM lends support to the latter argument. In this case, including related individuals in the analysis caused only a moderate increase in false positives, but greatly increased the power to find true signals. This proved to be particularly useful in these data because the signals associated with the phenotypes were particularly modest: with 1130 unrelated individuals, many of the signals did not exceed the level of background noise; with 6479 related individuals, they did.As we continue to try to determine factors contributing to common, complex phenotypes we will likely continue to find that we are looking for factors of modest effect size. Our results suggest that for a sufficiently large gain in sample size, it may be worth violating the assumption of unrelatedness.a priori that the cheapest approach, namely testing for interactions among the top univariate signals, would almost certainly have failed to detect either of the interactions in the models for CAC and CEs. Similarly, the intermediate method of testing a top univariate result against all other predictors might have found one of the interactions, depending on how low into the univariate list one was willing to go. However, it is extremely unlikely that both of the interactions could have been found without some sort of exhaustive search through all pairs.A second point relates to search strategies for detecting interacting trait predictors. All such strategies carry considerable computational and statistical costs. Given the design of the generating model , one canFinally, we note the effect of missing data. In these analyses we included SNPs that had approximately a 90% call rate. It is now common to require call rates of at least 98% for a SNP to be included in analysis. Although this has not proved to be a problem for recent datasets we have worked with, in the Framingham Heart Study Candidate Gene data it would have eliminated nearly 25% of the SNPs. However, we also found that lowering the call rate threshold caused a rapid increase in false-positive calls. We are not certain if this is due simply to the instability of the models produced from small samples or if the data from the low call rate SNPs are truly unreliable.CAC: Coronary artery calcification; CE: Coronary event; GAW: Genetic Analysis Workshop; GWAS: Genome-wide association study; LD: Linkage disequilibrium; RPM: Restricted partition method; SNP: Single-nucleotide polymorphismThe authors declare that they have no competing interests.RC conceived the study and drafted the manuscript. ALH and BKS assisted in the design and methodology. WJ and CHJ assisted in statistics and data management. All authors read and approved the final manuscript.


The ultimate goal of genome-wide association (GWA) studies is to identify genetic variants contributing effects to complex phenotypes in order to improve our understanding of the biological architecture underlying the trait. One approach to allow us to meet this challenge is to consider more refined sub-phenotypes of disease, defined by pattern of symptoms, for example, which may be physiologically distinct, and thus may have different underlying genetic causes. The disadvantage of sub-phenotype analysis is that large disease cohorts are sub-divided into smaller case categories, thus reducing power to detect association. To address this issue, we have developed a novel test of association within a multinomial regression modeling framework, allowing for heterogeneity of genetic effects between sub-phenotypes. The modeling framework is extremely flexible, and can be generalized to any number of distinct sub-phenotypes. Simulations demonstrate the power of the multinomial regression-based analysis over existing methods when genetic effects differ between sub-phenotypes, with minimal loss of power when these effects are homogenous for the unified phenotype. Application of the multinomial regression analysis to a genome-wide association study of type 2 diabetes, with cases categorized according to body mass index, highlights previously recognized differential mechanisms underlying obese and non-obese forms of the disease, and provides evidence of a potential novel association that warrants follow-up in independent replication cohorts. Genome-wide association (GWA) studies, such as those undertaken by the Wellcome Trust Case Control Consortium (WTCCC) , have prsub-phenotypes could be defined by severity of disease, age of onset, or the site and/or pattern of symptoms, such as we see in inflammatory bowel disease, for example. By doing this, we may detect associations with variants contributing different effects to sub-phenotypes that would otherwise be overlooked by considering all cases, simultaneously, as the same phenotype. However, by focusing on specific sub-phenotypes, we reduce sample size, and thus will lose power to map loci contributing homogeneous effects to the unified phenotype.One approach to advance our understanding of the biological mechanisms underlying a phenotype under investigation is to refine the trait, somehow. These In order to address this issue, we have developed a novel test for disease association, allowing for heterogeneity in genetic effects between sub-phenotypes, within a multinomial regression framework. We demonstrate, by simulation, that the multinomial regression approach has greater power to detect disease association, in the presence of heterogeneity in allelic odds ratios between sub-phenotypes, than do existing methods formulated in a logistic regression framework. Furthermore, when genetic effects are consistent across sub-phenotypes, the loss in power of the multinomial regression analysis is minimal, despite the additional parameters required in the model.FTO (trend test P 5 5.2 × 10−8). However, analysis of BMI as a continuous trait in the aforementioned case samples demonstrated strong evidence of obesity association with precisely the same variants (trend test P = 8.0 × 10−6). In particular, high-risk alleles for T2D were also associated with increased BMI [FTO and TCF7L2 [To demonstrate the utility of our multinomial regression approach, we have re-analyzed a GWA study of T2D from the main WTCCC experiment  by categased BMI . Our muld TCF7L2 , and higK possible disjoint sub-phenotypes. We denote the phenotype of the ith individual by iy, where iy = 0 for controls, and iy = k for cases with the kth sub-phenotype. Under the assumption of a linear trend in the allelic odds ratio (i.e. multiplicative disease risks), we can model the log-odds of the kth sub-phenotype for the ith individual in a multinomial regression framework, given byConsider a case-control sample of unrelated individuals, where cases are categorized according to iG denotes the SNP genotype of the ith individual, coded as 0,1, or 2, according to the number of minor alleles they carry. Furthermore, ix denotes a vector of their covariate measurements, with corresponding regression coefficients βk. The parameter λk represents the allelic log-odds ratio for the minor allele, relative to the major allele, for the kth sub-phenotype.In this expression, ith individual is given byWithin a multinomial regression framework, the log-likelihood contribution of the i = k)I of dominance in equation (1). Furthermore, we can test for association with imputed genotype data within this framework by replacing iG in equation (1) with the expected genotype from the posterior distribution of calls [mlogit function in R [The multinomial logistic regression framework described above is extremely flexible and can be easily extended to allow for non-multiplicative disease risks, for example, by including an additional indicator of calls . The mulion in R .We have performed simulations to investigate the power of the multinomial regression framework to test for disease association and heterogeneity in allelic odds ratios between sub-phenotypes, and to compare its performance to existing logistic regression-based approaches. We considered a disease for which cases are categorized according to two sub-phenotypes, and examined a wide range of association scenarios, parameterized in terms of: (i) the minor allele frequency (MAF) of the causal SNP; and (ii) the heterozygous log-relative risk, under a multiplicative disease model, for each sub-phenotype.For each scenario, we simulated 10,000 replicates of data, each consisting of causal SNP genotype data under the assumption of Hardy–Weinberg equilibrium (HWE) for 2,000 controls, 1,000 cases of sub-phenotype 1 and 1,000 cases of sub-phenotype 2. For each replicate of data, we performed the following tests of association and heterogeneity, and recorded the P-value for each.MULTINOMIAL: test of association of the causal SNP with disease, allowing heterogeneity of allelic odds ratios between sub-phenotypes, within a multinomial regression framework .LOGISTIC: test of association of the causal SNP with disease, assuming the genetic effect to be the same for both sub-phenotypes, within a logistic regression framework .SP1 and SP2: tests of association of the causal SNP with each sub-phenotype, separately, within a logistic regression framework .HETEROGENEITY: test of heterogeneity of the effect of the causal SNP between sub-phenotypes within a multinomial regression framework .SP1vSP2: test of heterogeneity of the effect of the causal SNP between sub-phenotypes within a logistic regression framework .For each test, we estimate power by the proportion of replicates for which the P-value meets a nominal significance threshold of 5%.The T2D component of the main WTCCC experiment  consists−2) and obese (BMI >30 kg m−2). Cases passing QC filters, but with unknown BMI, were unclassified and hence excluded from the analysis. For each SNP passing QC filters, the following tests were performed:For our analysis, each T2D case was assigned to one of two obesity sub-phenotypes: non-obese ;disease association within a logistic regression framework (i.e. controls against obese and non-obese T2D cases combined);heterogeneity of effects between obesity sub-pheno-types within a multinomial regression framework.−2, leading to similar frequencies of obese (997) and non-obese (916) individuals when categorized according to the traditional obesity threshold (BMI >30). A total of 4,851 samples from the T2D component of the main WTCCC experiment  passed QP<10−5) in a multinomial regression framework, with cases categorized according to obesity. The strongest signal of association was observed for variants in TCF7L2 (lead SNP rs4506565), with more convincing evidence obtained from the multinomial regression analysis (P = 4.0 × 10−14) than the logistic regression analysis of all T2D cases, combined (P = 3.0 × 10−12). There is clear evidence of heterogeneity in allelic odds ratios between obesity categories (P = 3.0 × 10−4). Our results confirm previous findings that variants in TCF7L2 have stronger effects on non-obese T2D cases than those that are obese [FTO and BMI [P = 7.2 × 10−7 at rs7193144). As a result, there is evidence of association with T2D obtained from the multinomial regression analysis (P = 9.2 × 10−13) is considerably more convincing than that from the logistic regression analysis of all cases combined (P = 2.8 × 10−8). Using the simulation procedure described above, we have estimated the power of the multinomial and logistic regression-based analyses, respectively, at a genome-wide significance level of P<5 × 10−7, to be 99.8 and 98.0% for the lead SNP in TCF7L2, and 99.3 and 77.1% for the lead SNP in FTO.re obese . Unsurpr and BMI , there iUnlike previous studies, we have not investigated association of SNPs with BMI as a quantitative trait in cases of T2D . If we wCAND1  and variants in CCDC33 . Previous analysis of the WTCCC T2D cohort, stratified by obesity, identified a signal of association with variants in CCDC33 in obese cases only [CAND1 with T2D has not been previously described. The association is limited to obese cases, demonstrating a similar pattern of heterogeneity in allelic odds ratios to those in FTO, and warrants follow-up in replication cohorts.Amongst the other signals of association with T2D identified through application of the multinomial regression model , two regses only , the samses only , the assWe have developed a novel test of disease association with SNPs, allowing for heterogeneity in allelic odds ratios between sub-phenotypes, within a multinomial regression framework. This framework is extremely flexible, and can incorporate covariates to account for non-genetic risk factors and confounders, such as axes of genetic variation defining underlying population structure. Although we have presented results based on a multiplicative disease risk assumption within each sub-phenotype class, applied to directly observed genotypes, the multinomial regression model can easily be extended to incorporate more general disease models by incorporating dominance, and can be utilized with imputed data. Within the multinomial regression framework, we can also perform formal tests of heterogeneity in allelic odds ratios between sub-phenotypes.The results of our simulation study highlight two general conclusions. First, the multinomial regression-based analysis performs well in comparison to existing methods formulated in a logistic regression framework over a range of models incorporating heterogeneity of genetic effects between sub-phenotypes. Second, when genetic effects are consistent across sub-phenotypes, the loss in power of the multinomial regression analysis is minimal. Given the multifarious genetic architecture underlying complex traits, it is not unreasonable to believe a model of heterogeneity of effects between sub-phenotypes. It is in this setting that the advantages of the multinomial regression approach will be maximized. Our results also highlight, in the context of two sub-phenotypes, that the multinomial regression-based test of heterogeneity has equivalent power to a direct comparison of the two case groups via logistic regression. However, the advantage of the multinomial regression approach is generalization to more than two sub-phenotypes in a unified analysis. In a logistic regression context, we would need to make comparisons between each pair of sub-phenotypes, making interpretation of heterogeneity statistics more complex, and would require correction for multiple testing.TCF7L2 and FTO according to obesity sub-phenotype in the same samples [(CAND1) in obese cases only. CAND1 is a regulatory protein that interferes with the assembly of the SKP1-CUL1-F-box protein (SCF) ubiquitin ligase complex and thereby down-regulates ubiquitination of target proteins, and is involved in ubiquitin-dependent protein catabolic process. In a meta-analysis of three GWA studies of T2D [CAND1 (P = 0.12). However, the meta-analysis did not focus on obese cases of T2D, and thus might not be expected to highlight the association we have identified through multinomial regression analysis of obesity sub-phenotypes. As a result, this signal warrants further follow-up in independent replication samples from the UK or closely related populations to confirm our findings, ideally focusing on obese cases of T2D, or by making use of multinomial regression to allow for heterogeneity of effects according to BMI.We have applied the multinomial regression analysis method to a GWA study of T2D from the main WTCCC experiment , where c samples ; and (iis of T2D , there wrelated phenotypes, such as CD and ulcerative colitis, against a combined control group. The multinomial regression approach will have greater power to detect pleiotropic loci, contributing the same, or different, effects to each phenotype, than would traditional analysis of each case-control cohort separately. Furthermore, by combining control cohorts, providing that they are suitably matched, we may also increase power to detect loci that contribute effects to just one phenotype.We have presented the multinomial regression framework as a powerful approach to the analysis of sub-phenotypes. However, the utility of this method can be utilized in other genetic association contexts. For example, we could consider applying multinomial regression to comparisons of The multinomial regression model assumes no ordering in the disease sub-phenotypes. However, for sub-phenotypes defined by severity, for example, we may wish to consider case categories as ordinal. In this setting, we can make use of the same statistical techniques as described above, but assume a proportional odds model for disease risk. This framework requires fewer parameters than the multinomial regression model, and thus may offer greater power to detect association if sub-phenotypes can be appropriately ordered.It is clear that, for many complex traits, it is difficult to define one unified phenotype with the same underlying genetic risk factors, and that to do so may, in fact, be misleading. For example, cases of T2D may be affected as a result of beta cell failure and/or insulin resistance, and we might naturally expect that there are different genetic effects contributing to these two distinct pathways. With larger, and more clearly refined disease collections, our multinomial regression approach thus provides a powerful approach to detect variants contributing to the phenotype overall, whilst also highlighting those that may be specific to one category of disease. In this way, we can further our understanding of the biological mechanisms underlying disease, ultimately leading to improved, and more targeted therapies.


The association between patterns of pigmentation and deafness in the dog has a long-documented history, with reports dating back over one hundred years. Long suspected of having a genetic basis, the search for loci with a pronounced influence in the expression of hearing loss in the dog has yet to be successful. No studies in the dog to date have found a possible influence of a specific colour locus associated with deafness. The present study is intended to evaluate the heritability of deafness in the Jack Russell Terrier (JRT), characterize the mode of inheritance, and evaluate the existence of a sex, coat colour, or coat texture influence on the expression of sensorineural deafness.The estimation of heritability of deafness in the JRT was 0.22 when deafness was considered a binary  trait and 0.31 when deafness was considered a three-category . The influence of coat colour in the incidence of JRT deafness was statistically significant, indicating that dogs with more white are more likely to be deaf. The influence of sex or coat texture was not statistically significant in the incidence of JRT deafness. Complex segregation analysis revealed a model of a single locus with a large effect on the binary measure of hearing loss is not supported.This is the first attempt, to our knowledge, to characterize a genetic component responsible for deafness in the JRT. The heritability of deafness in the JRT was found to be 0.22 and 0.31 considering deafness to be a two-category or three-category trait, respectively. There appears to be an influence of coat colour on the expression of deafness. In an attempt to characterize the mode of inheritance of deafness in the JRT, a model of a single locus with a large effect on hearing loss is not supported with this data. Further study is needed to determine if a single locus may be influencing deafness in the JRT. While the absence of a clear mode of inheritance complicates genetic dissection of deafness in the JRT, the assembling of this pedigree provides a tool for eventually defining the genetic bases of this disorder. The association between patterns of pigmentation and deafness in the dog has a long-documented history, with reports dating back over one hundred years. Long suspected of having a genetic basis, the search for loci with a pronounced influence in the expression of hearing loss in the dog has yet to be successful. One study  has disci.e., black or liver in the Dalmatian) associated with deafness ; γ1 is set to zero for computational convenience, with no loss in generality or impact on subsequent analysis. Accordingly, the combination of continuous genetic and environmental terms thought to control the unobservable θ are translated into a categorical observation through comparison to the fixed thresholds .We choose to estimate heritability through the use of threshold models , an appr0 = -∞; γ1 = 0; γ2; γ3 = ∞], where γ2 must be estimated from the data. Furthermore, normal hearing dogs would be observed when γ0 ≤ θ < γ1, unilaterally deaf dogs would be observed when γ1 ≤ θ < γ2, and bilaterally deaf dogs would be observed when γ2 ≤ θ < γ3.We also consider deafness as a trichotomous trait, in which normal hearing dogs are scored as a zero, unilaterally deaf dogs scored as a one, and bilaterally deaf dogs are scored as a two. Such a characterization of the auditory phenotype requires only minor modification of the threshold model. Specifically we add a fourth fixed threshold /25 = 10,000). Highest density regions (HDR) were computed as described . This extension of model [e1] requires estimation of two genetic variances, one for deafness and the second for coat colour, a genetic covariance between these two categorical phenotypes and a residual covariance between the two phenotypes. As described above for the univariate deafness model, unknown parameters were estimated from a Gibbs sample of 10,000 values.where θThe possibility that deafness in JRTs is influenced by the action of a segregating locus of large effect can also be examined. This technique, called complex segregation analysis , is inteAn outline of the criteria that must be satisfied before acceptance of the single major locus model has been provided . Adheren"q"). Given our scoring of binary phenotypes, where deaf  is 1 and normal is scored as zero, the "B" allele represents the putative disease-enhancing allele. Note also that the iBay software models the unobservable scale of this threshold trait such that the residual variance is fixed at 1.0 .The goal of this strategy was to simultaneously estimate the posterior density for a polygenic contribution to binary deafness disease along with the contributions of a putative Mendelian locus. Specifically, for this mixed-inheritance model, the strategy allowed the evaluation of a polygenic variance component, the additive and dominance contributions of a single locus  and the frequency of allele A of the putative major locus  prior densities, the polygenic variance component with a flat prior density, as well as flat prior densities for the additive, dominance, and allele frequency parameters. A Gibbs sample of 9,000 was generated, beginning with the creation of 350,000 total samples, a "burn-in" of 50,000 and a sampling rate of every 100-th Gibbs value. This process was repeated two additional times, to create three replicate chains. As outlined above, the post-Gibbs analysis was implemented with the packages boa  and codaTRF participated in design of the study, performed estimation of heritability and complex segregation analysis, and provided review of the manuscript. EJC participated in design of the study, analyzed the phenotypic data, and drafted the manuscript. GMS conceived of the study, participated in design of the study, collected the phenotypic data, and provided review of the manuscript. All authors read and approved the final manuscript.


P<5×10−8) in primary and secondary analysis, ten (PCCB/STAG1 (3q22.3), GMPR/MYLIP (6p22.3), BTNL2 (6p21.32), KLF14 (7q32.2), 8p23.1, JMJD1C (10q21.3), SBF2 (11p15.4), 12q23.2, CCDC92/DNAH10/ZNF664 (12q24.31.B), and WIPI1 (17q24.2)) have not been reported in prior genome-wide association studies for plasma lipid concentration. Associations with mean lipoprotein particle size but not cholesterol content were found for LDL at four loci , 12q24.31.B, and LIPG (18q21.1)) and for HDL at one locus (GCKR (2p23.3)). In addition, genetic determinants of total IDL and total VLDL concentration were found at many loci, most strongly at LIPC (15q22.1) and APOC-APOE complex (19q13.32), respectively. Associations at seven more loci previously known for effects on conventional plasma lipid measures reveal additional genetic influences on lipoprotein profiles and bring the total number of loci to 43. Thus, genome-wide associations identified novel loci involved with lipoprotein metabolism—including loci that affect the NMR-based measures of concentration or size of LDL, HDL, and VLDL particles—all characteristics of lipoprotein profiles that may impact disease risk but are not available by conventional assay.While conventional LDL-C, HDL-C, and triglyceride measurements reflect aggregate properties of plasma lipoprotein fractions, NMR-based measurements more accurately reflect lipoprotein particle concentrations according to class  and particle size . The concentrations of these lipoprotein sub-fractions may be related to risk of cardiovascular disease and related metabolic disorders. We performed a genome-wide association study of 17 lipoprotein measures determined by NMR together with LDL-C, HDL-C, triglycerides, ApoA1, and ApoB in 17,296 women from the Women's Genome Health Study (WGHS). Among 36 loci with genome-wide significance ( Genome-wide association studies (GWAS) of plasma lipoprotein fractions hold great promise for understanding lipid metabolism and its central role in cardiovascular disease and related disorders. Conventional assays for lipoprotein status determine total cholesterol content of low- or high-density lipoprotein particles  or total plasma triglyceride content (as an estimate of very-low density lipoprotein particle concentration [VLDL]). All three measures have been targets for recent GWAS. However, a more precise target for GWAS of lipoprotein metabolism would be the concentration of the individual lipoprotein particles according to class  and size , all of which can be measured by NMR-based methods. In a population of 17,296 women of European ancestry from the Women's Genome Health Study, we have performed a GWAS for 22 lipoprotein measures derived from NMR-based and conventional assays. We find 43 genetic loci involved in lipoprotein metabolism, including 10 novel loci. The results offer a clearer picture of common genetic influences on lipoprotein metabolism than available previously, including genetic effects on the distribution of LDL, HDL, and VLDL particle size, as well as on IDL and VLDL particle concentration, neither of which can be assessed by conventional measures. Standard measures of plasma lipoprotein concentration do not reveal heterogeneity in the size of lipoprotein particles or their content of cholesterol and triglycerides. Yet recognizing this heterogeneity may be essential for understanding qualitative differences in lipid metabolism among individuals. Some reports identify a pattern in the size distribution of lipoprotein sub-fractions as intimately connected with coronary heart disease The variation in particle size and lipid content can be quantified accurately by NMR-based methods that determine lipoprotein particle concentration according to lipid class and particle size. Thus, NMR methods can measure concentration of large and small low density lipoprotein (LDL) particles as well as concentration of the related intermediate density lipoprotein (IDL) particles, and similarly concentration of small, medium, and large high density lipoprotein (HDL) or very low density lipoprotein (VLDL) particles. HDL and LDL particle concentration can also be estimated by chemical measures of apolipoprotein A1 (ApoA1) and apolipoprotein B (ApoB) protein concentration, respectively, but neither these assays nor other standard clinical assays provide information about particle size distribution, and consequently the apportionment of cholesterol and triglycerides to different sized particles. The greater precision in characterizing lipoprotein profiles using NMR-based techniques provides an opportunity for correspondingly greater detail in understanding lipid metabolism, for example by genome-wide genetic analysis, as has been done recently for plasma concentration LDL-C, HDL-C, triglycerides, ApoA1, and ApoB P<5×10−8), genetic variation at total of 31 loci was associated with at least one of the lipoprotein fractions (ABCA1 (9q31.1), a locus that was identified in the whole sample on the basis of genome-wide significant associations with HDL-C and medium HDL particles but not for ApoA1. The other was an association with mean VLDL size at 8p23.1, a locus that appears only in analysis in the fasting sub-sample (P<1.6×10−5) even though they do not reach genome-wide significance. Statistics for the most significant genome-wide associations with P<5×10−8 at each of the candidate loci are shown in the Among 17,296 WGHS participants with confirmed European ancestry , we perfractions . Thirty ractions . Nearly b-sample . These aPCCB/STAG1), 6p21.32 (BTNL2), 7q32.2 (KLF14), 12q24.31.B (CCDC9/DNAH10/ZNF664) and 17q24.2 (WIPI1) are all near genes (KLF14 (7q32.2) and CCDC9/DNAH10/ZNF664 (12q24.31.B), both for triglycerides. The association at the novel locus 8p23.1 (which differentiated the fasting sample from the whole sample on the basis of mean VLDL particle size) is over 1.8 Mb from a recently described association at 8p23.1 between SNP rs7819412 and triglycerides Seven of the 31 unique loci reveal novel genome-wide significant associations with the plasma lipoprotein fractions , APOA2 (1q23.3), APOB (2p24.1), ABCG5/8 (2p21), HMGCR (5q13.3), LPL (8p21.3), APOA1-A5 (11q23.3), ABCA1 (9q31.1), FADS1-3 (11q12.2), LIPC (15q22.1), CETP (16q13), LIPG (18q21.1), LDLR (19p13.2), the APOC-APOE complex (19q13.32), and PLTP (20q13.12). Similarly, association at 9q34.2 implicating the ABO gene recapitulates and extends the known association between blood group antigen and total cholesterol ANGPTL3 (1p31.3), CELSR2/MYBPHL/PSRC1/SORT1 (1p13.3), GCKR (2p23.3), MLXIPL (7q11.23), and TRIB1 (8q24.13), HNF1A (12q24.31.A), and HNF4A (20q13.12). The association at COBLL1/GRB14 (2q24.3) with HDL-C was recently described elsewhere in this same cohort and validated by replication GRB14 is thought to inhibit receptors in the insulin receptor class The remaining 24 unique loci suggested genes recognized for a diversity of roles in lipid metabolism, broadly defined . Thus, SAPOB gene (2p24.1), where the ordering of the p-values, conditional analysis, and patterns of linkage disequlibrium (LD) among the top SNPs (2 = 1.0) had the strongest association; a second class included ApoB, large LDL particles, and total LDL particles for which either rs1713222 or rs506585 (LD r2 = 0.5) had the strongest association; and a final class including only LDL-C for which rs137117 was most strongly associated , p-values revealed two classes of associations seemingly segregating between effects nearer the APOA5 gene involving triglycerides and effects nearer the APOA1 gene involving HDL related lipoprotein fractions , at least one of the candidate associations was nominally significant  in at least one of the replication cohorts or in analysis combining p-values from the two replication cohorts when effect estimates (beta coefficients) indicated trends in lipoprotein measure consistent with the effects observed in the WGHS. Among the 7 novel loci from the primary analysis only, where the effect estimates for the WGHS were generally smaller and power for replication was less, concordance of the direction of effects remained high for the PROCARDIS sample [86% (25/29)], although only modest for the FHS sample [58% (22/38)], but these associations were not significant , BTNL2 (6p21.32), KLF14 (7q32.2), and 8p23.1 PCCB/STAG1 (3q22.3) and BTNL2 (6p21.32) were not fully concordant between the two studies (P<5×10−15). Finally, the associations at CCDC92/DNAH10/ZNF664 [12q24.31.B] and WIPI1 (17q24.2) were not confirmed either in the meta-analysis shown in Large, well-characterized cohorts with NMR-based measurement of lipoprotein fractions are scant, but sub-samples of about 2700 participants in the Framingham Heart Study Offspring cohort (FHS)  studies . IndepenAPOC-APOE complex (19q13.32), explain 8.9%, 8.4%, and 7.1% of the variance in ApoB particle concentration, the related total LDL particle concentration, and LDL-C, respectively. Fasting status had an influence on retention of SNPs in the model selection procedure, but only for loci with modest effects (Compare APOA2 (1q23.3) in the whole sample and at WIPI1 (17q24.2) in the fasting subsample, suggesting that these loci would not have been identified for genome-wide association with the five conventional lipoprotein fractions even in a much larger sample with the genome-wide SNP genotyping panel used in this study. Clustering loci on the basis of the profile of associated lipoprotein fractions suggests sub-groups of loci with related patterns of effects  for SNPs retained by the model selection procedure at the candidate loci, and repeated the genome-wide association testing. Quantile-quantile analysis confirmed that all of the excess of extremely small p-values in the original analysis could be explained by the variation at the candidate loci (not shown). Similarly, genotype-based statistical models  did not reveal other loci with genetic influences at the genome-wide significance level in the whole sample.LPA (6q25.3), LCAT (16q22.1), and APOH (17q24.2), and two additional loci, 6p22.3 and 10q21.3. All of the additional loci were present in the age-adjusted analysis. Associations at 6p22.3 and 10q21.3 appear to be novel and implicate, respectively the GMPR or MYLIP genes and the JMJD1C gene. The lead SNPs at each of these loci were significantly associated with at least one of LDL-C, HDL-C or triglycerides in the recently published meta-analysis (JMJD1C (10q21.3), the candidate SNPs have minor allele frequency near 0.5, and that available data does not allow us to determine whether the differences in the direction of the minor allele effect on VLDL fractions in the WGHS and triglycerides in the previously published replication study are truly physiological or rather that the frequency of the coded (i.e. minor) allele from the WGHS is greater than 0.5 in the replication cohort resulting in an opposite sign of the effect estimates.While we adjusted the lipoprotein measures with a full set of clinical characteristics to reduce variance and enhance power in the primary analysis, it remained possible that relevant SNPs would be overlooked if they acted through effects on the adjustment covariates. Similarly, subtle effects on the association estimates due to non-normality of the (possibly log-transformed) adjusted lipoprotein measures or due sub-European population stratification might confound hypothesis testing. To evaluate whether our discovery procedure was robust, we performed secondary analyses repeating the entire genome-wide discovery procedure for alternative nested subsets of clinical covariates with and without further adjustment for population structure and quantile normalization . Comparianalysis  [10]. Sianalysis . We noteSBF2 gene was associated with full-plus-triglyceride adjusted total HDL particle concentration. Again, internal replication provided support for this association although there was no association (P>0.05) with LDL-C, HDL-C, or triglycerides in the recent meta-analysis for replication.Since lipoprotein particle size is closely related to triglyceride content, we also performed secondary analysis examining genome-wide significant associations after adjustment of the lipoprotein fractions by the full set of clinical covariates and (log-transformed) triglyceride levels . This anLIPC (15q22.1), where rs1532085 had an estimated 0.11 nmol/l shift in particle concentration for each copy of the minor allele (p = 1.5×10−20). For total VLDL concentration, association with genetic variation was observed at many loci but none more strongly than at the APOC-APOE complex where rs439401, which is in perfect LD with rs7412 , had an estimated −2.4nmol/l shift in concentration per copy of the minor allele , LPL (8p21.3), CCDC92/DNAH10/ZNF664 (12q24.31.B), and LIPG (18q21.1). These loci implicate genes related to glucose or triglyceride metabolism as well as unrecognized biological function at one novel locus (CCDC92/DNAH10/ZNF664 [12q24.31.B]). The associations with mean LDL particle size were a consequence of strong inverse effects on large and small LDL particles  or of exclusive effects on small LDL (CCDC92/DNAH10/ZNF664 [12q24.31.B])  and PPP1R3B [8p23.1]) could not have been found at the genome-wide significance standard solely with conventional measures  of lipoprotein profile in the WGHS. Replication in independent cohorts of men and women as well as other observations provided confirmatory evidence for candidate variation at all novel, although only through internal replication at SBF2 (11p15.4), CCDC92/DNAH10/ZNF664 (12q24.31.B), and WIPI1 (17q24.2). The failure of external replication to validate these two novel loci may simply reflect intrinsic differences from the WGHS in NMR-based assay protocols (FHS) or clinical features of the cohort (e.g. lipid lowering treatment in PROCARDIS) as well as limiting power; alternatively, the associations observed in the WGHS may not reflect true genetic effects. Among the primary loci, total genetic effects were largest and appreciable for ApoB, total LDL, and others. They were the smallest for mean VLDL size. While the heritability for the NMR-based fractions has not been thoroughly explored, the present analysis suggests some aspects of lipoprotein profiles may be much less affected by common genetic variation than others. Combining the 31 loci in the primary analysis, the five loci in the secondary analysis (three novel loci plus APOH and LCAT), and the seven previously recognized loci for which the WGHS extends associations to the NMR-based lipoprotein measures brings the total to 43 loci characterized by the present study.By performing genome-wide association analysis among 17,296 Women with European ancestry for 22 NMR-based and conventional lipoprotein fractions, we identified 36 loci in the primary and secondary analyses for roles in lipoprotein metabolism, broadly defined. Ten of these loci have not been reported in other recent genome-wide association studies, including one identified only after adjustment for triglyceride levels. The functional bases for the associations are uncertain for five, including associations at 8p32.1 and 12q23.2 that map to intergenic regions. In spite of the high degree of correlation among some of the NMR-based and conventional measures, two of the novel loci  analysis. For p-values from all of the lipoprotein measures considered at once, the conventional standard requiring FDR<0.05 implied a P<2×10−5, more than two order of magnitude less significant than the genome-wide p-value threshold. Similarly, among the individual lipoprotein measures, FDR<0.05 implied at worst P<7×10−7 for the case of IDL, still less significant than our genome-wide standard by over an order of magnitude. Thus, on a post-hoc basis, applying the conventional genome-wide standard P<5×10−8 for all fractions appears to have been justified.The procedures in the primary analysis enforced a genome-wide significance standard of mple see  but doesmple see , but theBTNL2 (6p21.32) has been associated with Grave's disease, multiple sclerosis, and sarcoidosis, apparently independent of the neighboring HLA class DR genes B3GALT4 gene encoding a galactosyltransferase STAG1/PCCB (3q22.3), the genome-wide significant association with small HDL particle concentration is in the STAG1 gene, but a more likely candidate for lipid metabolism may be the adjacent PCCB gene encoding the propionyl coenzyme A carboxylase beta subunit, in which substitutions cause Mendelian forms of proprionic acidemia  have functional links to lipoprotein metabolism or disease status, even if strict biochemical roles of the candidate genes and protein are not yet known. Variation at P = 4.5×10−15). Previous reports, including our own, had also identified associations at GCKR, APOC-APOE complex, and HNF1A with both lipid fractions and CRP HNF4A to this list since rs4810479 at 20q13.12.A is associated in the WGHS with both CRP and the lipoprotein fractions  in a subset of the current population ractions . These lThe etiology of cardiovascular disease is complex, and is believed to include an interplay between cell-based processes, including inflammation, and blood components, including lipoprotein fractions. The latter aspect may be summarized by clinical measures of cholesterol or triglycerides, or by ApoA1 and ApoB concentration. However, none of these aggregate measures reflects the full diversity of lipoprotein species in blood. The current investigation not only identifies novel loci for lipid metabolism in general, but may also help delineate the impact of lipoprotein metabolic genes on lipoprotein profile viewed with the highest resolution currently available.All analyses were performed with approval of local institutional review boards (IRBs).All samples in the discovery analysis derive from the Women's Genome Health Study (WGHS), a prospective cohort of North American women with phenotypes related to cardiovascular disease, extensive clinical and demographic data, blood samples at baseline, and ongoing genome-wide genotyping 100 levels were all measured by direct assay and had low coefficients of variation In the WGHS, lipoprotein determinations were performed on baseline plasma samples that had been stored in liquid nitrogen (−170°C) since collection. LDL-C, HDL-C, triglycerides, ApoA1, and ApoBP = 10−6 in significance. A total of 335,603 unique SNPs, of which 32,521 derive from the custom content, remained in the final data. Although assays for two non-synonymous SNPs at the APOE locus (19q13.32), rs429358 and rs7412, which determine ApoE isotype, failed in the design of the Illumina custom content, genotypes for these two SNPs were determined separately by an allele-specific, PCR based method  APOE were included during the model selection procedures but not during the primary analysis to discover loci with genome-wide significant associations.Genotyping in the WGHS sample was performed using the HumanHap300 Duo “+” chips or the combination of the HumanHuman300 Duo and iSelect chips  with the Infinium II protocol. In either case, the custom SNP content was the same; these custom SNPs were chosen without regard to minor allele frequency (MAF) to saturate candidate genes for cardiovascular disease as well as to increase coverage of SNPs with known or suspected biological function, e.g. disease association, non-synonymous changes, substitutions at splice sites, etc. For quality control, all samples were required to have successful genotyping using the BeadStudio v. 3.3 software  for at least 98% of the SNPs. In the final dataset, SNPs were retained with MAF >1%, successful genotyping in 90% of the subjects, and deviations from Hardy-Weinberg equilibrium not exceeding P<5×10−8 was assumed for genome-wide significance Primary analysis to discover loci with highly significant associations in the WGHS discovery cohort was performed by linear regression in PLINK P<5×10−8) was already smaller than required by correction for the number of SNPs tested by a factor of three, and justified including testing the fasting subset in the primary analysis.The primary analysis also included association testing in a nested subset of 72% of the study participants who reported fasting for at least eight hours before providing the baseline blood sample. Analysis in this subset was expected to differ from the analysis in the whole sample by opposing trends: a loss of power due to reduced sample size was contrasted with possibly smaller variance among lipoprotein fractions that are influenced by prandial status, e.g. triglycerides. Because the majority of the sample was fasting, the association statistics in the two samples were expected to be highly correlated, and the statistical penalty for this additional testing in the Bonferroni framework was expected to be less than a factor of two. Our genome-wide significance threshold  from among all genotyped locus SNPs within 100 kb of the locus genome-wide SNP associations. Separately, these model selection procedures were performed also at each of the candidate loci with the unadjusted, but possibly log-transformed, lipoprotein fractions to estimate the proportion of variance explained without adjustment.2<0.2 and followed by quantile normalization of the residuals. Second, we adjusted with all of the clinical covariates except BMI, either with or without inclusion of the eigenvectors and subsequent quantile normalization. Finally, we adjusted only for baseline age, again either with or without inclusion of the eigenvectors and subsequent quantile normalization. In an additional secondary analysis, the genome-wide association procedures were performed with lipoprotein fractions transformed and fully adjusted as for the primary analysis, including also log transformed triglyceride levels among the adjustment variables (see text).To assess the degree to which the adjustment procedure or sub-European population stratification might influence the identification of genome-wide loci, we performed a secondary analysis to evaluate the sensitivity of the locus discovery procedure to the adjustments applied to lipoprotein fractions before association testing. First, we adjusted for all of the clinical covariates as well as ten eigenvectors corresponding to a principal component analysis of genotype frequency in EIGENSTRAT Additional analytic procedures, including the hierarchical clustering of loci according to effects on lipoprotein fractions, as well as the graphical representations were programmed in R http://www.sph.umich.edu/csg/abecasis/mach/) from raw genotypes collected with the Affymetrix  500K array, and the regression models assumed a linear relationship between the dosage of the minor allele (ranging from 0 to 2) and the lipoprotein measures In the Framingham Heart Study (FHS) sample, residual lipoprotein fractions were created by adjusting for gender, age at exam lipoprotein fraction collection (continuous), age-squared (continuous), and the top ten principal components from EIGENSTRAT Figure S1Locus p-values for lipoprotein fractions with at least one SNP reaching genomewide significance at each of the candidate loci. All plots correspond to analysis in the whole sample except for locus 8p23.1, for which genomewide association was observed only in the fasting subsample as shown.(0.41 MB PDF)Click here for additional data file.Figure S2Primary loci clustered hierarchically according to Cartesian distance corresponding to whether ( = 1) or not ( = 0) there were associations with each of the lipoprotein fractions in the model selection procedures see .(0.02 MB PDF)Click here for additional data file.Figure S3Dendorgram showing bierarchical relationships between loci clustered as in (0.01 MB PDF)Click here for additional data file.Figure S4Normalized SNP effects (beta coefficients) from univariate regression models. All plots correspond to analysis in the whole sample except for locus 8p23.1, for which genome-wide association was detected only in the fasting subsample as shown. Locus SNPs are shown if they were retained in the model selection procedure for at least one lipoprotein fraction. Absence of shading indicates the univariate beta coefficient was not significant (p>0.05). A small black dot for some combinations of SNPs and lipoprotein fractions indicates genomewide significance for the univariate beta coefficient.(0.10 MB PDF)Click here for additional data file.Table S1Best genome-wide associations with the lipoprotein fractions at each candidate locus.(1.10 MB DOC)Click here for additional data file.Table S2Correlations between all pairs of lipoprotein fractions.(0.12 MB DOC)Click here for additional data file.Table S3Replication of WGHS candidate associations from whole sample in PROCARDIS and the Framingham Heart Study.(0.56 MB DOC)Click here for additional data file.Table S4Replication of WGHS candidate associations from fasting sub-sample in PROCARDIS and the Framingham Heart Study.(0.45 MB DOC)Click here for additional data file.Table S5Proportion of variance in fully adjusted lipoprotein fractions explained in the whole sample by genetic variation at the candidate loci.(0.15 MB DOC)Click here for additional data file.Table S6Proportion of variance in fully adjusted lipoprotein fractions explained in the fasting sub-sample by genetic variation at the candidate loci.(0.15 MB DOC)Click here for additional data file.Table S7Total proportion of variance explained by candidate loci for each of the unadjusted lipoprotein fractions.(0.04 MB DOC)Click here for additional data file.Table S8Sensitivity analysis for locus discovery procedure.(0.10 MB DOC)Click here for additional data file.Table S9Lipoprotein associations in the whole sample at loci in previous lipid fraction GWAS.(0.34 MB DOC)Click here for additional data file.Table S10Lipoprotein associations in the fasting sub-sample at loci in previous lipid fraction GWAS.(0.16 MB DOC)Click here for additional data file.