Multifactor dimensionality reduction (MDR) is a powerful method for analysis of gene-gene interactions and has been successfully applied to many genetic studies of complex diseases. However, the main application of MDR has been limited to binary traits, while traits having ordinal features are commonly observed in many genetic studies .We propose ordinal MDR (OMDR) to facilitate gene-gene interaction analysis for ordinal traits. As an alternative to balanced accuracy, the use of tau-b, a common ordinal association measure, was suggested to evaluate interactions. Also, we generalized cross-validation consistency (GCVC) to identify multiple best interactions. GCVC can be practically useful for analyzing complex traits, especially in large-scale genetic studies.In simulations, OMDR showed fairly good performance in terms of power, predictability and selection stability and outperformed MDR. For demonstration, we used a real data of body mass index (BMI) and scanned 1~4-way interactions of obesity ordinal and binary traits of BMI via OMDR and MDR, respectively. In real data analysis, more interactions were identified for ordinal trait than binary traits. On average, the commonly identified interactions showed higher predictability for ordinal trait than binary traits. The proposed OMDR and GCVC were implemented in a C/C++ program, executables of which are freely available for Linux, Windows and MacOS upon request for non-commercial research institutions. Because most complex biological phenotypes are often affected by multiple genes and environmental factors, the investigation of gene-gene and gene-environment interactions can be essential in understanding the genetic architecture of complex traits . It has Many different methods have been proposed to analyze gene-gene interactions in genetic association studies ,5, and chttp://epistasis.org). In addition, because the mode of genetic inheritance of a common complex trait is usually unknown a priori, MDR can be more useful to study a complex trait in that it does not require any assumption on genetic model. Since the MDR method was first introduced, it has been extended in many directions. Examples include family data [While each method has its own advantages and disadvantages, the multifactor dimensionality reduction (MDR) method, a data-reduction approach, is known to have the advantages in examining high-order interactions and detecting interactions without main effects ,18-20, aily data , covariaily data , the quaily data , and theily data . HoweverIn the MDR analysis for binary traits, multi-locus genotype combinations of a set of genetic variables/markers  are induced to two levels  of a new binary variable, called an MDR classifier. The induction is conducted via assessing odds of two phenotypic classes for each genotype combination. Among MDR classifiers representing specific marker sets, the single best MDR classifier is selected by evaluating their classification performances, such as cross-validation consistency (CVC). As a result, the corresponding set of genetic markers is identified as having the strongest association with a trait of interest.While MDR was introduced for binary traits, there is no existing approach that is applicable to ordinal categorical traits. In many genetic association studies, examples of traits having ordinal features are commonly available, such as the obesity classification based on body mass index , the diabetes diagnosis based on glucose level  and the severity classification of metabolic syndrome. The current application of MDR to these ordinal traits requires to dichotomization of traits by combining several categories, which results in the loss of ordinal information and powers.In this study, we propose an ordinal MDR (OMDR) approach that enables one to analyze a joint effect of multiple genetic variables on an ordinal categorical trait. The proposed OMDR generates a classifier for each set of genetic markers in the form of a categorical variable with ordinal levels. The performance of each OMDR classifier is evaluated to select the best OMDR classifiers. For performance evaluation, we suggest the use of common ordinal association measures, such as tau-b , which tK) of the best classifiers are selected via this GCVC.In addition, we propose a way to report multiple candidates of gene-gene interactions in OMDR as well as MDR analyses. The original MDR approach reports only a single best candidate. This feature can be impractical and/or unreasonable when causal gene-gene interactions are searched for complex traits, especially in a genome-wide scale. Because genome-wide association studies with up to ~1 million SNPs became common, there is a growing need for more efficient criterion to report multiple candidates of gene-gene interactions in the MDR analysis. Thus, we propose a new evaluation measure, generalized cross-validation consistency (GCVC), according to which one can report multiple best gene-gene interactions associated with the ordinal trait. Specifically, a pre-specified number  of Age-Related Eye Disease Study data .L  subsets for L-fold cross-validation (CV). For example, L = 10 hereafter. Out of 10 subsets, one subset is taken as an independent testing dataset, and the remaining nine subsets are assigned to a training dataset. As a result, a total of 10 CV datasets are generated. Second, all possible OMDR classifiers are constructed for the corresponding combinations of m SNPs, and the K best ones are selected based on classification performance on a training data for each CV set (see the following two sections for details). Third, the best OMDR classifiers are chosen over all CV sets for the fixed m. The predictability of the selected OMDR classifiers is evaluated via the average value of the evaluation measure with a testing dataset over all the 10 CVs. In addition, the selection strength of a particular OMDR classifier is suggested via GCVCK which is the number of times the classifier is identified as one of the K best classifiers across all the CVs. The best OMDR classifiers across the CVs are chosen if having the maximum predictability and maximum GCVCK. Finally, the overall best OMDR classifiers are selected based on the predictability and GCVCK among the best ones for various values of m, which result from the previous steps. For additional details, refer to the original MDR procedure described in literature [The OMDR procedure is same as the MDR procedure for binary traits, and consists of multiple steps. First, the dataset is partitioned into terature ,27,28.J be classes for an ordinal phenotype of interest. For example, 'low blood pressure (BP)', 'normal' and 'high BP' classes can be viewed as classes 1, 2 and 3, respectively, in the analysis of the BP classification trait. Note that J = 2 for a binary trait .Let 1, 2,..., m-way interaction is under consideration. For the corresponding m SNPs, let ij nbe the number of individuals with the ith multi-locus genotype and let nj +be the total number of individuals in phenotypic class j, where i = {1, 2,...,3m} and j = 1, 2,..., J. As in MDR, the estimated OR of the class j against the class 1 is defined for the ith genotype asSuppose that an ith multi-locus genotype into the class c(i) as follows:Then the OMDR classifier corresponding to the m given SNPs will assign all individuals with the J×J confusion matrix. The th cell of the confusion matrix is denoted as jk xand indicates the number of individuals in class j, who are classified as class k:The final classification results of the OMDR classifier can be described in a J = 3. Because each of all possible multi-locus genotypes of m given SNPs is represented in a cell of an m-dimensional contingency table, the construction of the corresponding OMDR classifier allows one to reduce the m-dimensional space to one dimensional space. Each constructed OMDR classifier is evaluated by an ordinal association measure, such as tau-b, which assesses concordance between true classes and predicted classes [For example, see Table  classes .K selection (GCVCK). After constructing all possible MDR classifiers, each classifier is evaluated respectively with training and testing datasets via a certain evaluation measure of predictability . Then, a pre-specified number (K) of the best classifiers having the largest values of the evaluation measure with the training set are selected as top-K classifiers for each CV dataset.In order to report multiple causal SNP combinations, we propose the generalized CVC based on top-K is defined as below and calculated for each MDR classifier:Next, the selection results are summarized across all CV datasets in order to suggest multiple best classifiers. The proposed GCVCK indicates how many of the training-test sets support the classifier as the K best classifiers in L-fold CV. When K = 1, GCVC1 is equal to the original CVC. Note that the proposed GCVC is applicable to both MDR and OMDR.The GCVCK, multiple candidates of causal gene-gene interactions with the same order can be reported along with their performance measures . A criterion can be chosen appropriately according to the analysis purpose. We demonstrate possible choices in practice with the following three examples. First, all combinations with GCVCK  > 0 are reported to search all possible candidates . In other words, every combination that was selected as the K best classifiers at least once during CV will be reported. Second, one can report all combinations with GCVCK ≥ 9 in 10-fold CV, intending to identify candidates with high selection consistency . This criterion means that these combinations are likely selected with at least 90% chance. Third, 100 plausible candidates are listed up for further studies by reporting top 100 combinations that have the largest values of GCVCK.Via a certain criterion based on GCVCj = 1 for normal, j = 2 for low risk, j = 3 for high risk). Proportion of each class in the population  'prevalence' of jth class) was set as p1 = 0.3, p2 = 0.4 and p3 = 0.3. A total of 50 SNPs were considered. Among all the SNPs, one pair of SNPs were simulated as a causal factor that has a two-way interaction associated with the ordinal trait; and the remaining SNPs were simulated as non-causal factors. For generating the genotype data of the causal SNPs, five different interaction patterns were developed for the ordinal trait  'penetrance' of jth class for ith genotype) were computed under the Hardy-Weinberg equilibrium assumption for each SNP. As a result, 15 different genetic models were developed  and testing tau-b (TSTB) values across 100 replicated datasets. Average GCVC was used to assess selection stability. First, we observed fairly good empirical power across various genetic models Table . EspeciaWe compared the performance between the OMDR method and the original MDR method. Overall, the OMDR showed better performance than the MDR across all performance measures Figure . EspeciaK on the OMDR was examined with different K = 1, 2 and 3. Because we simulated with a single causal two-way interaction, selected classifiers must include false positives when K = 2 or 3 were chosen for top-K selection. In most genetic models, the causal interaction was identified as the best classifiers . Thus the second best or the third best classifiers were falsely identified . We compared the selection stability and predictability between true and false positives. While true positives were selected with high stability (average GCVC = 92.0~94.7%), false positives were selected with very low stability (average GCVC = 3.4~43.5%). These limited results imply that one can avoid false positives, which the OMDR produces with large K, by further screening out the selected classifiers with low GCVC. Thus incorrect choices of K would not fail the OMDR although further investigation on the choice of K is required. Note that predictability was higher for true positives (average TSTB = 0.285~0.288) that for false positives (average TSTB = 0.106~0.133).The effect of -3. As a result, a total of 87,260 SNPs remained for the analysis.In order to demonstrate the proposed OMDR, we applied it to a body-mass index (BMI) category phenotype from the National Eye Institute Age-Related Eye Disease Study (AREDS). While the AREDS was originally designed to investigate the clinical course of age-related macular degeneration (AMD), the data contains other information on medical history, clinical status, life condition, and physical measurements, including BMI. A total of 313 subjects with and 149 without AMD were genotyped on Affymetrix 100K genotyping platform. The detailed information on this data is available in Maller et al. . Prior tAccording to the international BMI classification , an adulK = 300 to select multiple best MDR classifiers for each of 1~4-way interactions. The 10-fold CV and tau-b were employed to assess the performance of classifiers. All 87,260 SNPs were first searched for one-way effects on obesity. Then, to reduce the computational burden, we examined all pairwise combinations of the top-300 SNPs with main effects. Similarly, three- and four-way combinations were searched only for the SNPs that were selected with top-300 two- and three-way interactions, respectively.For the ordinal phenotype (OD) and two binary phenotypes (B1 and B2), the proposed OMDR and the current MDR were respectively applied to identify SNPs associated with obesity. We used For the top-300 SNPs identified with main effects, the average GCVC was 6.67 for OD while it was 5.98 and 5.96, respectively for B1 and B2. We also observed that more SNPs were identified with high GCVC for OD than B1 and B2. For example, the number of SNPs showing GCVC = 10 is 58, 22 and 26 respectively for OD, B1 and B2. The number of SNPs with GCVC ≥ 9 for OD is also about twice the number of those for B1 and B2. These patterns are stronger for 2~4-way interactions  than by the original MDR . Note that the famous obesity-associated gene K  were further used to search for possible causal SNPs with main effects via the OMDR and the original MDR methods. As we increased K , we identified more obesity-related SNPs using the OMDR approach than using the current MDR, and the gap seems increasing. For example, with K = 1000, we identified four more SNPs in known obesity-related genes for OD than for B1 and B2.In addition, various values of In this paper, we developed the OMDR approach that facilitates the MDR analysis for an ordinal phenotype. The construction process for OMDR classifiers is a straightforward extension of the process for the existing MDR classifiers. For selecting good classifiers, the performance of the OMDR classifiers has to be evaluated via an evaluation measures. We proposed the use of an ordinal association measure, specifically tau-b, for some reasons. First, tau-b along with likelihood ratio and normalized mutual information has been known to outperform other evaluation measures in MDR, including balanced accuracy, misclassification error, specificity and sensitivity ,30. SecoWhile designed for the analysis of genuine ordinal categorical traits, the OMDR method can also be used to analyze a continuous trait by approximating it as an ordinary category trait. Currently, the MDR analysis for a continuous trait is conducted mostly by binarizing it with a certain cut-off. Compared to binary approximation, the ordinary approximation can be more powerful because it preserves more information on the continuous trait. The empirical study with a real data demonstrated that the OMDR approach would produce more consistent results and be more powerful than the original MDR approach for binary traits, in terms of GCVC and the number of the classifiers identified with high selection consistency, respectively.K selection to report multiple candidates of gene-gene interactions in OMDR as well as MDR analyses. When one searches for few but possibly strong candidates for gene-gene interactions, a small value of K would be appropriate. On the other hand, a large value of K can be used for detecting many candidates including ones with mild effects on traits. Note that the choice of K would be critical for both power increase and false-positive control, which requires a further investigation. However, our simulations suggested that false positives can be screened out with very low GCVC values and low predictability values. We also investigated the null distribution of GCVCK with different K = 1, 2, 3, based on a small simulation, and found that the choice of K did not dramatically affect the null distribution of GCVCK (data not shown).Nowadays, the genome-wide association studies with the genotype data produces up to ~1 million SNPs. Reporting one single best candidate is impractical and/or unreasonable when causal gene-gene interactions are searched for complex traits in a genome-wide scale. Thus, we proposed GCVC with the top-c(i)) in the OMDR approach. There might be many possible options to address this tie problem. For examples, the class with the smallest or largest K can be used as the predicted class among the tied classes. In our analysis, we chose the largest class for prediction in tied cases following the original MDR approach.The original MDR for binary traits  compares the estimated ORs between two classes , and determines the class with larger estimated OR as the predicted class. When the estimated ORs are same for both classes, one class is usually specified for the prediction purpose . Similarly, more than one class can happen to have the same maximum value of the estimated OR  of 0.5 are used in models with patterns 1 and 2; MAFs of 0.3 are used in models with other patterns.)Click here for fileGCVC value distribution of top-300 OMDR classifiers for 2~4-way interactions from real data analysis.Click here for file


We propose a nonparametric Bayes-based clustering algorithm to detect associations with rare and common single-nucleotide polymorphisms (SNPs) for quantitative traits. Unlike current methods, our approach identifies associations with rare genetic variants at the variant level, not the gene level. In this method, we use a Dirichlet process prior for the distribution of SNP-specific regression coefficients, conduct hierarchical clustering with a distance measure derived from posterior pairwise probabilities of two SNPs having the same regression coefficient, and explore data-driven approaches to select the number of clusters. SNPs falling inside the largest cluster have relatively low or close to zero estimates of regression coefficients and are considered not associated with the trait. SNPs falling outside the largest cluster have relatively high estimates of regression coefficients and are considered potential risk variants. Using the data from the Genetic Analysis Workshop 17, we successfully detected associations with both rare and common SNPs for a quantitative trait. We conclude that our method provides a novel and broadly applicable strategy for obtaining association results with a reasonably low proportion of false discovery and that it can be routinely used in resequencing studies. The two highly debated hypotheses on the genetic basis of complex human diseases are the common disease/common variant (CDCV) hypothesis and the common disease/rare variant (CDRV) hypothesis . The CDCi  we observe iy, a quantitative trait; iz, a p-dimensional vector of individual-specific covariates, such as age and sex; and ix =  , genotypes at J SNPs. Here, we assume an additive genetic model; thus ijx = 0, 1, or 2, representing the number of minor alleles present at SNP j of individual i. A regression model on the quantitative trait is given by:Suppose that for each individual i = 1, 2, …, n, where γ is a vector of regression coefficients, including the intercept and slopes for individual-specific covariates, the jβ are the SNP-specific regression coefficients, and iε is the error term. We specify the following prior distributions for the model parameters: jβ ~ G, G ~ DP, and σ ~ U. Here, v2 and b >a ≥ 0 are prespecified hyperparameters, p + 1)-dimensional normal distribution with mean vector μ and variance-covariance matrix Σ, 0 is a vector of zeros, I is an identity matrix, G denotes a random distribution, U denotes a uniform distribution between a and b, and DP is the Dirichlet process.for G0 and the precision parameter α (>0). If G ~ DP, then G0 is the prior expectation of G and α controls the variance of G. Here, we take U, d >c > 0, as the prior distribution for the precision parameter α.The Dirichlet process  is a proSethuraman  providedandthenα, G0), where kϕδ denotes a point mass at kϕ. It is clear that G is discrete with probability 1. Because of the discreteness, the jβ can take on the same value. That is why the Dirichlet process can be used for clustering analysis.is a random probability distribution generated from DP and included the resulting first two components as covariates, in addition to Age and Smoke. We built our model with 244 nonsynonymous SNPs selected from the vascular endothelial growth factor (VEGF) pathway [v2 = 1,000, a = 0, b = 100, c = 0.5, d = 20, µ0 = 0.5, and We illustrate our methods using the data from Genetic Analysis Workshop 17. The analyses were performed with the knowledge of the underlying simulation model . We stud pathway . These S pathway  with v2 µ0 ranging from 0.1 to 0.5 and We evaluated our results using two thresholds. When the number of clusters was small (2–5), we defined true positives as true associations identified in at least 2 of the 10 replicates. This threshold was selected to balance the reduced power resulting from small cluster numbers. Indeed, requiring at least two replications for each identified association yielded a reasonably low FDP. When we used the optimal cluster numbers, we defined true positives as true associations detected in no less than eight replicates. We carried out sensitivity analyses on the prior specification for the SNP-specific regression coefficients with β) used in the simulation, and frequency of detection. When we used two clusters, we found eight true positives with no false positives. Compared with false negatives, the true positives have either relatively high MAFs or relatively high effect sizes. With 3 clusters, we had 11 true positives and no false positives. With 4 or 5 clusters, we detected 12 and 13 associations, respectively. However, there was one false positive (data not shown) in both cases (FDP ≈ 8%). We also conducted single-SNP-based tests with Bonferroni correction for multiple comparisons. With the criteria that p ≤ 0.05/244 in at least 2 of the 10 replicates, 20 associations were detected and 10 of them were true discoveries, giving an FDP of 50%. Compared with single-SNP tests, our method gave a much lower FDP.Table F = 9 rows in Table As the number of clusters increases, more associations may be detected; however, the number of false positives may also increase. To strike a balance between sensitivity and specificity, we examined receiver operating characteristic (ROC) curves Figure  for eachWe then evaluated the performance of this method using a specified number of clusters, ranging from 50 to 100. Using only associations identified with 100% power, we had 8 to 10 true positives and at most 2 false negatives (FDP ranging from 10% to 18%). For 90% power, we had 8 to 16 true positives and at most 4 false negatives (FDP ranging from 8% to 20%). Thus cluster numbers of 50 to 100 seem reasonable.β compared with false negatives, as shown in Figures Using optimal cluster numbers and the threshold of true positives, we identified 12 of the 23 true associations with private SNPs. As we expected, true positives had overall higher effect sizes than false negatives Figure . Among tWe have demonstrated that a novel nonparametric Bayes-based clustering method can be used to identify associations with SNPs for quantitative traits. Importantly, this method is capable of detecting associations with both rare and common genetic variants. Compared with other methods that deal with rare variants, our methods detect genetic risk factors directly at the SNP level. Compared with single-SNP-based methods, the proposed method is more powerful and reliable. It can detect a relatively larger proportion of true associations independent of the MAF of the variants, and it produces a relatively lower proportion of false discoveries.The authors declare that there are no competing interests.LD conceived and performed the statistical analysis and wrote the manuscript. LJM contributed to the design of the statistical analysis and the writing of the manuscript. TMB, HH, XZ, and BGK helped with the writing of the manuscript. All authors read and approved the final manuscript.


Here we investigate the theoretical properties and performance of Wu et al.'s proposed statistics and explain why, in some circumstances, they outperform competing approaches. Unfortunately, we find minor errors in the formulae for their statistics, resulting in tests that have higher than nominal type 1 error. We also find minor errors in PLINK's fast-epistasis and case-only statistics, although theory and simulations suggest that these errors have only negligible effect on type 1 error. We propose adjusted versions of all four statistics that, both theoretically and in computer simulations, maintain correct type 1 error rates under the null hypothesis. We also investigate statistics based on correlation coefficients that maintain similar control of type 1 error. Although designed to test specifically for interaction, we show that some of these previously-proposed statistics can, in fact, be sensitive to main effects at one or both loci, particularly in the presence of linkage disequilibrium. We propose two new “joint effects” statistics that, provided the disease is rare, are sensitive only to genuine interaction effects. In computer simulations we find, in most situations considered, that highest power is achieved by analysis under the correct genetic model. Such an analysis is unachievable in practice, as we do not know this model. However, generally high power over a wide range of scenarios is exhibited by our joint effects and adjusted Wu statistics. We recommend use of these alternative or adjusted statistics and urge caution when using Wu et al.'s originally-proposed statistics, on account of the inflated error rate that can result.Recently, Wu and colleagues  Gene–gene interactions are a topic of great interest to geneticists carrying out studies of how genetic factors influence the development of common, complex diseases. Genes that interact may not only make important biological contributions to underlying disease processes, but also be more difficult to detect when using standard statistical methods in which we examine the effects of genetic factors one at a time. Recently a method was proposed by Wu and colleagues  Genome-wide association studies (GWAS) have been remarkably successful at identifying the genomic locations of variants involved in a variety of complex diseases biological and statistical interaction has been hotly debated over many years The relationship between In case/control studies, statistical interaction is generally modelled as departure from a simple linear model describing the individual (main) effects of predictor variables on the predicted log odds of disease Given the simpler logistic regression model (1), a variety of tests can be performed to assess the effects of the two contributing factors. (Similar tests can be derived for logistic regression model (2)). A 3df test of Recently, Wu and colleagues Wu et al. Wu et al. To test for interaction, Wu et al. In order to actually calculate Wu et al. fast-epistasis tests test whether correlation between alleles at the two loci exists (case-only test) or is different between cases and controls (case/control test) via the following Two fast approaches for testing interaction (in addition to a slower logistic regression based approach) are implemented in the computer program PLINK Apart from the difference in fast-epistasis statistics:Although the log odds ratio fast-epistasis tests implemented in PLINK operate by turning a question about statistical interaction into a question about allelic association (or correlation), namely, whether association between alleles two loci exists (case-only test) or is different between cases and controls (case/control test)). However, many different measures of allelic association  have been proposed. Arguably the most popular are Lewontin's Both the methods of Wu et al. interaction  or is different between cases and controls (case/control test)), it is possible that such a bias could be advantageous in terms of improving power. Since the method of Wu et al. If HWE does not hold, Wellek and Ziegler found the genotype-based estimator of Given a genotype-based estimator of Although designed to test specifically for  interaction, several of the test statistics proposed above can be shown to be sensitive to the situation where there is, in fact, no interaction, but one or both of the loci display main effects .In order to address this issue, we propose two new ‘joint effects’ tests that are sensitive only to either a) a genuine interaction effect or b) (if the disease is not sufficiently rare), main effects present at both loci. Our tests are motivated by a desire to test the same interaction parameter as tested by Wu et al. Our new tests are based on the counts in To construct our proposed tests, we therefore propose to use the four relationships in (16) as four estimating equations for We construct two separate estimates of nce  see  separateA difficulty with estimation arises when We performed computer simulations to evaluate the performance (type 1 error and power) of the various test statistics described above. For the Wu and adjusted Wu methods, haplotype frequencies in cases and controls were calculated from unphased genotype data using an EM algorithm as implemented in either PLINK or the R library ‘Genetics’. The general structure of the disease models we considered is shown in Loci not in LD: Loci in LD: When the two SNPs were not in LD, we examined the performance of both case/control and case-only statistics. When the SNPs were simulated to be in LD, we examined only the performance of case/control statistics (since we know that case-only statistics will show inflated type 1 error in this situation). To investigate type 1 error we considered 8 scenarios, each using 10,000 data replications. To investigate power we considered a further 4 scenarios, each using 1,000 data replications. The structure of the simulated models and the parameter values assumed are given in In addition to the test statistics described above, when comparing power (Scenarios 6–9) we also calculated several additional statistics. Firstly, as an ‘optimal’ test we considered analysing the data assuming the ‘correct’ model  except the original Wu et al. fast-epistasis tests  in case/control analysis, when the two SNPs considered are in LD in the general population.  for our adjusted Wu statistic.fast-epistasis test shows a slight deflation (rather than inflation) in type 1 error, while our adjusted Wu statistic shows a slight inflation. Correct type 1 errors are achieved by the ideal Wu statistics and by our new joint effects statistics. Results from Scenario 4 (in which locus G has an additive main effect) are shown in A similar pattern is seen for Scenario 3  shows generally lower power than the other tests considered, in this scenario.en shown , S3, S4 en shown , S3, S4 fast-epistasis tests show low power when applied to case/control data. The ideal Wu test also shows generally low power when applied to either case/control or case-only data.fast-epistasis method) give very similar results with respect to estimated haplotype frequencies and resulting correlation measures. The correlation measures  are correctly estimated as being close to 0. The slight departure from 0 results from the fact that the disease is not particularly rare, and so the presence of an interaction effect will cause unaffected controls, as well as cases, to show some slight correlation between alleles at the two loci.In cases (with no LD) however, the story is very different. All methods show correlation between alleles at the two loci, however the haplotype frequencies and resulting correlation measures estimated using PLINK's allele counting algorithm seem to be much closer to the true generating values. The EM algorithm  produces upwardly biased estimates, presumably because of the incorrect (within cases) HWE assumption made. This results in much higher apparent correlation, which could plausibly increase power when testing whether correlation between alleles two loci exists (case-only test) or is different between cases and controls (case/control test)). However, the power of any given test will depend not just on the level of apparent correlation, but also on the estimated variance of the correlation measure used, and our results overall suggest that the bias induced by the incorrect HWE asssumption does not necessarily always translate to a substantially improved power.In the presence of LD, for controls the EM algorithm  appears to better capture the true haplotype frequencies and resulting correlation measures, while the PLINK's allele counting algorithm produces results that are biased downwards (i.e. towards showing lower levels of correlation). For cases, PLINK's allele counting algorithm produces correlation measures that are biased downwards from the true values, while the EM algorithm produces correlation measures that biased upwards. Given that any analysis in the presence of LD needs to be based on the difference in correlations between cases and controls, it is unclear to what extent these biases will operate to improve power for one method over another, although the results shown in fast-epistasis and Wellek and Ziegler inspired methods, we only output results passing a fast-epistasis statistic, PLINK in fact only performed a total of 13,818,410 tests that passed its validity criteria).fast-epistasis and Wellek and Ziegler inspired statistics all follow the expected distribution under the null hypothesis, even in this tail . . fast-epistasis and Wellek and Ziegler inspired statistics against one another. The results from these three methods are seen to be broadly correlated, with the same SNP pairs tending to fall at the extreme of the distribution, regardless of which method is used.The results in Since we were unable to calculate the Wu and adjusted Wu statistics for all pairs of SNPs, at the suggestion of a reviewer, we used another approach for calculating these statistics, which we hoped would be computationally quicker. We used a phasing algorithm to infer haplotypes across chromosome 22, for each individual. We carried out this step using the program SHAPEIT Having generated 100 replicates of phased haplotypes, we then calculated, for each pair of SNPs, the mean (over the 100 replicates) haplotype frequencies in cases and controls. . We used these mean haplotype frequencies in the formulae for the Wu and adjusted Wu statistics (Equations 7 and 9 respectively). Note that these formulae were derived on the basis of sampling theory under the assumption of a certain number of observed haplotypes, and it is unclear whether the same theoretical arguments should apply to haplotype frequencies that have been estimated in a different way. In particular, SHAPEIT uses a hidden Markov model that is motivated by population genetics principles, resulting in a greater borrowing of information across SNPs and individuals than is used in the other approaches. This fact, together with the fact we averaged (over 100 replicates), suggests that the haplotype frequencies  be translated into Wu-like interaction tests, in our hands, implementation of these approaches was not computationally faster than the original Wu and AWu methods. Although generation of 100 replicates of phased chromosome 22 haplotypes in SHAPEIT was relatively fast (taking around 28 hours on our system), our program for generating the resulting SMBW and SVBW test statistics ended up taking about 3 seconds per SNP pair.  type 1 error in analysis of real data (see QQ plot shown in per se i.e. that test (or attempt to test) the interaction term in a linear model (such as Equation 1). As mentioned previously, if one prefers to test combinations of terms  Q-Q plot for Scenario 3 (Dominant effect at locus G). Top panels ((a), (b) and (c)): Case/Control not in LD; Middle panels ((d), (e) and (f)): Case/Control in LD; Bottom panels ((g), (h) and (i)): Case-Only not in LD; FE: Fast-Epistasis; AFE: Adjusted FE; Wu: Wu et al. statistic; AWu: Adjusted Wu statistic; IWu: Ideal Wu statistic; WZ: Wellek and Ziegler statistic; JE: Joint Effects statistic.(TIF)Click here for additional data file.Figure S2Chi-squared (1 df) Q-Q plot for Scenario 4 (Additive effect at locus G). Top panels ((a), (b) and (c)): Case/Control not in LD; Middle panels ((d), (e) and (f)): Case/Control in LD; Bottom panels ((g), (h) and (i)): Case-Only not in LD; FE: Fast-Epistasis; AFE: Adjusted FE; Wu: Wu et al. statistic; AWu: Adjusted Wu statistic; IWu: Ideal Wu statistic; WZ: Wellek and Ziegler statistic; JE: Joint Effects statistic.(TIF)Click here for additional data file.Figure S3Chi-squared (1 df) Q-Q plot for Scenario 5a (Additive effects at both loci). Top panels ((a), (b) and (c)): Case/Control not in LD; Middle panels ((d), (e) and (f)): Case/Control in LD; Bottom panels ((g), (h) and (i)): Case-Only not in LD; FE: Fast-Epistasis; AFE: Adjusted FE; Wu: Wu et al. statistic; AWu: Adjusted Wu statistic; IWu: Ideal Wu statistic; WZ: Wellek and Ziegler statistic; JE: Joint Effects statistic.(TIF)Click here for additional data file.Figure S4Chi-squared (1 df) Q-Q plot for Scenario 5b (Recessive effects at both loci). Top panels ((a), (b) and (c)): Case/Control not in LD; Middle panels ((d), (e) and (f)): Case/Control in LD; Bottom panels ((g), (h) and (i)): Case-Only not in LD; FE: Fast-Epistasis; AFE: Adjusted FE; Wu: Wu et al. statistic; AWu: Adjusted Wu statistic; IWu: Ideal Wu statistic; WZ: Wellek and Ziegler statistic; JE: Joint Effects statistic.(TIF)Click here for additional data file.Figure S5Power curves for Scenario 8 (Additive(TIF)Click here for additional data file.Figure S6Power curves for Scenario 9 (Dominant(TIF)Click here for additional data file.Figure S7QQ plots from analysis of pairwise (SNP(TIF)Click here for additional data file.Figure S8Correlations between three different methods applied to the WTCCC Crohn's data set. Each point represents a particular SNP(TIF)Click here for additional data file.Figure S9QQ plots from analyses based on the mean haplotype frequencies (over 100 replicates) estimated using SHAPEIT. Red crosses denote results calculated using the original Wu formula. Black plusses denote results calculated using the Adjusted Wu formula. Green circles denote results calculated using the SMBW formula, which corresponds to twice the original Wu statistic.(TIF)Click here for additional data file.Figure S10Panel (a): QQ plots from analyses based on the SVBW test statistic. Results from SNP pairs where the SNPs are less than 1 cM apart are shown in red. Panel (b): QQ plots from analyses based on the SVBW test statistic, having removed all SNP pairs where the SNPs are less than 1 cM apart. Panel (c): QQ plots from analyses based on the SMBW test statistic, having removed all SNP pairs where the SNPs are less than 1 cM apart. Panel (d): Plot of SVBW test statistic (y axis) against SMBW test statistic (x axis), for each SNP pair.(TIF)Click here for additional data file.Figure S11Panel (a): Plot of SMBW test statistic (y axis) against Adjusted Wu test statistic (x axis), for each SNP pair. Panel (b): Plot of SVBW test statistic (y axis) against Adjusted Wu test statistic (x axis), for each SNP pair. Panel (c): Plot of SMBW test statistic (y axis) against Joint Effects test statistic (x axis), for each SNP pair. Panel (d): Plot of SVBW test statistic (y axis) against Joint Effects test statistic (x axis), for each SNP pair.(TIF)Click here for additional data file.Figure S12SMBW (left hand panels (a) and (c)) and SVBW (right hand panels (b) and (d)) results, from haplotypes estimated by applying SHAPEIT to cases and controls separately (y axes) or together (x axes). Points shown in red on top panels (a) and (b) correspond to SNP pairs where the SNPs are less than 1 cM apart. These points have been removed from the plots shown in bottom panels (c) and (d).(TIF)Click here for additional data file.Text S1Details of the variance calculation for our various proposed statistics. (PDF)Click here for additional data file.Text S2Here we demonstrate that several of the test statistics described in this manuscript may show sensitivity to the presence of main effects at one or both loci, rather than showing sensitivity purely to interaction effects.(PDF)Click here for additional data file.Text S3A logistic regression view of the Wu et al. statistic.(PDF)Click here for additional data file.Text S4Here we consider the relationship between the fast-epistasis (FE) and Wellek and Ziegler (WZ) inspired statistics and standard logistic and linear regression.(PDF)Click here for additional data file.Text S5Here we show that the Wellek and Ziegler inspired case-only statistic can be viewed equivalently as a score test with respect to the interaction parameter δ in the model given in the second table on page 5 of (PDF)Click here for additional data file.


Complex traits may be defined by a range of different criteria. It would result in a loss of information to perform analyses simply on the basis of a final clinical dichotomized affected / unaffected variable.We assess the performance of four alternative approaches for the analysis of multiple phenotypes in genetic association studies. We describe the four methods in detail and discuss their relative theoretical merits and disadvantages. Using simulation we demonstrate that PCA provides the greatest power when applied to both correlated phenotypes and with large numbers of phenotypes. The multivariate approach had low type I error only with independent phenotypes or small numbers of phenotypes. In this study, our application of the four methods to schizophrenia data provides converging evidence of the relative performance of the methods.Via power analysis of simulated data and testing of experimental data, we conclude that PCA, creating one variable based on a linear combination of all the traits, performs optimally. We propose that our comparison will provide insight into the properties of the methods and help researchers to choose appropriate strategy in future experimental studies. For linkage and genetic association studies of biological markers, a complex trait can be defined by a range of multiple and often overlapping criteria. For example, obesity, usually defined by body mass index (BMI), is also related to waist-hip ratio (WHR) and body fat percentage. More than one indicator is usually used. It is possible that the specific type of the indicator selected may favor one susceptibility gene, while selection on another indicator may reveal another gene. In early genome-wide association studies, a common variant of the FTO gene was implicated in increased BMI and to predispose to childhood and adult obesity . Later, Multiple intermediate phenotypes have been proposed for a variety of neuropsychiatric disorders, in particular schizophrenia, bipolar disorder, and Alzheimer’s disease. For example in Alzheimer’s disease, impairment occurs in eight cognitive domains including attention, language, memory, perceptual skills, constructive abilities, orientation, problem solving and functional abilities . Typicalet al.[In a recent review, Ott et al. describeThe primary purpose of our study was to assess the performance of these four approaches. We introduce the four methods in detail and discuss their relative advantages and disadvantages. Then through power analysis of extensively simulated data and a real data application, we conclude that for genetic association studies, using PCA to create one variable based on a linear combination of all the traits performs optimally.p-value across phenotypes is less than a pre-determined threshold, we suspect the SNP is a genetic risk factor for the trait.The most intuitive and simplest way to deal with multiple phenotypes is to test each SNP against one phenotype at a time. In the case of quantitative traits, a one-way analysis of variance (ANOVA) is usually performed. It tests whether the mean of a phenotype is the same in the three genotypes, AA, AB, and BB. As an alternative to ANOVA, we can perform a simple linear regression for each phenotype as a response variable and the genotypes as predictors . Each of the phenotypes would measure a trait from a particular different angle. A given SNP could be associated with none, one or more of the phenotypes. In practice, researchers have to make decisions on the criteria for declaring significance and interpretation. Usually, if any of the phenotypes result in a statistically significant outcome, the SNP is retained for further investigation. This is also what we do in this study, that is, if the smallest p-values by controlling the overall type I error. In the situation of a single test, a result is declared significant when p ≤ 0.05 if the type I error α is controlled at 5% by convention. With m independent tests, the probability of making correct decisions on all the results is (1 – p)m, given the null hypothesis is true. So the probability of finding at least one false positive is 1 – (1 – p)m. This overall type I error α is called the family-wise error rate. It is approximated by mp when m is large and p is small and we want to keep α ≤ 0.05 [m as the threshold to declare a single test significant. This approach represents the well-known Bonferroni correction. Unfortunately, the disadvantage is that the correction tends to be too stringent when tests are dependent, which is often the case with endophenotypes. This correction causes more false negatives so power is decreased. An alternative to Bonferroni correction is to use permuted p-values as discussed in the next section.Since multiple tests are conducted at a SNP, we need to handle the resulting Fmax or Pmin, among associations with all phenotypes as our final test statistic for this SNP . In the first approach of one SNP at a time, we assess the significance level associated with a test statistic by looking it up in a known statistical distribution table. Since the null distribution of Pmin may not have a known distribution, we approximate it by simulating datasets under no association. The procedures are firstly to permute sample labels in phenotypes but keeping genotypes in their original order. Obviously, in this new dataset we destroy any association between phenotypes and genotypes by randomization. Secondly, we obtain and store the smallest p-value in such a dataset. We repeat the randomization a sufficiently large number of times. The smallest p-values stored would approximate the distribution of Pmin under the null hypothesis. Finally, we calculate the proportion of the smallest p-values in the distribution less than or equal to the observed Pmin to be the significance level associated with Pmin[p-value is not as conservative as a Bonferroni-corrected p-value and, thus, is more powerful. We will revisit this issue in the simulation section.For a given SNP, we define the best test statistic, with Pmin. It is oThe obvious drawback to the first two approaches is that they do not utilize information from the structure of multiple phenotypes, which may or may not to be correlated. Given there are not too many phenotypes, we could carry out regression or multivariate analysis of variance (MANOVA) with multiple phenotypes directly. In multivariate regression, the response variables are assumed to follow some specific multivariate distribution, most commonly a multi-normal distribution, although this is a strong and sometimes unwarranted assumption.Another method of analyzing several phenotypes simultaneously is to summarize them into one overall value. The simplest summary statistic is to take the mean or sum . But in real-life examples, directly adding phenotype values does not always make sense. For example, it is difficult to interpret one's height plus weight plus intelligence quotient (IQ). Instead of a simple sum, we may consider a weighted linear combination of phenotypes with weights based on the inverse of their variances. In principal component analysis (PCA), such a weighted sum is called the first principal component (PC). This technique of dimension reduction is often used in the presence of a large number of predictors in a regression model. Here, we apply the technique to condense information in outcome variables, that is, phenotypes.http://www.r-project.org).All the simulation and data analysis described in this paper was conducted in the R statistical programming language  [et al., [We first describe our analysis of a dataset on schizophrenia, followed by extensive simulation of computer-generated data. Investigators collected clinical, cognitive, MRI and genetic information of European subjects in families with schizophrenia and controls. Family members include mainly parents and siblings. All case subjects are individuals with a diagnosis of schizophrenia. Additional description of the studies, including methods for selecting control subjects and diagnosis is provided in Toulopoulou 7; 2010)  and Owen[et al.,  and in tWe select all available 216 unrelated schizophrenia patients and 240 unrelated controls and analyze genotypes in case and control subjects for each of 51 candidate SNPs potentially associated with schizophrenia. Phenotypes of interest are subjects’ cognition level measured from the angle of IQ and memory. More explicitly, they are two summary scores from the Wechsler Adult Intelligence Scale (WAIS) test to measure intelligence through verbal and performance subtests, one score from the National Adult Reading Test (NART) estimating premorbid intelligence levels, and two scores from the Wechsler Memory Scale (WMS) test that measures logical memory in the form of immediate memory capacity and delayed memory performance. We apply the four approaches described in the methodology section to conduct two sets of analyses: one with all five phenotypes and the other with the three IQ phenotypes only.p-value) regardless of which method is used. It has previously been identified to be associated with schizophrenia in the Scottish population with a relative risk of 5 [p-value of 0.002. The one-by-one and permutation approaches have similar p-values of 0.008 and 0.009, respectively, followed by MANOVA with a p-value of 0.031.Results are given in Table isk of 5 . Note thWhen we reduce the phenotypes to a highly correlated subset, the three IQ scores have a correlation coefficient of 0.72. We notice that MANOVA is then no longer able to pick up the potential risk variant, rs3738401, at a significance level of 0.05. The significance of this SNP in the other three methods also drops, possibly due to higher correlation, or fewer phenotypes, or both, although the sample size is slightly increased. We will investigate the relationship between power and correlation coefficient, number of phenotypes and so on in the next section.n, the number of phenotypes m, effect size δ, and the correlation coefficient r among the phenotypes. Here, δ means that if we set the mean of phenotypes for individuals with genotype BB to be unit 1, mean of phenotypes for individuals with genotype AB and AA would be equal to δ and δ2, respectively. This inheritance model is analogous to the genotypic relative risk model, in which the chance of an individual having the disease increases by a factor δ with an increasing copy of the risk allele in the genotypes [We simulate extensively to assess which of the approaches would give highest power under various settings. We assume a multivariate, normally distributed phenotype associated with a risk SNP. Frequency of allele A is set to 0.3 throughout the simulation study. Other parameters in the simulation are the number of individuals enotypes . We varyn, m and δ are fixed at 300, 10 and 1.2, respectively, r varies from 0 to 0.9, that is, from complete independence to a high correlation. We want to generate 10,000 replicates of the SNP of interest, that is, 20,000 of its alleles. To generate a genotype, we assume Hardy Weinberg equilibrium (HWE) so that the two alleles in a genotype can be ascertained independently. To achieve this, allele A is generated from a binomial distribution , and separately, allele B from a binomial distribution . Under the assumption of HWE, given an allele frequency of 0.3, the mean genotype frequencies of AA, AB and BB are 0.09, 0.42 and 0.49, respectively. Phenotype data are then generated from a multivariate normal distribution with mean values of δ2, δ and 1.Firstly, we examine the relationship between power and correlation among the phenotypes. While the parameters δ ≠ 1. The patterns for the change of power are quite different for the four approaches. When phenotypes are correlated, even to a mild degree, MANOVA performs the worst. Its power decreases dramatically with an increase of the correlation coefficient. Performance of the one-by-one and permuted p-value approaches also has an inverse relationship with the correlation coefficient, although their rates of decrease are slower. The PCA approach has the most interesting pattern, which does not show as a monotonic curve. Power first increases, then decreases. To take a closer look at where the peak occurs, we simulate another set of SNPs with all parameter settings the same as above except the correlation coefficient varies from 0 to 0.2. Figure In Figure r is fixed at 0.5. Interestingly, for all methods except MANOVA, power increases with more phenotypes included. The performance of the one-by-one and permuted p-value approaches goes hand in hand and PCA is the best.Next, we check the relationship between power and number of phenotypes, as shown in Figure In the end, we present two traditional graphs in power analysis, where power is plotted against effect size and sample size, shown in Figures p-values less than a pre-determined threshold. In practice, we often fix 0.05 as that threshold such that the estimated type I error is controlled at about 5% and, in principle, power is expected to be about 5% under the null hypothesis, H0: δ = 1. However, we do not know whether it is always the same case for the four approaches, especially when correlation coefficient and number of phenotypes also vary. In supplementary method in Additional file Note that for all simulations above, power is calculated as the proportion of We also want to check the performance of these four methods when phenotype distributions deviate from normal. Using the same parameter setting as above, we find similar patterns for the four methods (See supplementary Figures 2 and 3 in Additional file We have described four methods to analyze multiple observed phenotypes for linkage and association studies of complex traits. For any given marker, it is likely that a simple dichotomized phenotype of affected versus unaffected is not clearly associated with the marker due to relatively subjective definition and characterization of disease status, especially for psychiatric traits. Disease definition is not generally based on the genetics of the trait but is established for the purpose of unique classification. Thus, a range of phenotypes is required to capture all underlying genetic risk factors with different functions. Hypertension in Lyon hypertensive rats is a good example. It was shown that two different blood pressure measurements, diastolic and pulse, are associated with different genes which might have been missed based on the conventional measurement of systolic and diastolic blood pressure . FurtherIn this study, we investigate the performance of different approaches to analyse multiple continuous phenotypes and recommend PCA as the optimal method. When phenotypes comprise both discrete and continuous variables, each discrete phenotype can be non-linearly transformed  before bWhen phenotype distributions deviate from normality, we check the performance of the four methods and again conclude that PCA is optimal. Although a transformation of the non-normality, e.g. using Box-Cox or simply log transformations, would improve power to be similar to that for normally distributed variables, we show through simulation that the consequence would be decrease in power if we did not remove non-normality in our phenotype distribution. Comparing Figure In practice it is not uncommon to have missing values, which may differently affect the four methods. The univariate approaches may be less affected in the sense that if a missing value exists in one of the phenotypes, we are still able to select a minimal p-value among the other phenotypes. But the standard PCA and MANOVA require that all values be present for the phenotypes. Fortunately, there are methods available to get around the problem of missing data, for example imputation. So we can predict and fill in missing values before implementing any method to analyse the multi-phenotype data. Additionally, an R package, pcaMethods, allows performing PCA on incomplete data and may be used for missing values estimation .Working with the different methods brought several issues to our attention. We found that using Bonferroni correction and permuted p-value performed comparably in terms of power in the two univariate approaches. At first glance, this result seems surprising, given that the Bonferroni correction is known to be conservative when phenotypes are strongly correlated. However, it is worth noting that we use a calibrated threshold throughout such that power is 5% under the null hypothesis and, thus, we have a fair comparison in terms of power. As shown in the left panel of Supplementary Figure Using simulation we demonstrated that PCA provides the greatest power when applied to both correlated phenotypes and large numbers of phenotypes. The multivariate approach had low type I error only with independent phenotypes or small numbers of phenotypes. Despite increasing awareness of how to deal with multiple phenotypes, the one-by-one approach is still commonly employed by researchers. Examples of using the other methods in real data application are not often seen. In this study, our application of the four methods to schizophrenia data provides converging evidence of the relative performance of the methods. We propose that our comparison will provide some insight into the properties of the methods and help researchers to choose appropriate strategy in future experimental studies.The authors declare that they have no competing interest.JO conceived, designed, directed and helped to draft the manuscript. CS performed the statistical analysis, participated in the design of the study and drafted the manuscript. TT participated in the coordination of the study and helped to draft the manuscript. MP helped to draft the manuscript. TT, MP, EB, MW and RM contributed samples. All authors read and approved the final manuscript.Supplementary material and method. A PDF containing description in detail of schizophrenia data used for testing the four methods, methodology addressing the issue of selecting a proper threshold to declare significance, and results of the performance of the four methods when phenotype distributions deviate from normal.Click here for file


Drosophila melanogaster to identify the genetic basis of variation in susceptibility to viral infection. We found that there is substantially more genetic variation in susceptibility to two viruses that naturally infect D. melanogaster (DCV and DMelSV) than to two viruses isolated from other insects (FHV and DAffSV). Furthermore, this increased variation is caused by a small number of common polymorphisms that have a major effect on resistance and can individually explain up to 47% of the heritability in disease susceptibility. For two of these polymorphisms, it has previously been shown that they have been driven to a high frequency by natural selection. An advantage of GWAS in Drosophila is that the results can be confirmed experimentally. We verified that a gene called pastrel—which was previously not known to have an antiviral function—is associated with DCV-resistance by knocking down its expression by RNAi. Our data suggest that selection for resistance to infectious disease can increase genetic variation by increasing the frequency of major-effect alleles, and this has resulted in a simple genetic basis to variation in virus resistance.Variation in susceptibility to infectious disease often has a substantial genetic component in animal and plant populations. We have used genome-wide association studies (GWAS) in  D. melanogaster with viruses and have looked for genetic variants associated with resistance to infection. Using two viruses that naturally infect this species, we found a high level of genetic variation, much of which is due to a small number of genetic variants that have a large effect on virus resistance. Previous work has shown that two of these variants resulted from recent mutations that increased resistance and have been driven to a high frequency by natural selection. Furthermore, we did not find similar major-effect variants when we infected flies with viruses isolated from other species of insects. Therefore, selection for virus resistance appears to increase genetic variation in susceptibility to viral infection. Understanding the function of the genes, we have identified promises to give new insights into the antiviral defences of insects.In most animal populations, individuals vary genetically in how susceptible they are to infectious disease. To understand the genetic basis of this variation, we have infected a panel of inbred lines of the fruit fly  Variation in susceptibility to infectious disease often has a substantial genetic component in animal and plant populations Over the last decade, genome-wide association studies (GWAS) have provided a more complete picture of the genetic architecture of disease susceptibility Drosophila melanogaster, linkage mapping has been used to identify major effect resistance polymorphisms that affect susceptibility to both the sigma virus (DMelSV) ref(2)P and CHKov1), and they have been found to be common in natural populations In arthropods, several studies suggest that susceptibility to infectious disease may often be affected by major-effect polymorphisms e.g.. In DrosD. melanogaster both with viruses that naturally occur in this species and viruses isolated from other species. The two of the viruses that naturally infect D. melanogaster are Drosophila C Virus (DCV), which is a positive sense RNA virus in the Dicistroviridae that infects a range of Drosophila species D. melanogasterDrosophila affinisD. melanogaster viruses is high due to a small number of common major-effect polymorphisms. In contrast there is less genetic variation in susceptibility to viruses isolated from other species, and here there is no evidence of major effect polymorphisms.To understand how natural selection affects the genetics of disease susceptibility, we have used GWAS to examine the effects of selection for resistance to pathogens on patterns of genetic variation. To do this we infected D. melanogaster in nature. Comparing the two viruses where resistance was measured in terms of survival time—DCV and FHV—we found DCV resistance has significantly greater heritability  eV and gV in gV.To investigate genetic variation in resistance to viruses, we injected 47,220 flies from 185 different inbred lines from the Drosophila Genetic Reference Panel (DGRP) with four different viruses . The exttability . When thtability . While dariation ; CVg [27In all cases the genetic correlation in the level of resistance to different viruses is low, indicating that different genes are controlling resistance to different viruses . In partP-value across the entire genome. Quantile-quantile (qq) plots of the P-values show that there are highly significant associations in the experiments using DCV and DMelSV — the two viruses that infect D. melanogaster in the wild — but not in the experiments using FHV and DAffSV P that is known to cause resistance ,pastrel, which has not previously been implicated in antiviral defence. There were no significant associations with susceptibility to FHV or DAffSV using a genome-wide significance threshold of P<0.05 (When the together . In the f P<0.05 .ref(2)P, CHKov1 and pastrel. The quantile-quantile plots of the resulting P-values  can explain 47% of the heritability. In the case of DMelSV, ref(2)P explains 8% of the heritability, the doc element insertion in CHKov1 explains 29% of the heritability, and in combination these polymorphisms explain 37% of the heritability.To investigate how much of the genetic variation in susceptibility is explained by our GWAS, we calculated the proportion of the heritability that is explained by these genes. Assuming the polymorphisms have additive effects, then their contribution to additive genetic variation is 2ref(2)P, where heterozygotes have intermediate levels of resistance when injected with the virus pastrel allele is recessive and only half the remaining genetic variance is additive, this polymorphism will explain 84% of aV in an outcrossed population. Conversely, if the resistant pastrel allele is fully dominant and all the remaining genetic variance is additive, this polymorphism will explain just 7% of aV in an outcrossed population.The proportion of the heritability explained by these polymorphisms may be biased by two factors. First, we are injecting the virus, which is an unnatural route of infection, and in the case of the sigma viruses we are assaying a symptom of infection rather than viral titres or effects on host survival. Second, we can only estimate the amount of genetic variation explained in inbred lines, and this can only be directly extrapolated to outcrossed populations if all the genes affecting resistance are additive. Unfortunately, we cannot estimate the importance or direction of this bias as we only used inbred lines . This gene functions both as a pattern recognition receptor of bacteria Anaphase promoting complex 7 was associated with a 3.7 day increase in survival after injection with DCV . This was at a low frequency, with the resistant variant present in 4 of 145 lines. Furthermore, it is a synonymous polymorphism, suggesting that it may not be a causal variant. The QQ plots also show that there is an excess of small P-values in three of the analyses P have a large effect on resistance, we repeated the GWAS taking account of these polymorphisms by including them as fixed effects in the model. However, this did not lead to the identification of additional SNPs associated with resistance (Anaphase promoting complex 7 (X:6491634 G/T). For DMelSV it was a SNP in the intron of off-track , which is a transmembrane receptor that controls a variety of developmental and physiological processes As the polymorphisms in sistance . The mospastrel, CHKov1 and ref(2)P have highly specific effects, altering susceptibility to just one of the four viruses P polymorphism is associated with a 24% reduction in infection rates , two non-synonymous SNPs  and two SNPs in introns . All of these are in linkage disequilibrium, with the two SNPs in the 3′ UTR being perfectly associated . To try and disentangle which of the polymorphisms might be a causal variant, we fitted a general linear mixed-effects model in which all five variants were included as fixed effects. This allows us to calculate the marginal significance of each polymorphism . In this analysis only a non-synonymous SNP in the last coding exon of the pastrel remained highly significant . This SNP occurred in 21 of 142 lines that were sequenced at this site. We then tested the significance of each of the other four variants individually while controlling for the effects of 3L:7350895, by fitting general linear mixed-effects models and calculating sequential P-values from an ANOVA table. When we did this, all the other SNPs are significant . If we assume that we have included all the polymorphisms in this region in our analysis, this suggests that the non-synonymous polymorphism 3L:7350895 and at least one of the other sites are causal variants — but strong linkage disequilibrium prevents us from identifying which one(s). However, many polymorphisms, including indels, are missing from this dataset, so another polymorphism in this region that is not included in our analysis may be causing flies to be resistant to DCV.In pastrel, we used RNAi to knock down the gene in flies that were homozygous for the susceptible allele. To do this, we expressed hairpin RNAs that target the pastrel gene under the control of a constitutively and ubiquitously expressed Gal4 driver. When the flies were infected with a high dose of DCV, this resulted in a large reduction in survival rates relative to both a control with a similar genetic background  and a control where we knocked down a gene unrelated to viral resistance (z = 3.19 P = 0.001). To allow us to investigate viral titres, we also infected flies with a lower dose of DCV, which caused less mortality .To confirm the antiviral role of ortality . The virD. melanogaster to viral infection. These genes have either been previously identified by linkage mapping, or, in the case of pastrel, were verified by RNAi in this study. These polymorphisms are only seen when flies were infected with the two viruses that occur naturally in D. melanogaster populations — we were unable to detect any significant associations when using viruses that naturally infect other insects. The consequence of this is that the genetic variation in susceptibility to the naturally occurring viruses is substantially greater than to viruses from other species. Combined with previous data showing that two of these resistance alleles have been driven to a high frequency by positive selection We have found that a small number of major-effect polymorphisms can explain a substantial proportion of the genetic variation in the susceptibility of Our results support the suggestion that the genetic architecture of infectious disease susceptibility may be different from non-communicable diseases due to selection by parasites CHKov1 and ref(2)P both arose recently by mutation and natural selection has caused them to increase in frequency Parasites can result both in balancing selection maintaining polymorphisms in host resistance, and directional selection, which will ultimately fix the resistant allele Drosophila serrataref(2)P and CHKov1, previous work has suggested that they have undergone a ‘hard’ selective sweep, where selection has been acting on new or rare polymorphisms Directional selection on a trait can result in higher genetic variance when selection is acting on alleles that are initially at a low frequency Wolbachia also makes D. melanogaster more resistant to viral infection Wolbachia occurs in natural populations, and protects flies against two of the viruses we studied — DCV and FHV Wolbachia is transmitted vertically from mother to offspring, in many ways it can be regarded as another major-effect resistance polymorphism. We cured Wolbachia in our experiments with DCV and FHV and therefore have no data on its effects, but in natural populations of D. melanogaster it varies in prevalence from below 1% to near fixation Wolbachia is common.In addition to the genes that we have identified, the bacterial symbiont Drosophila, parasitoid wasps are one of the main causes of mortality in natural populations D. melanogaster and other organisms that we observed among our viruses Will the genetic architecture of resistance to other classes of pathogens be similar to the pattern we have seen for viruses? In ref(2)P resistance spread through European populations of D. melanogasterIn the long term, the spread of the resistance genes through populations could either result in the virus evolving to overcome host resistance, or a permanent increase in the levels of resistance seen in the host population. Due to their high mutation rates, short generation times and large population sizes, RNA viruses can evolve rapidly Drosophila is well-understood, we have only begun to understand in detail how Drosophila defends itself against viruses in the last six years D. melanogaster infected with vesicular stomatitis virus (VSV), which is another rhabdovirus that is related to DMelSV scavenger receptor C1 may be important in defence against DAffSV. This gene functions both as a pattern recognition receptor of bacteria While the antimicrobial immune response of CHKov1 and pastrel, in antiviral defence remain unclear, although pastrel is thought to play a role in protein secretion CHKov1 and pastrel in the immune system or the viral life cycle promises to yield new insights into both how animals evolve resistance to infection, and how viruses interact with their hosts.The functions of the two genes that have the largest effects on susceptibility, Wolbachia bacteria Wolbachia infection, flies were reared for two generations on food prepared by adding 6 ml of 0.05% w/v tetracycline to a vial containing 5 g instant Drosophila medium  and yeast. We checked the flies were uninfected by PCR as described in reference Wolbachia does not affect sigma viruses, Teixeira, Magwire and Wilfert, Pers. Comm.).Many of the DGRP lines are infected with D. melanogaster by DAffSV has not been characterised before, so we first injected flies with the virus and monitored viral titres and the characteristic symptom of sigma virus infection — sensitivity to CO2. These pilot experiments confirmed previous results that the virus can replicate in D. melanogaster2 P by PCR as described in reference Therefore, to assay for infection by DAffSV, flies were exposed to pure carbon dioxide for 15 min at 12°C at 15 days post-injection. By 30 min post-exposure, flies are awake from this anaesthesia were classed as uninfected, but flies that were dead or paralysed were classed as infected pastrel gene by RNAi. Males from line UAS-pst (P{KK105159}VIE-260B) were crossed to Actin-GAL4  virgins. As controls, males from a line with the same genetic background as UAS-pst  and UAS-CG10669 (P{KK105150}VIE-260B) were also crossed to Actin-GAL4 virgins. F1 females were injected with DCV. We used two doses of DCV (high: TCID50 = 1000 and low: TCID50 = 690). We note that these were from different viral preparations, which may explain why this small difference in TCID50 caused a large difference in mortality.We knocked down the 5′-CTTGCGGACCCTTTGTACGAC-3′) and DCV 7320R (5′-GCCATTCGAACTTGACCACGCAG-3′). As an endogenous control we amplified Actin5c using the primers qActin5c_for2 (5′GAGCGCGGTTACTCTTTCAC 3′) and qActin5c_rev2 (5′ AAGCCTCCATTCCCAAGAAC 3′).We performed three technical replicates of each PCR and used the mean of these in subsequent analyses. We calculated the titre of DCV relative to Actin5c as 2ΔCt, where ΔCt is the critical threshold cycle of DCV minus the critical threshold cycle of Actin5c. This approach assumes near 100% primer efficiency, which was confirmed using a dilution series of the template cDNA.We measured DCV titres by quantitative PCR using the SensiFAST™ SYBR & Fluorescein Kit . DCV was amplified using the primers DCV 6060F  of fly k from line i and vial j.β is the mean survival time across all lines, ib is a random variable representing the deviation from the overall mean of the ith line, jc is a random variable representing the deviation jth vial from the line mean, and i,j,kε is the residual error.We fitted a series of linear models to estimate genetic variances and covariances. For FHV and DCV, our data consisted of the lifespan of individual flies, which we treat as a Gaussian response in a general linear model. We fitted separate models for each virus, which were formulated as follows. Let i,kv be the probability of flies in vial k from line i being infected.β is the overall mean, ib is a random variable representing the deviation from the overall mean of the ith line, and ikε is a residual which captures over-dispersion within each vial due to unaccounted for heterogeneity between vials in the probability of infection.For DMelSV and DAffSV our data consist of numbers of infected and uninfected flies in each vial, which we treat as a binomial response in a generalized linear model. Let i,j,kv be the probability of flies, in vial k from line i and infected with virus j being dead.β is a vector of the mean survival times of the four virus types, and ix is a row vector relating this fixed effect to vial i. i,jb is the random effect of virus k on line j, and was assumed to be multivariate normally distributed, allowing us to estimate separate line variances for each virus type and covariances between all pairwise combinations of viruses. i,j,kε is the residual which captures over-dispersion within each vial. The residuals were assumed to be normally distributed with a separate variance estimated for each virus type.To estimate the genetic correlations between the viruses, we analysed data from all four viruses using a single model. To allow us to treat data from all four viruses as a binomial response in a generalized linear model, for FHV and DCV we used the numbers of dead and alive flies on a single day. Let The parameters of the models were estimated using the R library MCMCglmm gV, is half the between-line variance (assuming additive genetic variation). This allows us to calculate the heritability of DCV and FHV as:vV is the between vial variance and rV is the residual variance. As the DMelSV and DAffSV parameters are on a logit scale, we calculated heritability as:rV in this model. In eV as rV+gV after accounting for these polymorphisms, and then adjusted the numerators of As these fly lines are homozygous across most genes in the genome, the genetic variance, gCV, for DCV and FHV as pqa2, where p and q are the frequencies of the alleles in the population used to calculate 2h, and a is half the difference in the survival or infection probability of flies that are homozygous for the resistant and susceptible alleles . The maximum likelihood estimate of a, a2 was obtained as 2 minus the square of the standard error of We also calculated the coefficient of genetic variation, M estimator and used a robust F test to assess significance We used robust statistics to analyse data on viral titres due to the presence of an outlier in the data. We fitted a linear model by robust regression using an 2 assay. The DAffSV data was arcsine square root transformed to remove the dependence of the variance on the mean. To each SNP we fitted the linear model i,j = rβi+εi+m, where i,jr is the susceptibility of flies with SNP genotype i from line j, β is the overall mean, im is the SNP i genotype, and ikε the residual. As major-effect polymorphisms affect the susceptibility of flies to DCV and DMelSV, the analysis was then repeated including the genotype of these genes as an additional explanatory variable.To identify single nucleotide polymorphisms (SNPs) that were associated to susceptibility, we performed a GWAS using the published DGRP genome sequences P-value across the entire genome was recorded. This was carried out 400 times to generate a null distribution.Because we are performing multiple correlated tests, we determined a genome-wide significance threshold for the association between a SNP and phenotype by permutation. The phenotype data were permuted over the different recombinant lines, the genome-wide association study was repeated as described above, and the minimum Figure S1P-values for the association between SNPs and virus resistance in the region of three resistance genes. The data is the same as pastrel, CHKov1, CHKov2 and ref(2)P). The blue box shows the location of the doc element insertion that is believed to increase resistance to DMelSV.Manhattan plots of the (PDF)Click here for additional data file.Figure S2ref(2)P and CHKov1 genotypes as fixed effects in the DMelSV model, and included pastrel as a fixed effect in the DCV model. The horizontal lines are genome-wide significance thresholds of P = 0.05 (solid line) and P = 0.2 (dashed line) that were obtained by permutation.(PDF)Click here for additional data file.Figure S3D. melanogaster. The red circles shows the titre of DAffSV relative to actin 5c mRNA following injection of the virus. As is typical for sigma viruses, there is an initial drop in viral titre, presumably due to virions that were injected but do not infect cells. This is followed by an increase in titre as the virus replicates. The red line shows the predicted values from a second order polynomial regression. There was a significant effect of the second order term . The blue triangles show the proportion of flies that were paralysed after exposure to CO2, and the blue line shows the predicted values from a second order polynomial regression . Each data point is a vial of flies, with four vials per day and a mean of 16 flies/vial.DAffSV replicates in (PDF)Click here for additional data file.