The difficulty in elucidating the genetic basis of complex diseases roots in the many factors that can affect the development of a disease. Some of these genetic effects may interact in complex ways, proving undetectable by current single-locus methodology.We have developed an analysis tool called Hypothesis Free Clinical Cloning (HFCC) to search for genome-wide epistasis in a case-control design. HFCC combines a relatively fast computing algorithm for genome-wide epistasis detection, with the flexibility to test a variety of different epistatic models in multi-locus combinations. HFCC has good power to detect multi-locus interactions simulated under a variety of genetic models and noise conditions. Most importantly, HFCC can accomplish exhaustive genome-wide epistasis search with large datasets as demonstrated with a 400,000 SNP set typed on a cohort of Parkinson's disease patients and controls.With the current availability of genetic studies with large numbers of individuals and genetic markers, HFCC can have a great impact in the identification of epistatic effects that escape the standard single-locus association analyses. Most common diseases have an etiology so complex that years of research have yielded scarce results towards the elucidation of their causes. Technology and methodology are improving quickly but results have been arriving slowly. Nonetheless, optimism is in the air, because large studies of many individuals and genetic markers seem to finally be revealing some of the genetic factors behind these common diseases .The difficulty of elucidating the genetic basis of complex diseases roots in the many factors that can affect the development of a disease. Many factors, both genetic and environmental, each with possibly only a small effect, may be necessary for the expression of a particular disease phenotype. For example, most associations reported in the recent wave of genome-wide association studies of different common diseases exhibited small (1.1–1.4) to moderate 1.5–2) odds ratios [ odds ratThese small effects may only be detectable by means of genetic association analysis in very large samples, or in smaller sub-samples in which, by sample selection, this effect is enlarged: a sub-sample where the allele frequency of a particular risk gene is increased; or a sub-sample where a combination of other alleles or environmental factors act to increase the observable effect of a particular gene .Many genes may contribute to the expression of complex diseases. It is quite reasonable to expect that the effects of some of these genes do not sum up in a simple fashion. Epistasis generally refers to an interaction between the effects of genes at different loci, although the term has been used in different contexts by different disciplines . Some ofA wealth of current research in molecular genetics has discovered millions of genetic markers which provide a good coverage of common genetic variation across the entire human genome . At the -7, if a Bonferroni correction is applied. Nonetheless, many of these markers are correlated so this correction would be too strict, but in any case the required p-value would be very small.Although the arrival of genome-wide association testing is great news for the genetic dissection of complex traits, the large number of statistical tests involved raises the issue of statistical significance. For example, to maintain a Type I error of 5 percent when testing 100,000 markers for genetic association may require a test-statistic with a probability value of 5 × 10+9 two-locus combinations, which would require a Bonferroni-corrected p-value of 1 × 10-11 for a genome-wide significance level of 0.05, which again would be overly conservative due to the correlated nature of many of these tests. To achieve these significance levels it is necessary to study large samples and expect to find large epistatic effects.This problem of multiple testing is even more extreme for the test of epistasis. For example, for 100,000 markers, there are a total of 5 × 10Replication of findings in independent samples is sought for growing confidence in statistical results. The lack of replication of association results may be due to different causes, some technical  and some biological (heterogeneity of effects or population-specific risks). An approach to tackle the multiple testing issue is to divide the available sample into independent groups and to carry out the analysis in these independent groups to look for consistent results across the groups. Some true genetic effects will be missed due to lack of power (due to the reduced sample in each group) and to heterogeneity, but this approach may allow the identification of moderate/large-sized epistatic effects that are frequent and consistent.In this scenario, we have developed an analysis tool to search for genome-wide epistasis in a case-control design. Hypothesis Free Clinical Cloning (HFCC) is an standalone software which allows for single-locus genetic association testing, as well as epistasis testing for multi-locus combinations of markers. Due to the intense computational burden, it is programmed to take advantage of computer clusters by dividing the tasks into processes which can migrate to the available CPUs. We present here the method, as well as a genome-wide two-locus epistatic analysis performed on a real dataset of Parkinson's disease that illustrates the method. With the current availability of genetic studies with large numbers of individuals and genetic markers, HFCC can have a great impact in the identification of epistatic effects that escape the standard single-locus association analyses.The standard input to HFCC is a case-control sample with hundreds or thousands of individuals. Similarly to other association methods, it is convenient that cases and controls are matched for potentially important covariates like age, sex, ethnicity, geographical location, environmental factors, etc. Dichotomous phenotypes with a potential effect on the trait may be used as covariates in the analysis.If all cases have only one disease phenotype or trait, HFCC carries out a single-phenotype analysis. In the single-phenotype scenario, HFCC can analyze the full sample simultaneously for extra statistical power. In addition, we have developed a multi-group analysis strategy, explained in more detail in a later section, that allows the replication of consistent results, and it also aids the elimination of false positives results, a very attractive quality for genome-wide analysis of large number of genetic markers. For this single-phenotype multi-group analysis option, cases can be sub-divided into groups to allow for replication of consistent results across these groups. Controls can also be sub-divided into groups to eliminate spurious associations.Nonetheless, one of the strengths of HFCC is that it can analyze multiple phenotypes simultaneously. For this multiple-trait analysis, several groups of cases with different but related phenotypes are formed, each matched to its own control group. Indeed, the multi-group analysis strategy is especially convenient for the simultaneous analysis of several related diseases, or different symptoms of a syndrome, so that we can identify the genetic effects common to the different groups.HFCC can currently analyze di-allelic markers such as single nucleotide polymorphisms (SNP), and it can also accommodate other dichotomous markers such as the presence or absence of a particular allele of a multi-allelic marker or of a haplotype. HFCC can analyze anything from small sets of candidate gene markers to genome-wide arrays of hundreds of thousands of markers.Markers can be filtered out before analysis if they have low call rate, low minor allele frequency, or if they fail a Hardy-Weinberg equilibrium test. Nonetheless, data analysis filters inherent in the software can eliminate, at least partly, these problematic markers.Currently, linkage disequilibrium (LD) among markers is ignored during the analysis, although it is useful for the validation and interpretation of results.. The original genotyping was performed in the laboratory of Drs. Singleton and Hardy , Bethesda, MD USA [To illustrate the method we used data from the SNP Resource at the NINDS Human Genetics Resource Center DNA and Cell Line Repository , MD USA . We haveTo explore the power of HFCC we also analyzed a simulated dataset that was originally generated to evaluate the power of a different gene-gene interaction method . These cHFCC can perform a single-locus genome-wide association scan. A di-allelic marker with alleles A and B, has 3 possible genotypes: AA, AB and BB. For each genetic marker, HFCC performs three statistical tests, comparing each genotype against the other two. For example, the frequency of the AA genotype is compared against the combined frequency of the AB-BB genotypes, in cases and controls. This could be considered a dominance model test for the B allele. Similarly, recessive (BB versus AA-AB) and heterozygote models (AB versus AA-BB) are also considered. The test for association between the established genotypic classes and the case-control groups can be a Wald test or a chi-squared test with one degree of freedom (df).HFCC can also perform a multi-locus genome-wide association scan. For a two-locus scan, HFCC first forms all possible combinations of two markers from all available markers. For each two-marker combination , there are 9 possible genotypic classes , and a total of 512 fully penetrant disease models . For ourAs in the single-locus case, the statistical test involves comparing the frequency of two sets of genotypic classes in cases versus controls. The two sets of genotypic classes are defined by the model being tested. For example, in the case of the double-recessive model, the frequency of the BBDD genotypic class is compared against the combined frequency of all other genotypes (AACC through BBCD), in cases and controls, from which a Wald-test Z statistic, or a chi-squared statistic with one degree of freedom, can be obtained.Another analysis option is a more general multi-locus test  which coFor a three-locus scan, there are 27 possible genotypic classes, and the software is currently implemented to test the 27 simplest 3-locus genetic models, comparing the frequency of a genotypic class  against the combined frequency of all other genotypes.A variety of post-hoc statistical tests are included in the post-hoc analysis software, named Alambique. For single-locus analysis, it is possible to carry out Hardy-Weinberg equilibrium, heterozygous, homozygous, allele positivity (dominance), recessive, common odds ratio (Armitage's trend) , and genFor the two-locus analysis, all 255 fully-penetrant models can be tested. Moreover, interaction indices can be estimated to determine to which extent an observed two-locus association deviates from an additive model . FinallyThese post-hoc analyses are useful to determine which genetic model explains better an observed association, and to measure the epistatic component of associated multi-locus combinations.The statistical tests for association of a trait with a marker are based on the differential frequency between cases and controls of a particular allelic or genotypic combination. Comparing the full sample of cases versus the full sample of controls is the most powerful approach to find statistically significant associations. Nonetheless, to evaluate genomewide association or epistasis we need to test a very large number of markers or marker combinations, which in turn can produce a large number of spurious results. Therefore, we need to improve the filtering of false-positive results, at the expense of increasing the false-negative findings.We have approached this multiple-testing issue by partitioning the available sample into multiple replication groups. Cases are selected randomly to be part of one and only one case group, and similarly for control individuals and control groups. Then, the statistical analysis is performed on each of the paired case-control groups, and results that are consistent across all replication groups are selected. This sample-splitting technique may prove less powerful to detect positive results in general, but provides a powerful tool to eliminate false positives, thereby highlighting potentially true effects that are consistent across samples. The number of groups into which the sample is partitioned can be chosen by the user depending on the study design, and the number of subjects and markers available for analysis.This multi-group strategy is one of the differentiating aspects between HFCC and conventional association methods, and it is particularly useful for the analysis of multiple related phenotypes. Case groups are directly defined by phenotypic criteria, and control groups are matched to each case group. This type of analysis can reveal genetic associations that are common to these phenotypes, revealing a common etiology for multiple symptoms of a disease, or for several related diseases .HFCC has developed an efficient noise filter, by applying the association tests to independent groups of controls. Positive results that arise from a comparison of two groups of controls must be spurious associations due to marker or sample characteristics. These spurious associations can be filtered out of the results from the case-control analysis, providing an efficient sample-specific background noise filter.HFCC requires specific data and parameter files. The input data file is a simple-text matrix of integers in which rows represent genetic markers and columns represent individuals. Each integer represents the genotype for one individual at one marker, coded as 0 for missing, 1 for one homozygote, 2 for the heterozygote, and 3 for the other homozygote. These integers are entered sequentially, with no blank spaces or lines, to save space. There is one data matrix for each group of cases , controls  and noise-filter controls , as can be seen in Figure The following algorithm describes HFCC analysis flow Figure . GeneticThese selected marker variables can then be included in two sequential post-hoc analyses which aid in the interpretation of the results. The first post-hoc analysis yields odds ratios and chi-squared values for all selected marker variables. It also applies a direction filter, by selecting only those results which display the same direction of effect in all replication groups, and writes a new output file, which contains only those marker variables with a significant and consistent effect (same direction and same model) in all replication groups.The second post-hoc analysis (Alambique) identifies the best type of genetic model for each association selected in the first post-hoc analysis. For this reason, all replication groups are combined into a single group, that is, all cases in one case group and all controls in a control group. Alambique has its own noise elimination algorithm, denominated tracking filter. Many of the selected associations are due to what we call a tracking marker, a locus with a very large marginal effect. Many of these tracking markers are not in HWE and are filtered at this stage. In any case, having a large marginal effect makes a locus appear in many two-locus associations, because the large effect tracks other loci. Because our focus is on finding epistatic interactions, the many positive associations due to these tracking effects can be filtered out and analyzed independently. For the remaining marker variables, which have passed this tracking filter, there is one analysis option that groups the two-locus results into those with marginal effects for only one locus , or for both loci (simultaneous effect) or those without marginal effects (epistatic effect) . Some ofDue to the extremely time-consuming and computer-intensive nature of these analyses, especially for genomewide multi-locus analysis, it will often be necessary to run HFCC under a small selection of genetic models, and then use Alambique to identify the best genetic model for the selected markers. The number and selection of genetic models to analyze will depend on the phenotype, the dataset, previous knowledge and computer resources available.We have applied HFCC to both simulated and real datasets to illustrate the power and the functioning of the method.To evaluate the power of the method, we analyzed a simulated dataset published previously . Data weTo detect potential epistatic loci, we ran HFCC two-locus analysis with nine simple genetic models, the M1, M2 and M16 models . There aHFCC had excellent power (>96%), with a Type I error of 0.01, to detect the simulated two-locus interactions under most genetic models and noise conditions, including genotyping error and missing data , but were included in order to test the data filters inherent in HFCC, which are meant to eliminate, at least partially, these problematic markers.The 270 cases and 271 controls were separated into groups, to illustrate HFCC multi-group analysis strategy. We created 3 replication groups of 90 cases each  two-locus marker combinations. In order to be considered a preliminary positive result, the chi-squared (1 df) cut-off value was set at 6.64, which yields a probability value of 0.01 for each replication group . Although this p-value may be considered low compared to the number of statistical tests performed, this is only a cut-off to select preliminary positive results, which are then filtered and subjected to post-hoc analysis to select the most promising results. We obtained a total of 418,535 preliminary two-locus associations at this p-value cut-off  had effects in the same direction in all replication groups. These results can then be grouped into those with marginal effects in both loci (simultaneous), only one marginal effect , and no marginal effect (epistatic). A marginal effect was defined as a single-locus effect with a chi-squared (1 df) statistic larger than 3.84 . This liberal cut-off serves our goal of selecting as pure epistatic effects those marker combinations with no or small marginal effects. Under these criteria, 22.3%  of the results had simultaneous marginal effects, 77.7%  had conditional effects, and only 0.01% (35) had epistatic effects. At this point, out of the hundreds of thousands of preliminary results, only 35 two-locus associations without marginal effects remained, very likely to be epistatic interactions. The many thousand simultaneous and conditional results may also involve epistatic effects on top of the marginal effects, but the large number of them prevents a thorough post-hoc analysis.In order to distil further the post-direction-filter results we can apply the tracking filter. Many of these two-locus associations are due to what we have denominated tracking loci, that is, markers with large marginal effects, which therefore display significant two-locus effects with many other markers. Most of these tracking markers exhibit large association effects because they fail HWE, and they are filtered out at this stage. In this Parkinson dataset we detected 36 tracking markers, defined as those markers showing up in 270 or more two-locus associations (top 0.1% of post-direction-filter results). Most of these tracking markers (83.3%) failed HWE (p < 0.001 in controls or <0.0001 in cases), and others failed minor allele frequency (MAF<0.1) or call rate (CR<90%) criteria. Therefore, results involving these markers can be safely excluded.A few of these tracking markers represent the best single-locus association results which, due to their large marginal effects, also appear in a large number of two-locus association results. These large-single-locus-effect tracking markers need their own specific post-hoc analysis. Because of their large marginal effects, these markers are likely identifiable by single-locus analysis, but it is still noteworthy to discover if they have epistatic effects, and with which genes. However, it is hard to identify a significant epistatic interaction in the background of such a large marginal effect. Individual post-hoc analysis for each of these markers may identify the most likely multi-locus combination involving those marker.Interestingly, by filtering out the marker combinations involving the tracking markers, we can eliminate 91.8% of the previous positive results. Most of these results were conditional effects, involving the tracking locus (with a large single-locus effect) and a tracked locus . The post-tracking-filter results include a total of 35 marker variables with epistatic effects, 6,706 with conditional effects, and 19,630 with simultaneous effects.We can repeat this data filtering process, but this time starting by applying the control noise filter. The control filter was set to employ the same statistical cut-off (chi-squared = 6.64) used in the case-control comparisons. Association results above this cut-off value obtained in analysis of two control groups can be deemed problematic and excluded from further analysis. This control filter was able to eliminate 18.75% of the preliminary results, leaving a total of 340,043 associations (81.25%). Applying the direction filter to the post-control-filter results eliminates only a further 5.84% of preliminary results, yielding a total of 320,188 associations, almost exactly the same quantity as when the direction filter was used alone. Therefore, the control and direction filters seem to eliminate most of the same results, which reassures their correct functioning and also allow for different analysis strategies. On one hand, when enough control subjects are not available and consequently the control filter can not be used, these results suggest that the direction filter may work well alone. On the other hand, the direction filter may not be useful for some multiple-phenotype studies, expecting effects on different directions in different replication groups. Thus, in some scenarios, the control and tracking filters may provide enough noise elimination by themselves.When the tracking filter was applied to the results selected by the control and direction filters, we obtained 35 two-locus combinations with epistatic effects, 6,701 with conditional effects, and 19,611 with simultaneous effects. By applying three consecutive data filters , we excluded almost 94% of the preliminary results. The remaining 6.3% of results are subsequently analyzed for departures of additive or multiplicative two-locus models, to estimate their potential for epistatic effects.HFCC analysis yielded 35 two-locus combinations with epistatic effects and no noticeable single-locus marginal effects, ten of which are displayed in Table In order to validate to some extent these results, and without immediate access to a truly independent sample, we created 10 validation samples by randomly re-creating the case groups (F) from the full pool of cases (N = 270), and similarly for the control groups (C). In the described analysis of the Parkinson dataset, three replication groups were created randomly, to find consistent results across these groups. To examine the possible effect of this random group membership, the replication groups were re-created randomly and reanalysed in what we called validation experiments. These validation experiments are not permutation simulations to estimate the empirical significance level of parameter estimates, and are not a standard bootstrapping technique because they use sampling without replacement. The replication groups in each validation analysis were re-created under association (keeping cases as cases and controls as controls), and not under the null hypothesis of no association. These validation experiments are used to examine the consistency of results when the replication groups are re-created.2 > 3.84) of results into different types of effects , a large variability in results across validation analyses is reasonable.The control noise filter was not employed for these validations analyses to save computing time, since it was found that for this dataset the direction and tracking filters alone were sufficiently efficient. Because we are using the same set of cases and controls in all the validation groups, a high degree of consistency of results across validations analyses would be expected a priori. Nonetheless, due to the small sample size of each group, the many requirements for the selection of marker variables, such as the consistency of strength and direction of result in three replication groups, and the subjective categorization  showed up in the original analysis and the 10 validation samples. Five other combinations with simultaneous effects were consistent in 10 out of the 11 samples, and 28 combinations were consistent in 9 samples. Of the conditional results, thirteen marker combinations were consistent in 8 samples. Perhaps because their effect is harder to replicate, only one epistatic marker combination was present in as much as 5 samples, while 2 combinations were present in 4 samples, and three combinations in three samples.HFCC is a new computer software for exhaustive genome-wide analysis of multi-locus association effects in a case-control design. It carries out different types of statistical tests to assess a variety of genetic and epistatic models. HFCC differs from other association or multi-locus methods in that it can analyze simultaneously multiple samples or multiple phenotypes, and incorporates several complementary noise-signal filters, and also post-hoc analysis tools. To address the enormous computing task, it is elegantly designed to take advantage of the multiple CPUs available nowadays in computer servers or clusters.The goal of HFCC analysis is to find multi-locus marker combinations which are significantly associated with a phenotype, especially those displaying interaction effects which may not be detected in a single-locus analysis. By setting the type of genetic model, the number of subjects in each group, the number of replication groups, the statistical cut-offs for the different tests, and applying different noise elimination filters, HFCC can arrive at a selection of the most promising multi-locus combinations.Other multi-locus methods to detect gene-gene interactions exist. For example MDR  is a metFor this illustrative application of the software we have also analyzed an open-access dataset of Parkinson's disease patients and unaffected controls. We would like to emphasize here the importance of these public datasets of real data to improve the quality of applied research, and also to foster the development of new methodology.One of the pecularities of HFCC is the possibility of dividing the case-control sample into replication groups, to detect only those effects that are consistent across samples. The number of replication case-control groups to be used depends on the available dataset (sample size and number of genetic markers). It is an important analysis parameter because the overall significance level is a function of the selected critical value for the test statistic and the number of replication groups. For the current analysis, the sample of cases was divided into three replication groups, and so were the controls. This strategy focuses on the detection of large and consistent effects, which are hopefully detectable with the available datasets. It is reasonable to expect that the joint effect of a combination of genes is larger and more penetrant than each of the single-locus effects, and therefore under some circumstances , these multi-locus effects can be identified. The detection of small, rare or heterogeneous effects may need larger samples and more complex models.HFCC allows for a variety of different genetic models and tests. Different models may be necessary to detect different types of effects, such as recessive, dominant or heterozygote effects. The best analysis strategy may depend on prior knowledge or hypothesis about the trait. An optimal strategy would apply a selected subset of models which would maximize the chances of detecting a hypothesized effect. For example, for this Parkinson's disease study, we have employed a subset of nine epistatic models which typically detects recessive effects.Another characteristic of HFCC analysis is the successive application of noise-signal filters. Control groups can be compared against each other to remove background noise associations. Direction of effect can be taken into account, so that only those results consistent in strength and direction across replication samples are selected. A final filter is able to remove those multi-locus results which are primarily due to quality-control failing markers  or to large single-locus effects. The remaining multi-locus combinations can be categorized into epistatic, conditional and simultaneous effects, and interaction tests can be used to detect possible epistatic interactions over and above the marginal effects. The selected markers can then be included in a validation analysis in an independent sample. As an illustration, Table -6). Using a stringer significance level, such as a Bonferroni correction, may be overly conservative, sometimes potentially missing real effects. HFCC filters and post-hoc analyses help selecting the most promising two-locus interactions from a large set of preliminary findings. For example, all two-marker combinations in Table 2 (1 df) in the range 21–30), and they all also deviate from a multiplicative model (case-only X2 (1 df) in the range 7–33) suggesting an epistatic interaction.The Parkinson's disease study reported here can illustrate several issues regarding the search for epistatic effects in large datasets. One of the most difficult tasks in large dataset analysis is selecting the most promising candidate results. The huge number of statistical tests performed requires a severe statistical cut-off, or a protocol of data filtering, to be able to select only the most promising results. For example, the two-locus analysis of a genome-wide association SNP dataset presented here reveals several hundred thousands two-locus marker combinations at a liberal significance level  at a significance level of 0.01 per replication group. However, this small dataset is underpowered to find more moderate, and perhaps more realistic, effect sizes. The general lack of consistency suggested by our own sensitivity analysis may be a consequence of the small sample size analyzed. Fung et al. (2006) claimed that there is no common genetic variant that exerts a large genetic risk for late-onset Parkinson's disease in white North Americans. Multi-locus analysis may, however, reveal the existence of large complex (multi-locus) genetic effects.HFCC provides a tool for the genome-wide study of epistasis. Its use may depend heavily on the researcher's goals and the data available. For this reason, it is hard to provide general guidelines on the optimal parameters for analysis, but HFCC's flexibility to accommodate to the specific needs of each study is a great asset.-6 yields a total of 784,506 preliminary positive results. The analysis of the same data splitted in three replication groups, each with alpha = 10-2, yields only 418,535 results (53% of the single-group results).A key parameter is the number of replication groups. When the available sample size is fixed, dividing the sample into more replication groups decreases the power of the analysis, but also increases the confidence in the remaining results. For example, the two-locus analysis of the full Parkinson's dataset in one case-control group with a Type I error set at 10There is not an optimal number of replication groups. Researchers need to select this parameter as well as the significance level cut-off to fit their dataset and study design. For example, a study of three related diseases or phenotypes suggests the use of three replication groups. In the case of a single disease, the number of replication groups, the sample size in each group, and the statistical cut-off should be chosen depending on the nature of the study. A strict statistical correction may be necessary if the results are to be conclusive, while a more relaxed criterion may be used in a two-stage study where the goal of the preliminary analysis is to select a subset of markers for subsequent validation.HFCC's flexibility is also possible in the application of data filters. The results displayed in Table There are also 255 possible two-marker genetic models that can be tested. Many of them are correlated, so it is probably not necessary to test them all. We suggest using a small subsample of models that cover the researcher's hypothesis. For example, for the Parkinson's analysis in this paper we tested nine simple genetic models. To identify subsamples of models that may optimize the chances of discovering epistatic effects of different nature would need a thorough simulation analysis that is beyond the scope of the current paper. Another analysis option is to use more general tests of epistasis, which are also implemented in the software.9 statistical tests. The two-locus analysis of these data in one case-control group with a Type I error set at 10-6 yields a total of 784,506 preliminary positive results, about 10% more of those expected by chance. This false positive inflation is probably due to the tracking markers (mainly QC-fail markers) as well as to the correlated nature of some of the statistical tests, and can be controlled by the use of replication groups, or by applying more stringent cut-offs if necessary.The two-locus analysis of the full Parkinson's dataset as presented here comprises a total of 708 × 10-2 (chi-square 6.64), the Type I error was actually lower than expected (approximately around 0.006 on average). These results demonstrate that HFCC analysis is not only powerful but can also be conservative, preserving against Types I and II Errors. More thorough simulations to assess the impact of sample size, allele frequency, number of replication groups, and noise filter applications are needed in the future to understand these issues in detail.For the simulated dataset, analyzed with only one case-control group a significance level of 10Applying strict multiple testing correction (Bonferroni) to the Parkison's disease analysis, we do not find any significant two-locus interactions. The reason for this may be the small sample size available in the Parkinson's dataset. But we can still select the most promising two-locus results for subsequent validation. The key issue is whether we are concerned with achieving an absolute level of statistical significance, which may not be properly defined in this setting given the complexity of the analysis suggested , or selecting the most promising markers or marker combinations that pass a more or less stringent statistical criterion. In either case, the usefulness of HFCC for selecting marker combinations for later validation is doubtless.9 two-locus marker combinations. Nine genetic models were tested in the current study, resulting in a total of 708 × 109 statistical tests. Moreover, these tests may be carried out in as many as three case-control replication groups, and also in as many as three control-control noise-filter groups, so the computing task is staggering. HFCC is programmed to take advantage of computer resources by dividing the computing task into processes which can migrate to the available CPUs in a computer server or cluster. For the current analysis, we employed a computer cluster consisting of twelve 3.2 GHz CPUs, which was able to carry out the full genome-wide analysis in approximately 5 days.Multi-locus analysis is computationally intensive and is therefore limited by computing capabilities. HFCC is a relatively fast algorithm considering the huge number of computations it performs. The dataset analyzed in this study consists of 396,591 genetic markers, which results in 78.6 × 10Another computational complication for multi-locus analysis is related to RAM memory. The data matrices need to be loaded onto memory to speed computations, and therefore a limitation exists for the analysis of very large datasets  where RAM memory is rapidly exhausted. This limitation, however, can be solved with parallel processing techniques (MPI like), such as dividing the data matrices into smaller subsets which are distributed around the computer network.HFCC can perform more complex multi-locus analysis , but the number of computations grows exponentially with the number of interacting markers, and the analysis becomes dependent on computing resources and time limitations. Depending on these resources, genome-wide three- or four-locus analysis may require a two-stage strategy, where some markers are selected first by single-locus analysis, and then employed to guide the multi-locus testing . Our exhIt is also important to note that linkage disequilibrium (LD) is unaccounted for in our analyses. LD reflects an association among markers and therefore can affect the results of some tests. For example, it can produce a significant case-only chi-squared test. Nonetheless, HFCC's algorithm and analysis filters seem to prevent this bias. In the case where one marker is associated with several markers in LD, these results are detected in the last stage of marker selection.In summary, we propose that genome-wide multi-locus analysis is performed on available datasets of common diseases, because they can exploit the large genetic datasets and computing resources becoming available, to open a new phase of genetic analysis. The analysis of Parkinson's disease reported here represents the first exhaustive genome-wide epistasis search on a real dataset, effectively handling hundred of thousands of genetic markers, and demonstrating its feasibility. Due to the small sample size, however, these results are only illustrative and require re-analysis or confirmation in larger datasets. These multi-locus analyses would not substitute conventional single-locus analysis but add a new layer of genome-wide association studies, allowing the identification of new candidate markers for further validation. HFCC is a new genome-wide multi-locus software, which allows the user a high degree of control over analysis parameters, so that data analysis can be tailored to the specific needs of each project. HFCC can have a great impact on the discovery of the genetic causes of common diseases, especially to identify those multi-locus effects that may not be detectable using the available single-locus methods. The discovery of new genes affecting a disease may be useful as predictive tools or to find new therapeutic targets. HFCC has multiple applications, not only in the study of disease phenotypes, but also of other qualitative traits, and can be used in clinical trials or pharmacogenetics studies.HFCC is written in C and freely available for linux platforms from this Website: CPU: central processing unit; GE: genotyping error; GH: genotyping heterogeneity; HFCC: hypothesis free clinical cloning; HWE: Hardy-Weinberg equilibrium; LD: linkage disequilibrium; MS: missing data; PC: phenocopy; SNP: single nucleotide polymorphism; XOR: logical exclusive "or" statement.JG, AG–P, and AR conceived and designed the experiments. JG, AG–P and AR analyzed the data. JG and AR wrote the paper. AR conceived the analysis tool. All authors helped develop the analysis tool. FB and AQ wrote the analysis tool. All authors read and approved the final manuscript.As a declaration of competing financial interest, authors in the paper are employees and/or shareholders in Neocodex. Neocodex owns a patent on  the HFCC algorithm described in this paper (WO 2008010195 20080124).


Mortality due to cannibalism in laying hens is a difficult trait to improve genetically, because censoring is high  and it may depend on both the individual itself and the behaviour of its group members, so-called associative effects . To analyse survival data, survival analysis can be used. However, it is not possible to include associative effects in the current software for survival analysis. A solution could be to combine survival analysis and a linear animal model including associative effects. This paper presents a two-step approach (2STEP), combining survival analysis and a linear animal model including associative effects (LAM).Data of three purebred White Leghorn layer lines from Institut de Sélection Animale B.V., a Hendrix Genetics company, were used in this study. For the statistical analysis, survival data on 16,780 hens kept in four-bird cages with intact beaks were used. Genetic parameters for direct and associative effects on survival time were estimated using 2STEP. Cross validation was used to compare 2STEP with LAM. LAM was applied directly to estimate genetic parameters for social effects on observed survival days.Using 2STEP, total heritable variance, including both direct and associative genetic effects, expressed as the proportion of phenotypic variance, ranged from 32% to 64%. These results were substantially larger than when using LAM. However, cross validation showed that 2STEP gave approximately the same survival curves and rank correlations as LAM. Furthermore, cross validation showed that selection based on both direct and associative genetic effects, using either 2STEP or LAM, gave the best prediction of survival time.It can be concluded that 2STEP can be used to estimate genetic parameters for direct and associative effects on survival time in laying hens. Using 2STEP increased the heritable variance in survival time. Cross validation showed that social genetic effects contribute to a large difference in survival days between two extreme groups. Genetic selection targeting both direct and associative effects is expected to reduce mortality due to cannibalism in laying hens. Mortality due to cannibalism in laying hens is a worldwide economic, health, and welfare problem, occurring in all types of commercial poultry housing systems . Due to One of the possibilities is to use genetic selection ,3. Howevt [Heritabilities for survival traits are often estimated using a linear animal model ,13. Howet ,16.1/3 to 2/3 of the heritable variation in survival days is due to social interactions. To reduce mortality due to cannibalism, the classical model for a given genotype must be extended to consider not only the individuals' direct effect of its own genes, but also the associative genetic effect of the individual on the phenotypes of its group members [Social interactions occur when individuals are kept together in a group. Wolf  has ment members . Muir [2 members . Further members  has founDucrocq et al.  have proIn this paper, we apply a similar two-step approach to estimate genetic parameters for direct and associative effects on survival time in laying hens. In the second step, we will use the linear animal model including associative effects to estimate genetic parameters ,13,20. FFor this study, the same data were used as described in Ellen et al. . The maiData of three purebred White Leghorn layer lines from Institut de Sélection Animale B.V., a Hendrix Genetics company, were used in this study. The three lines were coded: W1, WB, and WF. For each line, observations on survival time of a single generation were used. Chickens of each line were hatched in two batches, each batch consisting of four age groups, differing by two weeks each. All chickens had intact beaks.When the hens were on average 17 weeks old, they were transported to two laying houses with traditional four-bird-battery cages. Each batch was placed in another laying house. In both laying houses, the 17-week-old hens were allocated to laying cages, with four birds of the same line and age in a cage. The individuals making up a cage were combined at random. In both laying houses, cages were grouped into eight double rows. Each row consisted of three levels . A feeding trough was in front of the cages, and each pair of back-to-back cages shared two drinking nipples.A). To avoid pedigree errors, hens with unknown identification or double identification were coded as having an unknown pedigree (n = 101). The observations on these hens were included in the analysis to better estimate fixed effects.Sires used for both laying houses were largely the same while dams were different. For all three lines, sires and dams were mated at random. Each sire was mated to approximately eight dams, and each dam contributed on average 12.3 female offspring. Five generations of pedigree were included in the calculation of the relationship matrix  at the end of the study. From these data, the survival rate was calculated as the percentage of laying hens still alive at the end of the study. Survival days were defined as the number of days from the start of the study (day of transport to laying houses) till either death or the end of the study. Hens that died before the end of the study were referred to as a failure (event = 1), whereas hens still alive at the end of the study were referred to as censored (event = 0). In total, 196 hens were removed from the study, due to reasons other than mortality. These hens were referred to as censored (event = 0). For the statistical analysis, 6,276 records were used for line W1; 6,916 for line WB; and 3,588 for line WF.Data were analysed separately for each line. Two methods to estimate genetic parameters were compared: 1) LAM, a linear animal model including direct and associative effects applied directly to the observed survival days; this procedure is described in detail in , and 2) Data were analysed using the Cox animal model . The Coxi a) and an associated weight (iω) for each hen i. It can be shown that i ωis the estimated cumulative risk of animal i from time 0 to censoring time or death, and is therefore a function of the (possibly censored) length of life of hen i, her censoring code (i δ= 0/1), and the fixed effects in the model [i was [Using survival analysis results in a breeding value (he model . The psel [i was :(1)i δis the censoring code of individual i ; i ais the estimated direct breeding value of individual i; and iω is the associated weight of individual i. Pseudo-records are functions of the data and of the effects estimated in the survival model, such that when a straightforward BLUP animal genetic evaluation is applied on these pseudo-records, the same estimated breeding values are obtained as in the initial survival model.where i. The correlation between the estimated breeding values of 2STEP and the estimated breeding values of the survival analysis was calculated [To verify 2STEP, pseudo-records with appropriate weights were analysed to estimate breeding values with a univariate BLUP animal model, with a heterogeneous residual variance lculated . As expeTo estimate variances and covariances for direct and associative effects, using the pseudo-records and associated weights from step 1, the model of Muir  and Bijmy is a vector of the pseudo-records aD is a vector of direct breeding values, with incidence matrix ZD linking observations on individuals to their direct breeding value; aS is a vector of associative breeding values, with incidence matrix ZS linking observations on individuals to the associative breeding values of their group members ; and e is a vector of residuals, where iω) and the !WT statement in ASReml [where n ASReml  and fixi[ to one .The covariance structure of genetic terms is e, is given by ij R= 1 when i = j, ij R= ρ when i and j are in the same group (i ≠ j), and ij Ris zero otherwise. The value of ρ was estimated in the analysis, using a CORU statement in the residual variance structure in ASReml [where a et al.  have shon ASReml .n - 1 group members. In this study, n = 4. The total heritable impact of an individual on the population, referred to as its total breeding value (TBV), equals the sum of its direct breeding value and n - 1 times its associative breeding value: TBVi = AD, i + (n - 1) Ai S,[T2 expresses the total heritable variance relative to the phenotypic variance and is, therefore, a generalisation of the conventional h2 to account for social interactions.When social interactions exist among individuals, each individual interacts with  1) AS,i . The tot1) AS,i [,34. WithWe compared 2STEP to LAM using cross validation . With crComparing the predicted phenotypes of both methods is difficult for two reasons. First, a scale difference exists between estimated breeding values (EBV) of 2STEP and EBV of LAM. EBV of LAM are on the observed scale for survival days, whereas EBV of 2STEP are on the hazard rate scale. Transforming EBV of 2STEP into survival days is somewhat difficult, because the transformation is non-linear. Therefore, the predicted phenotypes using 2STEP are on the hazard rate scale, whereas the predicted phenotypes using LAM are on the observed scale for survival days. Second, in our dataset approximately 50-70% of the data were censored . These animals do not have an observed phenotype. In other words, a large proportion of the "observed" phenotypes is censored, and cannot be compared directly to their prediction. However, we know that their observed phenotypes are larger than those of animals that are not censored, which is highly relevant information.To deal with these two difficulties, we used two approaches to evaluate both methods. The first approach is based on using groups of animals rather than single individuals. In this approach, for each subset and method, 25% of the animals with the best predicted phenotypes or hazard rates were selected as the best groups , and 25% of the animals with the worst predicted phenotypes or hazard rates were selected as the worst groups. The Kaplan-Meier estimate of the survival curve was plotted for the best and worst groups based on the observed phenotypes. It was expected that the best groups would yield the best Kaplan-Meier estimate of the survival curve, whereas the worst groups would yield the worst one. Moreover, for both methods the mean observed survival days were calculated for the best and worst groups. From these, the difference in survival days between the best and worst group was calculated. For the best groups the percentage of overlapping animals, between 2STEP and LAM, was calculated.D, i A); associative BV of the group members  classical BV (CBV); 2) direct BV of the individual itself  or lowest predicted hazard rate (2STEP) have the highest expected value for observed survival days. Therefore, the rank correlation between predicted and observed values can be used for both methods. Hence, the use of rank rather than Pearson correlation solves the scale issue. The remaining problem is animals with censored records, which have an unknown rank for the observed phenotype. However, the fact that animals were censored, represents an important information because those animals had the highest observed survival days. Animals with known phenotypes have a rank 1 through i is the sum of the estimated direct breeding value (or hazard rate) of hen Before calculating rank correlations, observed phenotypes were corrected for the fixed effects , . Next,rIH), the expected correlation between predicted and observed phenotypes would be equal to IH ris the accuracy of The rank correlation between predicted and observed phenotypes depends not only on the accuracy of the estimated breeding values underlying the predictions, but is also affected by non-genetic components of the observed phenotype. If breeding values underlying predicted phenotypes were estimated with full accuracy, the correlation between predicted and observed phenotypes would be equal to the square root of the proportion of phenotypic variance explained by breeding values,   Figure , where rt. The survival rate differed significantly between lines in both laying houses (p < 0.01). Line WF showed the highest survival rate i.e. 74.6%, whereas line WB showed the lowest survival rate i.e. 52.9%.The Kaplan-Meier estimate of the survival function  was plotT2 ), whereas line WF showed the highest T2 , ranging from 32% through 64%. The estimated genetic correlation between direct breeding value and associative breeding value (A r) was positive but not significantly different from zero in line W1 (0.13) and A line WF (0.55), and negative and not significantly different from zero in line WB (- 0.20). Table The estimated genetic parameters for direct and associative effects using 2STEP are given in Table Figure To quantify the contribution of social effects to the predicted phenotype or hazard rate, the phenotype or hazard rate is predicted using different breeding values, CBV, DBV, SBV and DSBV. Again, for each of the three lines, 25% of the animals with best predicted phenotypes or hazard rates were selected as the best group, and 25% of the animals with the worst predicted phenotypes or hazard rates were selected as the worst group. Table The rank correlations between the observed phenotype, adjusted for fixed effects and censoring, and the predicted phenotype, T2 ), ranged from 32% (line WB) through 64% (line WF). Using 2STEP, T2 is substantially larger than using LAM. However, results of the cross validation do not show any difference between the two methods. Using cross validation, we showed that the difference in survival days between two extreme groups is largest when selecting on DSBV. Furthermore, we showed that social genetic effects contribute substantially to the difference in survival days  ,39. FurtWe made a number of assumptions in the cross validation, when using the rank correlation, that may have affected the results. First, observed phenotypes were corrected for fixed effects using LAM, which may have favoured LAM compared to 2STEP. Second, when calculating the rank correlation, we assumed that ranks of censored records were in random order. This will probably not be true if censored animals were given the opportunity to actually produce a record. Alternatively, we could have used the ranks of the uncensored records only. However, in that case we would have ignored the information that the censored records are actually the "best records".For all three layer lines, censoring occurred at the same time, at the end of the study. It could be that when censoring occurs at different times during the study period, differences may occur between the two methods. To investigate this, 50% of the censored records of line W1 were censored half way the study period (at 200 days). Again cross validation was used to compare the two methods. For both methods, the difference in survival days between the group with best predicted phenotypes or hazard rates and the group with the worst predicted phenotypes or hazard rates was calculated. For 2STEP the difference was 25.9 days, whereas for LAM the difference was 15.7 days. This indicates that, when the censoring times differ between individuals, 2STEP can better identify the genetically superior individuals than LAM. Thus both methods are practically equivalent when all animals are censored at the same survival time; with variation in censoring time, the 2STEP is superior.This study shows that it is possible to use 2STEP, a combination of survival analysis and a linear animal model including associative effects, to estimate genetic parameters for the direct and associative effects on survival time in laying hens. We used cross validation to compare 2STEP with LAM. Based on the results in this paper, we can conclude that both 2STEP and LAM are practically equivalent when all animals are censored at the same survival time. Cross validation showed that selecting on a combination of the direct BV and the associative BV of the group members (DSBV) gave the largest difference in survival days between two extreme groups.Furthermore, this study showed that social genetic effects contribute substantial to the difference in survival days between two extreme groups, which means that social genetic effects do exist.2STEP: two-step approach; LAM: linear animal model including direct and associative effects; CBV: classical breeding value; DBV: direct breeding value: SBV: associative breeding value; DSBV: combination of the direct breeding value of the individual itself and the associative breeding value of its group members.The authors declare that they have no competing interests.EDE performed the data analysis and the cross validation, wrote and prepared the manuscript for submission. VD helped with the data analysis and cross validation and reviewed the manuscript. BJD helped with the data analysis and reviewed the manuscript. RFV helped with the data analysis and reviewed the manuscript. PB was the principal supervisor of the study and assisted with data analysis, cross validation and preparation of the manuscript. All authors read and approved the manuscript.Example and mathematical proof of rank correlation with censoring.Click here for file


Statistical power calculations inform the design and interpretation of genetic association studies, but few programs are tailored to case-control studies of single nucleotide polymorphisms (SNPs) in unrelated subjects.We have developed the "Power for Genetic Association analyses" (PGA) package which comprises algorithms and graphical user interfaces for sample size and minimum detectable risk calculations using SNP or haplotype effects under different genetic models and study constrains. The software accounts for linkage disequilibrium and statistical multiple comparisons. The results are presented in graphs or tables and can be printed or exported in standard file formats.PGA is user friendly software that can facilitate decision making for association studies of candidate genes, fine-mapping studies, and whole-genome scans. Stand-alone executable files and a Matlab toolbox are available for download at:  StatiThe principals for power calculation can be found in standard statistical textbooks. Moreover, the scientific literature describes the mathematics of power analyses for a variety of specialized experimental designs -6. Yet, The "Power for Genetic Association Analyses" (PGA) package was developed in Matlab and consists a toolbox of command line functions and three unifying graphical user interfaces (GUIs). Users with a Matlab software can run the three GUIs or the command line functions in Matlab environment. Users without a Matlab license can download and install the compiled versions of the three GUIs that run as stand-alone applications under Windows XP or Vista operating systems.The program assumes that SNPs are biallelic and in Hardy-Weinberg equilibrium. All statistical tests are two-sided. The GUIs called PGA1 and PGA2 can display up to 9 scenarios simultaneously. Hence, they can be used to identify a robust choice of sample size. The graphs produced by each GUI can be printed or exported as TIF files, and tables of numerical results can be exported as HTML or csv files.2 = 1.0) is 800 cases and 800 controls  for genetic loci, given a fixed number of cases and controls, according to their minor allele frequencies (MAFs). MDRR can calculate the smallest relative risk that can be detected, with sample in hand, at the target level of power. Hence, PGA2 can assist in designing fine mapping studies of prominent genomic loci, identified from familial linkage analyses or genome-wide association studies. For example, multiple markers along a 600-kb segment on human chromosome 8q24 have recently been associated with prostate cancer susceptibility -17. Cons2) among the SNPs in the dataset, and from these data computes a summary measure of the EDF [An important utility for PGA1 and PGA2 is the GUI EDF, which calculates the effective degrees of freedom (EDF) for a particular set of SNP genotypes in linkage disequilibrium. This tool allows the user to assess the extent of multiple testing that is often overestimated or underestimated in naive power analyses. The EDF calculator accepts as input genotype data files from Hapmap  or tab-d the EDF  .• Project home page: • Operating system(s): Windows XP & Vista.• Programming language: Matlab.• Other requirements: To run the stand-alone GUIs, users without Matlab licenses should install first the MATLAB Component Runtime (MCR) that is available in the PGA home page.• Any restrictions to use by non-academics: None• Reviewers access to the software: reviewers can download the software in a way that preserves their anonymity, through the following links:• Readme file: .PGA.exe file: MCRinstaller file: IM drafted the manuscript and assisted in the design and implementation of the software. PSR conceived of the study, assisted in the design and implementation of the software and in drafting the manuscript. BEC developed the software and helped draft the manuscript.Supplementary Methods.Click here for fileTable 1. Major features of four commonly used power software for case-control association studies.Click here for file


Quantitative traits often underlie risk for complex diseases. For example, weight and body mass index (BMI) underlie the human abdominal obesity-metabolic syndrome. Many attempts have been made to identify quantitative trait loci (QTL) over the past decade, including association studies. However, a single QTL is often capable of affecting multiple traits, a quality known as gene pleiotropy. Gene pleiotropy may therefore cause a loss of power in association studies focused only on a single trait, whether based on single or multiple markers.We propose using principal-component-based multivariate regression (PCBMR) to test for gene pleiotropy with comprehensive evaluation. This method generates one or more independent canonical variables based on the principal components of original traits and conducts a multivariate regression to test for association with these new variables. Systematic simulation studies have shown that PCBMR has great power. PCBMR-based pleiotropic association studies of abdominal obesity-metabolic syndrome and its possible linkage to chromosomal band 3q27 identified 11 susceptibility genes with significant associations. Whereas some of these genes had been previously reported to be associated with metabolic traits, others had never been identified as metabolism-associated genes.PCBMR is a computationally efficient and powerful test for gene pleiotropy. Application of PCBMR to abdominal obesity-metabolic syndrome indicated the existence of gene pleiotropy affecting this syndrome. Quantitative traits often underlie increased risk for complex diseases. To understand the genetic basis of such traits, each trait is often separately tested for association with one or more markers. This approach has two disadvantages: 1) independent tests of each trait may lead to issues related to multiple testing; and 2) if a locus affects two or more traits, a single-trait study may lose the power to detect a pleiotropic effect, where a single gene influences multiple phenotypic traits.In the past decade, simultaneous analysis of multiple traits in the context of linkage mapping of quantitative trait loci (QTL) has attracted much attention. Three approaches to simultaneous analysis have been developed and broadly applied, the first of which is generalization of maximum likelihood (ML) ,2. AlthoThe resolution of QTL linkage mapping is generally low  . Thus, aIn this study, we propose to integrate two common methods that test for association by analyzing multiple traits simultaneously: principal components and multivariate regression. However, there are no comprehensive evaluations of this principal-component-based multivariate regression (PCBMR). In our study, we comprehensively evaluated the power and type I error of PCBMR using simulations that varied pleiotropic effects, linkage disequilibrium (LD), proportion of contributed correlation, and number of traits. We also used PCBMR to examine the pleiotropic effects of multiple traits on human abdominal obesity-metabolic syndrome.Human abdominal obesity-metabolic syndrome , a clust1 Yand 2 Yvaried from -0.35 to 0.37, with means for traits increasing as effect b increases. PCBMR generated two canonical variables for all simulated data. Power and type I error for the PCBMR and single-trait association studies are summarized in Table b = 0, the QTL had no effect on 1 Yand 2 Yand the type I errors were 4.5%-5.6% for PCBMR, 4.9%-6.1% for single-trait association without Bonferroni adjustment (SATN), and 2.8%-3.0% for single-trait association with Bonferroni adjustment (SATB) for the different models . Power depends on the assumption of genetic model, with power in decreasing order for ADD, DOM, GEN, and REC. For each model, the following results were obtained: 1) power generally increased in PCBMR, SATN, and SATB as effect b got larger, and PCBMR generally had more power than SATB and SATN; 2) the binomial exact test showed that PCBMR was significantly more powerful than SATB for all b > 0 (results not shown), and more powerful than SATN for b > 0.2 (marked with star); and 3) for b ≤ 0.2, there was no significant power difference between PCBMR and SATN.The correlation coefficients between traits 1 Yand 2 Yvaried from -0.25 to 0.32, and two canonical variables were generated by PCBMR for pleiotropic association studies. Power and type I error for PCBMR, SATN, and SATB are presented in Table r) between tested markers and QTLs ranged from 0 to 1.0. A correlation of r = 0 indicated that the tested marker and the QTL were independent and that there was no association between them. Under the differing assumptions in different genetic models , type I error was 4.2%-5.8% for PCBMR, 5.3%-5.8% for SATN, and 2.5%-3.1% for SATB. Power depended on the assumptions of the genetic models, and ADD, DOM, GEN, and REC had powers in decreasing order for all methods. For each model, the following results were obtained: 1) the powers of PCBMR, SATN, and SATB increased as r became larger; 2) according to the binomial exact test, PCBMR had significantly greater power than SATB (results not shown) for all r > 0, and significantly greater power than SATN when r > 0.2 in all but the REC model (marked with star); and 3) for r ≤ 0.2, there was no significant power difference between PCBMR and SATN.Correlation coefficients between 1 Yand 2 Ywere ≥0.98. Based on this, PCBMR generated a single canonical variable for the pleiotropic association test. The tested QTL exerted a simulated effect b from 0 to 4, and based on equation 3, the percentage of trait correlation contributed by the QTL, ρ(b)P, ranged from 0 to 20%. The type I error and power related to ρ(b) Pfor different methods are summarized in Table b = 0 (or ρ(b) = 0P) indicates that the tested QTL had no pleiotropic effect on the simulated traits. The type I error was 3.9%-5.6% for PCBMR, 4.2%-5.7% for SATN, and 2.4%-3.3% for SATB under the four genetic models, GEN, ADD, DOM, and REC. Power depended on the assumptions of the genetic models, with power in decreasing order for ADD, DOM, GEN, and REC. All methods increased in power as ρ(b) Pincreased. When b = 0.5 (or ρ(b) = 0.4%P), power was small for all three analytical methods; 6.4%-8.8% for PCBMR, 6.1%-8.4% for SATN, and 3.3%-4.7% for SATB. When b equaled 3.5 and 4 (ρ(b) = 15.7% Pand 19.5%), all methods had power close to 1 under various genetic models, except recessive ones. For b > 0, the binomial exact test showed that PCBMR was not significantly different in power from SATN, but was significantly more powerful than SATB.The correlation coefficients between simulated traits Under this simulation strategy, the number of traits affected by the QTL ranged from 2 to 10. The correlation coefficients between any pair of simulated traits were all ≥0.97 and the expected percentage of correlation contributed by the tested QTL was 8.7%. For all numbers of traits, PCBMR generated one canonical variable for the association test. Results are presented in Table -5, leaving 4,769 SNPs in the study. The characteristics of the study participants are summarized in Table 2), hip circumference , plasma insulin level  and plasma insulin/glucose ratio (I/G). The pairwise correlation coefficients (r) among adjusted traits are presented in Table r = 0.97).A total of 1,196 subjects with 5,529 SNPs in the candidate region of chromosome 3 (at 182-227cM or 173.4-198.8 Mb) made up the study population. Quality control measures included the removal of SNPs with minor allele frequencies of ≤0.01 and Hardy-Weinberg equilibrium p-values of ≤1e-5) are summarized in Tables The results of the PCBMR pleiotropic association studies based on the GEN model are presented in Figures -51e)  Figure .For the second trait group of INSULIN and I/G, PCBMR also generated a single canonical variable, and this variable explained 98.6% of the variance. Using the GEN model, thirty-four SNPs passed Bonferroni significance level Figure , of whic-log(P) = 109.86). To validate these PCBMR results, this SNP was extracted for further study. The SNP's phenotype distribution, divided by genotype, is presented in Table A' and 'G' and the frequency of the minor allele 'A' is 0.02. The Hardy-Weinberg Equilibrium (HWE) exact test/2 c(z[Where 2πϕi)]/2 .i = Xβi+Wτiμ, where X and W are explanatory variables of tested markers and other controlled variables, respectively, and i βand i τare their corresponding parameter vectors, which denoting effects on the μ, of the i-th canonical variable. The null hypothesis of no association (0H) is:In multivariate regression, PCBMR takes the canonic link. The mean regression model is 0 Hand the nested model as the one with restriction of 0H. PCBMR uses the likelihood ratio test (LRT) for the goodness of fit between full and nested models. Suppose ij zis the observed canonical variable i zon jth subject . The sample likelihood L(θ) based on equation (1) is:We define the full model as the one without restriction of i = μi = Xβi+Wτiθ, is input into equation (2), the T statistic is simplified to:The LRT statistic T is -2[logL the extent of the QTL pleiotropic effect; 2) the extent of LD between the tested marker and the pleiotropic QTL; 3) the portion of the trait correlation contributed by the tested QTL relative to the portion contributed by other QTL and environmental factors; and 4) the number of traits in the study. For each simulation, 1,000 datasets were generated. Type I error and power were calculated as percentages of the datasets, with 0.2 (p = 0.2), and simple linear regression models, 1 Y= 1U+X*1b+ 1 Eand 2 Y= 2U+X*2b+ 2E, are used to simulate traits 1 Yand 2Y. To simplify the simulation, we set 1 U= 0 and 2 U= 50, 1 Eand 2 Eto a normal distribution of mean 0 and standard deviation 2 E), and 1 = b2 = b bwith 11 different effects from 0 to 1.0 with steps of 0.1.The minor allele frequency of QTL is 1 = 0.2p) is not known directly. Instead, a marker of minor allele frequency 0.2 (1 = 0.2q) with LD to the QTL is genotyped for the test. Linear regression models, 1U, 2U, 1E, and 2 Eare set as above. The additive effects of 1 band 2 bare fixed at 1. LD was measured using a correlation coefficient (r) set between 0 and 1 with steps of 0.1. For a pair of alleles of a tested marker, denoted 1 Aand 2A, and those of the QTL, denoted 1 Band 2B, the following equation was used to calculate the joint allele frequencies of the tested marker and QTL. Based on r, D is calculated as 1B1) = p1q1+Df = p1(1-q1)-Df = (1-p1)q1-D f(Aand 2B2) = (1-p1)(1-q1)+D f(A[f(AiAj|Bi'Bj') .In this situation, the QTL ((1-q1)+D . Assumin1 Y= 1U+X*1b+1+W*d1+E1 Q*cand 2 Y= 2U+X*2b+2+W*d2Q*c+ 2E, were used to simulate traits 1 Yand 2Y, where 1 U= 0, 2 U= 50, and 1~E2~NE. The effects of 1 = b2 = b bare from 0 to 4 with steps of 0.5. Q is the second QTL with pleiotropic effects 1 c= 2 c= 4. Both X and Q have minor allele frequencies of 0.2. W is an environmental covariate with a standard normal distribution N and effects 1 d= 2 d= 4. The correlation, ρ, between 1 Yand 2Yis:Two linear regression models, X, ρ(b)P, isThe proportion of the correlation contributed by QTL ρ(b) Pincreases as b increases.so i Y= iU+X*b+Q*c+W*d+E , 2 to 10 traits were separately simulated in each dataset. Without loss of generality, X, Q, and W were defined as above with b = 2.5, c = 4, and d = 4 set correspondingly. E is distributed as normal, 2)N*50 Ufor i = 1, 2,..., 10.Based on the linear regression model, X variable for genotypes, which take values 0, 1 and 2: 1) X is treated as a factor with three levels for the general model (GEN) without assumption of any genetic inheritance; 2) X is a linear variable in the additive model (ADD); 3) X is 0 for genotypes 0 and 1, and is 1 for genotype 2 in the dominant model (DOM); and 4) X is 0 for genotype 1 and is 1 for genotypes 1 and 2 in the recessive model (REC). All four assumptions were considered separately for association tests by PCBMR and single trait regression.Power and type I error were estimated for PCBMR under the four simulation conditions. For comparison, we conducted single-trait association studies using classical linear regression with (STAB) and without (SATN) Bonferroni adjustment. For single-trait association studies, only the trait with the largest power or type I error was presented in the paper. Based on different assumptions of the genetic models, there are four possible ways of processing the 1 Mand 2 Mfor methods 1 and 2, respectively, where method 1 is PCBMR and method 2 is either SATB or SATN. The value of the variables was 1 for a significant p-value and 0 otherwise. Matched pairs of 1 Mand 2 Mwere tested by the binomial exact test [iM1i|(ΣiM1i+ΣiM2i) = Nm Σhas binomial distribution , i = 1, 2, ....1000 for the simulated data above. For iM1i > Nm/2Σ, the null and alternative hypotheses are p ≤ 0.5 and p > 0.5 respectively. Rejection of the null hypothesis indicates that method 1 is significantly more powerful than method 2. For iM1i < Nm/2Σ, the null and alternative hypotheses are p ≥ 0.5 and p < 0.5, respectively. Rejection of the null hypothesis indicates that method 1 is significantly less powerful than method 2. To strictly evaluate the power of PCBMR, we compared it to method 2 for the trait with the largest power.Without loss of generality, we created indicator variables act test , based oi = U+AGE*b1+AGE2*b2+SEX+EiY, where residuals (iE) were used as adjusted traits for association studies by PCBMR. The inheritance model for markers underlying abdominal obesity-metabolic syndrome is generally not known before pleiotropic association tests. We thus applied a general model that estimates the effect of each possible genotype for an SNP association in the sample. After susceptibility markers were identified, different models  with the minor allele as reference were also examined in the comparisons. The p-value was adjusted for multiple tests by the Bonferroni method. The number of SNPs in the pleiotropic study was 4,769, so the significance level for testing an SNP association was 1e-5.We applied PCBMR to search for markers associated with multiple traits related to abdominal obesity-metabolic syndrome in the Bogalusa Heart Study, a community-based investigation of the evolution of cardiovascular disease risk beginning in childhood . Based oHM developed and implemented the method. HM and WC performed the simulations, analysis and interpretation of the data. All authors participated in planning and discussion of the study. All authors read and approved the final manuscript.Factor analysis-based study of pleiotropic association. Table of significant pleiotropic association and figure of p-values of SNPs in linkage region.Click here for file


To assess the utility of haplotype association mapping (HAM) as a quantitative trait locus (QTL) discovery tool, we conducted HAM analyses for red blood cell count (RBC) and high density lipoprotein cholesterol (HDL) in mice. We then experimentally tested each HAM QTL using published crosses or new F2 intercrosses guided by the haplotype at the HAM peaks.The HAM for RBC, using 33 classic inbred lines, revealed 8 QTLs; 2 of these were true positives as shown by published crosses. A HAM-guided (C57BL/6J × CBA/J)F2 intercross we carried out verified 2 more as true positives and 4 as false positives. The HAM for HDL, using 81 strains including recombinant inbred lines and chromosome substitution strains, detected 46 QTLs. Of these, 36 were true positives as shown by published crosses. A HAM-guided (C57BL/6J × A/J)F2 intercross that we carried out verified 2 more as true positives and 8 as false positives. By testing each HAM QTL for RBC and HDL, we demonstrated that 78% of the 54 HAM peaks were true positives and 22% were false positives. Interestingly, all false positives were in significant allelic association with one or more real QTL.Because type I errors  can be detected experimentally, we conclude that HAM is useful for QTL detection and narrowing. We advocate the powerful and economical combined approach demonstrated here: the use of HAM for QTL discovery, followed by mitigation of the false positive problem by testing the HAM-predicted QTLs with small HAM-guided experimental crosses. Model organisms facilitate the discovery of genes through classical experimental methodologies and, more recently, through the application of bioinformatics resources and tools. Inbred line crosses have been successfully uncovering quantitative trait loci (QTLs) of complex traits since the early 1990's [see review in -4.In silico QTL mapping, or as we prefer to call it, haplotype association mapping (HAM), has been proposed as a means of utilizing phenotypic data from inbred strains together with dense marker maps to determine associations of haplotypes with phenotypes [enotypes ,6. Initienotypes , while oenotypes .Subsequent reports have tempered these two 2 perspectives somewhat with investigations of the power of HAM when variables and algorithms are altered, such as the number of strains, the "population structure" of the strain panel, the density of markers, the size of the haplotypes, the haplotype inference method, and efforts to control family-wise error ,8-11. Incis) and unlinked markers (trans) are likely to be a problem in association studies such as HAM [Understanding the conditions under which HAM succeeds or fails to identify QTLs and the mechanisms by which type I errors  and type II errors  are generated will help researchers wisely use this powerful tool. The number and the genetic relatedness of the inbred strains used in HAM analyses are known to affect its statistical power ,9,17,18.h as HAM ,12.In this study, we evaluated the performance of HAM as a tool for discovering and mapping QTLs. We used it to predict QTLs for red blood cell count (RBC) and for plasma concentration of high density lipoprotein cholesterol (HDL) in mice. We then tested whether each HAM-predicted QTL was a real QTL, as determined by a previously reported QTL cross that fit the haplotype at the HAM-predicted QTL peak or by a new cross carried out specifically to test these HAM-predicted QTLs. Our results, which allowed us to calculate the rate of false positives, show that HAM can be a powerful, although not comprehensive, predictor of QTLs even for a highly polygenic trait such as HDL cholesterol. We also show that extensive allelic association, the matching of SNPs at true HAM peaks with SNPs elsewhere in the genome, is responsible for type I error control problems; and we demonstrate a method for mitigating this issue that involves conducting relatively small-scale experimental crosses to test HAM QTL peaks.With the trait of red blood cell count, our goal was to assess the usefulness of HAM in discovering new QTLs when working on a quantitative trait for which little was known about its genetic architecture. Haplotype association mapping of 33 classic inbred strains for RBC in females Figure  yielded The next question is which of these 8 HAM-detected peaks detected at a significance of 0.63 represents a true peak and which are false positives. To answer that question, we first examined the literature for red blood cell QTLs and found that 2 of these QTLs on Chrs 4 and 11 have been detected previously with classic inbred line crosses and the haplotype at the HAM peaks differed for the parental strains that detected the QTL ; thus thOne-way ANOVAs conducted at markers near, including, or flanking the 6 HAM peaks revealed that the significant peak on Chr 2 (124.8 Mb) and the suggestive peak on Chr 12 (73.8 Mb) were both significantly correlated with RBC  are significantly correlated with HDL Figure . The othSince most inbred line crosses conducted now re-find HDL QTLs mapped previously by other crosses, we feel that the QTL map for HDL is almost saturated. This allows us to ask the question of false negatives -- whether HAM misses QTLs found by crosses. To answer that question, we mapped the 95% confidence intervals of HDL QTLs for each inbred line cross onto a physical map and indicated the peak locations of the 46 HAM peaks  with the mean RBC for B6 at 9.186 n/uL and the mean RBC for CBA at 9.232 n/uL. Upon testing the F2 progeny from this cross, we confirmed the presence of RBC QTLs on Chrs 2 and 12, which represent QTLs not yet found by traditional crosses. Furthermore, a cursory examination of the genes underlying the Chr 2 HAM QTL reveals a likely candidate gene, erythrocyte protein band 4.2 (Epb4.2). EPB42 is a major component of the erythrocyte membrane skeletal network that regulates the stability and flexibility of erythrocytes, and is implicated in the maintenance of normal surface area and cation transport in red blood cells [Using HAM, even quantitative traits with completely unknown or little-known genetic architecture can be economically explored. An example is the exploration of red blood cell count reported here. Using one HAM-directed small-scale experimental cross with targeted genotyping, we discovered 2 novel RBC QTLs, including a QTL on Chr 2 that includes a strong candidate gene for red blood cell count. The parental strains of the RBC test cross were based solely on their haplotype differences at the RBC HAM peaks and, in fact, are not very different in terms of mean RBC count , ecto- and endo- parasites, and the microsporidium Encephalitozoon cuniculi http://jaxmice.jax.org/health[Mice were obtained from The Jackson Laboratory and housed under conditions meeting the guidelines issued by the Association for Assessment and Accreditation of Laboratory Animal Care. All animal protocols were approved by The Jackson Laboratory's Animal Care and Use Committee. Mice were housed in 31 × 31 × 214 cm polycarbonate cages that were divided into 2 pens with no more than 5 mice/pen (Thoren Caging Systems Inc.) in rooms maintained at a 12:12 light:dark cycle and an ambient temperature of 23°C. Each cage was pressurized and individually ventilated (PIV) with HEPA filtered air supply and exhaust. Mouse colonies were regularly monitored for 15 viruses, 17 bacterial species (including ®) and water ad libitum. About 200 uL of blood for hematological analysis was obtained from 8-10 week old mice in both the HAM strain panel and the (B6 × CBA)F2 intercross by retro-orbital bleeding. For lipid analysis, plasma was separated from blood by centrifugation.All mice were fed a regular chow diet .Red blood cell count was measured using a Bayer ADVIAhttp://www.jax.org/phenome[10 transformed. These trait data were input into our analysis as vectors. A SNP panel consisting of over 21,000 autosomal SNPs was compiled from SNP resources including Wellcome Trust, Broad Institute, and Perlegen, and missing SNPs were inferred from adjacent SNPs , were measured. Using 4-15 mice per strain, we calculated the sex specific trait means for HDL and RBC  to produce HAM scores for the scan plots. We controlled type I error rate for multiple testing due to genome-wide searching using family-wise error rate control [P value was recorded for each permutation, and percentiles of their distribution were used to provide approximate multiple test-adjusted thresholds. The genome-wide type I error thresholds were estimated based on 1000 permutation tests. 3-SNP windows, or "peaks" corresponding to P value thresholds adjusted for global significance were defined as follows: P < 0.05 as significant, P < 0.2 as highly suggestive, and P < 0.63 as suggestive [http://www.mathworks.com[We computed regression-based test statistics to measure the strength of association between 3-SNP haplotypes and averaged mean phenotypes to detect haplotype groupings with significantly different mean phenotypes. Since the segregation of strains into genotypic groups varies widely over haplotype blocks,  control . Permutaggestive . We estiworks.com.et al. [We examined the strain haplotypes at the significant and suggestive peaks and chose strains for intercrosses based on which strains had different haplotypes. Phenotype differences between strains were not considered. For RBC, the C57BL/6J (B6) and CBA/J (CBA) haplotypes differed at all of the 6 relevant peaks in females, so we set up a small F2 intercross of B6 females crossed with CBA males. The resulting F2 females (N = 108) were phenotyped for RBC at 8 weeks old. For HDL, the B6 and A/J (A) haplotypes differed at all 10 significant peaks that were not confirmed by published HDL QTLs. Because our lab had already conducted a large (B × A)F2 intercross for kidney disease , we usedet al.  as a tra® DNA Polymerase (Applied Biosystems) under the following amplification conditions: initial denaturation at 95°C for 5 minutes, 35 cycles of 95°C (30 seconds) + 55°C (30 seconds) + 72°C (1 minute), and a final elongation at 72°C for 7 minutes. PCR products were visualized on 2% agarose gels and scored by eye.Genomic DNA was extracted from the tail-tips of the F2 progeny using a standard phenol-choloform procedure. SNPs flanking, within, or nearby HAM peaks of interest were genotyped by the Allele Typing Service at The Jackson Laboratory in conjunction with KBiosciences Ltd. In 6 cases, microsatellite markers were used instead: D1Mit373, D2Mit1, D8Mit191, D8Mit25, D11Mit48, and D15Mit149. For these, genomic DNA was amplified in PCR reactions with 0.200 mM of each dNTP, 0.132 uM of each MIT marker primer, 1× AmpliTaq buffer, and 0.375 Units of AmpliTaq® by SAS, we tested each marker for correlations between phenotype and genotype with one-way ANOVAs. We tested the non-independence of the HAM peaks using an analysis of "linkage disequilibrium" in GENEPOP, http://genepop.curtin.edu.au[P < 0.63 threshold were tested for the non-random association of their haplotypes with each other, while for HDL, all significant HAM peaks above the significant P < 0.05 threshold were tested for the non-random association of their haplotypes with each other.Intercross progeny were genotyped at markers flanking, including, or nearby the HAM peak of interest. Using JMPin.edu.au,39. PairSLBH designed the experiments, carried out statistical analyses for peak testing and linkage disequilibrium, and wrote the manuscript. S-WT set up and conducted all final HAM analyses, carried out peak stability bootstrapping, participated in SNP panel construction, and guided initial HAM analyses. IMS planned and coordinated phenotyping, participated in SNP panel construction, and participated in initial HAM analyses. KW performed all genotyping. AC conducted RBC and HDL phenotyping and assisted with intercross experiments and manuscript revisions. BP conceived of the study, participated in its design and coordination, and helped write the manuscript. All authors read and approved the final manuscript.


The selective genotyping approach in quantitative genetics means genotyping only individuals with extreme phenotypes. This approach is considered an efficient way to perform gene mapping, and can be applied in both linkage and association studies. Selective genotyping in association mapping of quantitative trait loci was proposed to increase the power of detecting rare alleles of large effect. However, using this approach, only common variants have been detected. Studies on selective genotyping have been limited to single-locus scenarios. In this study we aim to investigate the power of selective genotyping in a genome-wide association study scenario, and we specifically study the impact of minor allele frequency of variants on the power of this approach. We use the Genetic Analysis Workshop 16 rheumatoid arthritis whole-genome data from the North American Rheumatoid Arthritis Consortium. Two quantitative traits, anti-cyclic citrullinated peptide and rheumatoid factor immunoglobulin M, and one binary trait, rheumatoid arthritis affection status, are used in the analysis. The power of selective genotyping is explored as a function of three parameters: sampling proportion, minor allele frequency of single-nucleotide polymorphism, and test level. The results show that the selective genotyping approach is more efficient in detecting common variants than detecting rare variants, and it is efficient only when the level of declaring significance is not stringent. In summary, the selective genotyping approach is most suitable for detecting common variants in candidate gene-based studies. The extreme sampling strategy in quantitative genetics is termed selective genotyping , involviThis selective genotyping approach was shown to be efficient in association mapping of quantitative trait loci (QTLs) in a statistical framework ,3. SinceBoth theoretical and applied studies to date have focused on limited number of loci in a candidate gene study scenario, and therefore their test levels were set high. They made no comparison between common and rare variants in a realistic situation in terms of sample size. In this study we investigated the empirical power of selective genotyping using the Genetic Analysis Workshop 16 (GAW16) rheumatoid arthritis (RA) genome-wide association study (GWAS) data from the North American Rheumatoid Arthritis Consortium (NARAC). The genome-wide data provided us an opportunity to investigate the power at different test levels and a full spectrum of allele frequency.p-value > 0.001), and 522,587 SNPs were retained. Note that we did not filter the data through a MAF criterion because the MAF was a primary variable we were investigating. To control for population stratification, we calculated the first two principal components, denoted PC1 and PC2, of 1,344 ancestry-informative SNPs [Nth, N ∈ {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}, percentiles of cases, and, correspondingly, a random N percent of controls were selected as a study dataset, i.e., there were 10 datasets generated in total. All subjects were included when N = 100. A total of three RA-related traits, including a binary variable of RA affection status and two quantitative phenotypes  measured only in cases were used in the analyses.The NARAC data consists of 868 cases and 1,194 controls. The samples were genotyped using the Illumina Infinium HumanHap550 chip, and in the current study we focused on 531,689 single-nucleotide polymorphisms (SNPs) across the autosomal genome. The data were filtered through genotype call rate (>90% completeness) and the Hardy-Weinberg equilibrium test  denotes the p-value corresponding to the test statistic Ti. We concentrated on results based on T3 in the subsequent analysis because it was shown to be more powerful than the other two [The statistical testing procedure included three steps. First, we tested association between affection status and genotype using both cases and controls by a logistic regression model, which yielded a statistic ormation  was alwap-values  to form p-value < 0.05 under control of the false-discovery rate (FDR) [N < 100) divided by the total number of significant SNPs using the whole data (N = 100). We studied the relative power as a function of three sets of parameters: the sampling proportion N%, N ∈ {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}, the test level α = 5.0 × 100, O ∈ {-2, -3, -4, -5, -6, -7, -8}, and the SNP MAF stratified by p, p ∈ {0.05, 0.10, 0.20, 0.30, 0.40}. All analyses were performed using the software PLINK [To investigate the empirical power of selective genotyping in GWAS, we only focused on SNPs that attained a te (FDR)  when usire PLINK  and R [1re PLINK .PTPN22 on chromosome 1, and TRAF1-C5 on chromosome 9 (data not shown), which proved the validity of the current method. To attain a p-value < 0.05 under FDR control, the nominal p-values for anti-CCP and IgM were 2.35 × 10-6 and 2.34 × 10-6, respectively. There were 336 SNPs for anti-CCP and 337 SNPs for IgM that met these criteria. Their distributions across chromosomes and allele frequency categories are summarized in Tables We first performed a genome scan using the whole sample, and were able to detect loci confirmed to be associated with RA such as the major histocompatibility complex on chromosome 6, -3; however, more than 50% of the sample needed to be genotyped at the test level of 5 × 10-5; when the test level was equal to or less than 5 × 10-6, the power decreased linearly with the sample size  decreases more rapidly for rare variants as we decrease the sampling proportion.Selective genotyping is commonly practiced by genotyping individuals with extreme phenotypes at both upper and lower extremes; however, in the current study we only selected those at the upper extremes in cases and then made random selection in controls. This study design was based on the trait characteristics, not constraints of the data available. Both anti-CCP and IgM are usually present only in cases, i.e., both quantitative traits are zero in unaffected persons. Therefore, the study population approximates a selected sample plus a random sample from the general population, similar to the design proposed by Slatkin .The selective genotyping approach is more efficient in detecting common variants than detecting rare variants even though it was initially proposed to detect the latter . This apanti-CCP: Anti-cyclic citrullinated peptide (anti-CCP); FDR: False-discovery rate; GAW16: Genetic Analysis Workshop 16; GWAS: Genome-wide association study; IgM: Immunoglobulin M; MAF: Minor allele frequency; NARAC: North American Rheumatoid Arthritis Consortium; QTLs: Quantitative trait loci; RA: Rheumatoid arthritis; SNP: Single-nucleotide polymorphism.The authors declare that they have no competing interests.CX conceived of the study, participated in data analysis, and drafted the manuscript. GX participated in study design, carried out data analysis, and helped to draft the manuscript. Both authors read and approved the final manuscript.