Biological systems are interacting, molecular networks in which genetic variation contributes to phenotypic heterogeneity. This heterogeneity is traditionally modelled as a dichotomous trait (e.g. affected vs. non-affected). This is far too simplistic considering the complexity and genetic variations of such networks.In this study on type 2 diabetes mellitus, heterogeneity was resolved in a latent class framework combined with structural equation modelling using phenotypic indicators of distinct physiological processes. We modelled the clinical condition "the metabolic syndrome", which is known to be a heterogeneous and polygenic condition with a clinical endpoint (type 2 diabetes mellitus). In the model presented here, genetic factors were not included and no genetic model is assumed except that genes operate in networks. The impact of stratification of the study population on genetic interaction was demonstrated by analysis of several genes previously associated with the metabolic syndrome and type 2 diabetes mellitus.The analysis revealed the existence of 19 distinct subpopulations with a different propensity to develop diabetes mellitus within a large healthy study population. The allocation of subjects into subpopulations was highly accurate with an entropy measure of nearly 0.9. Although very few gene variants were directly associated with metabolic syndrome in the total study sample, almost one third of all possible epistatic interactions were highly significant. In particular, the number of interactions increased after stratifying the study population, suggesting that interactions are masked in heterogenous populations. In addition, the genetic variance increased by an average of 35-fold when analysed in the subpopulations.The major conclusions from this study are that the likelihood of detecting true association between genetic variants and complex traits increases tremendously when studied in physiological homogenous subpopulations and on inclusion of epistasis in the analysis, whereas epistasis (i.e. genetic networks) is ubiquitous and should be the basis in modelling any biological process. Despite tremendous progress in our understanding of the human genome and the rapidly advancing ability to probe genetic variation, investigation of the human genome has yielded only modest insight into the pathogenesis of complex human traits such as glucose levels and insulin resistance. One possible explanation is inadequate modelling of complex polygenic interactions and phenotypic heterogeneity.First, as far as a condition or disease is monogenic in the sense that a single gene variant is sufficient to precipitate a condition or disease, family-based studies are powerful in detecting causal genes or at least in narrowing down the location of the genes on the chromosomes . HoweverAlthough it is acknowledged, that most common diseases are complex, the traditional Mendelian single-gene approach is still common . Although this strategy has been somewhat successful, it has rarely provided insight into the complex disorder itself. One reason for this is that, although dynamic, continuous traits are introduced, most genetic studies are still performed as case-control studies and thus dichotomise the trait or phenotype. This approach inevitably leads to loss of power . Anothera priori defined penetrance functions of interactions. These methods are to various extents based on coalescence theory and they use of genetic data for classification mostly in hierarchy tree-like structures, which is rather unrealistic in natural systems [Several methods have been developed to account for population heterogeneity and epistasis ,15-32. N systems . An alte systems -8,39, bustates that may or may not develop into type 2 diabetes mellitus, which is recognised to be a heterogeneous condition [Here we adopt a "naive" approach, focussing on resolving physiological heterogeneity related to the metabolic syndrome and thus predisposition to type-2 diabetes in the general population using structural equation modelling (SEM) in a latent class analysis (LCA) framework. The assumption is that all physiological processes examined are coded for and regulated by genomic structures in an extensive cellular and inter-cellular network and are modified by non-genetic factors to varying extents. The population as a whole is considered to consist of a finite amount of physiologically distinct subpopulations defined by the state of the genetic network. The purpose of this analysis is not to define the disease, but rather to define subpopulations that are characterised by physiologically distinct metabolic entities or ondition  with a londition . The secThe population used is that of the Danish Inter 99 study, which comprises all 61,301 individuals born at 5-year intervals between 1939 and 1970 in 11 municipalities in south-western Copenhagen County. From the original population an age- and sex-stratified random sample of 13,016 individuals was contacted and invited to participate in the Inter 99 study of which 6,775 responded to the invitation to participate .Fasting levels of glucose, insulin, C-peptide, lipids and cholesterol were analysed, and blood pressure and anthropometric measures such as height, weight, body mass index (BMI) and waist/hip circumference (WH) were obtained. In addition, an oral glucose tolerance test (OGTT) was performed in all individuals, and glucose, insulin and C-peptide were measured at 0, 30 and 120 min. BMI and WH are included as indices of obesity. Insulin resistance (HOMAres) and β-cell function (HOMAbeta) were calculated using fasting levels of insulin and glucose . Basic vA total of 30 single nucleotide polymorphisms (SNPs) in 21 genes previously shown to be associated with the metabolic syndrome and diabetes mellitus were included in the genetic part of this study [see Additional file The study was approved by The Ethics Committee of Greater Copenhagen, Denmark.f(y|z) = Σxπ(x|z)f. We are modelling the probability density of observing y (= insulin levels) given a set of covariates z . Here π(x|z) is the probability of having a certain set of values for the discrete latent variable  given an individual's observed covariates. π(x|z) is equivalent to the probability of belonging to a subpopulation and sums to 1 for each subject. At the population level, π(x|z) reflects the relative size of a subpopulation and sums to 1. The outcome of this modelling is a classification of the population sample in mutually exclusive subpopulations with significantly distinct physiological metabolic states differing in their propensity to evolve into a clinical endpoint, in this case diabetes mellitus. In this model, the dependent or indicator variable (insulin at time points during the OGTT) is modelled as a continuous normal distribution f(y|x) conditional on class membership in a perfect classification. A number of known physiological risk factors for the metabolic syndrome or type-2 diabetes were introduced as independent variables in the model (see Results section on Model building for details).Heterogeneity is modelled in a latent class framework combined with SEM. The modelling is performed by applying a finite mixture model or LCA ,45. The All subjects are assumed to possess exactly the same basic genetic structures, but these vary in expression because of variability in the genome, including SNPs, deletions, insertions and copy number variations, and due to environmental factors. Furthermore, it is assumed that the population consists of a mixture of subpopulations, within which all variables are presumed to be normally distributed and only correlated through a latent variable. Variables may not be exactly normally distributed in a tissue or organism because of asynchrony of the dynamic processes in the cells , but theThe structural model (SEM) of the metabolism of glucose and hence the metabolic syndrome is schematically shown in Figure It is presumed that no subject transitions between classes are possible. Only metabolic transitions from one level to another level of the metabolic status would be within a class, depending on the load of non-genetic factors and within the limits defined by the class-specific genotype, i.e., the non-genetic factors operate within the limits of a genetic framework that physiologically cannot be exceeded.SEM-LCA analysis is time-consuming and computer-intensive. Therefore, an exploratory ordinary linear regression analysis was performed as a mean of data-mining to select variables most correlated to insulin. The selected variables were used in the initial building of the model. After the basic model was developed, the remaining variables correlated to insulin or previously shown to be correlated to the metabolic syndrome were successively entered into the analysis and were retained in model if they increased its goodness of fit.The entire study population was genotyped using the SNPlex technique (ABI Biosystems) or Taqman chemistry (ABI Biosystems). SNPs with unresolved ambiguities (range 3.2 – 8.5%) were excluded from the analysis. The minor allele frequencies ranged from 0.08% to 48.83%. Hardy-Weinberg equilibrium (HWE) was analysed using the exact method of Wigginton et al. . The R-sThe heritability of traits was calculated for each SNP . For genThe exploratory data-mining procedure to select variables included in the model, and comparisons of variables in the classes were performed using the SPSS package v.15.0.Structural analysis is carried out using Mplus v.4.0, which can perform LCA and SEM in a single operation . The corAn exploratory linear regression analysis was performed for the entire population and for the two subpopulations stratified by gender. The latter is justified, as the variables related to the metabolic syndrome and diabetes are known to differ between genders  see bel. AnalysiC-peptide at 0 min did enter the regression at 30 min, but not at 120 min. This may reflect two processes in C-peptide (and insulin) metabolism: secretion and catabolism. In the initial phase of the glucose challenge, insulin secretion (as measured by C-peptide levels) proceeded, but in the later phase secretion decreased, perhaps even below fasting levels, and the decrease in C-peptide and insulin levels mainly reflect the removal and degradation of the peptides. This scenario may pertain to what is perceived as normal metabolism, but collapses as insulin resistance and β-cell dysfunction progress.In summary, insulin as an indicator and C-peptide and glucose as co-variates were used to build the basic model.Combined SEM and LCA was initiated by including insulin at the three time points as indicators without any co-variates. The number of classes was increased to the point at which the adjusted BIC value did not significantly change. Next, glucose and C-peptide were included separately and in all combinations as co-variates. Although glucose and C-peptide at 0 min were only significantly associated with the indicators in a fraction of the regressions, they were indispensable in the model, as assessed by the adjusted BIC criterion . The entropy measure  was almoClasses are ordered according to an increase in insulin resistance defined by the HOMAres index . The sizIt was anticipated that the fraction of frank diabetic cases in the classes would increase with increasing class number . However, this was clearly not the case, in particular not for men. A possible reason is that the HOMAres index is an inaccurate measure of insulin resistance, as it only includes glucose levels at 0 min, whereas insulin does not enter in the algorithm. Rather, the dynamics of glucose, insulin and C-peptide in the OGTT have to be implemented in analysing the metabolic status. Glucose levels in female classes 8 and 16–19 at 120 min and in class 18 at 0 min did indicate impaired glucose tolerance (IGT) according to the WHO criteria . These fNevertheless, the latter classes did show increasing insulin levels concomitant with normalised glucose levels at 120 min, i.e., full compensation of insulin resistance was obtained for these two classes (which would not be detected by the HOMAres index). The combined insulin resistance classes  amount to a total of 895 females, or 33.4% of the female study population. Only five classes, including 782 or 29.2% of the females, showed decreasing C-peptide levels after 120 min, indicating increased secretion of C-peptide (and hence insulin) in the remaining 70% of the female population. On an individual level, approximately one-third of the women had increased secretion of C-peptide . Concomitantly, the number and fraction of spurious LDs due to admixture decreased significantly. Most LDs were di-allelic, but a few tri- and quadri-allelic LDs were present, indicating stringent genotype-combinations influencing the traits.Interestingly, all the HNF4α polymorphisms were in mutual LD except for HNF4α-6 (data not shown) in both genders before stratification, but most LDs were lost after stratification, except for SNPs HNF4α-2 and HNF4α-3. In contrast, only a few physically unlinked SNPs were in LD before stratification, but this number was 15-fold greater after stratification. Only the LDs in the non-stratified gender population between HNF4α-2/HNF4α-3 and Arβ2-1/ARβ2-2 were recovered in almost all classes. Thus, most of the LDs detected in the non-stratified population disappeared after classification, whereas several new LDs emerged after classification. This finding may be interpreted as hidden epistasis in non-stratified populations, as the SEM-LCA was based solely on physiological variables . This suggests that the non-stratified but admixed population exposes two problems: the creation of false LDs and masking of true LDs .When the population sample was stratified according to gender, none of the SNPs showed even a marginal effect on any of the physiological variables Table . When gea priori not suspected to be causative in the metabolic syndrome and were not included in the final SEM-LCA model. For a nominal 5% level of significance, approximately 5% of all heritabilities were significant. This is, as expected, by pure chance and remarkably non-significant, considering that the genes were selected because several studies have shown that they influence various physiological variables related to the metabolic syndrome and type 2 diabetes mellitus [see Additional file However, these were variables To examine epistatic effects on the physiological variables that characterise the metabolic syndrom and type 2 diabetes, logistic regression analysis was performed on both genders prior to LCA stratification for all two-SNP combinations. The variance components of the analyses that were significant after correction for multiple testing (including the summary variables HOMAres and HOMAbeta) are shown in Table T3 [see Additional file Real epistasis in Table T3 [see Additional file The numbers for women were 208 and 70, respectively. Combined for women and men, 165 two-SNP interactions did not influence any traits in either gender group, and 40 two-SNP interactions influenced all variables in both genders, which seems to suggest the existence of gender-specific interactions. Between 87.6% and 92.3% of the possible two-SNP combinations between different genes were involved in epistatic interactions termed The single-gene multilocus genotypes HNF4α4, ARβ2, AGT and IL6 were explanatory of genetic variances even if single-locus SNPs were only explanatory in a few sporadic cases  were always included in the haplotypes of the HNF4α gene. This was also true for the AGT and ARβ2 genes. In the case of IL6, the two promotor SNPs were included for all the physiological variables examined, suggesting that they are both necessary in regulating IL6 expression.On average, almost 10% of the phenotypic variances were accounted for by separate two-gene interactions across all physiological variables and all classes. The total genetic variance ranged from 0% to 66.8%, and the epistatic variance ranged from 0% to almost 40% of phenotypic variance.The total number of possible two-SNP epistatic effects after classification into 19 subpopulations was 7,269 in women and 7,268 in men, or 87.9% of all possible interactions. Two-gene combinations in which one or both genes was monomorphic were excluded, as no interaction could be calculated. Combinations in which one or both genes was not in HWE were also excluded, as this was a prerequisite for the variance decomposition . Of the The most striking results were that: (1) a few classes did not show any interactions at all for any physiological variable; and (2) stratification into subpopulations increased the genetic variance tremendously. The average total genetic variance increased by 30- to 35-fold compared to the non-stratified study population Table . The smaAnalysis of epistasis was performed using corrected significance levels corresponding to the 30 SNPs studied. However, as the number of SNPs will be increased in future studies, the adjusted significance levels will dramatically decrease, which poses the question as to whether truly epistatic effects will still be detected. When the epistasis analysis was corrected for multiple testing corresponding to analysis of 30 SNPs (as performed above), the original number of nominally significant two-SNP interactions was reduced to 70%. Surprisingly, further correction for multiple testing corresponding to analysis in a 20-million-SNP scenario – the assumed number of SNPs in the human genome  – only rSome classes did not show any two-gene interactions at all. This is summarised in Table state of the participants by defining the metabolic process in a multivariate SEM. The most important conclusion emerging from this study is that LCA-SEM very efficiently defines metabolic substates and allows detection of epistasis and genetic variance. In contrast, analysis of single-gene polymorphism has very limited power to detect QTL. Only a small fraction of the single gene-variants (or SNPs) showed any influence on the physiological variables examined in this study . Thus, we consider it to be a strength that our population study targets a "normal" population, which in fact contain (at least) 18% insulin-resistant subjects and 4.2% with undiscovered diabetes mellitus. One interpretation of these results is that the variables excluded (most notably triglycerides and HDL) are in fact not causative, but inaccurate proxies for the actual underlying causative agents, such as free fatty acids [Instead, BMI entered as a general measure of fat content. One probable reason for the discrepancies is that previous studies have been performed on selected populations  whereas our approach has been to consider the metabolic ty acids , leptin ty acids , and othThe complexity of the network is indicated by the differences in gene variants that characterise the physiological variables in the classes. First, MCHR1 only contributes to phenotypic variance in one class for women (class 5), and not at all for men [see Additional file across tissues.Rather, in a particular class, the influence of a gene variant is overridden or neutralised by other interactions in the metabolic network to a point that is undetectable by the variables included in the model, or the genes are monomorphic in the class. It should be remembered that the model is a whole-body model: genes may be expressed in different tissues participating in different cellular networks, as well as expressing the epistatic effect per se would be detectable. Metabolic networks most probably follows a small-world scale-free distribution of interactions [All the genes (or SNPs) included in this study (except perhaps TCF1 and HNF4α-6) seem to be part of a genetic network or of sub-networks, as they are involved in epistatic interactions related to the metabolism of glucose and insulin, although the network or subnetworks cannot be exactly defined at the moment. TCF1 and HNF4α-6 did not show interaction with any of the SNPs included in this study. This, however, does not exclude the possibility that these transcription factors are embedded in a network. In the case of the HNF4α-6 SNP, six other SNPs in the HNF4α gene do show extensive epistatic action, so the gene is included in the network even if the HNF4α-6 SNP is functionally neutral. As for the TCF1 SNP examined, one obvious explanation for the lack of interaction is that the SNP is functionally neutral. Another reason may be that TCF1 is the sole representative of a subnetwork of the general network related to glucose and insulin metabolism and no interaction ractions ,60, implractions ,62. Thenractions .A strength of our approach is that allelic, genetic and trait heterogeneity, genetic admixtures, and phenocopies do not present an obstacle, because these entities are implicit in the SEM-LCA modelling framework. Allelic and genetic heterogeneity and genetic admixture  is that no genetic model is assumed other than that the genetic network shared by all participants is the basic structure of all biological processes. This does not mean that gene variability cannot or should not be included in the modelling. On the contrary, the ultimate purpose is to define the genetic network or networks, and genetic factors should be included in the modelling when they are solidly identified. This calls for various physiological, biochemical and cellular studies to eventually define the exact role of a gene and the nature of its regulation, which most probably is beyond the reach of classical associations studies. In recent years, several new approaches have been presented to elucidate complex biological structures -37,66-73These dynamic data mining and machine learning procedures include neuronal networks, genetic and evolutionary programming, and genetic algorithms, among others. These techniques are exciting, but are still in their infancy for complex biological systems, and have to be developed further.23 ways, meaning that the combinations in two merged meiotic cells run into the billions, far exceeding the human population. Of course, the variability is far from that number, but even in small networks the number of combinations is still daunting [Any subject in a population will belong to different subpopulations, depending on the physiological process being studied, which is simply the consequence of independent segregating chromosomes and random mating. The extent of this gene-mixing process is of course modified by chromosomal linkage of genes, recombination, mutation (of any kind), migration, and selection, and to what extent random mating is in fact random. However, for every new generation the chromosomes during meiosis can be picked in 2daunting . Howeverdaunting . This sedaunting .MF developed the SEM-LCA approach, carried out all the modelling and computations, and wrote the paper. TW participated in developing ideas and formulated parts of the paper. AL and TJ established the study population and provided all data.All authors read and approved the manuscript.Genes previously shown to be involved in the metabolism of glucose and insulin. Included are 21 genes with a total of 30 single nucleotide polymorphisms. The table lists the single nucleotide polymorphisms (SNPs) included in the study of heritability, linkage disequilibrium, and epistasis.Click here for fileComparisons of traits between the 19 classes. The table shows the number of significant differences of a trait between all two-class comparisons.Click here for fileSummary of two-gene genetic variance as the fraction of total phenotypic variance in gender before stratification into subpopulations by SEM-LCA. The number of significant two-gene interactions and the variance decomposition for each variable examined in the study are summarized before stratification of each gender by SEM-LCA.Click here for fileGenes characterizing classes. The table summarize genes involved in epistasis of insulin, C-peptide or glucose in a limited number of classes. In particular, the MCHR1 gene or SNP is only involve in epistasis in one class in women and none in men.Click here for file


Due to the growing need to combine data across multiple studies and to impute untyped markers based on a reference sample, several analytical tools for imputation and analysis of missing genotypes have been developed. Current imputation methods rely on single imputation, which ignores the variation in estimation due to imputation. An alternative to single imputation is multiple imputation. In this paper, we assess the variation in imputation by completing both single and multiple imputations of genotypic data using MACH, a commonly used hidden Markov model imputation method. Using data from the North American Rheumatoid Arthritis Consortium genome-wide study, the use of single and multiple imputation was assessed in four regions of chromosome 1 with varying levels of linkage disequilibrium and association signals. Two scenarios for missing genotypic data were assessed: imputation of untyped markers and combination of genotypic data from two studies. This limited study involving four regions indicates that, contrary to expectations, multiple imputations may not be necessary. Due to the growing need to combine data across multiple studies, several analytical tools for imputation and analysis of missing genotypes have been developed and assessed -4. TheseAn alternative to SI is multiple imputation (MI) in which multiple imputed or "augmented" datasets are created and then analyzed using standard statistical methods and models ,6. In thPTPN22, which has been reported to harbor the risk SNP rs2476601 . In contrast, the run-times for Scenario II, based on phased haplotypes, was around 10 minutes with little variation in run times between the four regions.Another consideration of whether one should employ MI is computation time. For the analyses presented, MACH was run on a Beowolf-style Linux cluster with compute nodes running CentOS 4.3 Linux x86-64 allowing 8-16 GB memory per job. Scenario I run-times (single imputation) ranged from 13-18 minutes. However, when MACH used the raw genotype data for the reference samples instead of the phased haplotypes, the run-time increased to more than 30 days [Ignoring variation due to imputation results in under-estimation of the variance in the parameter estimate, and hence an inflated type I error. For imputation of untyped markers (Scenario I), we observed larger variation in results as compared to imputation of missing genotypes (Scenario II). For Scenario II, we observed small differences in association results based on SI or MI, especially in regions of higher LD. In genome-wide association studies in which SI is often implemented for over two million markers, one appropriate approach is to use SI as the initial analysis and employ MI for any regions of interest detected with SI to assess variation due to imputation. On the basis of this study involving four regions, single imputation is reasonable, especially in regions of high LD where imputed genotype "dosage" is used in the analysis.GAW: Genetic Analysis Workshop; HWE: Hardy-Weinberg equilibrium; IQR: Interquartile range; LD: Linkage disequilibrium; MAF: Minor allele frequency; MI: Multiple imputation; NARAC: North American Rheumatoid Arthritis Consortium; ORs: Odds ratios; RA: Rheumatoid arthritis; SI: Single imputation; SNP: Single-nucleotide polymorphism.The authors declare that they have no competing interests.BLF conceived of the study and coordinated it. BLF, JMB, ELG, SKM, KGR, RT, JPS, and DNR participated in design of study. SKM, KGR, RT, and JPS ran statistical analysis. BLF, ELG, and JMB drafted manuscript. All authors read and approved the final manuscript.


Oxytocin (OXT) has been implicated in a suite of complex social behaviors including observed choices in economic laboratory experiments. However, actual studies of associations between oxytocin receptor (OXTR) gene variants and experimentally elicited social preferences are rare.We test hypotheses of associations between social preferences, as measured by behavior in two economic games, and 9 single nucleotide polymorphisms (SNPs) of the OXTR gene in a sample of Swedish twins (n = 684). Two standard economic games, the dictator game and the trust game, both involving real monetary consequences, were used to elicit such preferences. After correction for multiple hypothesis testing, we found no significant associations between any of the 9 single nucleotide polymorphisms (SNPs) and behavior in either of the games.OXTR genetic variant.We were unable to replicate the most significant association reported in previous research between the amount donated in a dictator game and an  The field of behavioral economics has made significant strides during the last three decades in painting a panorama of the diversity of human economic behavior, a panorama which in several ways challenges the behavioral assumptions made in standard economic models OXT is a nonapeptide synthesized primarily by the paraventricular (PVN) and supraoptic nuclei (SON) of the hypothalamus. Functioning as both a neurotransmitter and a neuromodulator, it exerts a wide range of effects both peripherally and centrally. The most notable peripheral targets of OXT include uterine and mammary tissue. OXT induces contractions during labor and milk “let down” during lactation. Recently, converging evidence from studies on human and non-human subjects has demonstrated central effects of OXT on a number of complex behaviors. For example, in studies of animals, including rodents, OXT has been shown to regulate maternal care, social recognition and other affiliative behaviors . Overall, this line of research suggests that OXT might also modulate human social relationships Some evidence in favor of this proposition came from studies using paradigms from experimental economics. For example, one early study A number of research teams have subsequently documented effects of exogenously administrated OXT on a wide spectrum of social behaviors, including trust OXTR deficient mice display pervasive social deficits. For instance, OXTR knockout mice lack maternal nurturing One candidate gene for genetic association studies involving social behavior, such as trust, is the OXTR gene. In humans, the OXTR gene, localized as a single copy on chromosome 3 While the molecular evidence suggests that more extreme phenotypes are likely associated with the OXTR gene and that severe aberrations in the OXTR gene, such as deletions, are associated with major social deficits in rodents, it still remains unclear whether polymorphic differences in the OXTR gene can help explain normal variation in human social preferences. To our knowledge, only one study has examined the relationship between social preferences and the OXTR gene. Using the dictator game, a simple one-shot game in which a subject decides under conditions of anonymity how to divide an endowment between themselves and an unknown individual, researchers examined the association between 16 tagging SNPs across the entire OXTR gene and dictator game donations OXTR polymorphisms (including rs1042778 and rs237887) and behavior elicited from two standard economic games, the dictator game and the trust game, in a sample of 685 individuals. The experiments were conducted with real monetary consequences, consistent with standard practice in experimental economics In this paper, we examine the relationships between nine The subjects were recruited in collaboration with the Swedish Twin Registry as part of a study on the heritability of experimentally elicited preferences. A detailed description of our sample, along with an analysis of non-response bias, is given in http://www.kbioscience.co.uk) using the KASPar chemistry, which is a competitive allele specific PCR SNP genotyping system using FRET quencher cassette oligos (http://www.kbioscience.co.uk/genotyping/genotyping-chemistry.htm). The remaining six SNPs rs4686302, rs237897, rs2254298, rs2268493 and rs1042778 were genotyped using commercially available 5′ nuclease (TaqMan) assays on an ABI Prism 7900HT instrument .Nine SNPs in and up- and downstream of the OXTR gene were chosen for genotyping. One of the SNPs encodes an aminoacid substitution (rs4686302) and eight SNPs have been associated with autism and/or other social behaviors. See Upon arrival, subjects were instructed not to talk to each other during the experiment and to raise their hands if they had any questions (such questions were rare and were answered in private). They were also told about the strong norm against deception in experimental work in economics. Twins in the same twin pair were always required to take part in the same experimental session, thus ruling out the possibility of communication about the experiments. The instructions also made it clear that subjects would never be paired with their twin sibling when playing the experimental games, but would rather be paired against some other anonymous participant. Below, we describe how we administered the dictator and the trust games.Dictator Game – To measure preferences for giving, we used a modified dictator game. In a standard dictator game Trust Game – We administered a standard trust game PC – Finally, because we were concerned that the elicitation of preferences using a one-shot game is quite noisy, we applied principal components analysis to the three variables and used the first principal component as a fourth measure of “social” preferences. The first principal component correlates moderately with dictator game giving  models. We augmented the model with an additional dummy variable which takes the value 1 if the individual is heterozygous at that locus, thus allowing for the possibility that the mean phenotypic value of the heterozygotes is not the midpoint of the phenotypes of the two homozygotes.Since we are analyzing twin pairs, the error terms are non-independent for observations within the same family. Let We use the genetic markers in our dataset to establish zygosity of the twin pairs. Specifically, twin pairs who differ in the number of minor alleles on at least one locus are assumed to be DZ and all other twins are classified as MZ. In analyses not shown here, we verified that the standard errors are substantively identical if we use the Twin Registry's algorithm for classifying zygosity rather than the genetic data.We begin with some summary statistics. Results from the additive specification are reported in Results from the non-additive specification are given in Finally, we also estimated the non-additive models allowing different coefficients in men and women and then tested the joint significance of either the male coeffients or the female coefficients. This entails a de facto doubling of the number of hypotheses being tested. The F-test of joint significance failed to reject the null hypothesis at the one percent level in all 72 cases, which is consistent with the overall pattern of null results. In a post hoc analysis we also verified that the replication failure does not appear to stem from the fact that Israel et al. Advances in human genetics have provided a large number of opportunities for studies of genetic association, but also a growing recognition that many published associations fail to replicate OXTR and pro-social behavior in men. We are reluctant to attach too much significance to this finding because it could easily be due to sampling variation, but we do note that two recent studies reported that this and another SNP in the 5′-region of OXTR were associated with autism OXTR.In the present study, we failed to detect any significant associations between 9 SNPs of the OXTR gene and social preferences as elicited from two standard economic games. Specifically, after correction for multiple hypothesis testing, we did not find any significant associations with allocations of funds in the dictator game or with trust or trustworthiness. The results reported here thus stand in contrast to a recent study which reported associations between variants of the OXTR gene and behavior in the dictator game as well as in the Social Value Orientation task Non-reproducibility does not necessarily demonstrate that the original association reported was spurious. True associations may not replicate across different data sets for a number of reasons, including insufficient statistical power. Indeed, while our sample is larger than previous studies that have examined associations between experimentally elicited preferences and genetic variants, our power to detect weak genetic effects is still limited. This, coupled with the fact that original studies tend to overestimate effect sizes because of a winner's curse effect OXTR polymorphisms in explaining phenotypic variation. An important implication of our results, however, is that sample sizes an order of magnitude greater than those used here will probably be necessary for understanding the pathways from causal variants to complex outcomes. This conclusion is of course in line with a growing consensus in molecular genetics that common genetic variants with large effects on complex outcome variables are unlikely to exist. While failed replications such as the one presented here are common and cautionary, they should not discourage further research in this promising field.Given that our research design only allows us to statistically reject moderate to large effect sizes, the results reported here are not inconsistent with the results of hormonal association studies involving OXT in trust and generosity and do not necessarily rule out a role for


As a simple example, a recessive locus that results in fetal lethality will result in live-born individuals sharing more alleles at this locus than expected under Mendel's laws. This could result in apparent linkage of the phenotype of 'being alive' to such a chromosomal regions. Further, this could result in false-positive linkage when 'affected-only' parametric or non-parametric linkage analysis is performed. Similarly, loci demonstrating TRD may be detectable in family-based association tests as deviant transmission of alleles. Therefore, TRD could result in confounding of family-based association studies of diseases. The Framingham Heart Study data available for Genetic Analysis Workshop 16 is a suitable dataset to determine whether there are loci in the genome that reveal TRD because of the large number of individuals from families, the high-resolution genotyping, and the population-based nature of the study. We have used both genome-wide linkage and family-based association methods to determine whether there are loci that demonstrate TRD in the Framingham Heart Study. Family-based association analysis identified thousands of loci with apparent TRD. However, the vast majority of these are likely the result of genotyping errors with application of strict quality control criteria to the genotype data, and automated inspection of the intensity plots, we identify a small number of loci that may show true TRD, including rs1000548 in intron 6 of S-antigen  on chromosome 2 ( A critical assumption for the majority of genetic mapping approaches (including both linkage and family-based association) is that Mendel's law of segregation is obeyed. Transmission-ratio distortion (TRD) refers to the deviation from the expected Mendelian inheritance of alleles. Violation of this assumption could result in false-positive linkage, particularly within 'affected-only' or 'non-parametric' linkage analysis frameworks. Futhermore, within a family-based association design, the presence of TRD could produce spurious association if transmissions are only assessed to affected, but not unaffected offspring. In addition, it is feasible that the presence of TRD could also reduce the power to detect true disease loci. The presence of TRD in humans has been addressed in only a few studies, using either linkage  or familFor a variety of reasons, including that of statistical power, the majority of genome-wide association studies have used a case-control design, which is not able to detect loci that are subject to TRD. However, some studies are employing a family-based design, but it is typical for them to study only affected offspring, and they are thus susceptible to identifying loci that demonstrate TRD and falsely concluding that they are associated with the disease of interest. Unless unaffected sibs are genotyped, one cannot determine whether association signals are the result of confounding by TRD. Therefore, we took advantage of the large sample size, pedigree-based design and genome-wide genotyping of the Framingham Heart Study Problem 2 data from Genetic Analysis Workshop 16 (GAW16) to determine whether we could identify loci demonstrating TRD.We used data from Affymetrix 500 k and 50 k single-nucleotide polymorphism (SNP) datasets from Problem 2 of GAW16, the Framingham Heart Study. Genotype data were called by the data providers using BRLMM , but no p-value > 0.05, individual genotype missing rate <5%, SNP missing rate <2%, pairwise r2 < 0.05, and Mendelian error rate <5%. Individuals from Cohort 1 were not used in the analysis, therefore large pedigrees were split into smaller pedigrees using the R kinship package ) to determine whether there are regions in the genome linked to the phenotype of 'being alive in the last generation' (Merlin v 1.1.2) . We dealfunction ) to allop > 10-5.We also performed family-based association tests  to examine the transmissions of alleles for all SNPs across the genome to all genotyped individuals in the dataset using PLINK v1.02 ,8 with tGenome-wide linkage analyses used ~5 k SNPs from 1,028 pedigrees that were informative. There were no loci that met genome-wide criteria for significant linkage.p < 10-8, which was an unexpectedly large number. However, when we investigated this further, we suspected that the majority of these results were false positives due to genotyping error. It has been reported previously that, in the presence of certain common types of genotyping error, there is a bias to excess transmission of the major as opposed to minor allele for SNPs [p < 10-8, HWE p > 10-5, and MAF>1% in which the major allele showed excess transmission. This compared to only 21 SNPs using the same criteria in which the minor allele showed excess transmission.Genome-wide TDT analysis was performed and identified 2,722 autosomal SNPs with TDT for SNPs . Indeed,p < 0.0001).To confirm our suspicions that genotyping error was the major cause of the large number of positive results, we took advantage of the fact that it is more difficult to detect Mendelian errors for SNPs with lower MAF . This wop < 10-5), and for these 4,501 SNPs we ran automated cluster plot analysis (ACPA) [p-value>10-4. Using a criteria for genome-wide significance of p < 10-8, only one SNP was predicted by the ACPA procedure to have good quality genotype clustering, rs1000548  are provided in Table p > 0.08).Visual inspection of the cluster-plots of thousands of SNPs is labor intensive, so we next investigated whether we could use automated methods to help distinguish which SNPs had good quality genotype calls. We then applied a less stringent criteria for TRD  . We limiThe results of TDT analyses performed here have highlighted the problems of using high-throughput genotype data with even a small proportion of genotyping errors to detect phenomenon such as TRD. The gross over-transmission of the common allele for SNPs with a pattern consistent with TRD, and the marked allele frequency difference between them and the SNPs where the minor allele shows excess transmission, are consistent with genotyping error being the major force behind the unexpectedly large number of apparent positive results. Further contributing to the bias described by Mitchell et al.  in whichIn addition to the complexities that have arisen in the interpretation of our analysis, there is concern that the use of HWE as a criterion to filter SNPs for the analysis of TRD is a double-edged sword. Some SNPs showing true TRD may also deviate significantly from HWE because of violation of the selection assumption, and may end up being removed from datasets in an attempt to remove genotyping errors. Similarly, automatic exclusion of SNPs with low MAF may bias against the detection of true TRD loci because it is likely that because of negative selection, SNPs which show TRD tend to have low MAF. Another caveat of this study is that at each of the eight regions with evidence for TRD Table , there iCTDP1  on chromosome 18; autosomal recessive mutations in this gene have been shown to results in 'congenital cataracts facial dysmorphism neuropathy' (CCFDN), a developmental disorder prevalent in Roma Gypsies [SAG  have been found in Oguchi disease, a rare autosomal recessive form of night blindness [SAG. It may be that in populations similar to Framingham, variation in these genes contributes to phenotypes that can result in TRD, including the failure of fertilization, implantation, or the differential survival of fetuses. Identifying loci that demonstration TRD could provide insight into the mechanisms of the processes.There are some interesting genes near the SNPs in Table  Gypsies . Similarlindness . In thisACPA: Automated cluster plot analysis; GAW: Genetic Analysis Workshop; HWE: Hardy-Weinberg equilibrium; MAF: Minor allele frequency; NPL: Non-parametric linkage; TDT: Transmission-disequilibrium test; TRD: Transmission-ratio distortion; SNP: Single-nucleotide polymorphism;The authors declare that they have no competing interests.ADP, CI-R and SBB conceived of the idea. DW, DP, and YJY performed the linkage and association analysis. AS ran the ACPA analysis. ADP wrote a draft of the manuscript which all authors edited, read and approved the final manuscript.


Variance-components and regression-based methods are frequently used to map quantitative trait loci. The normality of the trait values is usually assumed and violation of this assumption can have a detrimental effect on the power and type I error of such analyses. Various transformations can be used, but appropriate transformations usually require careful analysis of individual traits, which is not feasible for data sets with a large number of traits like those in Problem 1 of Genetic Analysis Workshop 15 (GAW15). A semiparametric variance-components method can estimate the transformation along with the model parameters, but existing methods are computationally intensive. In this paper, we propose the use of empirical normal quantile transformation to normalize the scaled rank of trait values using an inverse normal transformation. Despite its simplicity and potential loss of information, this transformation is shown, by extensive simulations, to have good control of power and type I error, even when compared with the semiparametric method. To investigate the impact of such a transformation on real data sets, we apply variance-components and variance-regression methods to the expression data of GAW15 and compare the results before and after transformation. The rapid expansion of the size of data sets poses new challenges to mapping genes associated with quantitative traits. Facing massive amounts of data, it is no longer feasible to analyze individual traits or genotypes manually. Many methods, though theoretically advantageous, cannot be used due to their requirements of user intervention or a high demand for computing power. Automatic and efficient algorithms become more and more important. In this paper, we seek such an algorithm for the normalization of a large number of quantitative traits.Many models are used to map genes responsible for quantitative traits. Some of the most commonly used ones are Haseman-Elston regression, variance components , and varNone of these methods can be used for data sets with a large number of quantitative traits, as those in Problem 1 of Genetic Analysis Workshop 15 (GAW15). In this data set, there are 3554 traits and 2882 SNP markers across 23 chromosomes, collected for 194 individuals in 14 families. Among all 3554 traits, almost half (45.8%) of them fail the Anderson-Darling normality tests at the 0.05 significance level. Given the large number of traits, it is not possible to analyze each trait and transform them according to their distributions or to use the computationally intensive semiparametric algorithm. Tossing away half of the traits because the uncertain impact of non-normality on subsequent data analyses is not a good idea either, even when there is an abundance of them.We propose the use of a rank-based transformation method called the empirical normal quantile transformation (ENQT). This method ranks the trait values and scales the ranks to . It then transforms the scaled ranks to a normal distribution using an inverse normal transformation. This method is computationally efficient and can be blindly applied to all the quantitative traits, resulting in perfectly normal trait values provided there are few tied values. The major concern is that ENQT uses only the rank information of the original trait values so it may not perform well compared to customized transformations for each trait, or transformation obtained from the semiparametric quantitative trait locus (SQTL) method .In this paper, we test the impact of ENQT on the power and type I error of the variance component method using extensive simulations. Then, we apply ENQT to the GAW15 data set and study the impact of the transformation on the subsequent data analyses.H(Yij) whereThe parental trait is determined by j in family i. H(Y) = ey 1++ (5 + y)2 transforms Yij to a distribution with an average kurtosis of 54.1 and skewness of 4.98 if Yij is normal N. Xij 1and Xij 2are fixed covariates mimicking standardized age ) and sex  with β1 = -0.5 and β1 = 0.5. gij is the major gene effect determined by the true QTL, which assumes value -a, 0, or a for genotype AA, Aa, or aa, respectively. The major genetic variance is therefore σg2 = 2pqa2 = Gij is the polygenic effect that follows a normal distribution with mean 0 and variance σG2. eij is a normal random environmental effect with mean of 0 and variance of σe2. The genetic heritability h2 and major gene heritability hg2 are calculated as h2 = (σg2 + σG2)/σ2 and hg2 = σg2/σ2, respectively, where σ2 = σg2 + σG2 + σe2 is the total sample variance. The trait of offspring is determined in a similar way but the offspring's polygenic effects are determined by GijP and GijM are the paternal and maternal polygenic effects of the parents, respectively.is the original trait value of individual σg2, σG2, and σe2 to , , , , , and  for schemes a through f, respectively. Among these schemes, schemes a and d serve as null hypotheses because their major gene heritabilities are 0. For each setting, we generated 20,000 data sets. The variance-components method was applied to original (H(Yij)), perfectly back-transformed (Yij), and ENQT-transformed trait values. The SQTL method was also applied to the original trait values. The percentage of simulations with p-values less than 5%, 1%, and 0.1% are reported.We simulated the same six schemes as those in Diao and Lin . Namely,p-values (>0.99) in normality tests. Besides descriptive statistics , we applied the Anderson-Darling normality test and variance-components method to estimate polygenic heritability. Using these initial statistics, we chose several groups of traits that are:We took the expression data of Problem 1 of GAW15 and transformed each trait by ENQT. The resulting traits are normal with high p-value of Anderson-Darling normality test >0.7) with before-transformation heritability >0.3. This group has 81 traits.1. Normally distributed  before transformation. This group has 37 traits.4. Having a high difference in heritability before and after transformation (>0.1). This group has 49 traits.5. Having low difference of heritability (<0.001), with before-transformation heritability >0.3. This group has 49 traits.We use heritability as a criterion because traits with low heritability may not be of interest. These groups sometimes overlap. For example, there are 16 common traits in the non-normal and high heritability groups, indicating potential exaggeration of the estimates of heritability due to non-normality.For traits in these groups, we performed and compared full genome-wide scanning using variance component  and varip-values less than the given significance levels. The four columns correspond to trait values after a perfect back-transformation, no transformation, and ENQT transformation, all analyzed by variance components method; and analyzed by SQTL. Only results for simulations with two offspring per family are reported.Table a and d reflect the null model for which there is no major gene effect. Non-normality causes highly inflated type I error for scheme a when no transformation is applied, but not for scheme d. This is because departure from normality only causes excess false positives when there is residual correlation in the relatives not explained by the major locus and kurtosis (or perhaps skewness), which is the case for a but not d [Scheme ut not d . The varENQT transformation can have significant impacts on the analyses of quantitative traits. Using trait 209785_s_at as an example, we compare the LOD scores at the SNP markers on all autosomes, before and after ENQT transformation. This trait has kurtosis of 1.54 and skewness of -1.17. Its heritability measures 0.41 before transformation and 0.44 afterward. After ENQT transformation, two large peaks on chromosome 9 and 11 decrease dramatically, with maximum decreases of LOD scores from 3.43 to 1.61 and from 2.63 to 1.34, respectively. Smaller but sometimes wider peak changes can also be found on chromosome 1 (from 2.03 to 0.66), 5 (from 1.74 to 0.10), and 8 (from 1.50 to 0.14). On the other hand, the transformation magnifies a narrow peak on chromosome 11 (from 2.06 to 3.63) and induces a wide peak on chromosome 19 (from 1.15 to 3.35).Table ENQT transformation has a different impact on traits in different groups. The average difference of LOD scores, and the number of changed markers of the variance-components method are larger than those of the variance-regression method. This suggests that the variance-components method is more sensitive to non-normality than the variance-regression method.For both mapping methods, ENQT transformation causes more reduced LOD scores than increased LOD scores, which may contribute to decreased false-positive rates. Among these five groups, the normal group has the least LOD score changes followed by the group with low changes in heritability. Groups with high heritability differences, significantly non-normal and high heritability, have large changes in LOD scores. Note that these three groups overlap and have seven traits in common. These traits are 201481_s_at, 203032_s_at, 204428_s_at, 205048_s_at, 209480_at, 219843_at, and 65588_at.In this paper, we show that normalization has a significant impact on the QTL mapping, using variance-components and regression-based methods. We also show that ENQT transformation is an efficient transformation that outperforms traditional and semiparametric transformation methods. This method is especially suitable for problems with a large number of traits for which customizing the transformation for each trait becomes infeasible.Our simulations show that ENQT transformation performs similarly to a perfect back-transformation and outperforms the SQTL method, which has been proven to have better power than square-root and logarithm transformations for this particular example . HoweverYij may be bi-normal or some other non-normal distribution. SQTL may perform better in such cases because it assumes conditional normality and can in theory normalize trait values after removing covariate effects.It should be pointed out that the optimal transformation does not have to normalize the trait values. In the cases when there are strong and discrete covariate effects, GAW15 Problem 1 has fewer and larger families than what we have simulated, and our simple transformation may discard delicate within-family structures. For example, we have seen traits that are associated with age, resulting in differences in normality test results for each generation as compared to the entire population. However, given the small sample size, it seems impractical to perform normalization at a finer scale.The results presented use Anderson-Darling normality test, even though other normality tests may produce different results. We repeated the normality tests using Sharpiro-Wilk's test, which is suitable for samples of size less than 200. The two tests largely agree with each other, and there are only a few changes to the five groups of markers we chose.In summary, we show that normalization can have a strong impact on the results of variance-components and regression-based method and ENQT can be a good candidate to blindly transform a large number of quantitative traits. It is therefore recommended that results based on untransformed data be repeated with normalized trait values using ENQT method. If there are significant differences, caution should be taken when making statistical inferences.The author(s) declare that they have no competing interests.


Genome-wide association studies raise study-design and analytical issues that are still being debated. Among them, stands the issue of reducing the number of markers to be genotyped without loss of efficiency in identifying trait loci, which can reduce the cost of studies and minimize the multiple testing problem. With this aim, we proposed a two-step strategy based on two analytical methods suited to examine sets of markers rather than single markers: the local score, which screens the genome to select candidate regions in Step 1, and FBAT-LC, a multiple-marker family-based association test used to obtain significance levels of regions at step 2. The performance of this strategy was evaluated on all replicates of Genetic Analysis Workshop 15 Problem 3 simulated data, using the answers to that problem. Overall, seven of the nine generated trait loci were detected in at least 87% of the replicates using a framework designed to handle either association with the disease or association with the severity of disease. This multiple-marker strategy was compared to the single-marker approach. By considering regions instead of single markers, this strategy minimizes the multiple testing problem and the number of false-positive results. Genome-wide association studies with hundreds of thousands of markers (SNPs), as made possible by new high-throughput genotyping technologies, raise many study-design and analytical issues, among which the multiple testing problem occupies a central role. Several strategies have been proposed to confront this problem, including one-stage and multiple stage study designs, analytical approaches in one or multiple steps, and use of one or multiple data sets ,2. The tp-values obtained are then corrected for multiple testing. Each of these two steps is independent from each other and can be modified according to the type of data collected. We chose to make full use of Problem 3 data, which included both case-control and family data, thus guiding the choice of the test statistics suited to these data.We propose a flexible multiple-marker analytical approach for genome-wide association studies made up of two steps. In the first step, the local score method is applied to case-control data in order to detect and rank candidate regions across the genome. It serves as a screening tool. In the second step, these candidate regions are tested for association with the studied phenotype in a sample of family data using FBAT-LC  and the The local score method used the Pearson chi-square statistic applied to the case-control genotypic contingency table for each marker to produce a sequence of scores .X = (Xi)i=1,...,n be a sequence of real random variables. In our context X represents a sequence of statistics of association attached to each marker along the genome. The statistic:Let X. In practice, it corresponds to the value of the region with the maximal sum of scores Xi. Consequently, the variables Xi must be negative on average otherwise the best region would easily span the entire sequence. This definition is restrained to the highest-scoring region. The next high-scoring ones are potentially interesting as well because the data set may contain more than one trait locus (TL). We define the kth best region as the local score of the initial sequence disjoint from the preceding k - 1 best regions. In this case H(1) > ... > Hk)  corresponding, in our case, to the Pearson chi-square test of case-control marker genotype frequencies. A constraint of this strategy is to have X negative on average; that does not happen with positive statistics such as Pearson chi-square, so a constant δ must be subtracted from the whole signal X. In this study, δ corresponds to the value of statistic Xi at the classical 5% level and we let X' = X - δ; ii) identifying the highest-scoring region: a simple approach to get the local score from X' consists of comparing the value of identifying the next high-scoring regions by using an iterative algorithm: find the highest-scoring region, remove it from X', and apply the algorithm again until there are no more positive local scores in the sequence. At the end, the number of tests has been reduced from M markers to N candidate genomic regions ranked according to their local scores.The algorithm of the local score approach includes the three following procedures: i) p-values obtained for all candidate regions, different corrections for multiple testing were compared: no correction, Benjamini and Hochberg correction, and Bonferroni correction. A region was considered significant if the corrected p-value was less than 5%.The new FBAT extension proposed by Xu et al.  was usedWe assessed the ability of our strategy to reveal regions containing the trait loci by comparing the results obtained from the analysis of all Problem 3 case-control and family data replicates with the answers that were provided. Because the local score was applied to case-control data in Step 1 and FBAT-LC to ASP data in Step 2, we formed 50 replicates of association-study data sets, each set being made of two independent samples: one replicate of case-control data and one replicate of family data. Each case-control data replicate included 1500 cases (one case drawn at random from each ASP) and 2000 controls genotyped for the 9187 SNPs. Each family data replicate included 1500 ASPs genotyped for all SNPs belonging to the candidate regions selected in Step 1.p-values. The average proportion of trait loci detected by our two-step approach over the 50 replicates of association-study data sets was also derived.To evaluate the performance of our strategy, we first identified, in each replicate, the true positive and the true negative regions among those selected in Step 1, a region being defined as positive if it contained at least one of the two flanking markers of any hidden trait locus. We then derived the three following quantities: 1) sensitivity, which is the proportion of true-positive regions that were correctly identified by FBAT-LC test; 2) specificity, which is the proportion of true-negative regions that were correctly identified by FBAT-LC test; 3) the false-discovery rate (FDR), which is the proportion of false positives among the declared significant results. An average estimate and standard deviation of each of these three quantities were computed over the 50 replicates of family data. The estimates of these quantities were compared according to the correction applied to the FBAT-LC p-values associated with the Pearson chi-square test applied to the case-control genotypic contingency table. A number, M, of markers with the smallest p-values to be analyzed in Step 2 was selected. M was equal to the average number of markers belonging to the regions selected by the local score method over 50 replicates. In Step 2, a single-marker FBAT was applied to each of the M selected markers and p-values were either not corrected or corrected using either Benjamini and Hochberg or Bonferroni corrections. To be comparable with the above definition of a true-positive region, true-positive markers among the M selected markers were those flanking each trait locus. Estimates of the same performance indicators, as defined above, were derived over the 50 replicates of association-study data sets.We then conducted a two-stage single-marker analysis to be compare with our multiple-marker strategy. All 9187 genotyped SNPs were ranked according to the In Step 1, the local score method revealed an average of 381 regions (standard deviation (sd) = 7.79) with positive scores. These regions contained 472 SNPs on average (sd = 3.30). The distribution of the number of SNPs per region showed that Region 1 contained 38 markers on average, Regions 2 to 6 had more than 2 SNPs and up to 4 SNPs on average, the next 18 regions contained 2 SNPs, and the remaining ones had only 1 SNP.As an illustration, Table p-values among all genotyped SNPs. The average sensitivity was very high (>94%), regardless of p-values correction and analysis of regions or single markers. The average specificity was higher when examining regions  than single markers . The FDR associated with FBAT-LC test decreased dramatically from 37% without correcting p-values to 3% when using a correction, while the FDR associated with single-marker FBAT remained higher than 74% even when p-values were corrected for multiple testing. We then examined all regions with positive local scores and found similar performance (results not shown). Moreover, the average proportion of trait loci detected by either the multiple-marker or single-marker two-step strategy was close to 55%: the DR, C, D, and E loci affecting RA risk directly and the F locus as a QTL for IgM were detected in at least 98% of the replicates, while the influence of Loci G and H on disease severity and the involvement of Loci A and B in more complex gene × gene (G × G) and gene × environment interactions (G × E) were almost never revealed. These results could be explained by the fact that the local score statistic was based on the Pearson chi-square test of association between genotype frequencies and affection status, and hence not dedicated to study severity or interactions.We first evaluated the performance of our strategy by selecting at the first step 50 regions with the highest local scores, which included 115 SNPs on average, thus representing 1% of the 9187 genotyped SNPs. Table p-values were corrected. Moreover, the two loci influencing RA severity were detected in at least 87% of replicates. Regarding the loci involved in G × G and G × E interactions, we used a logistic regression model incorporating either one of these interactions and the likelihood-ratio test of interaction served as input for computing the local scores. However, there was no improvement in the detection of Loci A and B.We repeated our two-step analysis by using other test statistics to compute the local score in Step 1. Regarding severity, we used the test of Spearman rank correlation between marker genotype  and severity (from 1 to 5). An average of 395 regions (containing 467 markers on average) with positive local scores was found. Applying the same selection criterion as before, we kept 50 regions with the highest local scores to be analyzed in Step 2. The performance of FBAT-LC is shown in Table Overall, our results show that the present two-step strategy based on sets of markers provides significant evidence for all four loci affecting RA risk , one QTL for IgM (F) and two loci influencing RA severity in almost all replicates, provided appropriate test statistics are used in Step 1 to compute the local scores. These regions were always detected at the first step for the five former loci and in 87% of replicates for the two severity loci. All of these regions were confirmed at least 94% of the time in Step 2. This shows the efficiency and flexibility of this overall strategy, which can use different test statistics within the same framework. However, loci involved in more complex interactions  were difficult to identify, which may be partly due to the relatively small importance of these interactions and/or weak linkage disequilibrium of these loci with the analyzed markers.p-values were corrected for multiple testing, the FDR associated with the single-marker FBAT remained high. Previous simulations had shown that the local score statistic was more powerful than the single-marker approach in case-control data [When comparing the proposed multiple-marker strategy to the single-marker approach, these two strategies showed similar power to detect RA loci and had both high sensitivity and specificity. However, while the FDR associated with the multiple-marker FBAT-LC decreased significantly when rol data . The preThe results presented here were obtained for the first 50 selected regions with highest local scores in Step 1, which were followed up in Step 2. However, varying the number of selected regions from 10 regions to all regions with positive local scores had a small impact on sensitivity, specificity, and FDR as well as on proportion of TLs detected. This shows that the performance of the proposed strategy was already satisfactory even for a small number of selected regions. However, this may be at least partly due to the strong effect of most TLs on RA. Nevertheless, selecting a small number of regions  in Step 1 might be an appropriate strategy that can minimize the multiple testing problem, although disease models other than the one simulated here need to be explored before drawing a definite conclusion.We used a two-stage analytical approach using two different statistical methods applied to two independent data sets. However, in the context of a two-stage design for genome-wide association studies, Skol et al.  have shoH0), the local score is known to follow the GUMBLE distribution asymptotically. However, this asymptotic approximation is only valid under linkage equilibrium, which generally does not hold. A Monte-Carlo simulation-based version taking these dependencies into account has been implemented (available at ), but simulations increase the time of execution notably. The simple use of the local score method to rank regions to be further tested in another data set, as proposed here, was fast to run because the overall two-step strategy took less than 10 minutes to analyze one sample of 2000 cases/1500 controls in Step 1 and one sample of 1500 affected sib pairs in Step 2. Finally, the proposed strategy is also flexible because it allows different types of data and different test statistics at each step to be considered. Use of a case-control sample in Step 1 might be preferred because it requires less cost and less time to collect data [We used here the local score method as a simple screening tool in a two-stage design. However, this approach can also stand on its own in genome-wide association studies. The significance of local scores can be determined via the extreme values theory. Indeed, under the null hypothesis  declare that they have no competing interests.


PedGenie software, introduced in 2006, includes genetic association testing of cases and controls that may be independent or related (nuclear families or extended pedigrees) or mixtures thereof using Monte Carlo significance testing. Our aim is to demonstrate that PedGenie, a unique and flexible analysis tool freely available in Genie 2.4 software, is significantly enhanced by incorporating meta statistics for detecting genetic association with disease using data across multiple study groups.Meta statistics  were calculated using formal Cochran-Mantel-Haenszel techniques. Simulated data from unrelated individuals and individuals in families were used to illustrate meta tests and their empirically-derived p-values and confidence intervals are accurate, precise, and for independent designs match those provided by standard statistical software.PedGenie yields accurate Monte Carlo p-values for meta analysis of data across multiple studies, based on validation testing using pedigree, nuclear family, and case-control data simulated under both the null and alternative hypotheses of a genotype-phenotype association.PedGenie allows valid combined analysis of data from mixtures of pedigree-based and case-control resources. Added meta capabilities provide new avenues for association analysis, including pedigree resources from large consortia and multi-center studies. In the study of common diseases and genes with modest effects, large consortium and multi-center efforts hold the promise of increased power to detect associations, but present analysis challenges. The study populations for the multiple centers may differ geographically and ethnically, and considerable differences in case-control ascertainment and pedigree structures between studies are likely. PedGenie, available as an analysis option in Genie 2.4 software, requires Java 1.6 for execution and extends the functionality previously available in PedGenie 1.2 .In addition to offering all the capabilities of version 1.2, PedGenie (version 2.4) includes allele and genotype association analysis across studies based on formal Cochran-Mantel-Haenszel (CMH) techniques to calculate the following meta statistics: chi-squared test of independence, chi-squared test of trend, and odds ratios and confidence intervals. An illustration of a meta-association analysis as implemented in PedGenie can be found in Curtin et al [PedGenie is a flexible, easily implemented, and freely available analysis tool that is enhanced significantly in Genie 2.4 software  by the ith and 97.5th percentile of odds ratios from the null genotype configurations.In epidemiologic studies, data are often collected that can be summarized in three-way contingency tables, the presence or absence of a disease phenotype cross-classified with allele or genotype, and controlling for a third categorical variable or 'group' . In a mui. The Mi meta statistic is from the null distribution since it was derived from data simulated under the null hypothesis. To match the information content of the real data, we limit calculation of the statistic of interest in the simulated data to only those individuals with genotype data in the observed sample. In this way, the missing data structure is captured. Steps 2 and 3 are repeated multiple (N) times, and the series of null meta statistics stored. Hence an empirical null distribution is created for the meta statistic of interest, conditional on the particular pedigree and phenotype structures contained across all studies in the total resource.An outline of steps for meta statistics in PedGenie follows. First, allele frequencies for the markers of interest are estimated from the data. This is performed separately for each study. As before, these can be estimated by four different methods: genotyped founders only, all genotyped individuals, all founders with statistically inferred genotypes, and user-defined . Second0, is computed based on the true genotype and phenotype data using the same meta statistic of interest, again ignoring any pedigree relationships that exist. This observed meta statistic is then compared to the empirical null distribution to determine significance as follows:Finally, the observed statistic, Mp-value is less than or equal to the required level of type I error (α).The specified null hypothesis is rejected if the To evaluate the accuracy of the meta association statistics available in PedGenie  and corresponding empirical p-values and 95% confidence intervals (95% CI), two simulated meta-datasets were constructed, each comprised of three studies, as described below. Briefly, two test set designs were used. The first 'independent' design was comprised of three separate studies of varying sample size, each being the standard association design of independent cases and 1:1 frequency matched controls. Results from this design should be in exact agreement with results from standard statistical packages for test statistics, and in asymptotic agreement for their associated p-values and confidence intervals. The second 'mixed' design was comprised of mixtures of study designs (independent and family-based), both within and between studies. This 'mixed' design is used to illustrate PedGenie's versatility.Within each of the two meta-analytic datasets (independent or mixed design), a variety of sample sizes and minor allele frequencies (MAFs) for one bi-allelic single nucleotide polymorphism (SNP) were used across the component studies as detailed in the following section. In each component study, a dataset was simulated under two scenarios: one under the null hypothesis of no association, and another under the alternative hypothesis of association of an allele of interest and phenotype. Under the null scenario, a sporadic rate of 0.10 for affected phenotype status was randomly assigned, regardless of genotype. Under the alternate scenario, penetrances for each genotype  were determined based on a multiplicative genetic model with a genotypic relative risk (GRR) of 1.5 and a sporadic rate of 0.10, according to the methodology described in Camp .® version 9.1). For each PedGenie analysis, either 1,000 configurations (for the null scenario) or 10,000 configurations  were used to determine the empirical null distribution and p-values and confidence intervals for meta (across studies) and within-study test statistics. Generally, the number of gene-dropping configurations was guided by the expected size and desired precision of a p-value. Clearly, the accuracy of the empirical p-value increases with the size of the empirical null distribution simulated; for example, an N of 2,000 gives a 95% confidence interval around α = 0.05 with a width of 0.02 under the null hypothesis.Since PedGenie is an empirical approach, we repeated this procedure 1,000 times for each test design (independent or mixed) and scenario  by randomly re-seeding the initial assignment of alleles in each analysis to demonstrates the reproducibility of the Monte Carlo method, as equivalent results are obtained if a different random number seed is used. The means and standard deviations of the 1,000 empirical p-values and confidence intervals for each meta study simulation were examined for stability and accuracy. For the 'independent' test design, the meta statistics and p-values were compared to statistics and p-values from a standard distribution using an established statistical software package  were simulated with the following sample sizes and MAFs: 1,000 independent cases and 1,000 random controls, MAF = 0.05 (study 1.1); 500 independent cases and 500 random controls, MAF = 0.10 (study 1.2); and 250 independent cases and 250 random controls, MAF = 0.20 (study 1.3). Data were constructed for this design under both the null and alternative scenarios as described above.Three separate studies with a mixture of both family-based and independent resources were simulated with the following sample sizes and MAFs: 1,000 independent cases and 1,000 random controls, MAF = 0.05 ; nuclear families consisting of 200 affected sib-pairs plus parents, 200 discordant sib-pairs plus parents, and 200 independent controls, MAF = 0.10 (study 2.2); and four-generation pedigrees consisting of 53 family members per pedigree ; and including 500 independent controls, MAF = 0.20 (study 2.3).Study characteristics resulting from the independent and mixed design simulations under the null and alternative scenarios are shown in Tables For the nuclear family study study 2.2), alleles were first randomly assigned to parents in families with two siblings in a "population" of over 15,000 families  based on the specified MAF. Second, alleles were assigned to siblings according to Mendelian inheritance. Third, phenotype was assigned to all individuals randomly, but according to penetrances under either the null or alternate scenario. Finally, 400 nuclear families (200 affected and 200 discordant sib-pairs and their parents) were selected randomly from the "source" population. In addition, 200 independent controls were randomly selected from case-control study 1.2 from the appropriate scenario  to create study 2.2, a mixed family and independent resource. Genotypes on all parents, affected and unaffected, were also included in the simulation to demonstrate the flexibility of PedGenie to handle any pedigree structure and use all information available in each pedigree. This resulted in additional family-based cases and controls as noted in Tables .2, allelSimilarly, in extended family study study 2.3), the initial step consisted of randomly assigning alleles to all founders in a "population" of 150 four-generation pedigrees (14 founders and 53 members per pedigree) based on the MAF specified previously. Second, a Mendelian gene-drop was performed in which alleles were assigned to offspring randomly based on parental alleles. Third, phenotype was assigned to individuals randomly, but according to penetrances under the either the null or alternate scenario. Genotype data for generations 1 and 2 were removed, such that genotypes were only considered available for the bottom two generations. Finally, pedigrees containing at least four related, genotyped cases were randomly selected until ~500 affected family members had been ascertained. This resulted in 90 pedigrees in the null scenario, and 83 pedigrees in the alternate scenario containing 501 and 503 family-based cases, respectively. In addition, 500 unaffected independent controls were randomly selected from a source "population" corresponding to the null or alternate scenario samples in case-control Study 1.3 to create a mixed pedigree and independent resource. All family members with genotypes, both affected and unaffected, were included in the simulation to demonstrate the flexibility of PedGenie to handle large pedigree structures and use all information available in each pedigree. This flexibility resulted in additional pedigree-based controls as detailed in Tables .3, the iThe Monte Carlo p-value and confidence interval assessment results, for 1,000 randomly seeded runs using the multi-study, independent-design meta-analytic datasets under both null and alternate scenarios, are shown in Tables For the independent design, all statistics were shown to be equivalent to those from a standard package Tables  and 4. TThe PedGenie software implements a Monte Carlo approach that corrects the null distribution, and not the observed statistic, for family relationships and hence the statistics for the mixed design are also the standard statistics. As shown in Tables ® Precision 670 computer with 4 gigabytes of memory, using a Red Hat® linux operating system. Runtime  with 10,000 null configurations took approximately 15 minutes per independent-design meta analysis and ~35 minutes per mixed-design meta analysis.To illustrate performance, runtime is reported. Runtime for PedGenie (null scenario) with 1,000 null configurations took approximately 1 minute, 30 seconds per single independent-design meta analysis and under 4 minutes per single mixed-design meta analysis on a DellFor common traits involving small effect genes, consortia and multi-center efforts are becoming commonplace. For example, CMH statistics for ordered genotypes have been used to assess association in multiple case-control studies in which cases are independent, either as probands or as randomly selected affecteds . ComplexPedGenie can incorporate all relationships in family-based resources, therefore all family members with phenotype and genotype data that are available can be included. For example, if only one affected sibling was chosen from each pedigree as some investigators are forced to do to appropriately utilize standard statistical packages, the sample size in study 2.2 would have been reduced under the alternate scenario from 694 cases, 200 independent controls, and 706 family-based controls to 400, 200, and zero, respectively. This may be particularly useful for linkage consortia interested in pursuing association testing, as PedGenie can provide valid meta analyses across multiple studies each containing family-based cases and family-based controls, in addition to any supplemental independent controls available. The ability to more fully utilize all data on hand both increases the utility of prior linkage resources and provides increased power to detect associations, particularly in stratified and subset analyses that likely lead to small sample sizes in individual studies. We anticipate that the new meta capabilities in PedGenie will provide new avenues for linkage consortia to explore in terms of association testing.A potential limitation of PedGenie meta analysis is the fixed-effects nature of the CMH approach, and interpretation of the meta odds ratio is dependent on an assumption of homogeneity in genetic effects across studies. Future work will include providing an option to test for heterogeneity across studies such as described in ,22,23, aIn this study, we have described allele and genotype tests for single SNPs. PedGenie also incorporates haplotype and composite genotype tests; these are based on the most likely haplotype configurations from expectation-maximization  rather than a full likelihood approach based on all possible haplotypes (which is not a feasible approach for pedigrees of arbitrary size). We are currently working towards more sophisticated haplotype methods. Future efforts will also include meta extensions for other quantitative and transmission statistics, such as the TDT test, and multiple logistic regression analysis (including a random-effects extension) with covariates.We have demonstrated PedGenie is a valid statistical software tool that offers a comprehensive way of performing valid meta association testing across studies of mixed design. PedGenie (freely available in Genie 2.4 software) can accommodate independent and family-based resources, allowing for more power to detect associations by allowing for valid combined analyses and maximal use of available data.[PedGenie is an analysis option in Genie 2.4 software, University of Utah Genetic Epidemiology Division, freely available at . Java 1.KC carried out the validation testing and statistical analysis, participated in software development, and drafted the manuscript. JW performed the Java programming and maintains the software home page. KAB participated in the design of the study and helped to draft the manuscript. NJC conceived of the study, and participated in its design and coordination and helped to draft the manuscript. All authors read and approved the final manuscript.genie. A compressed archive file of Genie 2.4.2, including Genie.jar, genepi.jar, and all PedGenie example files.Click here for filegeniesource. A compressed archive file with Genie 2.4.2 source code only.Click here for file


Risk of complex disorders is thought to be multifactorial, involving interactions between risk factors. However, many genetic studies assess association between disease status and markers one single-nucleotide polymorphism (SNP) at a time, due to the high-dimensional nature of the search space of all possible interactions. Three ensemble methods have been recently proposed for use in high-dimensional data . An intuitive way to detect an association between genetic markers and disease status is to use variable importance measures, even though the stability of these measures in the context of a whole-genome association study is unknown. For the simulated data of Problem 3 in the Genetic Analysis Workshop 15 (GAW15), we examined the variability of both rankings and magnitude of variable importance measures using 10 variables simulated to participate in gene × gene and gene × environment interactions. We conducted 500 analyses per method on one randomly selected replicate, tallying the rankings and importance measures for each of the 10 variables of interest. When the simulated effect size was strong, all three methods showed stable rankings and estimates of variable importance. However, under conditions more commonly expected to be encountered in complex diseases, random forests and generalized boosted regression showed more stable estimates of variable importance and variable rankings. Individuals endeavoring to apply statistical learning methods to detect interaction in complex disease studies should perform repeated analyses in order to assure variable importance measures and rankings do not vary greatly, even for statistical learning algorithms that are thought to be stable. The use of statistical learning methods to detect interactions between genetic and environmental risk factors is fuelled by the necessity of using methods developed for use with high-dimensional data ), in which explicitly considering all possible two-way, three-way, or higher-order interactions is computationally not feasible. Ensemble methods, or methods that consider multiple models such as classification trees, may be a more efficient way to detect interactions in a high-dimensional space. A simple and intuitive approach for selection of 'interesting' variables that may be involved in interaction is to use the associated importance measure for each variable to rank them  and to LogicReg package) [randomForest) [gbm package) [gbm) with decision stumps (decision trees with a single split) as the base classifier. Boosting algorithms can be seen as gradient-descent algorithms that seek to find a weak classifier that most reduces the error or loss function [The statistical methods assessed in this study included Monte Carlo logic regression  -6, randomForest) -9, and gpackage) -12. Logipackage) . The ranfunction . The conBecause the focus of this study was to examine the stability of variable importance rankings and scores for three ensemble methods on variables involved in simulated interactions, we requested the generating model for the simulated data before beginning analysis. After reviewing the generating model, we included data from all chromosomes containing SNPs simulated with gene × gene or gene × environment interaction: chromosome 6 (674 SNPs), chromosome 8 (442 SNPs), chromosome 16 (204 SNPs), plus lifetime smoking status and sex. On chromosomes 16 and 8 no linkage disequilibrium (LD) was simulated between the disease loci and observed SNPs, so the simulated disease loci were included in our data for analysis. Gene × gene interaction was simulated between the DRB1 locus on chromosome 6 and locus A on chromosome 16; the minor allele at locus A (frequency = 0.30) acted in a dominant fashion to increase risk with the DRB1*4 allele . An interaction between locus C on chromosome 6 and sex was simulated with the C allele (frequency = 0.50), acting log-additively to increase risk of RA in females. Women with one copy of the C allele were modeled to have 2.1-fold increased risk versus women with the cc genotype; women with two copies of the C allele showed 4.41-fold increased risk. Locus B on chromosome 8 was modeled to interact with lifelong smoking status in a dominant fashion; smokers with at least one copy of the B allele  had 1.5-fold higher risk of RA versus smokers with the bb genotype. To approximate a case-control study we used control data paired with a single randomly selected affected offspring from each family. One hundred replicates were created by the workshop organizers, no data sets had missing values, and no genotyping error or misclassification of sex and smoking status was assumed. All genotypes were recoded into a pair of binary variables: one as two-allele dominant and the other as two-allele recessive. Smoking status and gender were retained as binary predictors.r2 = 0.50) and because the generating model for simulation for the DRB1 disease locus was tri-allelic, we retained both SNPs as variables of interest. To assess the variability of ranking and magnitude of importance measures, we randomly selected a single replicate (number 19) and repeated our analyses using the three ensemble methods 500 times, tallying the ranking and influence measures of each of our 10 variables of interest. GBM tallies rankings only for variables with a non-zero importance score, so any variable with an importance score of 0 does not have a corresponding rank.The variables of interest  included sex, smoking status, and the disease loci on chromosomes 8 and 16. Because of the strong LD between SNPs 153 and 154 on chromosome 6 , all three methods place these SNPs near the top of the importance rankings Table . In factImportance scores (as measured by the interquartile range of importance scores for each method) were nearly identical for all variables with non-zero importance scores using GBM, with the largest difference between the first quartile and third quartile score being 0.2 Table . MCLR shOverall, the variability of importance rankings and scores using variables involved in modeled interactions was fairly consistent for all methods evaluated for the chromosome 6-sex interaction, which had a much larger effect size than the other two interactions (chromosome 8 × smoking and chromosome 6 × chromosome 16). With regards to the smaller effect sizes, GBM and RF seemed less variable in rankings and importance scores than MCLR, and GBM was superior to RF in stability of rankings and importance measures, which is not surprising because boosting is an averaging process across an additive expansion of trees .It should be noted that these results are specific to this simulation model, and might be very different under alternative simulation models. In particular, the very large effect size for the chromosome 6 locus might paint an overly optimistic picture of the stability of variable importance rankings and scores. This implies that the disease locus on chromosome 8  in particular may serve as a good benchmark for the variability of statistical learning rankings and importance scores as applied to complex multifactorial diseases when larger effect sizes are also present. In this particular case, it appears that GBM and RF show more stable estimates of variable rankings and importance measures. However, the comparison between RF/GBM and MCLR may not be completely fair, considering that the Gini index used for RF measures the reduction in impurity and GBM attempts to reduce the loss function across the additive expansion of trees, and MCLR is simply tallying variables included in the model across the Markov chain.Especially in situations in which the expected effect size is modest, researchers who use statistical learning methods to detect SNP × SNP (or gene × gene) interaction in complex disease studies should perform repeated analyses to determine the variability of importance measures and rankings, even for statistical learning algorithms that are thought to be stable.The author(s) declare that they have no competing interests.