In the analysis of complex traits, genetic effects can be confounded with non-genetic effects, especially when using full-sib families. Dominance and epistatic effects are typically confounded with additive genetic and non-genetic effects. This confounding may cause the estimated genetic variance components to be inaccurate and biased.In this study, we constructed genetic covariance structures from whole-genome marker data, and thus used realized relationship matrices to estimate variance components in a heterogenous population of ~ 2200 mice for which four complex traits were investigated. These mice were genotyped for more than 10,000 single nucleotide polymorphisms (SNP) and the variances due to family, cage and genetic effects were estimated by models based on pedigree information only, aggregate SNP information, and model selection for specific SNP effects.We show that the use of genome-wide SNP information can disentangle confounding factors to estimate genetic variances by separating genetic and non-genetic effects. The estimated variance components using realized relationship were more accurate and less biased, compared to those based on pedigree information only. Models that allow the selection of individual SNP in addition to fitting a relationship matrix are more efficient for traits with a significant dominance variance. Complex traits are important in evolution, human medicine, forensics and artificial selection programs -4. Most Traditionally, pedigree information has been used to estimate heritabilities and genetic effects for complex traits -10. In mRecently, it has become feasible to generate individual genotype information on large numbers of single nucleotide polymorphisms (SNP) across the whole genome, and genome-wide association studies have been performed in a number of species ,13. It iIn this study, we propose novel strategies that utilize dense SNP data for the genetic dissection of complex traits. First, we estimate a realized relationship matrix based on aggregate SNP information -18. The http://gscan.well.ox.ac.uk/. The total number of animals was 2,296 from 85 unrelated families. The available pedigree spanned four generations. In this complex pedigree, there were 172 full-sib families with an average size of ~11 (SD ~8). The mice were reared in a total of 536 cages, and the number of animals per cage ranged from two to seven. This number was considered as a cage density factor for analyses. Figure Publicly available data including pedigree, genotypic and phenotypic information on heterogeneous stock mice were used ; http://k based on pedigree information was estimated . For example, the intra-class correlation for the group with relationship k = 1/2 was that for full-sibs. However, for relationship k = 1/16, 1/8, and 1/4, it was difficult to group and classify them because of the complicated pedigree structure. In order to estimate intra-class correlations for the group with relationship k, pairs of relationship k were used, but in a way that there were no relationships between individuals of different pairs, i.e. relationship = k within each pair and relationship = 0 for individuals of different pairs. Because of this restriction, not all pairs of relationship k could be used simultaneously. Therefore, we sampled 10,000 independent pairs for each relationship k for each trait. The number of pairs for relationship k, and the average number of pairs in 10,000 samples are given in Table k. Estimated intra-class correlations were averaged over the 10,000 sampling sets. These correlations are, approximately, the summary statistics that are modeled in the variance component analyses.The intra-class correlation of phenotypes for groups having relationship A mixed linear model analysis was used to estimate random polygenic, cage and family effects, and the fixed effect of cage density. The model can be expressed as,y is a vector of Nr phenotypic observations, β is a vector of fixed effects including the overall mean and the cage density as covariates, f is a vector of Nf random environmental family effects, c is a vector of Nc random environmental cage effects, u is a vector of N random additive polygenic effects for all animals derived from pedigree information (N = 2296), and e is a vector of Nr residuals. It is assumed that f, c and u are normally distributed with a mean of 0 and a variance of X, W, U and Z are incidence matrices for the effects. The variance covariance matrix (V) of phenotypic observations for the model can be written as,where A is the numerator relationship matrix based on pedigree information only, and I is an identity matrix. In order to see if estimates for genetic and environmental family effects are dependent, a simple comparison is carried out for model 1, by omitting subsequently the term u (model 1-u) or f (model 1-f). Variance components and effects are estimated by a residual maximum likelihood (REML) method [where ) method ,25. The G) can be estimated and implemented in the model [G, we used the method introduced by Oliehoek et al. (2006) since it is robust and best-performed among tested methods in their study. The details to estimate G are in Appendix A. The model can be written as,When SNP information is available, the realized relationship matrix  may not be fully captured by model 2, and a Bayesian approach can be used to explicitly search for sets of SNPs that explain additional genetic variance. In the first instance, we model only additive effects of QTL. The model can be written as,nq is the number of SNP associated with the QTL, ∝i is the random additive effects of the ith SNP which is normally distributed with mean 0 and variance Λ i is a column vector having coefficients 0, 1 or 2 representing indicator variables of the genotype for each animal at the ith SNP. The variance covariance matrix of phenotypic observations is,where In addition to additive SNP effects, dominant SNP effects are modeled for SNP having three genotypes and its heterozygosity > 10%. The model can be written as,i is the random dominance effects of the ith SNP assuming a normal distribution with mean 0 and variance Δi is a column vector having coefficients equal to 1 for a heterozygous genotype and 0 for a homozygous genotype at the ith SNP. The variance covariance matrix of phenotypic observations is,where σG, and the ratio of variance due to family, cage and additive and dominance SNP effects over the total phenotypic variance were estimated using a reversible jump Markov chain Monte Carlo (RJMCMC) and REML.The polygenic heritability based on G. Therefore, solving dense MME and obtaining REML estimates in every MCMC round was almost impossible in models 3 and 4. Because of this obstacle, we used a computationally tractable strategy to estimate variance components. Initially, variance components were estimated using REML from model 2 (V) nor invert V for each set of sampled QTL effects, which made it possible to carry out a large number of RJMCMC rounds. Variance components for family, cage, polygenic and additive and dominance SNP effects were estimated every 1000 rounds using REML, and the estimated variance components were stored to obtain the posterior mean of the estimates. We used a total of 100,000 rounds of MCMC after 10,000 burn-in periods. Although the variance components were updated and stored only 100 times, the estimates reached convergence quickly probably because of a large number of iterations for the main process.In the estimation of variance components, solving mixed model equation (MME) was a heavy computing task because of very dense 2 > 0.95 in sliding 50 SNP windows using PLINK [In order to efficiently search for sets of significant SNP, we preliminarily pruned SNP, and excluded closely linked SNP having rng PLINK . After pŷ ) with models 1 to 4. In the Bayesian approach (models 3 and 4), averages of ŷ  over all RJMCMC rounds were used as predicted phenotypes. In order to quantify how well each model can disentangle genetic effects from environmental effects, we used two strategies to produce estimation and validation sets. First, we randomly selected approximately half of the individuals within each full-sib family, which divided the whole data into two subsets. One set was used as an estimation set, and the other set was used as a validation set. Since some individuals in the estimation and validation sets belonged to the same full-sib family, prediction was carried out within full-sib families. Second, approximately half of the full-sib families were randomly selected within each of the 85 unrelated families. This also divided the whole data into two subsets. In this case, no individual in the estimation and validation sets shared the same full-sib family although they would be related. Therefore, prediction was performed across full-sib families.We predicted phenotypes of individuals  were predicted from the estimation based on the phenotypes and genotypes for the rest of the population in the estimation set. For each comparison, we correlated the predicted value of an animal in the validation set with its phenotype (which was not used in the estimation phase). We term the correlation between predicted phenotypes and actual phenotypes as the accuracy of prediction.k = 1/16, 1/8 and 1/4 were relatively low and there was little increase until a highly increased correlation for k = 1/2. For FDC, the correlations for k = 1/16, 1/8 and 1/4 were close to zero with again a much higher value for k = 1/2. For WT, the pattern was similar; the correlations for 1/16, 1/8 and 1/4 were low, and not much different from each other, but increased dramatically with k = 1/2. The relative high correlations for k = 1/2 were probably due to the fact that members within this group (i.e. full-sib) had common dominance and environmental family effects in addition to common additive genetic effects.Figure Estimated variance components proportional to the total phenotypic variance and model log-likelihood are compared in Tables The results for the trait REP are shown in Table Table The results for the trait CC are shown in Table f and u were very high and negative for REP, WT and CC, ranging from -0.85 to -0.94. Correlations between c and u were moderate and negative for FDC (-0.41). This showed that the additive genetic effects derived from pedigree information were highly confounded with the environmental family or cage effects. However, correlations between f and g were low for all the traits (-0.1 ~ -0.23), and those between c and g were negligible, indicating that realized relationships based on aggregate SNP information could disentangle genetic effects from environmental effects. For all the traits, the sampling correlations between estimated variances due to genetic and non-genetic effects were close to zero when using models 3 and 4.Table Accuracies of the prediction of unobserved phenotypes for the various models are shown in Table The accuracies for predicting individuals within full-sib families were higher than those for predicting across full-sib families, which was expected since family information could not be used across the full-sib families. Interestingly, the difference between the accuracies for models 1 and 2 was larger when predicting phenotypes across full-sib families, compared to that when predicting phenotypes within full-sib families. The reduction in accuracy due to lack of family information was larger when using model 1 than when using model 2. This showed that the performance of model 2 was apparently less dependent on environmental family effects.Deviation from unity of the regression coefficient of true phenotypes on predicted phenotypes is an indication of bias in the estimation compared to the true value. The averaged values of regression coefficients were close to 1 when predicting phenotypes within full-sib families. However, when predicting phenotypes across full-sib families, the values were clearly biased probably because of lack of family information across the full-sib families. In general, models 3 and 4 would give more biased estimates, compared to models 1 or 2 although the difference was small.We have shown that a mixed linear model implementing a realized relationship matrix based on aggregate SNP information can efficiently disentangle genetic effects from environmental family and cage effects when the number of causal genes is large and their effects are additive, e.g. REP and WT in this study. When dealing with a trait having a limited number of causal genes with possibly dominance effects, e.g. FDC and CC in this study, a model with a finite number of individual loci can be used to help to disentangle efficiently genetic effects from non-genetic effects. Moreover, the latter model can separate additive and non-additive genetic effects and capture more of the total genetic variance. Therefore, the estimated variance components and resulting solutions from the models based on SNP information are more reliable and accurate, compared to those based on pedigree information only, and they allow a better dissection of the various genetic and non-genetic components of variation.For REP and WT there was no improvement in accuracies for models 3 or 4, compared to those for model 2, which may be due to the fact that the true model for the traits is probably an infinitesimal model like model 2, i.e. a large number of causal genes, each with a small effect. Another possible reason might be that we used a slightly unrealistic prior for the number of QTL in the RJMCMC process. We used a Poisson distribution with a mean of 1 as the prior distribution for the number of QTL (Appendix B). It has been reported previously that the method is robust to different priors for the number of QTL ,27,28. HSince we analysed a single data set we cannot be sure about all the causal factors and how they are  confounded. However, we have shown that the model likelihood increased Tables  to 5, thIn our study, we have estimated a variance covariance matrix of the variance components using average information from Fisher's scoring and the Hessian matrix . A full The better performance of the realized relationship matrix based on SNP information, compared to the numerator relationship matrix based on pedigree, is probably due to the fact that SNP-based analysis can better predict some of the variation within a family . In FiguG matrix nor to solve the mixed model equation. This resulted in much longer computing time to estimate variance components based on the realized relationship matrix. Therefore, we had to use the computationally tractable approach that was modified from the original approach. However, the estimated variance components for family, cage and polygenic effects were mostly consistent across the MCMC process. Therefore, we did not expect very different results when using the modified version.Because most elements of the realized relationship matrix based on SNP data are non-zero, sparse matrix techniques ,33 couldIn model 3, covariance between SNP was negligible probably because the model had a better fit when less dependent SNP were selected. However, this was not the case with model 4 because additive and dominance effects for a SNP were always fitted together whether they were correlated or not. This would cause a negative covariance between SNP effects, and overestimation of total phenotypic variance. When covariance between SNP is explicitly modelled, better estimates can be obtained although there is a risk of overparameterization in model 4.In conclusion, the proposed method implementing a realized relationship matrix based on aggregate SNP information is useful to genetically dissect complex traits especially when there are confounding factors between genetic and non-genetic effects. Resulting variance components are less biased and more accurate. A further analysis could be carried out using the proposed Bayesian approach to disentangle additive genetic and dominance effects. This novel strategy may help to understand the architecture of various complex traits.The authors declare that they have no competing interests.All authors conceived the idea, contributed to the study design, and method developments. SHL undertook the analysis. All authors drafted the manuscript and approved the final manuscript.


Systems genetic studies have been used to identify genetic loci that affect transcript abundances and clinical traits such as body weight. The pairwise correlations between gene expression traits and/or clinical traits can be used to define undirected trait networks. Several authors have argued that genetic markers  can serve as causal anchors for orienting the edges of a trait network. The availability of hundreds of thousands of genetic markers poses new challenges: how to relate (anchor) traits to multiple genetic markers, how to score the genetic evidence in favor of an edge orientation, and how to weigh the information from multiple markers.We develop and implement Network Edge Orienting (NEO) methods and software that address the challenges of inferring unconfounded and directed gene networks from microarray-derived gene expression data by integrating mRNA levels with genetic marker data and Structural Equation Model (SEM) comparisons. The NEO software implements several manual and automatic methods for incorporating genetic information to anchor traits. The networks are oriented by considering each edge separately, thus reducing error propagation. To summarize the genetic evidence in favor of a given edge orientation, we propose Local SEM-based Edge Orienting (LEO) scores that compare the fit of several competing causal graphs. SEM fitting indices allow the user to assess local and overall model fit. The NEO software allows the user to carry out a robustness analysis with regard to genetic marker selection. We demonstrate the utility of NEO by recovering known causal relationships in the sterol homeostasis pathway using liver gene expression data from an F2 mouse cross. Further, we use NEO to study the relationship between a disease gene and a biologically important gene co-expression module in liver tissue..The NEO software can be used to orient the edges of gene co-expression networks or quantitative trait networks if the edges can be anchored to genetic marker data. R software tutorials, data, and supplementary material can be downloaded from:  By definition, these undirected networks cannot be used to describe causal relationships between the traits. Causal information can be encoded by directed networks where A → B if trait A causally influences trait B. We refer to the process of assigning a causal direction to at least some of the edges in a trait network as 'edge orienting'. Experimental edge orienting approaches include transgenic modifications, viral-mediated over-expression, and chemical perturbation of genes. Edge orienting methods can also be based on various approaches that involve multiple perturbations, such as genetic- and time series experiments [The pairwise relationships between different clinical traits (e.g. cholesterol level) and/or gene expression traits (e.g. mRNA levels) have been successfully described with undirected gene co-expression networks -11. Whileriments , or by ieriments .A is significantly associated with a genetic marker M, variation in M must be a cause of variation in A (denoted by M → A) since the randomization of marker alleles during meiosis precedes their effect on trait A. Since the orientation of the edge between M and A is unambiguous, M is referred to as a causal anchor of A [Using genetic markers for orienting the edges of trait networks generated in genetic experiments provides significant statistical power and specificity for recovering directed edges -22. Sinchor of A .M → A → B implies that the genetic marker M has a causal effect on trait A, which in turn has a causal effect on trait B. A causal graph encodes independencies between variables. Conditional independence can be determined by the graphical property of d-separation [A and B are d-separated in the graph by a set of variables S, then the two traits are independent given the variables in S. For example, M → A → B implies that M and B are independent after conditioning on A.We follow the convention of path analysis to represent a causal model by a directed graph. For example, the directed graph paration -32. If tD-separation predicts the correlational consequences of conditioning in the causal graph . By testM and a trait A, we use the correlation coefficient cor. Ordinal variables are routinely used in path analysis and structural equation modelling [For simplicity, we assume that the genetic markers are single nucleotide polymorphisms (SNPs). For a given sample (e.g. a mouse), a bi-allelic SNP can take on one of three possible genotypes. By default, we assume an additive genetic effect and encode these genotypes as 0, 1, or 2, but alternative marker codings could also be considered. To quantify the linear relationship between a SNP marker odelling ,40.A mediates the effect of marker M on trait B (M → A → B) one can assess how conditioning on A affects the correlation between M and B. To quantify the linear relationship between M and B after conditioning on A, we use the partial correlation coefficient:To determine whether trait M → A → B is correct, then the partial correlation coefficient cor is expected to be 0.If the causal model r [We use Fisher's Z transform to assess the statistical significance of a sample correlation coefficient r :N denotes the sample size; ZFisher(r) asymptotically follows a normal distribution  with mean μ and variance 1. Under the null hypothesis of zero correlation, μ = 0 and ZFisher(r) follows a standard normal distribution. For brevity, we denote the Fisher transformations of the correlation coefficients cor and cor by Z = ZFisher) and Z = ZFisher), respectively.where M → A → B  follows a standard normal distribution. Thus, if the p-value corresponding to Z is high (non-significant), the data fit the assumed causal graph. Using path analysis rules, the causal graph M → A → B  of A and B. If the expected values of cor and cor are non-zero and the causal model holds, Eq. (2) implies that the genetic marker M will be significantly correlated with both A and B. Thus, the marker M can be confirmed as a pleiotropic anchor of A and B by confirming the fit of the causal model M → A → B. We will now consider a situation where the correlation between A and B stems from a hidden confounder C, i.e. M → A ← C → B. The graph implies that A and B are correlated due to the shared confounder C. The correlation cor is expected to be 0 since the arrows between M and B collide at A, i.e, M and B are d-separated without conditioning. In this situation Fisher)Z = Z follows a standard normal distribution. If the p-value corresponding to Z is high (non-significant), the data fit a confounded model. In contrast, the partial correlation cor is expected to be non-zero since conditioning on A 'activates' the causal flow through the collider node, i.e. it induces conditional dependence [We refer to the marker pendence .M → A ← B also implies that the expected value of cor is zero since the causal paths collide at A. Conditioning on A activates this collider node, and the partial correlation cor is expected to be non-zero.The opposite (reactive) causal graph A ← M → B implies that cor is expected to be zero. Under this causal model, Z asymptotically follows a standard normal distribution. In contrast, cor is expected to be non-zero.Similarly, one can show that the model These considerations illustrate that one can test the predicted correlational consequences of a causal model and thus evaluate its fit.We will now consider the situation of multiple markers Figure . Denote A and B. Analogous to Eq. (2), the causal model MA → A → B implies a set of candidate common pleiotropic anchors of MB is also available for trait B  with respect to the edge A → B. We will argue that the availability of orthogonal causal anchors significantly improves the recovery of the causal signal  to evaluate the fit of different causal scenarios.Figure local causal models depicted in Figure higher the model p-value, the better the causal model fits the data.While SEMs can be used to study the fit of multi-trait causal models ,20 we onA → B, we propose the use of edge orienting scores. The higher the value of an edge orienting score for the orientation A → B, the stronger genetic evidence favors this causal model.To summarize the genetic evidence in favor of a given edge orientation A → B. For a single genetic marker M and traits A and B, we consider the 5 different local causal models depicted in Figure A – B and (M – A or M – B) associations and (2) can be tested. The critical technical issue is having degrees of freedom (d.f.) remaining after estimating the model parameters. If the degrees of freedom are 0, the model p-values cannot be calculated. The 5 different local causal models depicted in Figure P(M → A → B), P(A ← B ← M), P(A ← M → B), P(M → A ← B), and P(A → B ← M). While a detailed analysis should consider all model p-values, we find it useful to summarize the genetic evidence in favor of a given orientation A → B (model 1) using a single number: the Local SEM-based Edge Orienting Next Best (LEO.NB) score. The LEO.NB score is defined by dividing the model p-value for A → B by the p-value of the best fitting alternative model, i.e. the best of models 2–5 in Figure In the following, we propose local SEM-based edge orienting (LEO) scores for orientation LEO.NB(A → B) score indicates that the p-value in favor of model A → B is higher than that of any of the competing models in Figure A → B model is inferior to at least one alternative model. In our simulations, we use a threshold of 1 for LEO.NB.SingleMarker(A → B|M).A positive MA (Eq. 3):It is straightforward to generalize the single marker LEO.NB score (Eq. 4) to a set of genetic markers } Figure . We refeM replaced by MA.Note that the multi-marker models used in the definition of LEO.NB.CPA correspond to the single marker models of Figure B is available  since the model A → B implies that these markers impact B, but are independent of both A and MA. We define the likelihood-based orthogonal causal anchor (OCA) score by assessing whether the model MA → A → B ← MB has a higher p-value than the alternative models depicted in Figure If an additional genetic marker set e Figure , we propC. The use of two independent genetic marker sets (MA and MB) alleviates the problem of model identifiability that may plague a CPA based edge orienting score.Note that model 4 in the denominator involves a hidden confounder A and B, and that no such model is included in the single anchor model comparisons. Such a model was found to be indistinguishable from the models with a collider node, such as single anchor models 4 and model 5. In the single marker case, both the collider node and the hidden variable models test for independence in the marginal relationship between the anchor and the more distal trait node. Future research may lead to an understanding of what type of data allow one to consider additional alternative models for the edge score computation. It should be straightforward to adapt the proposed LEO score to additional models as long as their model p-values can be calculated. Correlated markers, which are frequently encountered in practice such as in haplotype blocks, may compromise the performance of edge orienting scores. LEO scoring allows multiple parents of a node to be correctly accounted for within each model. Moreover, the parents  of a model are allowed to co-vary. By contrast, the orthogonal causal anchor set is, by definition, penalized for any covariation with the pleiotropic anchors.Model equivalence is also a key consideration in choosing which models to compare. From the standpoint of model equivalence, we note that the multiple anchor models presented in Figure LEO.NB.SingleMarker, we use a threshold of 1, which implies that the model p-value of the causal model is 101 = 10 fold higher than that of the next best model. For the LEO.NB.CPA and the LEO.NB.OCA, we use lower thresholds of 0.8 and 0.3, respectively. Using simulation studies presented in the Additional File, we found that these thresholds lead to false positive rates that are often substantially below 0.05. Similar to other statistical procedures, NEO is susceptible to the pitfalls of multiple testing that may inflate the false positive rate. Permutation procedures and data dependent schemes  may inform the user on how to pick a threshold for a particular application. Further, we provide R software code for carrying out both single edge and multi-edge simulation studies. Simulation studies can be used to determine the power and false positive rates in different settings .For the single marker score In practice, one often observes strong dependence relationships between genetic markers. Our simulations show that correlations between genetic markers can reduce the power of edge orienting scores. Further, we mention that the NEO software implements an option for removing redundant markers that are highly correlated with each other. The removal of redundant markers may alleviate the loss of power.We now provide a detailed step-by-step description of a typical NEO analysis. An overview is also provided in Figure A and B if the absolute correlation |cor| lies above a user-specified threshold. For each edge A – B, NEO generates edge orienting scores for both possible orientations: A → B and B → A. If an erroneous edge exists between two traits, then it is meaningless to orient it. The NEO software can be used to orient any edge that the user chooses to consider. To allow the user to judge whether the existence of an edge is supported by the data, the NEO software outputs a Wald test statistic of the path coefficient, the corresponding p-value, and the correlation between the two traits. If the Wald test p-value is insignificant, orienting the edge may be meaningless.NEO takes trait and genetic marker data as input. Traits can include microarray gene expression data, clinical phenotypes, or other quantitative variables. Each SNP or trait is a node in the network, and the NEO software evaluates and scores the edge between traits Edge orienting scores will only be generated for edges whose traits have been anchored to at least one genetic marker. Two basic approaches for anchoring traits to markers are implemented in the NEO software: a manual selection by the user or an automatic selection by the software itself.NEO provides great flexibility to the user on how to anchor traits to markers. For example, the user can manually assign SNPs to the traits . Toward this end, the user can choose 1) a greedy approach based on univariate linear regression models, 2) a forward-stepwise approach based on multivariate linear regression models, or 3) both. The greedy SNP selection approach defines M'A as the set of markers with the K highest absolute correlations with A. The greedy approach is equivalent to using univariate linear regression models to relate A to each marker separately and subsequently picking the K most significant markers.NEO can also be used to automatically relate (anchor) traits to SNPs. The automated SNP selection methods consider each trait For creating multivariate linear QTL models, NEO also implements forward-stepwise marker selection. The forward-stepwise marker selection method may avoid a pitfall that plagues the greedy SNP selection: if several genetic markers are located very close to each other (and are highly correlated), the greedy SNP selection may pick all of them before considering SNPs at other loci associated with the same trait. For this reason, we recommend combining greedy and forward-stepwise SNP selection methods.M'A and M'B are obtained, NEO evaluates the consistency of each set. We utilize a marker assignment consistency heuristic: a genetic marker can only serve as causal anchor for one trait. To fulfill this heuristic, a SNP is moved from M'A to M'B if its correlation with B is stronger than that with trait A. We denote the resulting consistent genetic marker sets by M"A and M"B. The resulting consistent genetic marker sets may be comprised of dozens of SNPs. Therefore, it can be useful to further filter the SNPs according to their joint predictive power for the trait. Toward this end, we use the Akaike Information Criterion (AIC) in conjunction with multivariate regression models to select genetic markers from within the consistent genetic marker sets [final genetic marker set MA for trait A, we use the AIC criterion to find a parsimonious multivariate regression model of A using predictors from within M"A. The final sets of markers MA and MB are thus comprised of consistent genetic markers that according to the AIC criterion best predict their respective traits; we use these final sets as causal anchors in computing the edge orienting scores.Once the preliminary sets of markers ker sets . SpecifiA and B are built independently, using AIC-based halting criteria. After consistency checks, these multivariate eQTL models are weighed by embedding them in causal models  and models are then compared using SEM fitting indices. When candidate CPA markers can be found for A and OCAs for B, the NEO method provides stringent consistency checks and balances against over-fitting. We consider automated SNP selection particularly useful when no prior evidence suggests causal anchors for the traits.The forward-stepwise approach based on multivariate linear regression models is akin to a legal courtroom where two cases are built, weighed, and judged. Broadly, the strongest genetic support (multivariate eQTL models) for the genetic influence on A → B and B → A). We recommend using the LEO.NB.OCA score (Eq. 6) as the primary edge orienting score if markers affect both A and B. However, if the results of the LEO.NB.CPA score strongly disagree with those of the LEO.NB.OCA score, the latter should not be trusted. As described in the next step, all fitting indices should be considered before calling an edge causal.Both LEO.NB.CPA and LEO.NB.OCA scores are computed for each edge orientation  also report a Wald test statistic for the path coefficient from A → B. If the Wald test for an edge is significant, the data support its existence. Apart from the model p-value, many other SEM model fitting indices have been defined by contrasting the observed covariance matrix Sm × m with the fitted covariance matrix Σ, a low RMSEA score (say ≤ 0.05), a low SRMSR (say ≤ 0.10), a high CFI (say ≥ 0.90), and a significant Wald test p-value (say p ≤ 0.05).Edges with high edge orienting scores may not necessarily correspond to causal relationships. Although edge orienting scores flag interesting edges, they are no substitute for carefully evaluating the fit of the underlying local SEMs. Since a LEO.NB score is defined as a ratio of two model p-values, it is advisable to check whether both p-values are small, as this would indicate poor fit of either model. If the model p-value of the confounded model  indices ,45 that ces [sem  includinA – B critically depend on the input genetic marker sets MA and MB, we also recommend carrying out a robustness analysis with respect to different marker sets. In particular, the automated SNP selection results should be carefully evaluated with regard to the threshold parameters that were used to define the marker sets. For example, when using a greedy SNP selection strategy, it is advisable to study how the LEO.NB score is affected by altering the number of most highly correlated SNPs. For a given edge and a given edge orienting score (e.g. LEO.NB.OCA), NEO implements a robustness analysis with respect to automatic marker selection  and a corresponding threshold Figure .MA and MB.The primary output of NEO is an Excel spreadsheet which reports likelihood-based edge scores  and other edge scores that are described in the NEO manual. For each edge, the NEO spreadsheet also contains hyperlinks that allows the user to access the log file for each edge. The log file contains a host of information regarding computation of the edge orienting scores including SEM model p-values, Wald test statistics for each path coefficient, and the SNP identifiers for the causal anchor sets sem [Although the main output of NEO are scores for every edge orientation, one can construct a global directed network by thresholding an edge orienting score. NEO uses the R software package sem  to compuautomatically select markers for edge orienting. Since the automatic marker selection entails certain parameter choices, we recommend carrying out a robustness analysis with respect to adding or removing genetic markers. (3) When dealing with a single trait A and manually selected genetic markers, the software can be used to screen for other traits that are causal or reactive to trait A. For example, in Table Insig1. (4) When dealing with multiple edges, NEO can be used to arrive at a global directed network. This can be done by thresholding a chosen edge score. If the resulting global network is acyclic  then d-separation [NEO can be used to address the following four research goals. 1) On the simplest level, NEO can be used to assign edge orienting scores to a single edge using manually chosen genetic markers (see the example in Table  On the sparation  and stanApoe null and C3H/HeJ.Apoe null). The strain C57BL/6J is susceptible to a variety of atherosclerosis, diabetes, obesity, and heart disease related traits to which C3H/HeJ is resistant. The F2 offspring mice are expected to show a significant spectrum of atherosclerosis and metabolic syndrome responses to a high-fat diet. The mice were genotyped at 1278 genetic markers (SNPs) across the mouse genome. A variety of physiological traits were measured, including mouse body weight, fat mass, insulin, glucose, free fatty-acid levels in the blood, and cholesterol fractions (HDL and LDL+VLDL). Here we focus on gene expression data in mouse liver tissue. Since significant differences in the gene expression profiles between male and female mice have been observed [We illustrate our methods using data from a previously studied F2 mouse intercross (referred to as BxH cross) ,11,47,48Insig1 serve as a sensitive proxy for the activation level of the SREBP transcription factors [Insig1 → Fdft1 and Insig1 → Dhcr7 result in high LEO.NB scores. For the female mice of the BxH cross, QTL analysis of Insig1 expression implicated two candidate pleiotropic anchors (SNPs) on chromosomes 8 and 16  of the variation of Insig1. As candidate orthogonal causal anchor of Fdft1, we selected a highly significant SNP on chromosome 9 as can be see from the single marker LOD score curve in Figure Dhcr7 chromosome 13. Figures LEO.NB.OCA(Insig1 → Fdft1) score and the LEO.NB.OCA(Insig1 → Dhcr7) score, respectively. In Table LEO.NB.OCA(Insig1 → Fdft1) = 1.4, which lies above the recommended threshold of 0.3. Further, we find that the Wald test of the path coefficient is highly significant (Z statistic = 10.7). The model p-value of the causal model is p = 0.75 and the RMSEA is ≤ 0.001. These results suggest that there is indeed a causal relationship Insig1 → Fdft1. For the edge orientation Insig1 → Dhcr7, LEO.NB.OCA(Insig1 → Dhcr7) = 1.2 and the Wald test is highly significant at Z = 16.1, and the RMSEA is 0.051. These results confirm the known causal relationship: Insig1 → Dhcr7.Here we use both manually and automatically selected SNP markers to compute edge orienting scores to the known causal relationships between genes in the cholesterol biosynthesis pathways. The gene expression levels of  factors , allowin factors ,51Insig16 Figure . TogetheInsig1 → Dhcr7 and Insig1 → Fdft1, the results of a robustness analysis are presented in Figures Insig1 → Fdft1  and LEO.NB.OCA(Insig1 → Fdft1), respectively. Overall, we find that automatic marker selection with the LEO.NB.OCA and LEO.NB.CPA scores provide evidence of the reported causal relationships in both male and female mouse liver data.For the female BxH mice, we also used automatic SNP selection to compute LEO.NB scores. For edge orientations 1 Figure  shows thInsig1) and manually selected genetic markers NEO can be used to screen for other traits that are reactive to the trait in question.In this application, we illustrate that for a single trait , and assuming that there are 200 known genes downstream of Insig1 (a conservative estimate), we compute the Fisher exact test for the set of 9 predicted versus 14 known downstream genes giving a p-value of 1.0 × 10-13 for the predicted novel gene set.We again used the above-mentioned genetic markers on chromosomes 8 and 16 as causal anchors for Moreover, our analysis also implicates nine novel genes as being affected by the same pathway in female liver. A PubMed literature search on these genes did not suggest known relationships to liver or sterol impacted gene expression.Tlcd1, Slc25a44, and Qdpr. The disparity between male and female mice may reflect the tissue-specific expression and regulation of sexually dimorphic genes [NEO gene screening requires careful validation. For example, we report the results of a NEO analysis in male mouse liver data in Table ic genes .Insig1. Here we contrast this NEO based gene screening method to a related gene screening method [The above application describes the use of NEO for finding reactive genes to g method  that utiFsp27 → MEblue where Fsp27  corresponds to a pro-apoptotic gene that is related to metabolic syndrome: Fsp27-null mice have been found to be resistant to obesity and diabetes; Fsp27 expression is halved in obese humans after weight loss; and Fsp27 regulates lipolysis in white human adipocytes [MEblue, represents the activation status of an entire pathway. More specifically, MEblue is the module eigengene  of the biologically important 'blue' gene co-expression module described in [MEblue is a summary gene expression trait that best represents the expressions of the blue module genes.Here we illustrate how NEO can be used to assign edge orienting scores to a single edge using manually and automatically chosen genetic markers. Specifically, we computed edge orienting scores for the edge ipocytes . The othribed in . This geFsp27 causally affects MEblue, we conducted both manual and automatic SNP selection approaches. We used a previously identified SNP marker on chromosome 19 (SNP19) that affected the expression of the blue module genes [Fsp27 and MEblue. The LEO.NB.OCA scores passed the threshold of 0.3 and the LEO.NB.CPA scores passed the threshold of 0.8. We also used the automatic SNP selection strategies to assess the causal relationship between Fsp27 and MEblue. The results of a robustness analysis can be found in Figure Fsp27 → MEblue is highly robust with respect to different automatic marker selection methods.To study whether le genes  and of sE1 through E5) and a trait (denoted by Trait).NEO analysis can orient the edges of a multi-trait network by automatically selecting markers for each trait separately. The analyses proceed in a stepwise fashion: edges are oriented one at the time. For each edge, NEO computes edge orienting scores . By thresholding these edge orienting scores, one can arrive at a globally oriented trait network. The details of the simulation model and relevant R code is presented in an R software tutorial on our webpage. Briefly, we simulated a causal network between five gene expressions  = 1 - |cor|. Figure E4 → Trait. The LEO.NB.OCA and the LEO.NB.CPA scores exceed their respective threshold of 0.3 and 0.8 for all steps of the robustness analysis, i.e., they retrieve the orientation correctly. Alternative simulation models can be explored using our online tutorial.Note that the correlation between traits A and B that are anchored to genetic marker sets MA and MB, respectively. The correlation cor results from both a causal influence of B on A and from a hidden confounder C. This single edge model is used i) to study the choice of thresholds for the LEO.NB scores, ii) to compare the LEO.NB.CPA with LEO.NB.OCA scores, and iii) to evaluate automatic SNP selection methods. The results of these simulations are described in Additional File In Additional File We propose methods for using multiple genetic markers to recover causal trait-trait relationships in systems genetic studies. NEO will be particularly useful for the analysis of experiments in which common genetic variations are leveraged to explore complex genetic traits.A → B. While several methods exist for constructing undirected gene co-expression networks based on thousands of genes, we have evaluated the NEO method for inferring directed networks involving relatively few genes (fewer than 10 in our simulations). Future research could explore the use of the method for inferring directed networks involving thousands of genes.We propose several edge orienting scores that measure the genetic evidence in favor of a given edge orientation Our simulation studies show that orthogonal causal anchors lead to powerful edge scores that may outperform scores based only on candidate pleiotropic anchors  is quite robust to noise SNPs in our simulations, false-positive input SNPs will result in unreliable edge scores. The automatic SNP selection is particularly vulnerable to false positives and its results should be carefully validated using biological experiments or causality analysis of independent data.The second limitation is that the resulting global trait network may contain loops, i.e. it may be cyclic. In contrast, a directed acyclic graph (DAG) has no cycles. DAGs appear in models where it does not make sense for a trait to have a path to itself. While local DAGs are used for orienting individual edges, the reconstructed global trait network may no longer be acyclic. Acyclicity is theoretically desirable since it allows one to test causal predictions using Pearl's formalism of d-separation -32. The The proposed LEO.NB scores are local in that they orient one edge at a time without regard to the orientations of the other edges. The reconstruction of the global network should be taken with a grain of salt. While we report one simulation model where the global network was reconstructed correctly, future research should carefully evaluate the performance of the NEO approach for inferring global networks. A potential use of NEO is to use it for initializing an iterative edge orienting algorithms for large networks that maximizes a global SEM fitting index.The third limitation is that the SEM-based edge orienting scores assume linear relationships between traits and SNP markers. This is mathematically convenient but non-linear effects are common and have been reported in the literature . The NEOInsig1. The sem R package can be used to evaluate the global fit of an acyclic multi-trait network.Causal inference and structural equation modeling assume that relevant traits and causal anchors have been included in the causal model. Under-specified causal models, i.e. models that omit important variables, may mislead the user to detect spurious causal relationships. NEO leads to relatively simple causal networks that do not incorporate dynamic or hierarchical properties (compare to -58). GivThe NEO algorithm computes an edge score for each edge without regard to the information gained from neighboring edges. NEO aims to harness the power of the established upstream causal anchors (markers) as fully as possible; thus, it is appropriate when genetic variations are a major source of the variation in the traits. To the extent the environment (e.g. diet) is also varied, the NEO approach may be less effective. It is plausible that additional assumptions may allow one to use unshielded colliders to improve the causal inference . This isWe focused on the use of SNP markers which capture only a limited amount of the sequence information of each individual. In the not too distant future, it will be economically feasible to obtain the sequence information of each study subject. Since sequence information is likely to enhance the causal anchor assignment, sequence data may greatly improve the power of the NEO method. Apart from the common genetic variation that perturbs gene expression in mouse crosses, NEO can also be applied to orient edges on the basis of causal anchors from population-based allelic association studies, cell hybrids, or transfected cells.Natural randomization of alleles that occurs during meiosis can be used to study the causal information flow through trait networks. For example, we use mouse cross data to retrieve known causal relationships in the sterol biosynthesis pathway. We find that the proposed edge scores  are quite robust with respect to adding extraneous noise SNPs. Combined with the use of orthogonal causal anchors, the proposed edge orienting scores can provide a strong basis for further experimental evaluation of the predicted causal relationships.A detailed description of our methods, the data, and the R software scripts can be downloaded from our webpage. Here we will briefly outline the main points.Structural equation modelling descends from Sewall Wright's path analysis and is a generalization of multivariate linear regression analysis. Since maximum likelihood testing procedures were incorporated into the analysis, SEMs have become a widely used tool to explore the causal relationship between multiple variables ,46,59,60m observed traits, we denote the observed sample covariance matrix by Sm × m and the expected covariance matrix under the causal model by Σ(θ). For the models considered in this article, the parameters θ include path coefficients between the traits and variances of the genetic markers. To arrive at a maximum likelihood estimate of the model covariance matrix SEM analysis typically starts with variables centered on their means and focuses on the covariance relationships. Traits or nodes are connected by arrows denoting causal relationships. The causal relationships define a systems of linear regression models where the parents of a node are used to predict the child node's response. The system of resulting linear equations imposes constraints on the structure of the expected covariance matrix. Given θ by F = P(data|M → A → B) denotes the p-value for the model in which SNP marker M causally affects trait A which in turn affects trait B. X2 tests the null hypothesis that the model is correct. A small model p-value (say p < 0.05) indicates that the causal model does not fit well. Following the logic of an 'accept-support' context [where  context ,61 whereX2 fit statistic and the corresponding model p-value have several limitations, e.g. they are sensitive to the size of correlations and they depend on the sample size N [relative fitting index that contrasts the fit of the causal orientation to that of the other models. Alternative edge orienting scores could be defined by replacing the model p-value by another fitting index for which high values indicate good fit, e.g. the comparative fitting index (CFI). Studying the performance of these generalizations of the LEO.NB score is beyond the scope of this article.The e size N . DespiteProject name: Network Edge Orienting (NEO) R softwareProject home page: Operating system(s): Platform independentProgramming language: RLicence: GNU GPL 3JEA and SH jointly developed the methods and wrote the article. JEA implemented the NEO software. TFF evaluated the method in several real data applications, helped with the R software tutorials, and the write-up. SH and AJL directed the methodological research and applications, respectively. All authors read and approved the final manuscript.Single edge simulation study. This document describes our single edge simulation studies involving the LEO.NB.CPA score (Eq. 5) and the LEO.NB.OCA score (Eq. 6). We describe the parameters used in the single edge A ← B simulation model. A hidden confounder C affects the correlation between A and B. The effect of SNP markers on traits A and B is parameterized with the restricted heritabilities. The single edge simulation model is used i) to study the choice of thresholds for the LEO.NB scores, ii) to compare the LEO.NB.CPA with LEO.NB.OCA scores, and iii) to evaluate automatic SNP selection methods.Click here for file


We performed association analysis under a previous linkage peak on chromosome 16 with genome-wide single-nucleotide polymorphism (SNP) data to identify genetic variants underlying body mass index (BMI). Data from all subjects with baseline measures and a subgroup who had complete data at four selected time points from the Framingham Heart Study were analyzed. The cross-sectional measures include BMI at baseline for all subjects, as well as BMI at selected time points for the subgroup. The longitudinal measure is the within-subject mean of BMI for the subgroup at the four time points.Association analysis was first performed using PLINK after dividing large pedigrees into nuclear families. We then followed up the identified regions by variance-components methods as implemented in SOLAR using the extended pedigrees.p = 0.00002, QTLD p = 0.005), on the FTO gene, and at 48.1 Mbp  on chromosome 16, which are directly under the previous identified linkage peak. This association was consistently observed for all samples at baseline, and for the subgroup at time point 2, 3, 4 and MEAN, both by PLINK and SOLAR. In addition, another SNP/region at 46.7 Mbp on same chromosome was found to be associated with several BMI measures in the subgroup. Fine-mapping with more markers provided further evidence for SNP association with BMI in the same region .The strongest evidence for associations were observed at 52.3 Mbp (PLINK These results suggest the existence of genes/DNA variations in these regions that contribute to BMI variation. Obesity, which is influenced by both genetic and environmental factors, is an independent risk factor for coronary heart disease (CHD). However, the reported quantitative trait loci (QTLs) for body mass index (BMI) are not consistent. The discrepancy among various studies represents the difficulty in identifying susceptibility genes for common complex traits. Many factors, including, but not limited to sample size, ascertainment method, long-term or short-term environmental influences, and genetic heterogeneity, all may contribute to the discrepancy among studies. Age-dependent penetrance of a trait is another factor that may complicate the identification of susceptibility genes.Cross-sectional study designs collecting phenotypic data at one time point are used in most genetic studies, mainly due to their relative feasibility. However, longitudinal data may answer questions that cross-sectional data cannot. A longitudinal study with measures at multiple time points might be the best solution for gene mapping studies of traits with age-dependent penetrance. Furthermore, serial observations over time of the same trait may allow more accurate partitioning of genetic and environmental components than would a single observation . Thus, lThe Framingham Heart Study (FHS) is a successful longitudinal study of cardiovascular diseases. Started in 1948, FHS has obtained longitudinal cardiovascular-related phenotypic measures in two generations of participants. A 10-cM genome-wide scan in subjects from 330 families was carried out in the late 1990s and several suggestive linkage regions were identified for BMI . The higOur goals in this study were: 1) to identify QTLs for BMI using an association approach, taking into account the linkage information we had obtained in the previous genome-wide linkage studies ; and 2) Three cohorts were recruited in the FHS. Both the Original Cohort (Generation 1) and Offspring Cohort (Generation 2) had data collected at baseline and three follow-up visits. The Generation 3 had only baseline measures. Using the cross-sectional measures from baseline, a total of 960 extended pedigrees consisting of 6475 subjects were used in the genome-wide association analysis of BMI.In order to evaluate the longitudinal effect and to make association analysis results from different time points comparable, we also analyzed those subjects with phenotypic data at all the four selected visits as a subgroup . Only families with at least two blood-related individuals who met such criteria were included in the analysis.2] was selected as the quantitative trait because of its completeness and uniform method of measurement over time. Baseline BMI was denoted as BMI-B. For the subgroup of the Original and Offspring Cohorts, five measures of BMI, denoted as BMI1, BMI2, BMI3 and BMI4  as well as MEAN (the within-subject mean of the four visits over years), were analyzed.BMI [weight (kg)/height (m)Data quality control (QC) was performed using PLINK to remove SNPs with minor-allele frequency (MAF) less than 0.05 and to zero out mendelian inconsistencies . SNPs wip < 0.0001 and being located under the identified linkage peaks.Because of the limitations of the analysis program and time constraints, the association between each SNP and BMI was first evaluated using nuclear families (by dividing the large pedigrees) and the program PLINK  with 100Follow-up association analysis for the selected region and fine-mapping were conducted using extended families by the variance-components analysis method as implemented in the SOLAR program ,6. ThreeAssociation test for quantitative traits was performed on BMI-B, BMI1-BMI4, and the MEAN under the additive model. Age, sex, and cohort were included as covariates in the association analyses.n = 6475 subjects), 5 SNPs (52.3 Mbp) met the selection criteria, i.e., p < 0.0001 and located under the previous identified linkage region (highest LOD = 3.0 at 45 cM) [p = 0.001 and were within 10 cM of the peak (45-55 Mbp) , while the SNPs identified by PLINK at 52.3 Mbp remained significant. The top SNP in the latter region was rs9926289  and so we only reported the p-value from QTLD in Table Applying SOLAR to extended families, the top SNP was found to be rs11647781 at 48.1 Mbp (PLINK n = 2702) may reduce the power to identify the association, we observed SNP associations similar to BMI-B for BMI2, BMI3, BMI4, and MEAN (Table Although using a subgroup of samples (AN Table . Interesp = 0.0004) for baseline BMI for all subjects. Another fine-mapping SNP , which is in the same region as the SNP identified in the subgroup samples (rs16845869), also remained significant (QTLD p = 2 × 10-6 for BMI1 and MEAN) in this subgroup.Within the same region, we selected 150 additional SNPs from the fine-mapping markers to further test the associations for all subjects and the subgroup samples. Only one fine-mapping SNP in the same region  showed significant association  were identified in the subgroup only.We performed association analyses on chromosome 16 using genome-wide scan SNP data for BMI measured at different time points and the mean of BMI over a number of years on the FHS sample. The strongest evidence for association was observed at 52.3 Mbp and 48.1 Mbp, which are directly under the previously identified linkage peak. The most consistent associations were observed in baseline BMI for all samples and most time points and MEAN for the subgroup by different analysis methods. The p-value and several tentative associations was observed under the previous identified linkage region, and the evidence for association were consistently observed by different statistical analysis methods as well as for different samples. Considered these together, we believe that there must be some genes or DNA variants in this region that contribute to the determination of BMI. The most significant region we identified (52.3 Mbp) harbors FTO, a gene which was found to be associated with fat mass and obesity. Recent studies have reported that the variants of this gene are associated with body fat distribution and a variety of metabolic traits, such as insulin resistance, diabetes, and high-density lipoprotein cholesterol level [One of the major issues for GWAS is separating true and false positives due to the huge number of multiple tests. Combining the information from previous linkage studies may provide additional power to identify true associations. On chromosome 16, the second most significant ol level .Using longitudinal observations of BMI, we derived MEAN as a longitudinal phenotype that represents an overall status of BMI over years. Although the sample size was much smaller (2702 vs. 6475), we identified similar SNPs as those found in the analysis of all samples at baseline only. In general, BMI4 (at time point 4) and MEAN yield similar associations. Even though it is expected that longitudinal measures provide more information, this was not proven in the study. One possible explanation is the much-reduced sample size when using the longitudinal data.It is intriguing that two top hits (one from fine-mapping) were identified in the subgroup only. After adding more samples from Generation 3 (mean age at baseline was 40.1 compared with 33.8 for the subgroup), the association in the subgroup at 47.6 Mbp was diluted. It is noteworthy that the three different generations in the FHS may have different environmental exposures. Thus, unmeasured environmental factors that may interact with genes might be a major issue in genetic studies.A limitation of our study is that we only performed univariate analyses, which may not be able to identify causative genes or SNPs that are individually weak but collectively informative. Multivariate approaches will be helpful in identifying those SNPs. As far as we know, however, the available machine-learning methods were developed for random individuals or case-control data, which restricts their applications to the FHS data, which contained extended pedigrees.FTO gene. Another region (47.6 Mbp) may contain genes contributing to BMI by interacting with environmental factors.In summary, there appears to be genetic variation(s) on chromosome 16 that contribute to BMI. In addition to age, environmental factors, and major genes with marginal effects, there may also be different genes that determine BMI variations at different age periods. Nevertheless, when we analyzed cross-sectional BMI data at different time points and the mean for all time points, we observed consistent associations with BMI at 52.3 Mbp, i.e., the BMI: Body mass index; BMI-B: Baseline BMI; CHD: Coronary heart disease; FHS: Framingham Heart Study; GWAS: Genome-wide association study; MAF: Minor-allele frequency; QC: Quality control; QTDT: Quantitative trait transmission disequilibrium; QTL: Quantitative trait locus; QTLD: Quantitative trait linkage disequilibrium; SNP: Single-nucleotide polymorphism.The authors declare that they have no competing interests.XL participated in the design and analysis and drafted the manuscript. LM and KY participated in data cleaning and analysis. JIR helped to draft the manuscript. XG participated in coordination and helped to draft the manuscript. All authors read and approved the final manuscript.


In families segregating a monogenic genetic disorder with a single disease gene introduction, patients share a mutation-carrying chromosomal interval with identity-by-descent (IBD). Such a shared chromosomal interval or haplotype, surrounding the actual pathogenic mutation, is typically detected and defined by multipoint linkage and phased haplotype analysis using microsatellite or SNP genotype data. High-density SNP genotype data presents a computational challenge for conventional genetic analyses. A novel non-parametric method termed Homozygosity Haplotype (HH) was recently proposed for the genome-wide search of the autosomal segments shared among patients using high density SNP genotype data.The applicability and the effectiveness of HH in identifying the potential linkage of disease causative gene with high-density SNP genotype data were studied with a series of monogenic disorders ascertained in eastern Canadian populations. The HH approach was validated using the genotypes of patients from a family affected with a rare autosomal dominant disease Schnyder crystalline corneal dystrophy. HH accurately detected the ∼1 Mb genomic interval encompassing the causative gene UBIAD1 using the genotypes of only four affected subjects. The successful application of HH to identify the potential linkage for a family with pericentral retinal disorder indicates that HH can be applied to perform family-based association analysis by treating affected and unaffected family members as cases and controls respectively. A new strategy for the genome-wide screening of known causative genes or loci with HH was proposed, as shown the applications to a myoclonus dystonia and a renal failure cohort.Our study of the HH approach demonstrates that HH is very efficient and effective in identifying potential disease linked region. HH has the potential to be used as an efficient alternative approach to sequencing or microsatellite-based fine mapping for screening the known causative genes in genetic disease study. SNP genotyping technology is developing very rapidly. Phase II of the International HapMap Project has characterized over 3.1 million single nucleotide polymorphisms (SNPs) with the resulting SNP density of approximately one per kilobase High-density SNP genotype data presents a computational challenge for genetic analyses. Disease gene mapping methods, including linkage, haplotyping and association studies, identify candidate regions containing a disease susceptibility gene by exploiting the cosegregation of the disease phenotype and markers in cases as well as the difference of allele sharing between cases and controls. The determination of haplotype sharing may represent the future direction of linkage analysis due to its better adaptation to high-density SNP genotype data It is currently still difficult to obtain haplotype information on a genome wide basis for high-density SNP genotype data from either a general pedigree or a population. Performance of haplotype inference methods in a general pedigree relies on whether enough informative individuals have been genotyped. Inference of haplotypes from a diploid population is a NP-hard problem et al. The non-parametric Homozygosity Haplotype (HH) method (HH is not homozygosity mapping employed to search for segments inherited homozygous by descent in inbred recessive pedigrees) was proposed by Miyazawa In this study, the applicability and the effectiveness of the HH approach in localizing causative genes are presented and discussed for a series of monogenetic disease projects with high-density SNP genotype data. A large Canadian family with Schnyder crystalline corneal dystrophy  for which the disease susceptibility gene was discovered recently Schnyder crystalline corneal dystrophy  is a rare autosomal dominant disease characterized by progressive opacification of the cornea resulting from the local accumulation of lipids, and associated in some cases with systemic dyslipidemia. A large multigenerational family  in Nova et al.Samples from 10 affected individuals were genotyped with Illumina HumanHap550 chips. The HH program was first run with the genotypes of all 10 patients with a cutoff value of 3.0 cM, which is the recommended cutoff of HH approach m+n = 10) were selected first, and the HH analysis result is shown in We next sought to determine whether it was necessary to include all 10 patients in order to identify the correct locus in this pedigree. According to equation (1), the ratio of RCA shared by patients decreases with the number of generations removed from their common ancestor. Therefore, samples from the youngest generation of different family branches should be more informative in general. By selecting samples according to this rule, subject 1351 and 1425  and (3)), which were developed to study multigene diseases using genotypes of both patients and controls, can be extended to include unaffected family members. This is similar in spirit to a family-based association approaches 10P value of 3.35. The region was confirmed later by the whole genome scan results of two point and multipoint linkage analyses. Two point linkage analysis was carried out using the MLINK routine of FASTLINK v4.1P We ascertained a large Canadian family with a specific pericentral retinal disorder (PRD) . Thirty-The whole-genome screening approach was further validated using a Canadian family ascertained with myoclonus dystonia (MIM 159900). Three causative genes are known for this genetic condition: SGCE The selection of the cutoff value and samples is critical in employing the HH method. We used a family we ascertained with generalized renal failure as an example to illustrate the selection procedure. Four patients S1, S2, S3, and S4 from the family  were genm = 1, n = 1), or S2-S3 . However, all subsets with more distantly related patients, including S2-S4  and S3-S4 , were successful in ruling out the PKD1 and PKD2 genes as compared to the full analysis using all four samples. The results show that the selection of more distantly related samples would give a higher success rate for the screening of known causative genes. In addition, the performance of screening can be improved by adding more genotype data of affected individuals. For cutoff value selection, the HH analyses with a small cutoff of 1.0 cM were not able to exclude PKD1 and PKD2 when the patients were more closely related, e.g. subset S1-S2, S2-S3 and S1-S3. For the two descendants / patients from a family with 2≤m+n≤6, a condition suitable for a general family, a cutoff of 2.0 cM is recommended for the screening of known causative genes because the ratio of type II errors in identifying candidate region to the total length of the RCAs is lower than 0.01 e.g. an affected sib pair with m+n = 2, it is suggested to genotype more affected individuals.The genotyping error simulation method was applied to study the error possibilities using 550k genotype data of two affected subject s1 and s4. The Monte Carlo simulation of genotyping error was run 10,000 times for each test. As shown in As other statistical genetics methods, the accuracy of HH approach is also affected by genotyping errors. Genotype errors may impact HH results in two ways. Genotype errors may break down a large RCHH to a few smaller RCHHs or intervals, and make the RCHH undetectable if the intervals are smaller than the cutoff value. Second, genotype errors may create a false RCHH. An interval with discordant homozygous SNPs can be identified as a false RCHH if all the discordant SNPs are changed to concordant SNPs by genotyping errors.ε, the chance of generating a false dhSNP by genotype error is ≤ε/2. For the second potential impact, genotype errors may create a false RCHH by changing all dhSNPs of an interval to non-dhSNPs. Given an error ratio of ε, an interval with total For the first possible impact, a genotype error must change a non-dhSNP (either a non-comparable SNP or a matched comparable SNP) to a dhSNP (a mismatched comparable SNP). For a non-dhSNP, when at least one sample is homozygous for the SNP, there is a half chance to cause an error if an AB call was changed to AA or BB. Whereas the change of a homozygous call AA or BB to AB has no effect, the changing to the opposite homozygous call will cause an error only if other homozygous calls of the tested samples are also present. Given an error ratio P value. The interval was confirmed by the two point and multipoint linkage analyses, and for which the causative mutation was found by direct resequencing. Clearly the HH approach can be effectively applied to study monogenic traits in large families by utilizing the genotypes of both affected and unaffected family members. HH can also be applied to test known causative genes or loci quickly for potential linkage. The whole-genome screening approach was further validated using a Canadian family ascertained with myoclonus dystonia and a renal failure cohort. HH correctly detected the potential linkage of myoclonus dystonia, and excluded the known causative genes for the renal failure cohort. These applications demonstrate that HH is an efficient and reliable tool in identifying the potential linkage for monogenic diseases. In addition, the successful application of HH to our projects indicates that HH is well suited for founder populations like those in Atlantic Canada. The population is considered a geographically isolated population derived from thousands of ancestors with m = n = 20.In this study, we investigated the applicability and the effectiveness of HH in identifying genetic disease genes with a series of monogenetic disorders ascertained in eastern Canadian populations. We applied HH to identify the known locus using the genotypes of 10 affected subjects of a family with a rare dominant eye disease SCCD. HH analysis successfully detected the 1 Mb shared segment of the affected members with a minimum of four samples. This study of sample subsets also demonstrates that the optimal genotype data set for HH analysis should be those from the youngest generation or otherwise most distantly related affected individuals in a pedigree. This suggests that important upstream efficiencies can be realized in the clinical phase of genetic studies by the adoption of a sparse recruitment strategy focused on the most informative individuals. We also explored the applicability of HH to the family based case and control study. Thirty-four family members from a large Canadian family with a specific retinal disorder PRD were genotyped with the Illumina HapMap300 beadchip. With 13 affected samples in the patient pool and 19 samples in the control pool, HH identified an RCHH on chr3 with the lowest O(2n). It was reported that the calculation for a family with Marfan syndrome that contains nine subjects is completed in 6 s on a laptop, and another analysis composed of two pools containing 45 subjects each took 5 min The HH approach is very efficient and easy to implement. In comparison to other linkage analysis programs, the most significant advantage of HH is its high computational efficiency. The time complexity of HH algorithm is et al.et al.One feature of the HH method that can be improved is the usage of cutoff value. In our applications, we found it difficult to determine an optimal cutoff value. A cutoff value of 3.0 cM was used by the Miyazawa et al.In this study, we analyzed the impact of genotype errors on HH analysis. The major impact of genotype errors on HH analysis is breaking down a large RCHH. Several approaches may be useful to reduce the impact of genotype errors. Miyazawa et al. Our study of the HH approach with Illumina high-density SNP genotype data from a series of Atlantic Canadian monogenetic disease projects demonstrates that HH is very efficient and effective in identifying disease linked and unlinked regions. The method can be used as an efficient alternative approach to sequencing or microsatellite-based fine mapping for the research and clinical diagnosis of genetic diseases.An HH is a haplotype described by only homozygous SNPs. It is obtained by deleting heterozygous SNPs. Then, the haplotype of each chromosome is uniquely determined by the combination of the allelic type in each homozygous genotype.A comparable SNP is a SNP that is homozygous in two subjects. HH can be compared between two subjects using the comparable SNPs. The mismatched comparable SNP has discordant homozygous SNP genotypes in two subjects, one is AA and the other is BB. We used dhSNP (discordant homozygous SNP) to represent the mismatched comparable SNP.RCHH is a run of matched comparable SNPs with genetic length longer than a cutoff value. A RCHH is bounded by either dhSNPs or by the ends of the chromosome. HH approach searches RCHHs between each pair of subjects. The overlapped RCHH shared by multiple subjects is used to predict the presence of region of conserved ancestry (RCA) or identity by descent (IBD).m and n generations removed from a common ancestor, the ratio of the total genetic length of the derived RCA to the entire length of the autosomes is denoted as RCA, which can be calculated withFor the two descendants with x1 and x2 are the numbers of subjects sharing RCHHs in the patient pool and the control pool, respectively, and 1n and 2n are the total numbers of subjects in the patient pool and the control pool, respectively. The significance of each representative RCHH is expressed with the P value, which is calculated by The HH program also has a statistical method developed to identify candidate regions for multigene diseases in genetically isolated populations by comparing the shared RCHHs between the patient pool and the control pool Samples were genotyped with the Illumina HumanHap300K or HumanHap550K SNP genotyping beadchips. The Illumina HumanHap300 chip has a total of 318,237 SNPs, and the HumanHap550K genotype has a total of 561,466 SNPs. Genotype data of subjects were transformed to the input format of HH program.The source code of HH program Two commonly used error models were implemented. Genotyping error was introduced randomly in the SNP genotypes of each individual with a given error rate.o is the observed genotype of a SNP, G is the underlying genotype, the genotype error rate is ε. The error rate is the same for all possible underlying genotypes.The model was first introduced by Lincoln and Lander τ is the allelotyping error rate. Thus, the penetrance of error genotype followsτ can be approximated to ε/2 when τ is small This model uses mean error rate per allele to quantify genotype errors An RCHH will be broken down if genotyping errors change non-dhSNPs to dhSNPs. Furthermore, the RCHH will not be identified if the resulted segments are smaller than the cutoff in genetic distance. As a result, the causative gene will be excluded mistakenly because of the impact of genotyping error. To investigate the possibility of this type of error, Monte Carlo (MC) simulation was used to simulate the influence of genotyping error.First, the genotype of all tested samples in the region with a known causative gene was modified by replacing the dhSNPs with non-dhSNPs; thus the modified genotypes had consistent homozygosity haplotype. Given a gene/loci at chrN with start position at P1(bp) and stop position at P2 (bp), the region with a known gene/loci is defined as on chrN, starting at P2-1.0 Mb, and ending at P1+1.0 Mb. Then, the MC simulation was performed on the modified genotypes with the selected genotyping error model and error rate. After a large number of runs of MC simulation on each individual's genotype, the distribution of the number of dhSNPs created by genotyping errors was analyzed using the Poisson distribution with the probability density function in equation (4). The Poisson distribution is discrete, and has only a single parameter λ that is both the mean and the variance.i.e. the number of dhSNPs for each run, can be imported to R e.g. P<0.001, that is, the dhSNPs in the region are not likely created by genotyping error. Consequently, the genotype and HH results are reliable.The error simulation results,


Population-based investigations aimed at uncovering genotype-trait associations often involve high-dimensional genetic polymorphism data as well as information on multiple environmental and clinical parameters. Machine learning (ML) algorithms offer a straightforward analytic approach for selecting subsets of these inputs that are most predictive of a pre-defined trait. The performance of these algorithms, however, in the presence of covariates is not well characterized.In this manuscript, we investigate two approaches: Random Forests (RFs) and Multivariate Adaptive Regression Splines (MARS). Through multiple simulation studies, the performance under several underlying models is evaluated. An application to a cohort of HIV-1 infected individuals receiving anti-retroviral therapies is also provided.Consistent with more traditional regression modeling theory, our findings highlight the importance of considering the nature of underlying gene-covariate-trait relationships before applying ML algorithms, particularly when there is potential confounding or effect mediation. The primary aim of many population-based genetic association studies is to characterize the relationship among multiple single nucleotide polymorphisms (SNPs) and a continuous or binary trait. Crucial to this endeavor is consideration of environmental, demographic and clinical factors that may themselves be associated with one another, the genotype and/or the trait under consideration. In this manuscript we consider several different approaches to handling covariates in the context of applying two machine learning (ML) algorithms, random forests (RFs) and multivariate adaptive regression splines (MARS). Specific consideration is given to underlying models of association and sensitivity of each approach for detecting true effects. Measures of false discovery are also reported.RFs is a non-parametric approach, originally proposed by Breiman, L. 2001) [ [1], andStudies of the performance of ML algorithms include investigations of additive effects, statistical interaction, correlation among predictors, false positive rates and instability resulting from slight perturbations of the data ,11-13. TWe present results of a simulation study aimed at characterizing the comparative performance and interpretation of several approaches to handling covariates. Specifically, we consider four strategies for handling covariates in the context of uncovering genotype-trait associations: (1) including covariates as predictors; (2) stratifying by covariates; (3) residualizing the outcome by covariates; and (4) ignoring the covariates. Several underlying models are also considered, namely additive models with and without predictors that are themselves associated, models with statistical interaction (i.e. effect modifiers) with and without main effects, and models of conditional association.Y = T be the vector of responses where n is the number of individuals in our sample and suppose X is an n × p matrix of genotype (SNP) variables with ith row given by Xi =  and corresponding to individual i, i = 1,..., n. Further suppose Z is an n × q matrix with ith row given by Zi =  corresponding to the vector of covariate values for individual i. We assume throughout this manuscript that primary interest lies in correctly identifying associations between Y and X while accounting for Z.We begin by briefly outlining our notation. Let Y, node impurity is typically measured by the Gini index while for a regression tree on a continuous Y impurity is often measured by the mean square error. Splitting continues until a pre-specified criterion is reached, usually a minimum number of observations in terminal nodes. Finally, to obtain optimal trees that balance complexity and predictive power, some nodes may be removed in a pruning process  with 5, 2, 3 and 4 SNPs, respectively, as potential predictors. First stage analysis results, including complete demographic and clinical information on this cohort are presented in Foulkes, A. et al. (2006) . An appln = 512 individuals with a known duration of ART exposure and complete data in HDL-c. Among these are 317 Whites/non-Hispanic, 92 Blacks/non-Hispanic and 103 Hispanics. Some studies have shown that genetic variation plays a role in lipid differences across various races or ethnic groups , EL [rs12970066] and HL [rs6084] unless a stratified analysis is performed. Notably, for the Whites/non-Hispanic group, which makes up the majority of the sample, the two most predictive SNPs match those that were selected using other approaches.We begin by log transforming HDL-c and fitting a model with all 14 SNPs as well as race/ethnicity as potential predictors of log(HDL-c) levels. Secondly, we fit a model in which race/ethnicity is excluded from input. Thirdly, we fit a model after residualizing by race/ethnicity and lastly, we fit separate models for the three different ethnic groups. The results are given in Table tability . Table 5ODELS 5 and 6) under the include approach. Interestingly, for the Hispanics group, none of the SNPs are selected under MARS, though several SNPs appear in the RF analysis. This may reflect the loss in power associated with subset analyses.Table The aim of this investigation is to characterize the relative performances of RF and MARS algorithms for different models of association in genetic studies of unrelated individuals. Our study was motivated by the fact that even though there exists extensive genetic epidemiology literature about applications of ML algorithms in this setting, it is not well established how these algorithms perform under different approaches to handling covariates and various models of association. Overall, our investigation found that for a binary covariate: (1) machine learning algorithms perform relatively poorly in the context of effect mediation and the best approach in this setting is to ignore the mediator variable; (2) in the context of confounding, for high levels of correlation (> 0.5), it is best to use MARS and include the confounder or residualize. While TDR is lower for RF, MARS maintains control of FDR in these cases and is preferable; and (3) in the presence of interaction with no main effects and conditional association MARS performs better and it is best to include or stratify by the covariate.The results of a continuous covariate vary and suggest that RFs perform better in most cases, though MARS and RFs are equally powerful when there is interaction with main effects. In a recent manuscript, Strobl, C. et al. (2007)  demonstrNotably, machine learning algorithms are highly amenable to the analysis of a large number of input variables, as documented in the literature referenced in the introduction. We found that the computational burden of RFs using the randomForest package in R is greater than that of MARS, using the earth package which is also implemented in R. This is likely due to the fact that RFs involves fitting an ensemble of trees while MARS fits the equivalent of a single tree. This discrepancy will increase as the number of inputs increases. In this manuscript, we limit our simulation study to include 8 genotype indicators for the purpose of a coherent presentation. We also limit our analysis of the importance of genes and covariates to the relative rankings in RF and appearance in the final MARS model for ease of comparison between the two algorithms. A formal test of significance can be achieved using the robust inference approach described in van der Laan, M. (2006) . ControlFor the purpose of a concise presentation, we focus our approach and discussion on the evaluation of alternative strategies for incorporating covariates. Several important concepts require further consideration. Specifically, the simulation study focuses on a quantitative trait as the primary outcome of interest; and the impacts of genotyping errors, missing (genotype or covariate) data, variable penetrance and allelic heterogeneity are not considered. Extensive research supports the relevance of these factors on TDRs and FDRs. We further note that genetic association studies often involve a large number of SNPs. While our simulation study involves a small number of genotype predictors for clarity of presentation, ML algorithms have been widely applied to genetic studies of much higher dimensions ,14,15. FIn this manuscript we present the results of the study whose main aim was to compare approaches for handling the combination of SNPs and covariates within and across two ML algorithms. Based on the simulation study and the example, we conclude that both RFs and MARS are powerful algorithms for selecting subsets of significant predictors, but careful consideration of how to deal with underlying gene-covariate-trait relationships is important, particularly if confounding or effect mediation is likely. This study may be easily extended to other existing ML algorithms.BAS drafted the manuscript, assisted in the design of the simulation study, developed software and implemented the simulations, and analyzed the example data. ASF conceptualized the problem and assisted in design of the simulation studies and drafting the final manuscript.