Many complex disease syndromes, such as asthma, consist of a large number of highly related, rather than independent, clinical or molecular phenotypes. This raises a new technical challenge in identifying genetic variations associated simultaneously with correlated traits. In this study, we propose a new statistical framework called graph-guided fused lasso (GFlasso) to directly and effectively incorporate the correlation structure of multiple quantitative traits such as clinical metrics and gene expressions in association analysis. Our approach represents correlation information explicitly among the quantitative traits as a quantitative trait network (QTN) and then leverages this network to encode structured regularization functions in a multivariate regression model over the genotypes and traits. The result is that the genetic markers that jointly influence subgroups of highly correlated traits can be detected jointly with high sensitivity and specificity. While most of the traditional methods examined each phenotype independently and combined the results afterwards, our approach analyzes all of the traits jointly in a single statistical framework. This allows our method to borrow information across correlated phenotypes to discover the genetic markers that perturb a subset of the correlated traits synergistically. Using simulated datasets based on the HapMap consortium and an asthma dataset, we compared the performance of our method with other methods based on single-marker analysis and regression-based methods that do not use any of the relational information in the traits. We found that our method showed an increased power in detecting causal variants affecting correlated traits. Our results showed that, when correlation patterns among traits in a QTN are considered explicitly and directly during a structured multivariate genome association analysis using our proposed methods, the power of detecting true causal SNPs with possibly pleiotropic effects increased significantly without compromising performance on non-pleiotropic SNPs. An association study examines a phenotype against genotypic variations over a large set of individuals in order to find the genetic variant that gives rise to the variation in the phenotype. Many complex disease syndromes consist of a large number of highly related clinical phenotypes, and the patient cohorts are routinely surveyed with a large number of traits, such as hundreds of clinical phenotypes and genome-wide profiling of thousands of gene expressions, many of which are correlated. However, most of the conventional approaches for association mapping or eQTL analysis consider a single phenotype at a time instead of taking advantage of the relatedness of traits by analyzing them jointly. Assuming that a group of tightly correlated traits may share a common genetic basis, in this paper, we present a new framework for association analysis that searches for genetic variations influencing a group of correlated traits. We explicitly represent the correlation information in multiple quantitative traits as a quantitative trait network and directly incorporate this network information to scan the genome for association. Our results on simulated and asthma data show that our approach has a significant advantage in detecting associations when a genetic marker perturbs synergistically a group of traits. Many complex disease syndromes, such as diabetes, asthma, and cancer, consist of a large number of highly related, rather than independent, clinical phenotypes. Differences between these syndromes involve a complex interplay of a large number of genomic variations that perturb the function of disease-related genes in the context of a regulatory network, rather than each gene individually Numerous recent studies have shown that it is often more informative to map intermediate steps in disease processes, such as various disease-related clinical traits or expression levels of genes of interest, rather than merely the binary case/control disease status, to genetic marker loci quantitative trait network (QTN). From a visual inspection of this network, it is apparent that it contains several groups of inter-correlated traits that are connected with weighted edges among them. Further investigation reveals that each subnetwork in this QTN corresponds to different clinical aspects of asthma, such as quality of life , asthma symptoms , and lung physiology . It is natural for one to suspect that such highly correlated traits in a subnetwork may share some common genetic causes, and that analyzing a group of traits in each subnetwork jointly rather than each trait independently may help to better uncover such causes.In several recent attempts on expression quantitative trait locus (eQTL) mapping, a significant focus has been placed on identifying modules of co-expressed genes and the genotype markers that perturb the whole module rather than a single gene. For example, a genotype variation in a putative transcription factor is likely to affect the expression levels of all of the genes regulated by this common transcription factor. Under this scenario, once a group of genes are mapped to a common locus in the genome, it is possible to examine whether the locus harbors a transcription factor that targets the group of genes jointly in order to understand the functional relationship between the genotype marker and the gene module e.g., . Anotherad hoc cluster analysis for finding gene modules from the co-regulation network. Subsequently, each cluster would undergo an examination to determine whether it contains a significantly large fraction of genes that are mapped to a common locus in the genome with a potential pleiotropic effect. This primitive approach is essentially a multitude of single-marker/single-trait analyses which involved no direct integration of information across traits within a QTN during the association tests themselves, since the clustering information was used only in the post-processing step.Recent advances in high-throughput sequencing and molecular profiling technologies have made it both affordable and efficient to observe DNA sequence variations over millions of genomic loci, to measure the abundance of transcripts of virtually all known coding sequences, and to measure a wide range of clinical traits in various disease populations In a different approach to eQTL mapping, a module network graph-guided fused lasso (GFlasso), that can effectively address the general problem of association mapping of multivariate traits related as a quantitative trait network. Instead of using a two-stage method that performs single-trait analyses and combines the results afterwards in light of clusters of traits, our method directly infers markers with a pleiotropic effect by combining information across multiple traits in a single statistical framework, and does not require subnetworks or trait clusters to be extracted a priori or at any point of running the algorithm. The proposed GFlasso approach represents the correlation pattern in multiple traits explicitly as a QTN, and searches for genotype markers that are significantly and jointly associated with multiple highly correlated traits that often appear as a densely connected subnetwork within the whole network. Indeed, the extent of the “jointness” in a marker-to-multitrait association is automatically determined by the connectivities among traits in the QTN, and is subject to the modulation of the strengths of the trait correlations. Thus, the clustering information is just one form of relationship implicitly captured in the network, as the QTN is strictly richer than a trait-cluster. In addition, a QTN may carry other relational information such as weak correlations, heterogeneous  correlations, and pathways, etc. For example, the QTN of asthma-related traits in We believe that explicitly incorporating the molecular and/or clinical phenotype network as a trait correlation structure while searching for genetic associations can significantly increase the power of detecting pleiotropic effects. In this article, we present a new statistical approach, called lasso. Lasso achieves “sparsistancy” in the estimated model by setting the regression coefficients for irrelevant markers to exactly zero graph-constrained fused lasso  variations among a large number of candidate polymorphic loci, we use a linear regression formalism with an topology , and gra the QTN . In thisThe problem of estimating the regression coefficients in GFlasso involves solving a convex program, in which a global optimum solution can be efficiently obtained by exploring the large body of existing work on fast algorithms for convex optimization. In this article, we develop a fast coordinate-descent algorithm to estimate the regression coefficients under GFlasso, from which markers relevant to the (possibly multiple) traits in questions can be identified from the non-zero elements in the estimated regression coefficients. The results on two datasets, one simulated from HapMap SNP markers and the other collected from the SARP asthma patients, show that our method has a significantly greater power with fewer false positives in detecting pleiotropic effects of markers than other methods that do not exploit the correlation structure in traits.To capture correlated genome associations to a QTN, we employ a multivariate linear regression model as the basic model for trait responses given inputs of genome variations such as SNPs, with the addition of a sparsity-biasing regularizer to encourage selection of truly relevant SNPs in the presence of many irrelevant ones. Then, we introduce an additional regularizer of fusion penalty to encourage the sharing of association patterns from a common SNP to multiple inter-related traits.There is a large literature on multivariate linear regression in statistics In a standard regression approach for a single-trait association analysis, we assume a linear relationship between the covariates (SNPs) and each response (trait) parameterized by a set of regression coefficients, and estimate the parameters by optimizing a loss function defined on SNP-trait samples given the parameters. Based on the magnitudes of estimated regression coefficients, we draw conclusions on which SNPs are most significantly associated with the given trait. When data are available for multiple traits, we can apply this single-trait approach to each trait separately as we detail below.Let In a typical genome-wide association mapping, one examines a large number of marker loci with the goal of identifying only a small number of markers associated with the given phenotype. A naive application of the method in Eqn 2 to association mapping with large The lasso for multiple-trait association mapping defined in Eqn 3 is equivalent to solving a set of In order to estimate the association strengths jointly for multiple correlated traits while maintaining sparsity, we introduce another penalty term called graph-guided fusion penalty into the lasso framework. This novel penalty makes use of the complex correlation pattern among the traits represented as a QTN, and encourages the traits which appear highly correlated in the QTN to be influenced by a common set of genetic markers. Thus, the GFlasso estimate of the regression coefficients reveals joint associations of each SNP with the correlated traits in the entire subnetwork as well as associations with each individual trait.relevance network, and has been widely used as a representation of gene interaction networks We assume that a QTN, denoted by Below, we first introduce Given a QTN, it is reasonable to assume that if two traits are highly correlated and connected with an edge in the QTN, their variations across individuals are more likely to be explained by genetic variations at the same loci. In The idea of using a fusion penalty has been first proposed in the classical regression problem for a univariate response  and high-dimensional covariates to fuse the regression coefficients of two adjacent covariates when the covariates are assumed to be ordered such as in time When applied locally to a pair of regression coefficients for each edge When this edge-level fusion penalty is applied to all of the edges in the entire QTN as in the graph-guided fusion penalty, the overall effect is that differences of regression coefficients, by combining information among multiple correlated traits according to the topology of the QTN. As we demonstrate in our simulation study, in a typical association study that involves many irrelevant SNPs, this bias towards sparsity in the difference of regression coefficients for neighboring traits helps increase power while reducing false positives, since the information of a SNP being relevant or irrelevant is shared across traits. A balance among the three terms in Eqn 4 that jointly define the objective function, the regression error, the sparsity penalty, and the fusion penalty, will be reached if the optimal regularization parameters Although, in principle, the graph-guided fusion penalty has a smoothing effect on the rows of Now, we describe an enhanced version of Compared to The optimization problems in Eqn 4 and Eqn 5 are convex, and can be formulated as a quadratic programming problem using the similar approach for solving the fused lasso problem In this section, we describe a procedure for obtaining estimates of the regression coefficients in This coordinate-descent procedure finds the optimal The coordinate-descent algorithm for We determine the initial values We performed a simulation study to evaluate the power of the proposed GFlasso methods, and compared the results with those from single-marker/single-trait regression analyses as well as other multivariate regression methods.We simulated genotype data of 50 SNPs for 250 individuals based on the HapMap data Given the simulated genotype, we set the number of phenotypes to 10, and simulated the matrix of true regression coefficients by first choosing SNP-trait pairs with true associations and assigning values for the strengths of associations for the selected pairs as we describe below. We assumed three groups of correlated traits of sizes 3, 3, and 4. Three causal SNPs were randomly selected for the first group of traits, and four causal SNPs were selected for each of the other two groups, so that the shared relevant SNPs induce correlation among the traits within each cluster. In addition, we assumed another causal SNP for traits in both of the first two clusters in order to model the situation of a higher-level correlation structure across two subnetworks. Finally, we assumed one additional causal SNP for all of the phenotypes. In our simulation study, we assumed that shared causal SNPs are the only factors that induce correlations among traits, although in general there might be other genotypic effects or environmental factors that influence the correlation structure among traits.Once the SNP-trait pairs with true association were selected, we considered the following two cases of association strengths for these pairs, while setting the rest of the regression coefficients to 0.The regression coefficients for all of the SNP-trait pairs with true association were set to the same value. This corresponds to the situation where the basic assumption of the fusion penalty holds, and each SNP has the same effect across the traits in each subnetwork.The regression coefficients for the SNP-trait pairs with true associations were set to different values randomly generated from a uniform distribution over an interval Then, we simulated phenotype data based on the linear regression model with noise distributed as We compared the results from the GFlasso methods with those from other methods given below:We used  into a smaller number of variables that explain most of the variability in the original data, performs a standard multivariate regression on each of the transformed output separately, and then transforms the estimated regression coefficients back into the original space For methods that require a specification of the values of the regularization parameters such as ridge regression, lasso, and the GFlasso methods, we used As an illustrative example of the behaviors of the different methods, a graphical display of the QTN and the estimated QTL sets Next, we systematically and quantitatively evaluated the performance of the association methods based on two criteria, sensitivity/specificity on the uncovered QTL sets First, we varied the sample size of the dataset to see how the sample size affects the performance of the different methods for association analysis. We used datasets of sizes 50, 100, 150, 200, and 250, with association strength fixed at 0.5 for all associated SNP-trait pairs (Case 1), and we set the threshold We examined how varying the signal-to-noise ratio affects the performances of the different methods. We simulated datasets with regression coefficients set to 0.3, 0.5, 0.8, and 1.0, respectively, with sample size Next, we examined the sensitivity of the GFlasso methods to how the trait correlation network is generated, by varying the threshold entirely . When thrlapping . OverallGiven the SNP-trait pairs that the association methods found as associated, and the corresponding regression coefficients, we computed prediction errors to see if these SNPs with non-zero regression coefficients had a predictive power for traits of previously unseen individuals. reshold  . In thisSince the fusion penalty tends to fuse the regression coefficients to be the same value within a densely connected subgraph, one may suspect that the bias introduced by this penalty can reduce the power when the true association strengths of a SNP to different traits are not the same within each subgraph. In order to examine how the performance is affected in this case, we considered the situation where the association strengths of each causal SNP are not uniform across traits within each subnetwork, but vary within the interval of The scalability of our methods can be assessed from IL-4R gene that spans a 40 kb region on chromosome 16. This gene has been previously shown to be implicated in severe asthma PHASEIL-4R gene were associated with a subnetwork of correlated traits rather than an individual trait. We standardized measurements for each phenotype to have mean 0 and standard deviation 1 so that their values were roughly in the same range across phenotypes.We applied our methods to a dataset collected from 543 asthma patients as a part of the Severe Asthma Research Program (SARP) Before searching for associations between SNPs and traits, we first examined the correlation structure in the 53 clinical traits in question. We first computed the pairwise correlations between these traits as depicted in A comprehensive comparison of QTL mapping using GFlasso and other methods is presented in IL-4R, and codes for amino-acid changes in the intracellular signaling portion of the receptor. It has been previously found to be associated with severe asthma and its traits for lung physiology As can be seen from In addition, the results from the single-marker analyses in  to zero . When weBecause of the fusion penalty, the regression coefficients estimated by our methods formed a block structure, where each block corresponds to a SNP associated with several correlated traits. It is clear that the horizontal bars in In order to see how the threshold In summary, the GFlasso methods identified the previously known causal SNP (SNP Q551R) as significantly associated with the lung physiology traits, while maintaining an overall sparse pattern in estimated regression coefficients to reduce false positives. The property of the GFlasso estimates having a block structure for a SNP jointly associated with a set of correlated traits led to an interesting new hypothesis that two additional SNPs (rs3024660 and rs3024622) on the upstream of SNP Q551R may be jointly influencing the same set of traits on lung physiology as SNP Q551R, which may be validated in a future follow-up study.When multiple phenotypes are involved in association mapping, it is important to combine the information across phenotypes and make use of the full information available in data in order to achieve the maximum power. Most of the previous approaches either considered each phenotype separately, or used relatively primitive types of phenotype correlation structures such as surrogate phenotypes transformed through PCA or the mean values of subgroups of phenotypes found by clustering algorithms. Networks or graphs have been extensively studied as a representation of the correlation structure of phenotypes such as gene expression or clinical traits because they provide a flexible and explicit form of representation for capturing dependencies In this article, we proposed a new family of regression methods called GFlasso that directly incorporates the correlation structure represented as a QTN and uses this information to guide the estimation process. These methods considered a multitude of phenotypes jointly, and estimated a joint association model in a single statistical framework. Often, we are interested in detecting genetic variations that perturb a sub-module of phenotypes rather than a single phenotype, and GFlasso achieved this through a fusion penalty, in addition to the lasso penalty, that encourages parsimony in the estimated model. The fusion penalty locally fused two regression coefficients for a pair of correlated phenotypes, and this effect propagated through edges of the QTN, effectively applying fusion to all of the phenotypes within each subgraph. The fusion penalty in GFlasso introduced a bias that the amount of influence of a shared QTL is similar over the set of correlated traits in order to increase the power for detecting weak signal and reduce false positives. The simulation results showed that the benefit of information sharing due to the fusion penalty outweighed the risk of low-variance bias on fused regression coefficients when in reality the magnitudes of the coefficients can be highly variable. Perhaps a more effective approach and a promising future direction would be to encourage each SNP marker to be jointly relevant or irrelevant to the subset of correlated traits, but still allow the marker to have a different amount of influence on each of the traits. This would reduce the bias introduced by the fusion penalty and further improve the performance of GFlasso, since the only information shared across correlated traits is the sparsity pattern but not the magnitudes of the regression coefficients.We have used a simple scheme of a thresholded correlation graph for learning the QTN of phenotypes to be used in GFlasso. Many different types of network-learning algorithms have been developed previously. For example, graphical Gaussian models (GGMs) Geronemo and Lirnet, both the module network structure and the markers of regulators regulating the modules were learned simultaneously, although these methods only focused on modeling the relationship between regulators and target genes In this study, we assumed that the graph structure of a QTN is available from a pre-processing step. One of the possible extensions of the proposed method is to learn the QTN and the regression coefficients jointly by combining GFlasso with the graphical lasso For any new multivariate genetic-association methods, a natural question is whether the new method can scale to a genome-scale analysis. The current implementation of GFlasso leaves this to be determined by a user-specified tradeoffs between power and computation time. As shown in Finally, it is important to point out that as of now GFlasso considers only dependencies among phenotypes, and does not assume any dependencies among the markers. Since recombinations break chromosomes during meiosis at non-random sites, segments of chromosomes rather than an individual nucleotide are inherited as a unit from ancestors to descendants, creating a relatively low diversity in observed haplotypes than would be expected if each allele were inherited independently. Thus, SNPs in high LD are likely to be jointly associated with a phenotype in a regression-based penetrance function. In our future research, we plan to apply the same idea of the graph-guided fusion penalty for phenotypes to incorporate the LD structure among genotypes. It is straightforward to introduce another fusion penalty for correlated markers based on the genotype correlation graph and weight each term in the penalty using values that reflect the recombination rates and distances between each pair of genetic markers. This would allow a genome-phenome association analysis for identifying a block of correlated markers influencing a set of correlated phenotypes.http://www.sailing.cs.cmu.edu/gflasso.html. A preliminary version of this method was presented at the 19th international conference on intelligent systems for molecular biology (ISMB 2009).Software for our proposed method is available at


During the past two decades, the field of human genetics has experienced an information explosion. The completion of the human genome project and the development of high throughput SNP technologies have created a wealth of data; however, the analysis and interpretation of these data have created a research bottleneck. While technology facilitates the measurement of hundreds or thousands of genes, statistical and computational methodologies are lacking for the analysis of these data. New statistical methods and variable selection strategies must be explored for identifying disease susceptibility genes for common, complex diseases. Neural networks (NN) are a class of pattern recognition methods that have been successfully implemented for data mining and prediction in a variety of fields. The application of NN for statistical genetics studies is an active area of research. Neural networks have been applied in both linkage and association analysis for the identification of disease susceptibility genes.In the current review, we consider how NN have been used for both linkage and association analyses in genetic epidemiology. We discuss both the successes of these initial NN applications, and the questions that arose during the previous studies. Finally, we introduce evolutionary computing strategies, Genetic Programming Neural Networks (GPNN) and Grammatical Evolution Neural Networks (GENN), for using NN in association studies of complex human diseases that address some of the caveats illuminated by previous work. The identification of disease susceptibility genes for complex, multifactorial disease is arguably the most difficult challenge facing human geneticists today . Most coComplex genetic diseases present several difficult challenges for linkage analysis. First, there is no clear mode of inheritance for most of these diseases. Many linkage methods require the specification of a genetic model (mode of inheritance) for the analysis. Model-independent methods have been developed to account for this, but suffer a reduction in power compared to parametric counterparts. Second, it is likely that multiple loci with varying effects interact to yield an increased risk of disease. The degree and type of interactions will influence the ability to detect genes through linkage analysis. If the interacting loci exhibit strong independent effects, they should be detectable by linkage analysis. However, linkage analysis may not be able to detect a locus that has a small effect . It is hSimilarly, potential caveats exist for association analysis methods for detecting interactions. First, with methods such as logistic regression, the interaction effects must be explicitly modeled. That is, one needs to have knowledge about the interaction that is being tested in advance. Second, current association analysis methods were developed to detect single-locus main effects and thus were not designed for detecting complex gene-gene interactions or epistasis . EpistasTo deal with the limitations of traditional linkage and association analysis methods in detecting susceptibility genes, alternative statistical and computational approaches must be explored. In the search for new statistical methodologies, it is helpful to look to other fields that deal with similar problems in modeling data with many variables and complex interactions. Certainly some of the approaches that have been successful in other areas such as computer science, economics, and engineering, may translate to genetic epidemiology.A computational approach that has been proposed for the study of disease susceptibility genes is neural networks (NN). NN are a class of pattern recognition methods developed in the 1940's to model the neuron, the basic functional unit of the brain . The moti) in the input layer is then connected to one or more nodes in a hidden layer (Σ). The nodes in the hidden layer are in turn connected to nodes in additional hidden layers or to each output node (O). The number of hidden layers can range from zero to as many as computationally feasible. In Figure i) or coefficient associated with it. The signal is conducted from the input layer through the hidden layers to the output layer. The output layer, which often consists of a single node, generates an output signal that is then used to classify the input pattern.Neural networks can be thought of as an acyclic directed graph Figure . They coThe input pattern vector that is propagated through the network can consist of continuous input values or discrete input values. The output node(s) can also be continuous or discrete values. Designing the network architecture must take into account the representation of the input pattern vector and how it will interact with the network while propagating information through the network . Thus, tAs mentioned earlier, learning and memory are thought to be associated with the strength of the synapse. In NN the connections (or synaptic weights) are representative of the strength of the synapse. Therefore, setting the connection strengths is what allows the network to learn . The conSeveral research groups have suggested NN as a useful approach for genetic epidemiology. The features of NN that make them appealing are: 1) they are able to handle large quantities of data, 2) they are universal function approximators and therefore should be able to approximate any genetic penetrance function, 3) they are genetic model free, therefore no assumptions of the genetic model need to be made, 4) they can be implemented in a variety of software packages. Therefore, using NN does not necessarily require a computer programmer and the development of new statistical software. Through the remainder of this review, we briefly discuss several studies in genetic epidemiology where NN have been applied. We look at the types of studies where NN were implemented, the different data types analyzed, and we give an overview of results from the different studies. Next, we compile the results to demonstrate that, while NN appear to be a promising approach for genetic epidemiology, questions remain that need to be addressed. Finally, we introduce evolutionary computation strategies that will improve the utility of NN for genetic epidemiology studies by addressing the previous limitations.As mentioned earlier, there are two main analytical approached in human genetics for the identification of disease susceptibility genes: linkage analysis and association analysis. NN have been utilized for both types of analyses. The design of the NN architecture varies depending on whether the focus is detecting linkage between a marker and a disease locus , or detecting linkage disequilibrium between a marker and a disease locus . Thus, while NN can be used for both types of studies, the inputs and outputs of the NN will be dependent upon the type of study that is conducted. Presently, we examine NN approaches in linkage analysis followed by a review of NN for association analysis. The studies reviewed are summarized in Table Several research groups have explored NN as an analysis tool for linkage studies ,18-25. NAlthough each study that utilized NN for linkage analysis had the same underlying goal, the primary questions and hypotheses were different for each paper. Lucek and Ott  planned For a typical linkage analysis, the raw data consist of genotypes at many genetic markers for a collection of individuals from one or more families and a measured phenotype that is either discrete or continuous. In terms of NN architecture, the genotypes are used as NN input, and the phenotype values are used as NN output. There are a number of encoding strategies that have been employed for both inputs and outputs of a NN for linkage analysis. One type of encoding for NN inputs is based on the presence or absence of a marker allele ,18,23. TThe encoding of NN outputs in linkage analysis has also been quite variable. When the target output of the NN is disease status, a common type of encoding is a simple binary output unit, using the value 1 = affected and 0 = unaffected ,23. An aFor quantitative trait output values, one encoding scheme utilizes one output unit for each quartile of the trait. Then each quartile is coded as either "on" (x = 1) if the trait falls in that quartile, or "off" (x = 0) otherwise . AnotherAnother important aspect of NN analysis is the design of NN architecture. There is no rule of thumb for how to select the best NN architecture. Several different strategies have been used in genetic epidemiology. One approach is to select a single NN architecture for the NN analysis. This architecture will consist of an input layer (with a number of input nodes based on the input encoding scheme selected), one or more hidden layers with an arbitrary number of hidden units and an output layer (with the number of nodes being determined by the strategy previously selected to represent the data). Lucek and Ott , for exaThe number of hidden layers and units in each layer is an important choice in a NN analysis, and are often determined experimentally through trial and error. One strategy to address this potential problem is to systematically try a range of architectures. Saccone et al.  evaluateWhile NN have been successful for pattern recognition in many fields, their success in linkage studies is debatable. Several linkage studies reported results demonstrating that the NN approach was able to detect at least one of the functional loci ,18-24. MEach study describing NN applications for linkage studies indicate that further research is needed in this field. First, more work is needed to determine the best approach for selecting the most important loci in the NN ,18,19,24In addition to selecting the most important loci and determining statistical significance, several other areas of uncertainty remain. For example, the interpretation of the weights needs to be investigated . FurtherIn addition to linkage studies, NN can be used for association studies. The same issues with data encoding and NN architecture exist for association analysis as well. As mentioned earlier, in association analysis, the data collected consist of genotypes for multiple markers in a sample of either case-control data or cases with family-based controls. The data can be encoded using three genotype levels   or as duIn contrast to linkage analysis, the number of publications using NN for association studies is slightly larger, and more real data applications have been performed ,29-38. SIn their conclusion, Curtis et al  suggest Their work is continued in North et al . In thisWhere Curtis et al  and NortReal data applications in association studies have been largely positive. Serretti and Smelaldi  successfThus far, we have reviewed several studies in linkage and association studies utilizing NN. While the successes of each study illustrate the potential of NN for genetic epidemiology, each study also highlights the potential caveats of the approach. Many studies detected the functional marker loci in simulated data, but also identified several false positive loci. Nearly every paper reviewed here discussed that NN appear to be a good approach for gene mapping studies especially when the goal is to identify multiple susceptibility genes simultaneously. However, more studies are needed to answer important questions about this approach. The following questions were posed by several of the papers reviewed here. First, how can we select important loci when we use a large set as input to the NN? Second, what is the best measure of loci relevance? Third, how can we put statistical significance on this measure of input relevance? Finally, what NN architecture is optimal for gene mapping studies? In the remainder of this review we discuss NN architecture as a potential area for improvement in the use of NN in genetic epidemiology.The selection of the appropriate loci from a large pool of potential predictors is a concern with any model building approach, including NN. As genotyping technology rapidly advances, and genome-wide association studies become increasingly important in the field, the importance of variable selection in model selection is highlighted. Previous NN applications in genetic epidemiology have only addressed the variable selection problem in relatively small-scale studies.Training of NNs is an artful challenge in any context. General concerns about over-parameterization are important to consider with any application of NNs. Concerns with selection of the appropriate NN architecture have been previously discussed, and choosing appropriate starting weights is an additional consideration. Typically, starting weights are randomly chosen values near zero . This inThe study by Marinov and Weeks  addresse43 possible solutions. If these networks could be trained and tested in one microsecond of CPU time, to test all these networks would take 1.41 × 1030 years [One potential explanation of the results in the Marinov and Weeks  study isH = 2(NPNS)/(NI + NS), where NH is the number of hidden units, NP is the number of observations, NS is the number of output nodes, and NI is the number of input nodes [There are a variety of strategies utilized for selection of the network architecture, in particular the number of hidden layers and nodes in the hidden layer. For example, the nodes in the hidden layer can be defined by Nut nodes . Anotherut nodes . Many ofut nodes , while out nodes . These mut nodes ,45.While these approaches seem reasonable, there are an effectively infinite number of architecture variations that can be selected. In addition, when the underlying model of the data varies from one data set to the next, an additional optimization procedure must be run on each data set to find the most appropriate architecture for each type of data. Therefore, we need to come up with new ways to select NN architecture to avoid the trial and error approach that has been previously employed.One potential solution to the architecture selection problem in NN is to evolve the NN architecture for each data set analyzed using an evolutionary computation approach. This will allow the user to avoid common pitfalls associated with having the wrong network architecture. Several evolutionary computation approaches have been proposed in the literature, including genetic algorithms , geneticWe have developed a genetic programming optimized NN for association analysis , inspireGenetic programming begins with an initial population of randomly generated computer programs, all of which are possible solutions to a given problem. This step is essentially a random search or sampling of the space of all possible solutions. Next, each of these computer programs are executed and assigned a fitness value that is proportional to its performance on the particular problem being solved. Then, the best computer programs, or solutions, are selected to undergo genetic operations based on Darwin's principle of survival of the fittest. Reproduction takes place with a subset of the best solutions, such that these solutions are directly copied into the next generation. Crossover, or recombination, takes place between another subset of solutions. This operation is used to create new computer programs by combining components of two parent programs. Thus, the new population is comprised of a portion of solutions that were copied (reproduced) from the previous generation, and a portion of solutions that are the result of recombination (crossover) between solutions of the parent population. This new population replaces the old population and the process begins again by executing each program and assigning a fitness measure to each of them. This is repeated for a set number of generations or until some termination criterion is met. The goal is to find the best solution, which is likely to be the solution with the optimal fitness measure.To use GP to evolve NN architecture, the GP is constrained in such a way that it uses standard GP operators but retains the typical structure of a feed-forward NN. A set of rules is defined prior to network evolution to ensure that each GP solution maintains a structure that represents a NN. The rules used for this GPNN implementation are consistent with those described by Koza and Rice . The fleAn overview of the GPNN method is shown in Figure GPNN is implemented using 10-fold cross validation. Here, the data are divided into 10 equal parts. The GPNN evolves NN architecture using 9/10 of the data, and then tests this NN model on the 1/10 of the data left out. This is done 10 times, each time using a different 1/10 of the data for testing. The loci that are consistently present in the GPNN models are selected as the functional loci and are used as input to a final GPNN evolutionary process to estimate the classification and prediction error of the GPNN model.While GPNN is effective in searching highly nonlinear, multidimensional search spaces, it is still susceptible to stalling on local minima . To addrIn summary, GPNN optimizes the inputs from a pool of variables, the weights, and the connectivity of the network, including the number of hidden layers and the number of nodes in the hidden layer. Thus, the algorithm attempts to evolve appropriate network architecture for a given data set. GPNN also eliminates the need for the contribution value statistic, as GPNN selects the functional variables as input for the NN.We have compared our GPNN to a traditional feed forward NN trained by back propagation using simulated data. The type of data simulations that we are most interested in consist of gene-gene interactions, where there are minimal main effects but strong interaction effects ,56. For We had two separate goals for our initial study comparing these two approaches. First, we wanted to determine if the GPNN was able to model gene-gene interactions as well as or better than a traditional NN. This was important to determine that the NN we evolved were functioning similar to a traditional NN. Since it is well known that NN can model nonlinear interactions, we wanted to validate that the GPNN performed as well at this task. For this question, the input to the NN included only the two functional loci. We used a dummy variable encoding for the genotypes where n-1 dummy variables are used for n levels . Thus, fSecond, we wanted to determine whether the GPNN was able to perform simultaneous variable selection and modeling of gene-gene interactions, as well as or better than a traditional NN . In thisUsing simulated data, we demonstrated that GPNN was able to model nonlinear interactions as well as a traditional NN. When given the functional SNPs, one would expect the NN to accurately model the data. We have shown that GPNN is also capable of accurately modeling the data. This demonstrates that GPNN is able to optimize the NN architecture such that the NN evolved is able to model data as well as a traditional NN. In addition, GPNN had improved power and predictive ability compared to a NN when applied to data containing both functional and non-functional SNPs. These results provide evidence that GPNN is able to detect the functional SNPs and model the interactions for a set of epistasis models. In addition, these are the two criteria we specified for considering GPNN an improvement over a traditional NN .Since empirical studies suggested that GPNN has excellent power for identifying gene-gene interactions, a comparison of GPNN with traditional statistical methods was our next step. The goal of the next study was to compare the power of GPNN, Classification and Regression Trees (CART) and stepwise logistic regression (SLR) for identifying gene-gene interactions using data simulated from a variety of gene-gene interaction models. Our goal was to determine if GPNN is more powerful than traditional methods in the field . Using sAdditionally, after demonstrating that GPNN out-performed both a traditional NN and more traditional statistical methods, we wanted to know if GPNN would outperform a simple GP program . Here weNext, we wanted to evaluate the power of GPNN for identifying high-order gene-gene interactions. Previous studies involved a relative small range of models, and we wanted to extend our simulation studies. We were interested in two, three, four, and five locus gene-gene interaction models with varying allele frequencies and heritability, and a constant relatively small sample size. Using simulated data, we showed that GPNN has high power to identify gene-gene interactions in the two and three locus interaction models, with small genetic effects. However, GPNN has reduced power for models with a very small genetic effect (heritability less than 1%) in addition to all four or five locus interaction models .We were also interested in applying GPNN to a real data analysis in Parkinson's disease. GPNN was able to replicate the detection of a gene-environment interaction that had previously been detected using an exhaustive method, Multifactor Dimensionality Reduction (MDR) .Based on the results of these studies, we have concluded that the GPNN is able to evolve NN architecture and perform as well as or better than a traditional NN. GPNN is able to model gene-gene interactions as well as a traditional NN when only the functional loci are used as input to the NN. More importantly, when non-functional loci are included as input to the NN, GPNN had much higher power than the traditional NN in identifying the functional loci and modeling the gene-gene interactions . We haveCurrently, we are exploring the use of another type of machine learning method-grammatical evolution (GE) – to evolve the inputs, weights, and architecture of NNs . GrammatLike GPNN, GENN improves upon the trial-and-error process of choosing an optimal architecture for a pure feed-forward back propagation neural network ,63. GENNWe anticipate these machine learning NN approaches will be important pattern recognition methods in the search for complex disease susceptibility genes. It will be important to understand the performance of these methods in the context of many of the challenges facing genetic epidemiology. Currently, the effect of several types of error common to genetic studies is being evaluated in the context of GENN . Additionally, the scalability of the method is being evaluated. As the field has approached genome-wide association scans, it has become crucial that methods detect associations in the presence of thousands of genetic variables.In this paper, we have reviewed traditional back-propagation NN and their previous applications in genetic epidemiology for linkage and association studies. We have limited our discussion to back-propagation NN because they are the type of NN most commonly used in genetic epidemiology. Thus we did not examine the strengths or weaknesses of Hopfield nets, Radial basis function nets, or Bayesian networks. Additionally, we did not examine NN applications to haplotype estimation, phenotype assessment, or genetic counseling. While NN have been useful in many other fields such as economics, computer science, and engineering, their application in genetic epidemiology is in the exploratory phase. There are many heuristics that are required to perform a NN analysis including encoding the data, selecting the number or inputs and outputs, and constructing the NN architecture. With all of these choices, the results from NN analyses in genetic epidemiology have shown that NN can be effective in identifying functional loci. However, NN also tend to identify false positives as well and the results may vary from one NN analysis to the next. In addition, there is no solid foundation for selecting the functional loci from the set of inputs used in the NN. In order to evaluate the usefulness of NN for genetic epidemiology, it will be important to develop a strategy for selecting functional loci and constructing NN architecture. The GPNN strategy of Ritchie at al. and the GThe authors declare that they have no competing interests.MDR conceived the concept for and the original draft of the manuscript. AAM compiled the up-to-date list of neural network applications, and updated the review.


Our results suggest that careful pre-filtering and partitioning of data are crucial for controlling false positives and allowing detection of genuine effects in genetic analysis of gene expression.We applied a simple and efficient two-step method to analyze a family-based association study of gene expression quantitative trait loci (eQTL) in a mixed model framework. This two-step method produces very similar results to the full mixed model method, with our method being significantly faster than the full model. Using the Genetic Analysis Workshop 15 (GAW15) Problem 1 data, we demonstrated the value of data filtering for reducing the number of tests and controlling the number of false positives. Specifically, we showed that removing non-expressed genes by filtering on expression variability effectively reduced the number of tests by nearly 50%. Furthermore, we demonstrated that filtering on genotype counts substantially reduced spurious detection. Finally, we restricted our analysis to the markers and transcripts that were closely located. We found five times more signals in close proximity ( Association mapping is commonly used in detecting quantitative trait loci (QTL). For analyzing data collected from pedigrees, transmission disequilibrium test-based methods  are ofteAnother major challenge in this type of analysis is the massive inflation in the false positive (type I error) rate due to multiple-testing. Reducing the number of tests is one obvious way to control the number of false-positive results. In addition, many researchers have opted for the use of false-discovery rates (FDR)  to monitcis-acting expression QTL (eQTL).In this article, we present our analysis of the Genetic Analysis Workshop 15 (GAW15) gene expression data set (Problem 1) originating from Morley et al. . We cond version 1.8.0. From the 2882 SNPs provided, 2695 were selected because these were polymorphic among the individuals genotyped.All microarray files were pre-processed by "GCRMA" from the Bioconductor Project Genes that are not expressed are not relevant to this study. Signal levels for non-expressed genes are typically above zero due to the background signals and other inherent systematic noises. Nonetheless, such genes can be detected on the basis that the background variation tends to be much less than real biological variation across samples. We adopted the interquartile range (IQR) as a measure of variability and used IQR of 0.1 as the threshold for this data set.The full mixed model for detecting marker association can be written as:y is the expression trait values, a, b, u, and e are vectors of marker effect, other fixed effects (sex and generation), additive polygenic effect (random), and random residuals, respectively. W, X, and Z are incidence matrices related to marker, fixed, and polygenic effects, respectively.In Eq. (1), The fast and robust method proposed by Aulchenko et al. is composed of two steps; the first step accounts for the familial dependence among family members and covariates of nuisance effects, and the second step tests the single SNP (single-nucleotide polymorphism) effect on the remaining variation by analysis of variance (ANOVA).Step 1: For the expression values of each probe set we fitted the following mixed model without the marker effect: version 1.0. Narrow-sense heritability (h2) was estimated for each expression trait using the -P option in ASReml.We fitted the models using ASReml Step 2: Using the residuals from Step 1 as the new quantitative traits, the marker genotype effect of each SNP on each trait was tested by ANOVA. We used the lm and anova functions in R  version 2.3.1. FDR was calculated using the approach proposed by Storey and Tibshirani as implemented in the R package "q-value" [q-value" .cis-acting. Besides conducting the analysis at genome-wide level, we isolated a subset of 8462 probable cis-acting candidates (expression trait-SNP pairs), which comprised 2066 SNPs and 2797 expression traits, for mapping cis-acting eQTL separately. This was a much smaller search space and FDR was applied separately to obtain a new, group-wise significance threshold.eQTLs that associate with transcripts within 1 Mb of themselves are considered as We sampled 10,000 expression trait-SNP combinations for comparing the performance of the two-step approach and the full mixed model. Tests using the full mixed model described above were conducted using ASReml.p-values of the marker effect to the full mixed model . We observed that many significant hits were associated with the same SNPs. Although this phenomenon could be interpreted as some loci being the master regulator for a large number of transcripts, there is evidence that these vertical bands are likely to be artifacts. Table Using the two-step approach described in the Methods, we detected 2282 associations at 20% FDR (p cut-off = 9.78 × 10-7). This finding suggests that the vast majority of associations previously detected were due to small sample size in SNP genotype classes, and therefore, unreliable. Note that the p-value threshold for the same FDR was much lower after having avoided the detection of many putative artifacts. FDR estimation is strongly influenced by the distribution of the p-values. If a large number of spurious effects are present due to violation of the underlying assumptions of the test statistic, excessive detection of false positives will not be prevented by the use of FDR.Subsequently, we employed a screening strategy on the SNP data by excluding any genotype classes with four or fewer individuals. We found 423 SNPs possessing at least one such genotype class. When the ANOVA tests were repeated, only 61 associations were detected at 20% FDR . The latter approach is not sensitive to detect SNPs with a small genotype class because rare homozygous genotypes can be observed with minor alleles of moderate frequency under Hardy-Weinberg equilibrium, given the sample size of the current study.p = 1.13 × 10-7. Hence, our screening method is not only effective in excluding spurious effects, but also preserves genuine effects in the presence of rare genotype classes.It is also important to note that we only masked out genotype classes with small number of individuals rather than omitting all of the data for such SNPs. This has the advantage that the information from the remaining genotype classes could still be used for the tests. For example, having masked out the rare 4/4  genotype class from SNP rs1491846, its association with probeset 204133_at was detected at cis-acting eQTL). Detecting so few cis-acting eQTLs is perhaps not a surprise because the SNP density in this data set is very low for whole-genome association mapping. Much of the genome would not be in strong linkage disequilibrium with the SNPs used in the genome scan. Effectively, only a small proportion of the genome has been screened. On the other hand, the tests for cis-acting eQTL are a tiny proportion of the total number of tests performed genome-wide. Therefore, they are heavily penalized by multiple-testing in the analysis above. Subsequently, we restricted the testing to only the SNPs and transcripts that were less than 1 Mb away from each other. This gave rise to 8462 cis-acting "candidates" . At 20% FDR (p cut-off = 3.54 × 10-4), this analysis led to detection of an additional 12 cis-acting eQTLs . Without laboratory-based validation, it is difficult to conclude whether partitioning the data in this way can increase power of detecting real cis-acting eQTL. Nonetheless, we would consider this strategy a practical way for improving the chance of detecting real cis effects. Because of the technical, statistical limitations and uncertainties in studying trans-regulation as described by Pastinen et al. [cis-acting eQTL over trans-acting eQTL. This strategy increases the detection of cis signals and provides more "prioritized" candidate loci. In the present study, the number of candidates generated is still practically feasible to be followed up in laboratories.Out of the 61 eQTLs detected, 3 eQTLs are within 1 Mb of their transcripts  declare that they have no competing interests.


H2). We evaluate two approaches to measuring H2 in natural parasite populations using relatedness inferred from genetic marker data. We collected single-clone Plasmodium falciparum infections from 185 patients from the Thailand–Burma border, monitored parasite clearance following treatment with artemisinin combination therapy (ACT), measured resistance to six antimalarial drugs and genotyped parasites using 335 microsatellites. We found strong relatedness structure. There were 27 groups of two to eight clonally identical (CI) parasites, and 74 per cent of parasites showed significant relatedness to one or more other parasites. Initially, we used matrices of allele sharing and variance components (VC) methods to estimate H2. Inhibitory concentrations (IC50) for six drugs showed significant H2 , demonstrating that this study design has adequate power. However, a phenotype of current interest—parasite clearance following ACT—showed no detectable heritability  in this population. The existence of CI parasites allows the use of a simple ANOVA approach for quantifying H2, analogous to that used in human twin studies. This gave similar results to the VC method and requires considerably less genotyping information. We conclude (i) that H2 can be effectively measured in malaria parasite populations using minimal genotype data, allowing rational design of genome-wide association studies; and (ii) while drug response (IC50) shows significant H2, parasite clearance following ACT was not heritable in the population studied.Malaria parasites vary in phenotypic traits of biomedical or biological interest such as growth rate, virulence, sex ratio and drug resistance, and there is considerable interest in identifying the genes that underlie this variation. An important first step is to determine trait heritability ( In contrast, the ANOVA method estimates the broad-sense heritability (H2), because genetic variation among CI parasites can be both additive and epistatic. We have used the notation for broad-sense heritability (H2) throughout the manuscript for both methods, both for clarity and because dominance is not relevant to haploid organisms such as blood-stage malaria.We evaluate the use of inferred relatedness for estimating l plants . The VC H2 for this trait are of particular interest as genome-wide association studies (GWASs) have been proposed to try to identify the parasite genes that underlie variation in CR. Evidence of strong heritability for this trait comes from a recent study of Cambodian parasites (We examined two different types of traits. Drug resistance is known to have a strong genetic basis  and so p2.(a)Plasmodium falciparum-infected blood samples with greater than 0.5 per cent parasitaemia from patients visiting the malaria clinic at Mawker-Thai on the Thailand–Burma border, prior to treatment with ACTs. This clinic serves people on both sides of the border; 90 per cent of patients travel from within a 10 km radius around the clinic . We excluded patients who (i) had taken malaria treatment within 60 days, (ii) were pregnant, or (iii) were co-infected with P. vivax.We collected 5 ml of (b)24 or 48 h)/(1 + parasite densityadmission). For the subset of patients monitored every 6 h, we measured the first-order CR. This was quantified by plotting the natural log of parasite density against time since treatment in hours and measuring the slope.Thin smears were collected prior to parasite treatment and at 24 and 48 h post-treatment for all patients. We measured the parasite reduction ratio (PRR), defined as (1 + parasite density(c)in vitro response to six drugs using a 48 h [3H] hypoxanthine incorporation assay (3H] hypoxanthine in parasites cultured in 96-well plates. The drugs tested were chloroquine (CQ), quinine (QN), mefloquine (MFQ), lumefantrine (LUM), artesunate (AS) and dihydro-artemisinin (DHA). Tests were performed in duplicate at each of 11 doubling drug concentrations using a starting parasitaemia of 0.5 to 1 per cent We initially genotyped seven microsatellite loci to identify and exclude infections containing multiple clones ((e)opTools v. 3.2.0. (http://www.cse.csiro.au/poptools/index.htm).Relatedness is generally estimated for diploid species . Parasit(f)H2 using two different methods.We measured (i)all pairs of parasites in the dataset to estimate H2 and is equivalent to the methods used for the analysis of multi-generational family studies of humans , I is an identity matrix, H2 is then estimated as H2 of both log-transformed measures of in vitro drug resistance, PRR24 and PRR48.The VC approach uses relatedness between f humans  as a sim(ii)50 phenotypes within and among clonal lineages of parasites, and estimated H2 from the mean-squares terms in the ANOVA as described in MSe and MSb) for each trait. The total genetic variance n is the weighted mean number of patients infected with each CI genotype and is calculated as follows: T is the total number of patients, N is the number of different clones and ni is the number of patients infected with the ith clone. The environmental variance MSe, and so For this analysis, we used only CI parasite genotypes recovered from two or more individuals. We compared the variance of CR and IC(g)−1) + artesunate (4 mg kg−1) for 3 days (MAS3) or 7 days (MAS7); (ii) group 2: dihydroartemisinin 7 mg kg−1/piperaquine 56 mg kg−1 body weight into four doses at 0, 8, 24 and 48 h (DP4) or into three daily doses (DP3); and (iii) group 3: fixed dose combination tablets  as six doses over 3 days, administered by patient weight (COA6a). We evaluated the influence of these three independent variables on PRR24, PRR48, CR and IC50. To correct for the effects of these covariates, we used residuals from the regression analysis to examine H2.Patient age, patient gender and treatment type may potentially influence phenotype and were therefore included in the analysis. Each patient was treated with one of five different ACT treatment regimens. These five ACTs were divided into three groups for analysis: (i) group 1: mefloquine hydrochloride (8 mg kg3.(a)50 for six drugs and microsatellite genotype data (335 markers) are available. The microsatellite loci were highly polymorphic with 1–23  alleles per locus and expected heterozygosity of 0–0.92 . No more than seven (3.7%) genotypes were missing at any locus. The relationships between the parasites are summarized in figure 1a).The analysis is based on 185 infections containing a single parasite clone, for which measures of clearance, ICb shows the distribution of allele sharing between all pairwise comparisons for the 185 parasites (30 340 comparisons). The main peak is situated around 0.20–0.35. There is a tail to the right of this, suggesting parasites of intermediate relatedness. Finally, the peak at 0.95–1.0 shows parasite pairs that are CI. For comparison, we plotted the simulated distributions of allele sharing for different relatedness classes (c). The main peak in the observed data corresponds precisely with allele sharing expected for unrelated genotypes. We used the upper value of the simulated distribution for unrelated parasites (0.3556) to evaluate the proportion of parasites that show significant relatedness. Seventy-four per cent of parasite isolates showed ps > 0.3556 to one or more other parasites in the dataset, suggesting strong relatedness structure. Thirty-six per cent of these parasites were CI (ps = 0.95–1.00) to one or more other parasites in the dataset. Our simulations suggest that parasites that show significant relatedness but are not CI are either derived from the same zygote (0.5317 < ps < 0.7425) or share one common parent (0.3474 < ps < 0.5616).Figure 1 classes c. The ma(b)50 data for the six drugs is summarized in H2 estimates for IC50 values are shown in H2 for five of the six drugs using VC methods. Three drugs  showed high H2 , while the three other drugs  showed more marginal H2 . Analysis of residuals to remove the effect of covariates  generated marginally lower H2 for all six drugs. Analysis of the same dataset using the ANOVA method  also gave similar results, with all drugs except CQ showing significant H2. The estimates of H2 were marginally lower for four of the six drugs using ANOVA compared with variance components, with an average difference of 0.07 (0.01–0.16).IC(c)H2 of PRRs (PRR24 and PRR48). These calculations were performed on the natural logs of the phenotype data, as well as on the residuals following removal of the effects of gender, age and treatment type. H2 estimates derived from both simple ANOVA and more complex VC methods are shown in H2 for both PRR24 and PRR48  using both estimation methods and using analysis with and without covariate effects.We calculated r2 = 0.90 ± 0.06; H2 for clearance-related parameters. Furthermore, statistical analysis using both VC- and ANOVA-based methods did not reveal significant effects of parasite genotype on CR , and remained insignificant after correction for age, sex and treatment type .There were 61 patients for whom 6-hourly measures of parasite density were made allowing estimation of first-order CR. Slopes for parasite density against time post-treatment ranged from 0.12 to 0.43 (mean (±1 s.d.) = 0.24 ± 0.07) and fitted well with a linear model  in vitro drug resistance is strongly heritable and (iv) parasite CR following ACTs is not strongly influenced by parasite genotype on the Thailand–Burma border. We divide the discussion into three sections. First, we discuss the efficacy of two methods for measuring H2. Second, we evaluate the implications of these results for genetic mapping of ART resistance. Finally, we discuss the utility of H2 estimation in malaria.These data demonstrate that (i) Thai parasite populations show strong relatedness structure, (ii) (a)H2. The genetic data reveal strong relatedness structure in the data. However, given the number and allelic diversity of the microsatellites genotyped, we were surprised that pairwise relatedness plots  did not clearly demarcate common relatedness categories. There are two likely reasons for this. First, gamete fusion between related parasites (i.e. inbreeding) may result in IBS information poorly defining relatedness categories. Second, the two parasite genomes that fuse to form a zygote may be unequally represented in the meiotic products. This has been well documented in Plasmodium genetic crosses in the laboratory, where selection results in over-representation of one of the two parental genotypes  owing to additive and/or epistatic genetics, while the VC approach explicitly models narrow-sense heritability (h2). The close correspondence between measures derived from both VC and ANOVA approaches strongly suggests that additive variation is a principal determinant of phenotypic variation at the traits studied and that epistasis makes little contribution.We were extremely successful in measuring heritability using inferred relatedness. Encouragingly, both the VC method, using matrices of inferred relatedness between all parasites, and ANOVA methods that use only CI parasites gave very similar estimates of fficient —so largevariance , this doeDi (H2 (data not shown). The lack of bias may be due in part to the size of the dataset used.We used a simple allele-sharing measure to infer relatedness between parasites. This metric has the virtue of simplicity, but does not take into account background allele sharing that occurs by chance between unrelated parasites. We also computed kinship coefficients between pairs of parasites following eDi , which a50 values for LUM, QN and MFQ, but between 17 and 39 per cent of the variance for AS, DHA and CQ. By implication, factors other than genetics explain much variation in these drugs. The low H2 estimate of CQ response seems especially surprising given that the major gene determining resistance, the chloroquine resistance transporter (pfcrt), is well characterized 24, PRR48 and CR), these data provided no evidence that these measures are influenced by parasite genetic factors on the Thailand–Burma border. There are two possible explanations for this result. First, our measures of clearance may not be sufficiently accurate to detect significant H2, because we recorded parasite density at 24 h intervals for most patients. More frequent measures may be needed to accurately document CR. We note that detailed (6-hourly) CR information was available for a subset of 61 patients. However, this subsample also failed to detect significant H2 for clearance.We examined clearance following ART as an example of a trait that cannot be measured in the laboratory, but is of considerable biomedical interest. Slow clearance of parasites following treatment with ACTs has been widely interpreted as a sign of impending resistance to artemisinin derivatives , as different life stages vary in their response to artemisinin derivatives. Similarly, heterogeneity in patient immune status as a consequence of exposure to infection could influence clearance patterns , patient gender and treatment regimen. However, of these three, only gender marginally influenced PRRpatterns . The keyH2 for CR in a population in western Cambodia, where extremely slow clearance and high failure rates have been reported (H2 in western Cambodia (0.56–0.58), clearly implicating parasite genetic factors H2 estimates provide one way to achieve this. We provide one example of a trait of enormous public health significance that does not have a genetic basis in the population studied: clearance following ART. GWASs of this trait would therefore be unlikely to succeed in this population. Virulence and sex ratio are two other traits where the role of parasite genetics is uncertain, yet both are envisaged as adaptive traits with a genetic basis (H2 would provide a test for such models and would provide preliminary data to justify GWASs on such traits. To extend this argument further, the magnitude of H2 is also useful for estimating sample sizes for GWASs, as traits with strong H2 require smaller sample sizes than traits with weak H2. Typically, sample size scales with the square of H2, so n for a trait with H2 = 1 is four times less than n for a trait with H2 = 0.5 (H2 (Our ability to rapidly genotype or sequence malaria genomes now make GWASs an attractive alternative to linkage mapping for locating genes that underlie traits of biomedical or biological importance (ic basis . StudiesH2 = 0.5 . HoweverH2 measures are also useful for assessing the robustness of phenotype measures that are known to have a strong genetic basis. In laboratory studies, precision of phenotypes can be directly assessed by repeated measurement. For many malaria traits, such repeated measurement is not feasible. However, as related parasites are sampled within populations, estimating H2 provides an alternative approach to assessing robustness of phenotype measures. The IC50 data presented here, which were measured directly using parasite-infected blood from patients, provides an example of this application. Our results indicate that IC50 data collected in this way showed poor repeatability for three or six drugs examined.H2 is strongly dependent on the existence of related or identical parasites within population samples. In P. falciparum, the proportion of CI parasites within populations is dependent on levels of transmission and inbreeding (H2 is easiest in low-transmission regions such as southeast Asia and South America. However, even in high-transmission African countries, a large proportion of meioses are expected to result from inbreeding (H2.Our ability to measure breeding , and cou


Sequencing technologies are becoming cheap enough to apply to large numbers of study participants and promise to provide new insights into human phenotypes by bringing to light rare and previously unknown genetic variants. We develop a new framework for the analysis of sequence data that incorporates all of the major features of previously proposed approaches, including those focused on allele counts and allele burden, but is both more general and more powerful. We harness population genetic theory to provide prior information on effect sizes and to create a pooling strategy for information from rare variants. Our method, EMMPAT (Evolutionary Mixed Model for Pooled Association Testing), generates a single test per gene , facilitates graphical summaries, and improves the interpretation of results by allowing calculation of attributable variance. Simulations show that, relative to previously used approaches, our method increases the power to detect genes that affect phenotype when natural selection has kept alleles with large effect sizes rare. We demonstrate our approach on a population-based re-sequencing study of association between serum triglycerides and variation in ANGPTL4. Studies correlating genetic variation to disease and other human traits have examined mostly common mutations, partly because of technological restrictions. However, recent advances have resulted in dramatically declining costs of obtaining genomic sequence data, which provides the opportunity to detect rare genetic variation. Existing methods of analysis designed for an earlier era of technology are not optimal for discovering links to rare mutations. We take advantage of 1) the advanced theoretical understanding of evolutionary mechanics and 2) genome-wide evidence about evolutionary forces on the human genome to suggest a framework for understanding observed correlations between rare genetic variation and modern traits. The model leads to a powerful test for genetic association and to an improved interpretation of results. We demonstrate the new method on previously confirmed results in a gene related to high blood cholesterol levels. Over the past 20 years, positional cloning guided by linkage analysis and genome wide association studies (GWAS) have identified many loci relevant to human disease and other quantitative phenotypes such as height, body mass index, and serum lipid composition. However, in most cases the total amount of phenotypic variance explained is small compared to the heritability observed in twin or adoption studies There are three signatures of association in a resequencing study which we want to use to assess candidate genes. Some SNPs could have effect sizes large enough that they have individually noticeable impact on phenotype; this is the information underlying regression procedures, like those put forward by Hoggart et al We present a method capable of detecting all three signatures of association. Our method generalizes allele count and rare-variant-burden methods by explicitly constructing a model relating disease impact, selective pressure, and SNP frequency in a candidate gene. By doing so, we will be able to provide intuitive interpretations to detected associations, allowing investigators to answer additional questions with their data. Our approach will yield substantially more power if the model is close to correct without introducing bias or sacrificing much efficiency when our assumptions are not met.Evolutionary Mixed Model for Pooled Assocation Testing)We propose to estimate the evolutionary fitness burden of each SNP using its observed frequency and population genetic parameters inferred by other authors. That estimate of fitness burden will act as prior information on the variant effect, acting like a burden function In what follows, we will briefly introduce the population genetics ideas which underly our approach. Next, we construct our statistical model and discuss estimation and testing within it. Finally, we illustrate the method both in simulation studies and on a real candidate gene resequencing study examining serum triglyceride levels in a multi-ethnic prospective community-based sample Several authors have reviewed the potential contribution of low frequency alleles to variation in phenotypes In Hartl and Clark distribution of fitness effects (DFE). Just as a fixed Rather than assume that all variants in the region have the same With these facts in mind, in what follows we will use fitness effects to operationalize the construct of functional status for each SNP. Whereas Johnson and Barton Assume the context of a simple random cross-sectional sample of We can write a regression model for person Using standard least-squares regression to estimate such a model will pose several problems. First, because there will be many rare variants, j's effect on phenotype from the average of SNPs with the same observed frequency. The variance of To overcome these problems, we need to make more assumptions and model the Equation (4) asserts that phenotype-effect and fitness-effect are linearly related; that seems correct for the scenario in Our model is quite general in that existing methods correspond to submodels of (4). An allele count method tests the model with only When i's phenotype and what we would expect were there no effects of this gene. As a result we can empirically estimate the overall phenotypic variability due to observed genetic variants, The specification of equations (1), (4), and (6) yields a natural interpretation to the fitted model. After estimating the population parameters of phenotype effects, we will be able to jointly estimate individual SNP effects An important consideration is how to interpret the results when multiple ethnic groups are analyzed simultaneously. Because some genetic variation is fixed between ethnic groups in the sample, the average effect of single-population variation will be absorbed into the fitted mean for that group. As a result, the interpretation for “total explained variation” is actually “total explained within-ethnic-group variation;” genetic variation may explain some of the phenotypic difference between groups, but we do not include it in our estimate because of confounding between environmental exposures and ethnic background.Another point requiring clarification is the assumption that genotype effects are independent. In the context of GWAS, nearby SNPs often are thought to have correlated effects because they mutually tag a functional variant. Additionally, estimates of SNP effects will be correlated due to LD making their true separate effects difficult or impossible to identify. However, in the underlying data generating mechanism true genotype effects are independent. Because sequencing identifies all the variation within the region and eliminates much of the correlation due to untyped alleles, we believe that the independence assumption is a useful approximation in this case. Non-independence of the true effects could be accommodated by imposing a covariance structure on SNP effects, for example using their spatial distance in the genome or folded protein. Alternatively, the phylogenetic approach of TreeLD Model (4) relies on a prediction Take as given the fitted distributional form of fitness effects and population history since out-of-Africa Use existing software SFS_CODE For each variant in the real dataset, find variants in the pseudo-data with the same sampled frequency, and calculate the mean To reduce computational requirements, steps 2 and 3 above can be replaced by simulating a smaller number of large populations and calculating the expected mean and variance of fitness using simple random sampling. An advantage of this method is that because it refers to a feature of genetic history rather than a phenotype, it need only be done once for any trait under study on the same cohort. While the fitness - phenotype relationship will be different for all traits, that is modeled by the fitted parameter Our model fitting procedure will be likelihood-based, so we will use a standard hypothesis testing method: likelihood ratio tests. To improve robustness, our examples will use permutation p-values obtained by comparing the likelihood ratio of the fitted model to that generated under the null hypothesis by randomly swapping genotype vectors between members of the same ethnicity. Permuting genotype labels simulates the null hypothesis that no relationship exists between any genotype and any aspect of the response, which in our parametric setup is equivalent to For numerical convenience and statistical robustness, we will use only the first two moments of the model in equations (1), (4), and (6), and assume We allow the procedure to exploit the possibility that individuals with a high burden of rare alleles not only have drift in their mean phenotype because of We will fit the mixed effects model (8)–(9) using modified Newton-Raphson optimization of the implied likelihood. The linear mixed effects approach is equivalent to assuming normality for the error terms mixed procedure As discussed above, we will be interested in fitting distinct http://home.uchicago.edu/~crk8e/papersup.htmlAlternatively, if we use a single Our model is easily recast in a purely Bayesian framework. One would need to write priors for The Bayesian analyst could continue to use our normal approximation of the distribution of the latent About 3500 prospectively sampled individuals from the population in Dallas, Texas, were sequenced at a candidate gene for dyslipidemia: ANGPTL4 (Ensembl Acc:16039). These individuals come primarily from three ethnic backgrounds: non-Hispanic white (N = 1043), non-Hispanic black (N = 1832), and Hispanic (N = 601). We will exclude from our analysis the 75 individuals listed as “Other” ethnicity. Our outcome phenotype is log-transformed serum triglyceride levels. Details of the cohort For ANGPTL4, we observe a p-value of .006 on 10,000 permutations versus the strong null hypothesis that no SNPs have any effect. Previous authors An interesting data point in We can understand this model fit by looking at the green OLS estimates in An interesting potential story about natural selection on ANGPTL4 activity emerges from In order to determine the power and robustness of our procedure, we simulated variation in a gene with the exon structure of the gene ANGPTL4 in a study population using SFS_CODE We chose several levels of the phenotype parameters to correspond to potential cases of interest while keeping the total fraction of variation explained by the gene about the same: a weak mean variant effect, a strong fitness-related component of the phenotype, and a strong fitness independent component of the phenotype. We chose the baseline values such that Two additional batches of simulation examine the robustness of our procedure to incorrect assumptions. First we created violations of the assumed population model. We mis-specified the assumed DFE in our analysis, making the scale parameter a factor of 5 too large or too small and keeping the truth the same. We also simulated violation of our demographic assumptions using a population which experienced an additional 100 fold exponential growth over the last 11% of generations since out-of-Africa. Second we created violations of the assumed statistical model. We simulated three scenarios violating the linearity assumption. First, with To compare power with existing methods, we included several proposed methods of analysis. First, we test the method of Bonferroni corrected minimum p-value of SNPs with minor allele frequency >1% or >5%. Other proposed methods using allele counts like CAST To demonstrate the gain (or loss) in information by considering the marginal variance, we apply a similar regression with an optimal mean model, that is (8) either for all SNPs or treating common SNPs as free. We tested our model both with a single We propose a novel method, EMMPAT, for association between sequenced genes and phenotype which utilizes population genetic theory to pool information among rare variants. Our method generalizes allele-count and allele-burden techniques, and presents several advantages. Of greatest importance to the practicing scientist will be increased power and interpretability. As shown above, our method allows us to leverage allele frequency as auxiliary data related to SNP effects and to substantially increase power to detect association in many scenarios. The availability of a well motivated pooling strategy allows an omnibus test which incorporates common and rare variation simultaneously. Our approach provides clear interpretations for the fitted model, such as the attributable variance in phenotype due to all polymorphisms observed in a gene, particular types of SNPs, or only the rare variation. Furthermore it facilitates tests of meaningful parameters  and group differences (such as non-synonymous versus non-coding). The regression toolbox allows model checking and exploration, such as in A relevant question is how important our method will be for diseases which have not been strongly selected against. There are three answers to consider. First, when selection and disease effect are completely independent, common SNPs will tend to have just as large effect sizes as rare SNPs and explain much of the heritable variation in phenotype We have planned several extensions to this method. In addition to improved techniques of estimating fitness effects, we need to incorporate evidence for adaptive selection. Signatures of positive selection Text S1Supplementary methods and discussion.(0.05 MB PDF)Click here for additional data file.