Bayesian epistasis association mapping via SNP imputation

Genetic mutations may interact to increase the risk of human complex diseases. Mapping of multiple interacting disease loci in the human genome has recently shown promise in detecting genes with little main effects. The power of interaction association mapping, however, can be greatly influenced by the set of single nucleotide polymorphism (SNP) genotyped in a case-control study. Previous imputation methods only focus on imputation of individual SNPs without considering their joint distribution of possible interactions. We present a new method that simultaneously detects multilocus interaction associations and imputes missing SNPs from a full Bayesian model. Our method treats both the case-control sample and the reference data as random observations. The output of our method is the posterior probabilities of SNPs for their marginal and interacting associations with the disease. Using simulations, we show that the method produces accurate and robust imputation with little overfitting problems. We further show that, with the type I error rate maintained at a common level, SNP imputation can consistently and sometimes substantially improve the power of detecting disease interaction associations. We use a data set of inflammatory bowel disease to demonstrate the application of our method.     

Large-scale genetic epistasis networks using RNAi

Pairwise quantitative genetic interactions are mapped by combinatorial RNA interference in metazoan cells.     

Bayesian neural networks

A neural network that uses the basic Hebbian learning rule and the Bayesian combination function is defined. Analogously to Hopfield's neural network, the convergence for the Bayesian neural network that asynchronously updates its neurons' states is proved. The performance of the Bayesian neural network in four medical domains is compared with various classification methods. The Bayesian neural network uses more sophisticated combination function than Hopfield's neural network and uses more economically the available information. The naive Bayesian classifier typically outperforms the basic Bayesian neural network since iterations in network make too many mistakes. By restricting the number of iterations and increasing the number of fixed points the network performs better than the naive Bayesian classifier. The Bayesian neural network is designed to learn very quickly and incrementally.     

Learning genetic epistasis using Bayesian network scoring criteria

Background  

Gene-gene epistatic interactions likely play an important role in the genetic basis of many common diseases. Recently, machine-learning and data mining methods have been developed for learning epistatic relationships from data. A well-known combinatorial method that has been successfully applied for detecting epistasis is Multifactor Dimensionality Reduction (MDR). Jiang et al. created a combinatorial epistasis learning method called BNMBL to learn Bayesian network (BN) epistatic models. They compared BNMBL to MDR using simulated data sets. Each of these data sets was generated from a model that associates two SNPs with a disease and includes 18 unrelated SNPs. For each data set, BNMBL and MDR were used to score all 2-SNP models, and BNMBL learned significantly more correct models. In real data sets, we ordinarily do not know the number of SNPs that influence phenotype. BNMBL may not perform as well if we also scored models containing more than two SNPs. Furthermore, a number of other BN scoring criteria have been developed. They may detect epistatic interactions even better than BNMBL.     

Recognizing recurrent neural networks (rRNN): Bayesian inference for recurrent neural networks

Recurrent neural networks (RNNs) are widely used in computational neuroscience and machine learning applications. In an RNN, each neuron computes its output as a nonlinear function of its integrated input. While the importance of RNNs, especially as models of brain processing, is undisputed, it is also widely acknowledged that the computations in standard RNN models may be an over-simplification of what real neuronal networks compute. Here, we suggest that the RNN approach may be made computationally more powerful by its fusion with Bayesian inference techniques for nonlinear dynamical systems. In this scheme, we use an RNN as a generative model of dynamic input caused by the environment, e.g. of speech or kinematics. Given this generative RNN model, we derive Bayesian update equations that can decode its output. Critically, these updates define a 'recognizing RNN' (rRNN), in which neurons compute and exchange prediction and prediction error messages. The rRNN has several desirable features that a conventional RNN does not have, e.g. fast decoding of dynamic stimuli and robustness to initial conditions and noise. Furthermore, it implements a predictive coding scheme for dynamic inputs. We suggest that the Bayesian inversion of RNNs may be useful both as a model of brain function and as a machine learning tool. We illustrate the use of the rRNN by an application to the online decoding (i.e. recognition) of human kinematics.     

Bayesian meta-analysis of genetic association studies with different sets of markers

Robust assessment of genetic effects on quantitative traits or complex-disease risk requires synthesis of evidence from multiple studies. Frequently, studies have genotyped partially overlapping sets of SNPs within a gene or region of interest, hampering attempts to combine all the available data. By using the example of C-reactive protein (CRP) as a quantitative trait, we show how linkage disequilibrium in and around its gene facilitates use of Bayesian hierarchical models to integrate informative data from all available genetic association studies of this trait, irrespective of the SNP typed. A variable selection scheme, followed by contextualization of SNPs exhibiting independent associations within the haplotype structure of the gene, enhanced our ability to infer likely causal variants in this region with population-scale data. This strategy, based on data from a literature based systematic review and substantial new genotyping, facilitated the most comprehensive evaluation to date of the role of variants governing CRP levels, providing important information on the minimal subset of SNPs necessary for comprehensive evaluation of the likely causal relevance of elevated CRP levels for coronary-heart-disease risk by Mendelian randomization. The same method could be applied to evidence synthesis of other quantitative traits, whenever the typed SNPs vary among studies, and to assist fine mapping of causal variants.     

Integration of biological networks and pathways with genetic association studies

Millions of genetic variants have been assessed for their effects on the trait of interest in genome-wide association studies (GWAS). The complex traits are affected by a set of inter-related genes. However, the typical GWAS only examine the association of a single genetic variant at a time. The individual effects of a complex trait are usually small, and the simple sum of these individual effects may not reflect the holistic effect of the genetic system. High-throughput methods enable genomic studies to produce a large amount of data to expand the knowledge base of the biological systems. Biological networks and pathways are built to represent the functional or physical connectivity among genes. Integrated with GWAS data, the network- and pathway-based methods complement the approach of single genetic variant analysis, and may improve the power to identify trait-associated genes. Taking advantage of the biological knowledge, these approaches are valuable to interpret the functional role of the genetic variants, and to further understand the molecular mechanism influencing the traits. The network- and pathway-based methods have demonstrated their utilities, and will be increasingly important to address a number of challenges facing the mainstream GWAS.     

Bayesian graphical models for genomewide association studies

As the extent of human genetic variation becomes more fully characterized, the research community is faced with the challenging task of using this information to dissect the heritable components of complex traits. Genomewide association studies offer great promise in this respect, but their analysis poses formidable difficulties. In this article, we describe a computationally efficient approach to mining genotype-phenotype associations that scales to the size of the data sets currently being collected in such studies. We use discrete graphical models as a data-mining tool, searching for single- or multilocus patterns of association around a causative site. The approach is fully Bayesian, allowing us to incorporate prior knowledge on the spatial dependencies around each marker due to linkage disequilibrium, which reduces considerably the number of possible graphical structures. A Markov chain-Monte Carlo scheme is developed that yields samples from the posterior distribution of graphs conditional on the data from which probabilistic statements about the strength of any genotype-phenotype association can be made. Using data simulated under scenarios that vary in marker density, genotype relative risk of a causative allele, and mode of inheritance, we show that the proposed approach has better localization properties and leads to lower false-positive rates than do single-locus analyses. Finally, we present an application of our method to a quasi-synthetic data set in which data from the CYP2D6 region are embedded within simulated data on 100K single-nucleotide polymorphisms. Analysis is quick (<5 min), and we are able to localize the causative site to a very short interval.     

A flexible computational framework for detecting, characterizing, and interpreting statistical patterns of epistasis in genetic studies of human disease susceptibility

Detecting, characterizing, and interpreting gene-gene interactions or epistasis in studies of human disease susceptibility is both a mathematical and a computational challenge. To address this problem, we have previously developed a multifactor dimensionality reduction (MDR) method for collapsing high-dimensional genetic data into a single dimension (i.e. constructive induction) thus permitting interactions to be detected in relatively small sample sizes. In this paper, we describe a comprehensive and flexible framework for detecting and interpreting gene-gene interactions that utilizes advances in information theory for selecting interesting single-nucleotide polymorphisms (SNPs), MDR for constructive induction, machine learning methods for classification, and finally graphical models for interpretation. We illustrate the usefulness of this strategy using artificial datasets simulated from several different two-locus and three-locus epistasis models. We show that the accuracy, sensitivity, specificity, and precision of a na?ve Bayes classifier are significantly improved when SNPs are selected based on their information gain (i.e. class entropy removed) and reduced to a single attribute using MDR. We then apply this strategy to detecting, characterizing, and interpreting epistatic models in a genetic study (n = 500) of atrial fibrillation and show that both classification and model interpretation are significantly improved.     

Validation in genetic association studies

Validation of genetic associations is understood to be a cornerstone for the scientific credibility of the results. To approach this topic, the general concept of genetic association studies is introduced briefly, followed by how the term 'validation' is used in the context of genetic association studies. As a central issue, reasons for the importance of validation and for failure of validation will be described.     

U-statistics in genetic association studies

Many common human diseases are complex and are expected to be highly heterogeneous, with multiple causative loci and multiple rare and common variants at some of the causative loci contributing to the risk of these diseases. Data from the genome-wide association studies (GWAS) and metadata such as known gene functions and pathways provide the possibility of identifying genetic variants, genes and pathways that are associated with complex phenotypes. Single-marker-based tests have been very successful in identifying thousands of genetic variants for hundreds of complex phenotypes. However, these variants only explain very small percentages of the heritabilities. To account for the locus- and allelic-heterogeneity, gene-based and pathway-based tests can be very useful in the next stage of the analysis of GWAS data. U-statistics, which summarize the genomic similarity between pair of individuals and link the genomic similarity to phenotype similarity, have proved to be very useful for testing the associations between a set of single nucleotide polymorphisms and the phenotypes. Compared to single marker analysis, the advantages afforded by the U-statistics-based methods is large when the number of markers involved is large. We review several formulations of U-statistics in genetic association studies and point out the links of these statistics with other similarity-based tests of genetic association. Finally, potential application of U-statistics in analysis of the next-generation sequencing data and rare variants association studies are discussed.     

A Bayesian multilocus association method: allowing for higher-order interaction in association studies

For most common diseases with heritable components, not a single or a few single-nucleotide polymorphisms (SNPs) explain most of the variance for these disorders. Instead, much of the variance may be caused by interactions (epistasis) among multiple SNPs or interactions with environmental conditions. We present a new powerful statistical model for analyzing and interpreting genomic data that influence multifactorial phenotypic traits with a complex and likely polygenic inheritance. The new method is based on Markov chain Monte Carlo (MCMC) and allows for identification of sets of SNPs and environmental factors that when combined increase disease risk or change the distribution of a quantitative trait. Using simulations, we show that the MCMC method can detect disease association when multiple, interacting SNPs are present in the data. When applying the method on real large-scale data from a Danish population-based cohort, multiple interactions are identified that severely affect serum triglyceride levels in the study individuals. The method is designed for quantitative traits but can also be applied on qualitative traits. It is computationally feasible even for a large number of possible interactions and differs fundamentally from most previous approaches by entertaining nonlinear interactions and by directly addressing the multiple-testing problem.     

Probabilistic graphical models for genetic association studies

Probabilistic graphical models have been widely recognized as a powerful formalism in the bioinformatics field, especially in gene expression studies and linkage analysis. Although less well known in association genetics, many successful methods have recently emerged to dissect the genetic architecture of complex diseases. In this review article, we cover the applications of these models to the population association studies' context, such as linkage disequilibrium modeling, fine mapping and candidate gene studies, and genome-scale association studies. Significant breakthroughs of the corresponding methods are highlighted, but emphasis is also given to their current limitations, in particular, to the issue of scalability. Finally, we give promising directions for future research in this field.     

Statistical genetic issues for genome-wide association studies

Genotyping technology now allows the rapid and affordable generation of million-SNP profiles for humans, leading to considerable activity in association mapping. Similar activity is anticipated for many plant species, including Brassica. These plant association mapping activities will require the same care in quality control and quality assurance as for humans. The subsequent analyses may draw upon the same body of theory that is described here in the language of quantitative genetics.