A hierarchical Bayesian network approach for linkage disequilibrium modeling and data-dimensionality reduction prior to genome-wide association studies

Mourad et al. BMC Bioinformatics 2011, 12:16 http://www.biomedcentral.com/1471-2105/12/16 RESEARCH ARTICLE Open Access A hierarchical Bayesian network approach for linkage disequilibrium modeling and data-dimensionality reduction prior to genome-wide association studies Raphaël Mourad1*, Christine Sinoquet2*, Philippe Leray1 Abstract Background: Discovering the genetic basis of common genetic diseases in the human genome represents a public health issue. However, the dimensionality of the genetic data (up to 1 million genetic markers) and its complexity make the statistical analysis a challenging task. Results: We present an accurate modeling of dependences between genetic markers, based on a forest of hierarchical latent class models which is a particular class of probabilistic graphical models. This model offers an adapted framework to deal with the fuzzy nature of linkage disequilibrium blocks. In addition, the data dimensionality can be reduced through the latent variables of the model which synthesize the information borne by genetic markers. In order to tackle the learning of both forest structure and probability distributions, a generic algorithm has been proposed. A first implementation of our algorithm has been shown to be tractable on benchmarks describing 105 variables for 2000 individuals. Conclusions: The forest of hierarchical latent class models offers several advantages for genome-wide association studies: accurate modeling of linkage disequilibrium, flexible data dimensionality reduction and biological meaning borne by latent variables. Background Genetic markers such as SNPs are the key to dissecting the genetic susceptibility of common complex diseases, such as asthma, diabetes, atherosclerosis and some cancers [1]. The purpose is identifying combinations of genetic determinants which should accumulate among affected subjects. Generally, in such combinations, each genetic variant only exerts a modest impact on the observed phenotype, whereas, in contrast, the interaction between genetic variants and, possibly, environmental factors is determinant. Decreasing genotyping costs now enable the generation of hundreds of thousands of * Correspondence: ; 1 LINA, UMR CNRS 6241, Ecole Polytechnique de l’Université de Nantes, rue Christian Pauc, BP 50609, 44306 Nantes Cedex 3, France 2 LINA, UMR CNRS 6241, Université de Nantes, 2 rue de la Houssinie’re, BP 92208, 44322 Nantes Cedex, France Full list of author information is available at the end of the article SNPs, spanning the whole human genome, across cohorts of cases and controls. This scaling up to genome-wide association studies (GWASs) makes the analysis of high-dimensional data a hot topic [2]. Despite recent technological advances and extensive research effort, the genetic basis of the aforementioned diseases remains to a large extent unknown. Yet, the search for associations between single SNPs and the variable describing case/control status requires carrying out a large number of statistical tests. Since SNP patterns, rather than single SNPs, are likely to be determinant for complex diseases, a high rate of false positives as well as a perceptible statistical power decrease, not to mention intractability, are severe issues to be overcome. The simplest type of genetic polymorphism, single nucleotide polymorphism (SNP), involves only one nucleotide change, which occurred generations ago within the DNA sequence. To fix ideas, we emphasize that one single individual can be uniquely defined by © 2011 Mourad et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Mourad et al. BMC Bioinformatics 2011, 12:16 http://www.biomedcentral.com/1471-2105/12/16 Page 2 of 20 Table 1 Comparison of running times, dimension reduction rates and entropy compression rates between CFHLC and other algorithms, for Daly et al.’s dataset: Daly et al.’s method [29], Gerbil [25], HaploBlock [13] and Zhang et al.’s algorithm [16] Algorithm Running time Dimension reduction rates Entropy compression rates Daly et al.’s method - 0.107 0.313 Gerbil 40 s 0.107 0.300 HaploBlock 158 mn 0.066 0.241 Zhang et al.’s algorithm 168 s 0.078 0.229 CFHLC 84 s 0.146 0.231 We ran the last three programs on a standard computer. As we had no access to Daly et al.’s software, we could only compare the dimension reduction rates and entropy compression rates calculated from their results with the dimension reduction rates and entropy compression rates obtained with the other methods. only 30 to 80 independent SNPs and unrelated individuals differ in about 0.1% of their 3.1 billion nucleotides [3]. Compared with other kinds of DNA markers, SNPs are appealing because they are abundant, genetically stable and amenable to high-throughput automated analysis. Consistently, advances in high-throughput SNP genotyping technologies lead the way to various downstream analyses, including GWASs. Exploiting the existence of statistical dependences between neighboring SNPs, also called linkage disequilibrium (LD), is the key to association study achievement [4]. Indeed, a causal variant (i.e. a genetic factor) may not be a SNP. For instance, insertions, deletions, inversions and copy-number polymorphisms may be causative of disease susceptibility. Nevertheless, a welldesigned study will have a good chance of including one or more SNPs that are in strong LD with a common causal variant. In the latter case, indirect association with the phenotype, say affected/unaffected status, will be revealed (see Additional file 1). Interestingly, LD also offers solutions to reduce data dimensionality in GWASs. In the human genome, LD is highly structured into the so-called “haplotype block structure” [5]: regions where statistical dependences between contiguous markers (called blocks) are high alternate with shorter regions characterized by low statistical dependences (see Additional file 2). The most likely explanation of this phenomenon is related to the presence of large regions with low recombination rates separated by recombination hotspots (i.e. small specific regions with high recombination rates) [6]. Relying on this feature, various approaches were proposed to achieve data dimensionality reduction: testing association with haplotypes (i.e. inferred data underlying genotypic data) [7], partitioning the genome according to spatial correlation [8], selecting SNPs informative about their context, or SNP tags [9] (for more references, see [10] for example). Recent methods, such as HaploBuild [11], have permitted to construct more biologically relevant haplotypes where the “haplotype cluster structure”, instead of the “haplotype block structure”, is assumed: haplotypes are not constrained by (...truncated)