Hierarchical Naive Bayes for genetic association studies.

Genome Wide Association Studies represent powerful approaches that aim at disentangling the genetic and molecular mechanisms underlying complex traits. The usual "one-SNP-at-the-time" testing strategy cannot capture the multi-factorial nature of this kind of disorders. We propose a Hierarchical Naïve Bayes classification model for taking into account associations in SNPs data characterized by Linkage Disequilibrium. Validation shows that our model reaches classification performances superior to those obtained by the standard Naïve Bayes classifier for simulated and real datasets. In the Hierarchical Naïve Bayes implemented, the SNPs mapping to the same region of Linkage Disequilibrium are considered as "details" or "replicates" of the locus, each contributing to the overall effect of the region on the phenotype. A latent variable for each block, which models the "population" of correlated SNPs, can be then used to summarize the available information. The classification is thus performed relying on the latent variables conditional probability distributions and on the SNPs data available. The developed methodology has been tested on simulated datasets, each composed by 300 cases, 300 controls and a variable number of SNPs. Our approach has been also applied to two real datasets on the genetic bases of Type 1 Diabetes and Type 2 Diabetes generated by the Wellcome Trust Case Control Consortium. The approach proposed in this paper, called Hierarchical Naïve Bayes, allows dealing with classification of examples for which genetic information of structurally correlated SNPs are available. It improves the Naïve Bayes performances by properly handling the within-loci variability.