Bayesian nonparametric clustering and association studies for candidate SNP observations

Clustering is often considered as the first step in the analysis when dealing with an enormous amount of Single Nucleotide Polymorphism (SNP) genotype data. The lack of biological information could affect the outcome of such procedure. Even if a clustering procedure has been selected and performed, the impact of its uncertainty on the subsequent association analysis is rarely assessed. In this research we propose first a model to cluster SNPs data, then we assess the association between the cluster and a disease. In particular, we adopt a Dirichlet process mixture model with the advantages, with respect to the usual clustering methods, that the number of clusters needs not to be known and fixed in advance and the variation in the assignment of SNPs to clusters can be accounted. In addition, once a clustering of SNPs is obtained, we design an individualized genetic score quantifying the SNP composition in each cluster for every subject, so that we can set up a generalized linear model for association analysis able to incorporate the information from a large-scale SNP dataset, and yet with a much smaller number of explanatory variables. The inference on cluster allocation, the strength of association of each cluster (the collective effect on SNPs in the same cluster), and the susceptibility of each SNP are based on posterior samples from Markov chain Monte Carlo methods and the Binder loss information. We exemplify this Bayesian nonparametric strategy in a genome-wide association study of Crohn's disease in a case-control setting.