A BAYESIAN APPROACH TO QUANTIFY ENRICHMENT IN GWAS TEST STATISTICS

Background In Genome-wide association studies (GWASs), biologically determined subsets of the single nucleotide polymorphisms (SNPs) can exhibit an increased proportion of extreme statistics compared to the whole set of SNPs. The excess of extreme statistics—which we refer to as "enrichment"—provides a means to improve gene discovery. This approach has proven valuable for polygenic traits like schizophrenia, for which pleiotropy [O. Andreassen et al. PLoS Genet. 9.4, e1003455 (2013)] and annotation categories in the genome [A. Schork et al. PLoS Genet. 9.4, e1003449 (2013)], successfully have been used as selection criteria. The degree of enrichment is, however, challenging to quantify; current enrichment claims are mainly based on visual inspection of QQ plots or fold enrichment plots. Methods We outline here a Bayesian method to quantify the degree of enrichment, based on a mixture model where each SNP is either null or non-null. What sets this apart from previous work, is that we incorporate the z-score covariance matrix for the multivariate (global) null distribution into the model, thereby accounting for the linkage disequilibrium dependence. By assuming that the z-scores with low absolute value are dominated by the null distribution, we can express the posterior distribution for the proportion of non-null SNPs in terms of the multivariate null distribution only, avoiding more specific assumptions about the unknown non-null distribution. We calculate this posterior distribution for the selected subsets of SNPs and its compliment, and quantify the level of enrichment by comparing the two. Results The method is tested on synthetic data, and shows promising results. We further compare the method to other approaches, like permutation tests. Finally, we show how this method can be applied to map out enrichment of SNP subsets for different psychiatric phenotypes. Discussion The proposed method seems to be a promising tool for quantifying enrichment in the context of GWAS summary statistics.