posterior predictive p values are therefore defined by where M is the set of models under consideration, p $^{∗}$( m ) is the colocalisation testing p or ppp value under the SNP model m , P ( m ) is the posterior probability of model m given the data and under the assumption that one of M is the true model. To minimize the degrees of freedom of the test, we explore all two SNP models and, in the absence of any independent evidence to favour one SNP over another, we assume the prior is evenly spread over the set of models. Approximating the posterior probabilities by means of the Bayesian Information Criterion approximation [Schwarz, 1978; Hoeting et al., 1999] and discarding highly improbable models at the outset, this could be done without excessive computational burden (see Supplementary Material for full details). Both the PC and BMA approaches are available in our R [R Development Core Team, 2010] package, coloc, available from the Comprehensive R Archive Network ( http://cran.r-project. org/web/packages/coloc ). We used simulation to demonstrate the effects of variable selection on the power and type 1 error rate for colocalisation testing. Full details are given in supplementary material. Briefly, we sampled, with replacement, haplotypes of SNPs with a minor allele frequency of at least 5% found in phased 1000 Genomes Project data [Consortium et al., 2012] across all 49 genomic regions outside the major histocompatibility complex (MHC) which have been identified as type 1 diabetes (T1D) susceptibility loci to date, as summarized in T1DBase [Burren et al., 2011]. These represent a range of region sizes and genomic topography typical of GWAS hits. We excluded the MHC region which is known to have high variation, strong LD and exhibits huge genetic influence on autoimmune disease risk involving multiple loci and hence requires individual treatment in any GWAS [Nejentsev et al., 2007]. Using a single “causal variant” SNP chosen at random, we sampled case and control haplotypes according a multiplicative disease susceptibility model with relative risks of ranging from 1.1 to 1.3 to represent GWAS data. To simulate a quantitative trait, and to extend our exploration to two 8 Simulation ppp = ∑ m ∈M p $^{∗}$( m ) P ( m ) (4)