Now the question of prior is always difficult. Here is a quick computation which may be used as a guide: taking the minimac reference files as a guide, and scaling down to a 400 kb around a gene (in cis, 200 kb on each side), I find an average of 2,000 variants (SNPs/indels). So 10^-4 means that one out of 5 genes has a cis-eQTL, give or take. That seems about right to me.

The important thing to mention is that we applied the method to metaboChip data so known regions involved in metabolic type disorders. Hence, 10^-4 is also perhaps OK given the design. But if one were working with a true GWAS discovery type design, I would probably make the prior for the biomarker/disease stricter. But keep the eQTL prior as it is.

Prior really matters here. If a region is already known to be disease/biomarker associated, a single SNP with 10^-4 for both eQTL and lipid trait, say, is quite convincing evidence for a shared causal variant. If you have not seen that region before, you probably should remain unconvinced. Our settings are probably OK for a metaboChip/immunoChip type setup, but the best we can do is let the users play a bit with these values if the experimental design is not the same.

Hopefully what I wrote makes sense!

Vincent and Claudia may wish to comment in more detail on the priors, which are the prior probabilities of a causal association. Myself, I don’t think a causal eQTL for a specific gene is necessarily more common than a GWAS association, perhaps even less common if you are looking genomewide as many diseases are now known to have 50+ GWAS hits whilst most genes have only a limited number of eQTLs. Looking cis to a gene, perhaps the prior should be larger. Varying the priors would be interesting to explore, and Claudia did some work on varying p12 in the paper. Of course, priors can be individually specified in the software, so you are not restricted by our defaults.

I was also slightly confused about the priors. “We assigned a prior of 10e-4 for p1 and p2, the probability that a SNP is associated with either of the two traits.” In modern eQTL analyses, a few percent of all variants are significant eQTLs, although the number of causal variants is on the order of the authors’ prior. eQTLs are much much more common than GWAS associations – shouldn’t the priors be different?