Setting per-SNP priors to maintain per-hypothesis priors when number of SNPs is large?

[porchard]

Hi Chris,

I have SuSiE results for a large number of GWAS traits and a larger number of e/sQTL signals from a range of tissues, and am using these for a big colocalization analysis.

The range of GWAS traits and tissues makes it a difficult to select ideal priors for each trait - tissue combo (barring perhaps some kind of empirical Bayes approach), so let's say I wish to stick to something like the default coloc priors for p1/p2/p12. But even then, one needs to handle the case that the default coloc priors become invalid once the number of SNPs grows too large (e.g. for 8k SNPs H1+H2+H3+H4 > 1 when p1/p2/p12 are kept at their default values)

I think one solution to this would be to set per-SNP priors in order to maintain constant per-hypothesis priors. So for example, if I wanted to use the default coloc per-SNP priors of p1=p2=1e-4, p12=5e-6 in a region with 1k SNPs, then in a second region with 8k SNPs I could set p1 = p2 = 1.25e-05 and p12 = 6.25e-07. Then, in each case H0 = 0.785, H1=0.1, H2=0.1, H3=0.01, H4=0.005

Is this a reasonable solution? Do you have any other suggestions?

Thanks!