Unusual hypothesis priors when using coloc.abf() ?

[HarrietRB]

Hello!

I hope you're well! I was wondering whether you can help. I have been performing coloc analysis using the coloc.abf() function. Here is an example code for one I have been running:

my.res <- coloc.abf(
  dataset1 = list(snp = eqtl$snp, beta = eqtl$beta, pvalues = eqtl$pvalues, N = eqtl$N, MAF = eqtl$MAF, s = 0.5, type = "quant"),
  dataset2 = list(snp = risk$snp, beta = risk$beta, pval = risk$pval, varbeta = risk$varbeta, MAF = risk$MAF, s = 0.5, type = "cc"),
  p1 = 1e-04, p2 = 1e-04, p12 = 1e-05
)

my.res 

Coloc analysis of trait 1, trait 2

SNP Priors
   p1    p2   p12 
1e-04 1e-04 1e-05 

Hypothesis Priors
         H0     H1     H2        H3      H4
 -0.2832397 0.4946 0.4946 0.2445797 0.04946

Posterior
       nsnps           H0           H1           H2           H3           H4 
4.946000e+03 5.868596e-33 3.848770e-22 1.199395e-12 7.773699e-02 9.222630e-01 

I noticed that for many of my results, the hypothesis priors for H1 and H2 are rather high (0.4946), and actually H0 in some cases has a negative value (-0.283). I had a play with randomly sampling a given number of SNPs for the coloc analysis above (randomly sampling either 50, 100, 250, 500, 1000, 2000 and 4000), which had an impact on the hypothesis priors. Overall, it seems with less SNPs, there are more sensible H0, H1 and H2 values in comparison to the actual number of SNPs.

Results for SNPs_50 :
Coloc analysis of trait 1, trait 2
SNP Priors
   p1    p2   p12 
1e-04 1e-04 1e-05 
Hypothesis Priors
        H0     H1     H2        H3      H4
 0.9930594 0.0033 0.0033 1.056e-05 0.00033
Posterior
       nsnps           H0           H1           H2           H3           H4 
3.300000e+01 5.323039e-05 8.503882e-07 7.462310e-01 1.167946e-02 2.420355e-01 
Results for SNPs_100 :
Coloc analysis of trait 1, trait 2
SNP Priors
   p1    p2   p12 
1e-04 1e-04 1e-05 
Hypothesis Priors
       H0     H1     H2        H3      H4
 0.984406 0.0074 0.0074 5.402e-05 0.00074
Posterior
       nsnps           H0           H1           H2           H3           H4 
7.400000e+01 1.178955e-26 2.191645e-21 5.380269e-09 1.773215e-07 9.999998e-01 
Results for SNPs_250 :
Coloc analysis of trait 1, trait 2
SNP Priors
   p1    p2   p12 
1e-04 1e-04 1e-05 
Hypothesis Priors
        H0     H1     H2         H3      H4
 0.9612369 0.0183 0.0183 0.00033306 0.00183
Posterior
       nsnps           H0           H1           H2           H3           H4 
1.830000e+02 3.322876e-28 1.146457e-21 1.704888e-09 4.887084e-03 9.951129e-01 
Results for SNPs_500 :
Coloc analysis of trait 1, trait 2
SNP Priors
   p1    p2   p12 
1e-04 1e-04 1e-05 
Hypothesis Priors
        H0     H1     H2         H3      H4
 0.9213694 0.0368 0.0368 0.00135056 0.00368
Posterior
       nsnps           H0           H1           H2           H3           H4 
3.680000e+02 1.662104e-31 2.100897e-22 2.822728e-12 2.570495e-03 9.974295e-01 
Results for SNPs_1000 :
Coloc analysis of trait 1, trait 2
SNP Priors
   p1    p2   p12 
1e-04 1e-04 1e-05 
Hypothesis Priors
        H0     H1     H2        H3      H4
 0.8355322 0.0756 0.0756 0.0057078 0.00756
Posterior
       nsnps           H0           H1           H2           H3           H4 
7.560000e+02 5.649781e-32 5.230989e-22 1.288070e-12 1.093685e-02 9.890632e-01 
Results for SNPs_2000 :
Coloc analysis of trait 1, trait 2
SNP Priors
   p1    p2   p12 
1e-04 1e-04 1e-05 
Hypothesis Priors
        H0     H1     H2         H3      H4
 0.6536217 0.1537 0.1537 0.02360832 0.01537
Posterior
       nsnps           H0           H1           H2           H3           H4 
1.537000e+03 3.524917e-32 6.044386e-22 1.200514e-12 1.960554e-02 9.803945e-01 
Results for SNPs_4000 :
Coloc analysis of trait 1, trait 2
SNP Priors
   p1    p2   p12 
1e-04 1e-04 1e-05 
Hypothesis Priors
        H0     H1     H2         H3      H4
 0.2616244 0.3068 0.3068 0.09409556 0.03068
Posterior
       nsnps           H0           H1           H2           H3           H4 
3.068000e+03 1.049009e-32 3.717408e-22 1.362260e-12 4.732220e-02 9.526778e-01 

I was trying to understand how coloc actually calculates these numbers, but couldn't find much information. I wondered if you can give any advice and explain how coloc calculates these values?

Would you say these hypothesis prior values are a concern to the validity of the posterior probability results?

Thanks for the help!

Harriet