In the video on the munge() function, it was mentioned that for meta-analyses nEff needed to be calculated as the sum of nEff from each contributing sample rather than an overall nEff based on overall case/control prevalence in the combined data.
I am curious if the complications of meta-analysis data affect the ability to calculate liability-scale h2 as well when the trait is binary. You have different case prevalences in each contributing sample, and then you also often don’t have data for every SNP in every sample, so sometimes which cohorts are included (and therefore likely overall case prevalence) will also differ by SNP.
Is a per-SNP Neff calculated as the sum of per-sample Neffs from contributing samples sufficient to handle all of that, or does the issue of case prevalence varying by SNP (when some samples don’t have data for that SNP) require a separate correction to be able to get a meaningful estimate of h2 and accurate conversion to liability-scale h2?
And what do you do when you can only calculate an overall Neff for “all cohorts included”, but there are no per-SNP Ns, just say a “number of cohorts” field for each SNP or the line of + - ? you get if the meta-analysis was done with metal?
I remembered that logistic regression is invariant to prevalence. You’ll get the same odds ratio whether you have a sample of 10% cases or a sample of 50% cases.
But that just raises a different question - if odds ratios (and therefore log odds) are invariant to prevalence, how is sample prevalence making it into our LDSC heritability estimates to begin with? (It must be making it somehow if we need the liability-scale correction…)
I think yes you will get the same odds ratios per SNP despite oversampled cases, but not the same SE. For h2 from LDSC you are considering the slope of chi-squared statistics over LD scores, in this case chi-squared is inflated by oversampled cases in true phenotype linked SNPs (because chi-squared is inflated by smaller SE). Oversampling cases is how you find disease linked SNPs in GWAS, via giving our test more genetic variance than is in the full population, I.e. making the slope of chi-squared stats over LD steeper (h2 inflated). So the LDSC software converts the final observed scale h2 with a simple correction penalty at the end proportionate to the oversampling, its doesn’t change the chi-squared or h2 calculation.