Ok. So you mean: measured snp X1 correlates with unmeasured causal snp X2. But not perfectly. So there is some estimated error from the people who do or don’t have X1. But there is also some error from people who do/don’t have X2, and this won’t be picked up by the reported SEs? Or will it? Thinking about it, I don’t see why it wouldn’t be. But need to think more.
> Correcting for correlation among the SNPs (“linkage disequilibrium”). I have no idea what to do about this, or if it matters. I’m using corrected standard errors from the summary statistics, blindly hoping this helps.
This is my first thought. The summary statistics wouldn't tell you the standard error from measurement error in the causal variant. So there's hidden inflation of error: you have simple sampling error from the rare variant being rare, yes, but you also have sampling error from all of the people who do/do not have the rare variant which is driving the signal. This would create a steadily increasing bias the rarer the variant is, I'd think?
Hmm. So the idea is, there's a measured variant X1 which is correlated with an unmeasured variant X2 which is truly causal. But not perfectly correlated. And this inflates the standard error because some people have X2 but not X1 or vice versa, so the "effect" of X1 is measured with noise.
OK, I agree with this, but I think it would be reflected in the reported standard errors, no? Like, it will increase the variance of the difference between those with and without X1.
You would have to work it out, yeah. The differences between measurement error in the predictors and outcomes can get subtle... But I find it suspicious that it seems like LD error would change with MAF, and a change with MAF is also what you're trying to explain here.
Ok. So you mean: measured snp X1 correlates with unmeasured causal snp X2. But not perfectly. So there is some estimated error from the people who do or don’t have X1. But there is also some error from people who do/don’t have X2, and this won’t be picked up by the reported SEs? Or will it? Thinking about it, I don’t see why it wouldn’t be. But need to think more.
> Correcting for correlation among the SNPs (“linkage disequilibrium”). I have no idea what to do about this, or if it matters. I’m using corrected standard errors from the summary statistics, blindly hoping this helps.
This is my first thought. The summary statistics wouldn't tell you the standard error from measurement error in the causal variant. So there's hidden inflation of error: you have simple sampling error from the rare variant being rare, yes, but you also have sampling error from all of the people who do/do not have the rare variant which is driving the signal. This would create a steadily increasing bias the rarer the variant is, I'd think?
Hmm. So the idea is, there's a measured variant X1 which is correlated with an unmeasured variant X2 which is truly causal. But not perfectly correlated. And this inflates the standard error because some people have X2 but not X1 or vice versa, so the "effect" of X1 is measured with noise.
OK, I agree with this, but I think it would be reflected in the reported standard errors, no? Like, it will increase the variance of the difference between those with and without X1.
You would have to work it out, yeah. The differences between measurement error in the predictors and outcomes can get subtle... But I find it suspicious that it seems like LD error would change with MAF, and a change with MAF is also what you're trying to explain here.