What to do about lambda_GC?

[privefl]

Currently, lambda_GC(X2) = lambda_GC(Z)^2.
This can be confusing when comparing Q-Q plots using different statistics.
What to do about it?

[earosenthal]

Can you elaborate on what you mean by this? It looks like you are calculating lambda_GC using the Z-scores. What do you mean by 'other statistics'?

[privefl]

I think the one usually reported in papers is the one for X2, right?

[earosenthal]

I'm no expert, but it is my understanding that the inflation factor is based on the chi-square distribution (I think that is what you mean by X2). It looks like getLambdaGC may be calculating the square root of the inflation factor. Can you verify this? I calculated the inflation factor in my data using two ways (z-score, p-value) and compared it to what getLambdaGC output:

# using the z-scores
> chisq <-obj.gwas$score^2
> median(chisq)/qchisq(0.5,1)
[1] 0.9829162

# using the p-values 
> chisq <- qchisq(1-obj.gwas$p.value,1)
> median(chisq)/qchisq(0.5,1)
[1] 0.9806252

> bigsnpr:::getLambdaGC(obj.gwas)
[1] 0.9902582
> (bigsnpr:::getLambdaGC(obj.gwas))^2
[1] 0.9806112

[privefl]

Yes, currently big_univLinReg() uses t-scores and big_univLogReg() uses Z-scores, so you need to square the lambda_GC.

This is also my understanding that it is usually reported for chi-squares (X2), therefore this question/issue.

[privefl]

Also, maybe think about exporting the function to get the lambda_GC, which for now can be run using bigsnpr:::getLambdaGC().