Why should binary data have a 1:1 case:control ratio? my understanding is that you can get more power/accuracy with a 1:4 case: control ratio for less common diseases?
unfortunately the answer is it depends on h2 and covariates
There isn’t really a single optimal ratio. But you can calculate “N effective” based on your number of cases and controls, and see how adding more cases or more controls affects “N effective”
“N effective” is what will more directly affect the power in your GWAS.
Adding more people isn’t bad, even if they’re controls, but there’s a point of diminishing returns where adding more controls doesn’t do much to increase N effective anymore.
N effective = 4 / ((1 / cases) + (1 / controls))
There are a few different formulas for it, but that’s one of the most common.