The key error in the field standard approach is that it does not account for variation in ascertainment across cohorts. As such, the expectation for the degree of bias in liability-scale heritability for the field standard approach can be indexed using the ratio of the sum of effective sample sizes (our proposed approach) over the effective sample size calculated using the total number of cases and controls (statistically equivalent to the field standard approach). In other words, (13) %Bias=hl2EstimateforvTotalhl2estimatefor∑EffNk−1=∑vk(1−vk)nk(∑vknk)∑nk(∑(1−vk)nk)∑nk(∑nk)−1 Note that equation 13 makes it explicit that bias with respect to the heritability estimate is an inverse function of bias with respect to the computation of EffN.
