Figure 3.

MSE and bias given different values of liability-scale heritability, population prevalence, and sample prevalence

Results about MSE and bias are shown in (A) and (B), respectively. We observe that for the scenarios of small to moderate heritability ($h^2<0.5$), small population prevalence ($K\le 0.02$) and sample prevalence smaller or slightly larger than the population prevalence ($P\le 1.25K$), it is preferred to use our proposed expression, as it gives a lower MSE while not increasing the bias too much. In the case of ascertainment, we suggest using the proposed expression with the adjustment. We evaluated the observed scale heritability using GREML and then transformed it to the liability scale either by using the previous expression from Lee et al., by our proposed expression without adjustment for ascertainment, and by our proposed adjustment with ascertainment adjustment. In addition, we directly estimated the liability-scale heritability by using the PCGC method with summary statistics. Datasets were created under simulation scenario 2, and the number of simulation replicates was 100. 95% CI for MSE and bias values are provided in Data S1.