We simulated case-control data assuming increasing β. We present the results for a disease prevalence of 0.01. This value is relevant to complex traits such as BD or schizophrenia. Results for other prevalence values can be found in the Table S1 and S2. In all analyses, the admixture level significantly affected the sample size required to reach 90% power at the significance level of p<5×10−8. Specifically, there was a substantial loss of statistical power that was disproportionately larger than the degree of heterogeneity. An increase in the proportion of “non-cases” resulted in a non-linear increase of the sample size needed to achieve 90% of statistical power. As shown in Figure 1, this effect was evident both in the dominant and multiplicative models and for different relative risks (RR = 1.2, 1.5 and 2). For instance, with β at 50%, the sample size needed to achieve the same statistical power without admixture was three times larger, particularly with genetic effect sizes equal to or larger than 1.5.
