Next, we performed simulations with real LD patterns to further assess the robustness of the LCV method. These simulations and their results are described in detail in the Supplementary Note. In null simulations with a wide range of parameter settings, LCV produced approximately well-calibrated or conservative false positive rates, except for simulations at low sample size with noisy heritability estimates (Supplementary Table 6 a-s and Supplementary Table 7). (We exclude real datasets with noisy heritability estimates). We determined that LCV can be confounded by uncorrected population stratification (Supplementary Table 8). In non-null simulations, LCV was usually well-powered to detect a causal or partially causal effect (Supplementary Table 6 t-bb). In simulations with a range of gcp values, we determined that our posterior mean gcp estimates are approximately unbiased and that our posterior standard errors are approximately well-calibrated (Supplementary Figure 3 and Supplementary Table 9).
