In order to evaluate the accuracy of the SEs, we analyzed the ratio of the mean SE estimate across the 100 simulations over the empirical SE (calculated as the standard deviation of the parameter estimates across the 100 simulations). A value above 1 for this ratio indicates conservative SE estimates. This ratio was calculated within each of the annotations and for each cell of the covariance matrix. The average ratio across annotations and cells of the covariance matrix was 1.030 (see Supplementary Fig. 9 for distribution across all annotations and Supplementary Table 7 for ratio within causal annotations). Thus, we have produced a SE estimate for stratified heritability and covariance that performs as expected. In fact, our estimates are very slightly conservative as the mean SE was slightly larger than the empirical SE. Moreover, the average z statistic for heritability and covariance estimates within the causal annotations were all highly significant, suggesting more than adequate power under the conditions of the current simulation.
