In order to evaluate the improvement in accuracy, we performed a permutation test to compare the CORs of AnnoPred and LDpred. Suppose the CORs of LDpred and AnnoPred in simulations are x1, x2, …, xn and y1, y2, …, yn, respectively. And the hypothesis we want to test is H0:μx=μy↔H1:μx≠μy where μx and μy represent the population mean of accuracies of LDpred and AnnoPred. We used |x¯−y¯| as the test statistics and the p value can be calculated as p=Pr(|x¯−y¯)>|x¯obs−y¯obs||H0), in which x¯−y¯ represents the random variable and x¯obs−y¯obs represents the actually observed values. We used permutation to approximate the distribution of (x¯−y¯) when H0 is true. Specifically, we first pooled xi′s and yi′s together. Then x˜1,x˜2,…,x˜n and y˜1,y˜2,…,y˜n were sampled from the pooled data for N = 106 times and we calculated (x˜¯−y˜−) for each x˜i′s and y˜i′s sampled, which formed the empirical distribution of (x¯−y¯) under H0. And the p value could be approximated by p^=∑k=1NI{|x˜¯k−y˜¯k|>|x¯obs−y¯obs|}N, in which x˜¯k−y˜¯k represents the sampled test statistic of the kth permutation.
