For the confidence interval check, we created 1050 SNPs in each of the iterations and count the number of times the TATES false positive p-values fell outside of the corresponding 95% confidence interval, which in the case of 1050 SNPs is 1050·0.05+1.645·1050·0.05·0.95=64.12. The last column “out of CI ratio” is the proportion of counts of p-values <= 0.05 among 1050 exceeding 64.12 (>= 65). As the values in this column show, the false positive rate exceeded the expected level of 5%, and increased with increasing correlations between the two phenotypes. This table shows that with highly correlated phenotypes, TATES p-values fall out of the 95% CI up to 18% of the time, which is much more than expected 5%. With small correlations this percent drops to 6–7%. The reason for this is that if the correlation is small then the TATES p-value structure for two phenotypes is min{(1+correlation) min(p1,p2),max(p1,p2)}meaning that only one of the p-values (the smallest one) could multiply by (1 + correlation) which is close to one when the correlation is small.
