Fast and Accurate Construction of Confidence Intervals for Heritability  Regev Schweiger, Shachar Kaufman, Reijo Laaksonen, Marcus E. Kleber, Winfried März, Eleazar Eskin, Saharon Rosset, Eran Halperin  The American Journal of Human Genetics  Volume 98, Issue 6, Pages 1181-1192 (June 2016) DOI: 10.1016/j.ajhg.2016.04.016 Copyright © 2016 American Society of Human Genetics Terms and Conditions

Figure 1 Accuracy of CIs The left panels depict the true coverage probabilities of the GCTA CIs (according to the normal approximation) on the GTEx, LURIC, and NFBC datasets. The right panels depict the coverage probabilities of the ALBI CIs. The coverage probabilities are shown for CIs designed to have coverage probabilities of 90% and 95%. The GCTA CIs are often far from the correct confidence level, whereas ALBI CIs achieve accurate coverage. The American Journal of Human Genetics 2016 98, 1181-1192DOI: (10.1016/j.ajhg.2016.04.016) Copyright © 2016 American Society of Human Genetics Terms and Conditions

Figure 2 Accuracy of SEs The ratio between the square root of the mean variance derived from GCTA and the empirical SD of the REML estimator hˆ2 is shown as a function of the true h2 for the studied datasets. The discrepancy is high (ratios up to 1.7×). The American Journal of Human Genetics 2016 98, 1181-1192DOI: (10.1016/j.ajhg.2016.04.016) Copyright © 2016 American Society of Human Genetics Terms and Conditions

Figure 3 Distributions of the Heritability Estimator The density of hˆ2 for h2 = 0.1, 0.2, and 0.3 in the studied datasets under the LMM. Because the distribution of hˆ2 is continuous in the open interval (0, 1), we divided this range into equally sized bins of a fixed size (0.01) and instead estimated the probability mass function of a random variable taking values in the set {0, (0, 0.01), (0.01, 0.02), …, (0.99, 1), 1}. Estimator distributions are often far from normal, so the normal approximation seems highly questionable. The American Journal of Human Genetics 2016 98, 1181-1192DOI: (10.1016/j.ajhg.2016.04.016) Copyright © 2016 American Society of Human Genetics Terms and Conditions

Figure 4 Probability of Boundary Heritability Estimates The probability of estimating hˆ2 = 0 as a function of the true underlying heritability values h2 for the studied datasets. The probability of hˆ2 = 0 is high, especially for small values. The American Journal of Human Genetics 2016 98, 1181-1192DOI: (10.1016/j.ajhg.2016.04.016) Copyright © 2016 American Society of Human Genetics Terms and Conditions

Figure 5 Comparison of CI Width The ratio between the mean width of CIs derived from GCTA and the width of the ALBI CIs is shown as a function of the true h2 for the studied datasets. The American Journal of Human Genetics 2016 98, 1181-1192DOI: (10.1016/j.ajhg.2016.04.016) Copyright © 2016 American Society of Human Genetics Terms and Conditions