Confidence and coverage for Bland–Altman limits of agreement and their approximate confidence intervals

Bland and Altman described approximate methods in 1986 and 1999 for calculating confidence limits for their 95% limits of agreement, approximations which assume large subject numbers. In this paper, these approximations are compared with exact confidence intervals calculated using two-sided tolerance intervals for a normal distribution. The approximations are compared in terms of the tolerance factors themselves but also in terms of the exact confidence limits and the exact limits of agreement coverage corresponding to the approximate confidence interval methods. Using similar methods the 50th percentile of the tolerance interval are compared with the k values of 1.96 and 2, which Bland and Altman used to define limits of agreements (i.e. d ¯ +/− 1.96Sd and d ¯ +/− 2Sd). For limits of agreement outer confidence intervals, Bland and Altman’s approximations are too permissive for sample sizes