Exact Parametric Confidence Intervals for Bland-Altman Limits of Agreement

Purpose The previous literature on Bland-Altman analysis only describes approximate methods for calculating confidence intervals for 95% limits of agreement (LoAs). This article describes exact methods for calculating such confidence intervals based on the assumption that differences in measurement pairs are normally distributed. Methods Two basic situations are considered for calculating LoA confidence intervals: the first, where LoAs are considered individually (i.e., using one-sided tolerance factors for a normal distribution); and the second, where LoAs are considered as a pair (i.e., using two-sided tolerance factors for a normal distribution). Equations underlying the calculation of exact confidence limits are briefly outlined. Results To assist in determining confidence intervals for LoAs (considered individually and as a pair), tables of coefficients have been included for degrees of freedom between 1 and 1000. Numerical examples, showing the use of the tables for calculating confidence limits for Bland-Altman LoAs, have been provided. Conclusions Exact confidence intervals for LoAs can differ considerably from the Bland and Altman approximate method, especially for sample sizes that are not large. There are better, more precise methods for calculating confidence intervals for LoAs than the Bland and Altman approximate method, although even an approximate calculation of confidence intervals for LoAs is likely to be better than none at all. Reporting confidence limits for LoAs considered as a pair is appropriate for most situations; however, there may be circumstances where it is appropriate to report confidence limits for LoAs considered individually.