To tolerate or to agree: A tutorial on tolerance intervals in method comparison studies with BivRegBLS R Package.

The well-known agreement interval by Bland and Altman is extensively applied in method comparison studies. Two clinical measurement methods are considered interchangeable if their differences are not clinically significant. The agreement interval is commonly applied to assess the spread of the differences. However, this interval is approximate (too narrow) and several authors propose calculating a confidence interval around each bound. This article demonstrates that this approach is misleading, awkward, and confusing. On the other hand, tolerance intervals are exact and can include a confidence level if needed. Tolerance intervals are also easier to calculate and to interpret. Real data sets are used to illustrate the tolerance intervals with the R package BivRegBLS under normal or log-normal assumptions. Furthermore, it is also explained how to assess the coverage probabilities of the tolerance intervals with simulations.