Errors-in-variables regressions to assess equivalence in method comparison studies

Analytical laboratories continuously assess the uncertainties and reliability of their measurement systems so that their clients can take the right decision. This leads to the development of new measurement methods which should be more precise, less expensive but chiefly equivalent. To assess equivalence in method comparison studies, two main methodologies are presented separately in the literature. First, the approach based on errors-in-variables regressions that focuses on confidence intervals. Two devices are considered equivalent when they provide similar measures notwithstanding the random measurement errors. In this thesis, several regressions are reviewed and compared; several new results are proposed as well as charts and tips for the user. The second methodology is the well-known Bland and Altman approach with its agreement intervals. Two devices are considered interchangeable when the differences in their measurements are not meaningful in practice. Tolerance intervals are presented as better alternatives and two new consistent regressions are proposed to compute predictive intervals. Finally, this thesis reconciles the two methodologies, shows their similarities and how they complement each other.