Assessing individual agreement.

Evaluating agreement between measurement methods or between observers is important in method comparison studies and in reliability studies. Often we are interested in whether a new method can replace an existing invasive or expensive method, or whether multiple methods or multiple observers can be used interchangeably. Ideally, interchangeability is established only if individual measurements from different methods are similar to replicated measurements from the same method. This is the concept of individual equivalence. Interchangeability between methods is similar to bioequivalence between drugs in bioequivalence studies. Following the FDA guidelines on individual bioequivalence, we propose to assess individual agreement among multiple methods via individual equivalence using the moment criteria. In the case where there is a reference method, we extend the individual bioequivalence criteria to individual equivalence criteria and propose to use individual equivalence coefficient (IEC) to compare multiple methods to one or multiple references. In the case where there is no reference method available, we propose a new IEC to assess individual agreement between multiple methods. Furthermore, we propose a coefficient of individual agreement (CIA) that links the IEC with two recent agreement indices. A method of moments is used for estimation, where one can utilize output from ANOVA models. The nonparametric and bootstrap approaches are used for inference. Five examples are used for illustration.