Fiducial Confidence Intervals for Agreement Measures Among Raters Under a Generalized Linear Mixed Effects Model

A generalization of the classical concordance correlation coefficient (CCC) is considered under a three-level design where multiple raters rate every subject over time, and each rater is rating every subject multiple times at each measuring time point. The ratings can be discrete or continuous. A methodology is developed for the interval estimation of the CCC based on a suitable linearization of the model along with an adaptation of the fiducial inference approach. The resulting confidence intervals have satisfactory coverage probabilities and shorter expected widths compared to the interval based on Fisher's Z-transformation, even under moderate sample sizes. Two real applications available in the literature are discussed. The first application is based on a clinical trial to determine if various treatments are more effective than a placebo for treating knee pain associated with osteoarthritis. The CCC was used to assess agreement among the manual measurements of the joint space widths on plain radiographs by two raters, and the computer-generated measurements of digitalized radiographs. The second example is on a corticospinal tractography and the CCC was once again applied in order to evaluate the agreement between a well-trained technologist and a neuroradiologist regarding the measurements of fiber number in both the right and left corticospinal tracts. Other relevant applications of our general approach are highlighted in many areas including artificial intelligence.