Overall concordance correlation coefficient for evaluating agreement among multiple observers

Accurate and precise measurement is an important component of any proper study design. As elaborated by Lin (1989, Biometrics 45, 255-268), the concordance correlation coefficient (CCC) is more appropriate than other indices for measuring agreement when the variable of interest is continuous. However, this agreement index is defined in the context of comparing two fixed observers. In order to use multiple observers in a study involving large numbers of subjects, there is a need to assess agreement among these multiple observers. In this article, we present an overall CCC (OCCC) in terms of the interobserver variability for assessing agreement among multiple fixed observers. The OCCC turns out to be equivalent to the generalized CCC (King and Chinchilli, 2001, Statistics in Medicine 20, 2131-2147; Lin, 1989; Lin, 2000, Biometrics 56, 324-325) when the squared distance function is used. We evaluated the OCCC through generalized estimating equations (Barnhart and Williamson, 2001, Biometrics 57, 931-940) and U-statistics (King and Chinchilli, 2001) for inference. This article offers the following important points. First, it addresses the precision and accuracy indices as components of the OCCC. Second, it clarifies that the OCCC is the weighted average of all pairwise CCCs. Third, it is intuitively defined in terms of interobserver variability. Fourth, the inference approaches of GEE and the U-statistics are compared via simulations for small samples. Fifth, we illustrate the use of the OCCC by two medical examples with the GEE, U-statistics, and bootstrap approaches.