Assessing agreement with intraclass correlation coefficient and concordance correlation coefficient for data with repeated measures

The intraclass correlation coefficient and the concordance correlation coefficient are two popular scaled indices for assessing the closeness between observers who make measurements for quantitative responses. These two indices are usually based on subject and observer effects only, and therefore we cannot use these indices if the observer produces repeated measurements rather than replicated readings. In this paper, we consider not only subject and observer effects, but also time effects for data with repeated measurements since it is difficult to obtain the true replications in practice. We compare these two agreement indices for different combinations of random or fixed effects of observer and time. Finally, we use image data of 2D-echocardiograms to illustrate the proposed methodology and the comparison of these two indices. If there is a need to choose between these two indices for repeated measurements, we recommend to use the new concordance correlation coefficient since it does not need ANOVA assumptions.