Carrasco JL, Caceres A, Escaramis G, Jover L. Discernment and agreement with continuous data. Med Stat. 2014;33 (1):117-28. The correlation coefficient (CCC) method was developed by Lin in 1989 , with the longitudinal, repeated measurement version of the CCC developed by King et al. , Carrasco et al.  and Carrasco and Jover . The CCC is a standardized coefficient that takes values from 1 to 1, 1 indicating perfect match and 1 the perfect match. For the CCC model, individual measurements are modeled with a combination of random and fixed effects. The terms of interaction are often included.
In particular, in the context of our COPD example, we start from the linear mixed effect model: Before applying the individual agreement coefficient to COPD data, we test whether the residual variance is appropriate by calculating the Bland and Altman repeatability coefficient, which is equal to 1.96rt, 2.sigma, _e, 8.98. This tells us that there is about a 95% chance that repeated breathing frequencies are within 9 breaths per minute. In the context of the study, less than 5 is ideal, so the repeatability coefficient is unacceptable in this context. This means that we have to be careful in over-interpreting CIA results, as they are compared to a high benchmark. The CIA was calculated at 0.68 (IC 95% 0.56 to 0.70). It was proposed that an agreement be considered « acceptable » only if the CIA exceeded 0.8 [8, 27, 28]; in other words, if the disagreement between the devices lies within 25% of the level of disagreement of repeated measurements inside the devices and inside the patients. Therefore, the CIA results suggest a poor agreement between the devices, in accordance with the results of the other methods. Estimates of model variance components (2) allow us to identify the main sources of disagreement. There is significant variability due to subjects and activities (- – Sigma » Alpha alpha-2-11.4, gamma-gamma »2-16.6) « Sigma »), which may be the reason we came to the conclusion at the CCC that the thoracic ligament apparatus is in low compliance with the gold standard apparatus.
But it is important that the rest of the individual is high (-) (`sigma `varepsilon`2-10.5`Big`) and the interaction between the activity of the device is moderate » (`left`sigma` sigma« ` The relatively large variability of activity does not matter in the calculation of CP, TDI and CIA, which could explain the difference in conclusion compared to the CCC. Barnhart HX, Yow E, Crowley AL, Daubert MA, Rabineau D, Bigelow R, Pencina M, Douglas PS. Selection of contractual indices to assess and improve the reproducibility of measurements in a central laboratory. Med Res Stat Methods. 2016;25(6):2939-58. doi.org/10.1177/0962280214534651. All five methods are based on parametric assumptions. Non-parametric approaches to evaluating chords, such as the perez-jaume and Carrasco method , are not often seen in the literature, but should be considered; especially in cases where the data is distorted or not normal.