## Methods Of Agreement

(mu}_0 ^ast } ) is the average distortion of interest. Compliance limits are calculated in such a way that, if the assumptions described above are not valid, non-parametric methods should be considered. For example, Perez-Jaume and Carrasco propose a non-parametric alternative to the calculation of the ID, more stable and reliable than the parametric method when working with distorted data [30]. It is also relatively easy to calculate and less influenced by outliers or extremes than the parametric approach. The method is simply to calculate the quantils of an ordered list of paired differences to calculate the TDI. A bootstrap method can then be used to calculate the upper limit by recalculating at the patient level and then recalculating the TDI for each new bootstrap calculation. This seems to be the same as a perzentile method first described by Bland and Altman [5], except that, in the case of repeated measures, we use the start resampling to get the upper limit. Although it does not adopt a normal distribution, we must nevertheless consider that the differences are independent and distributed identically. Other non-parametric methods are available [31, 32]. Stevens [33] also developed a generalization of the probability of concordance based on the moment method, which does not require any distribution assumptions for true values. Full versions of the Limits of Agreement method have also been proposed, for example the Schluters Bayes tuning method [34].

In addition, Barnhart [12] and Barnhart et al. [11] an interesting method that uses generalized estimation equations to provide a non-parametric estimate of CP. Recently, Jang et al. [35] proposed a new set of correspondence indices adapted to contexts where there are several heterogeneous evaluators and variances. The Coefficient of Individual Agreement (CIA) was developed by Haber and Barnhart [8] and Barnhart et al[9]. This is an evolutionary coefficient that directly compares the disagreement between the devices and the disagreement within the devices within the subjects [27, 28]. The CIA`s main focus is on quantifying the magnitude of variability between different devices versus variability within devices. The CIA value ranges from 0 to 1.1 indicating that the use of different devices makes no difference in the variability of repeated measurements made under the same conditions within the same subject. The residual error variation ({sigma}_e^2 ) represents the variability of repeated measurements made under the same conditions within the same subject, and it is therefore important that it is a reliable comparison measure. As recommended by others [27, 28], we check whether this value is appropriate by calculating the repeatability coefficient of Bland and Altman, which is 1.96sqrt {2 { sigma} _e^2}. There are different variants of the CIA, but we follow others using the mean quadratic deviation as a measure of disagreement [27, 28]. We follow in particular that of Haber et al.

[28] the approach of repeated concordant measures, which indicates that the CIA`s calculation should be based on Carrasco JL, Caceres A, Escaramis G, Jover L. Distinction and compliance with continuous data. Stat Med. 2014;33 (1):117-28. Barnhart HX, Haber MJ, Lin LI. An overview of conformity assessment for continuous measures. J Biopharm Stat. 2007;17 (4):529-69.

Symbolically, the common method of conformity and difference can be presented as: Carstensen B, Simpson J, Gurrin LC. Statistical models to assess compliance with comparative studies of methods with replication measures. Int J Biostat. 2008;4(1):16. The common method is to apply both the concordance method and the difference method as shown in the graph above. The application of the common method should therefore tell us that this time it is beef that is the cause. . . .