where the square root of the total variance gives an estimate of the standard deviation to be used in the conventional Bland-Altman formula for compliance limits. Before applying the individual correspondence coefficient method to COPD data, let us verify whether the residual error variance is appropriate by calculating the Bland and Altman repeatability coefficient, which is ( 1.96sqrt{2{sigma}_e^2} ) =8.98 when applied to COPD data. This tells us that there is a probability of about 95% that the repeated respiratory rate values are within 9 breaths per minute. In the context of the study, less than 5 is ideal, so the repeatability coefficient in this context is unacceptably high. This means that we must be careful when overinterpreting the CIA`s results, as they are compared to a high benchmark. The CIA was calculated at 0.68 (95% CI 0.56 to 0.70). It has been suggested that an agreement will only be considered «acceptable» if the CIA exceeds 0.8 [8, 27, 28]; or in other words, if the inconsistency between devices is within 25% of the disagreement of repeated measures within devices and in patients. Therefore, the CIA results indicate a poor match between the devices, in accordance with the results of other methods. From the estimates of the variance component of the model (2), we can explain the main sources of disagreement. There is considerable variability due to themes and activities (( {sigma}_{alpha}^2=11.4,{sigma}_{gamma}^2=16.6 )), which may be the reason why we at the CCC have come to the conclusion that the breast band device slightly matches the reference device. It is important to note, however, that the residues in the subject are high (( {sigma}_{varepsilon}^2=10.5Big) ) and the interaction between the device and the activity is moderate ( left({sigma}_{beta gamma}^2=3.7right) ), which contributed to our conclusion that the agreement between the two devices is not satisfactory for the CP, TDI and CIA methods. The relatively large variability of activity and subject plays no role in the calculation of CP, TDI and CIA, which could explain the difference in the conclusion compared to the CCC.

Haber M,Gao J., Barnhart HX. Evaluation of the agreement between the measurement methods from the data and the corresponding repeated measurements via the individual correspondence coefficient. J Data Sci. 2010;8( 3):457. I think random-effects and mixed CCIs have different underlying definitions, it`s just that their calculation from the variance components in an ANOVA framework is identical. This may amount to something similar to the distinction between sample statistics and demographic statistics (e.B. n vs N as the size of a sample or population). If you look at the left column of Table 4 in McGraw and Wong (1996), the CCI(A,1) definitions differ in how they denote the variance of the columns. ICC random effects (case 2A) are sigma and are an estimate from samples in the population. The mixed-effects CCI (case 3A) uses theta and reflects the assumption that you have evaluated all the evaluators of interest to you.

However, they calculate the ratio of variance components in the same way! The reason for the outliers in the remnants of the model or the null values returned by the devices was unknown, but we think it could be due to technical problems with some of the devices or problems with the equipment. That is why it was appropriate for us to include results with and without outliers; Otherwise, if we exclude all outliers and zeros, it can give a false impression of the agreement for some devices. Only a few of the outliers in the remnants of the model can be traced back to the zero values generated by the devices; and it could be that most of the other outliers were caused by inaccurate readings of the devices, but these can be difficult to detect just by looking at the raw data. At the limit of compliance analysis, we must assume a constant level of agreement over the entire measurement range. In some of the Bland-Altman diagrams presented in Figures 11 and 2.2, the validity of this hypothesis is doubtful, as in some diagrams the variability appears to increase with the average respiratory rate. This could be due to a floor effect where the respiratory rate is unlikely to be below a certain threshold (for example, 10 breaths per minute) and in fact impossible for it to be below zero. This artificially limits the range within which the differences between devices should be at low respiratory rate values. while there is no such restriction for high values. Therefore, the compliance limit method is best applied in situations where the measurement range is completely unlimited and the effects on the floor and ceiling are negligible. but if there is evidence of floor or ceiling effects, this should be taken into account when interpreting Bland-Altman properties and compliance limits. If there are floor or ceiling effects, researchers should be aware that an acceptable agreement (at least in part) may be a consequence of the limited scope and does not necessarily reflect the ability of different methods/devices to agree.

Floor and ceiling effects can also lead to non-normal differences in outcomes. [20] All five methods are based on parametric assumptions. Nonparametric approaches to chord evaluation, such as the perez-Jaume method and Carrasco [30], are not often seen in the literature, but should be considered; especially in cases where the data is distorted or abnormal. Even in case you know by chance: from my experience, as well as based on the confidence intervals around icc estimates, it seems that ICC(1,1) and other ICC estimates of absolute agreement for single-rate reliability seem to fit together quite well and will not be easily differentiated, except in absolutely huge samples.. .