# Agreement Between Two Measurements

Taking into account repeated measures by subject, we began to adapt the model (2) to COPD data using the lmer function of the R lme4 packet [38, 39]. Diagnostic diagrams are shown in Figures 3 and 4 of the add-on material. The estimates of the variance components are as follows: (sigma} {{alpha}^2=11.4, {gamma} ^2=16.6, {sigma}_{alpha beta} 2=0.4, {sigma_ {alpha gamma} 2=6.0, {sigma}{beta gamma}^2=3.7 ) and (sigma}_{varepsilon}^2=10.5. ) Activity and subject declare a significant part of the total variance and are therefore the main sources of disagreement. The interaction between the subject and the device is negligible, which indicates no difference in the effect of the device between the subjects. For both the compliance limits and the TDI method, it is important to remember that the calculated limit values are only estimates (just as the CCC is a point estimate) and therefore there is uncertainty about the actual values of these values . Different samples of the total population may produce different limit values and a different DDI. In particular, when the sample size is reduced, the observed concordance limits may be removed from the “true” concordance limits due to the distortion of the finite sample. For this reason, for statistical purposes, it is often recommended to calculate confidence limits around borders, or even to calculate separate prediction intervals [44, 45]. Conformity studies examine the distance between measured values performed by different devices or observers that measure the same quantity. If the values generated by each device are close most of the time, so there is no practical difference between the device used, we conclude that the devices match. An example of a compliance study is that if we are interested in determining the extent to which two observers using the same instrument produce similar measurement values.

A second example is the determination of the importance of the method of notification of a questionnaire when it is given on the same day to the same group of participants. For example, Chen and colleagues examined whether two different versions of the epworth Sleepiness Scale (electronic and paper) produced the same values when both patients were given the same day with obstructive sleep apnea . Since the differences between the electronic and paper versions were mostly in the ± 4, this was considered an acceptable agreement . Compliance has elements of precision and precision: discrepancies between devices may be due to systematic distortion of one device in relation to the other or if at least one of the devices is inaccurate . Zou GY. Estimated confidence interval for Bland Altman compliance limits with multiple observations per individual. Stat Methods Med Res. 2013;22:630. The five statistical methods for assessing conformity to repeated measurement data are described below using appropriate modelling formulas. As described above, linear models of mixed effects are particularly suitable for the analysis of data from gratified and non-symmetrical designs, as they contain random effects stories. .

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