The average distortion is then quantified by (2, 1) and further: Var-left (`from ilt`ast`right) `2`sigma`_alpha `alpha`2`2`sigma`. That`s why the limits of the agreement are calculated like Parker RA, Weir CJ, Rubio N, Rabinovich R, Pinnock H, Hanley J, et al. Application of Mixed Effects Compliance Limitations in the presence of multiple sources of variability: an example from the comparison of several breathing frequency measurement devices in COPD patients. PLoS One. 2016;11 (12):e0168321. Lin LI. Overall difference index for measuring individual compliance with laboratory performance and bioequivalence applications. Med Stat. 2000;19:255-70. Barnhart HX, Lokhnygina Y, Kosinski AS, Haber M. Comparison of correlation coefficient and coefficient of individual agreement in the assessment of the agreement. J Biopharm Stat. 2007;17(4):721-38.
Considering the probability of coverage if we take δ 5 as a predetermined limit (CAO – ± 5), the probability of coverage is only 0.63 (95% from 0.56 to 0.70), indicating a relative mismatch between methods. This is well below the 0.95 threshold that we used to reach a satisfactory agreement. We offer a tutorial to help practitioners choose different methods of evaluating agreements on the basis of a mixed linear acceptance of models. We illustrate the use of five methods in a one-on-one comparison based on actual data from a study of patients with chronic obstructive pulmonary disease (COPD) and repeated respiratory frequency observations. The methods used were the correlation coefficient, the match limits, the overall difference index, the probability of coverage, and the coefficient of the individual agreement. To calculate CP in practice for our COPD example, we first use the linear mixed effect model in (2) to calculate the average square difference which is the expected quadritelic difference between the measured values of two different devices on the same person who simultaneously performs the same activity: Bland JM, Altman DG. Agreement between measurement methods with multiple observations per person. J Biopharm Stat. 2007;17(4):571-82. The timing of the measurements was not considered clinically important in this study, as the other covariates were dependent, so we did not adjust to the measurement period in the models. However, in other studies and attitudes, measurement time can be influenced and should be taken into account in models.
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