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Nor is it possible to use these statistics to determine that one test is better than another. Recently, a British national newspaper published an article about a PCR test developed by Public Health England and the fact that it did not agree with a new commercial test in 35 of the 1144 samples (3%). Of course, for many journalists, this was proof that the PHE test was inaccurate. There is no way to know which test is good and which is wrong in any of these 35 disagreements. We simply do not know the actual state of the subject in compliance studies. Only by further examining these disagreements will it be possible to determine the reason for the discrepancies. The term ( MSDleft({Y}_j,{Y}_j^{prime}right) ) refers to the average square deviation between two replicated (hypothetical) measured values, Yj and ( {Y}_j^{prime } ), which could be achieved by device j on the same subject under the same activity at the same time. In our COPD context and assuming model (2) for respiratory rate measurements, despite the many obvious options for analyzing match data, the basic questions are very simple. Usually, there are one or two methods that are best suited for a particular application. However, it is necessary to clearly identify the purpose of the analysis and the substantive questions to be answered. Stevens et al.

[14, 29] have developed the probability of agreement (PoA) method as an alternative to the approach to the agreement boundary, which has the advantage of taking into account two different types of bias and uneven accuracy between devices. Proportional bias, where the extent of disagreement depends on the actual value in each topic, is considered in addition to additive bias, and this information can be used to clarify the different sources of disagreement if the devices do not match. The PoA method provides a flexible and informative summary of the agreement, but currently the methodology does not adapt to confounding factors (e.g. activity . B in our study on COPD) and is therefore not yet as widely applicable as other alternatives. For more information about this method, see the supplement file. 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. Schluter PJ. A multivariate hierarchical Bayesian approach to measuring agreement in comparative studies of repeated measurement methods. BMC Med Res Methodol. 2009;9(1):6. Parker RA, Weir CJ, Rubio N, Rabinovich R, Pinnock H, Hanley J, et al. Application of mixed-effects compliance limits in the presence of multiple sources of variability: Example from the comparison of several devices for measuring respiratory rate in COPD patients.

PLoS one. 2016;11(12):e0168321. Various methods have been proposed in the literature to assess the correspondence of continuous data, of which the concordance correlation coefficient [3, 4] and compliance limits [5] are the most commonly used. The probability of coverage [6], the total deviation index [6, 7] and the coefficient of individual matching methods [8, 9] were also described. All five methods can be calculated using linear mixed-effect models. With a focus on practical application and interpretation, the aim of this study is to show how these five approaches can be applied to the same matching problem and to highlight the strengths and weaknesses of each method so that researchers can decide which methods to use in their own studies. Reviews of agreement indices have already been presented in the literature by Barnhart et al. (2007) [2], Obuchowski et al. (2015) [10], Barnhart et al. (2016) [11] and Barnhart (2018) [12]; with the last three articles that contain real examples to compare contract indices. However, the examples given came almost exclusively from the fields of quantitative imaging and nuclear laboratory research.

In this article, we extend the methodological work already done to the field of analysis of unbalanced data grouped in applied clinical research, particularly in the field of respiratory rate measurement in copD patients. In addition, we focus specifically on the implementation of the linear mixed-effects model of the methods and not on the more general approach used in the above articles. Especially for match limits, this implementation of the method is not taken into account in previous controls. The reason for this focus is that mixed-effect modelling is increasingly used in clinical research and has advantages over fixed-effect methods (e.g. analysis of variance (ANOVA)) for several reasons described in Brown (2015) [13]. In particular, (i) missing or unbalanced data pose fewer analytical problems, and (ii) conclusions can be drawn based on a larger patient population [13]. We also focus on problems of correspondence with repeated observations, as these are recommended during conformity assessment [14]. Finally, to help practitioners of the agreement methods, we also provided the R code needed to implement the methods in an additional hardware file. .