# Assessing Agreement with Continuous Measurements

Zaki R, Bulgiba A, Ismail R, Ismail NA. Statistical methods used to test the match of medical devices that measure continuous variables in method comparison studies: a systematic review. PLoS one. 2012;7(5):e37908. If the assumptions described above are not valid, nonparametric methods should be considered. For example, Perez-Jaume and Carrasco propose a non-parametric alternative to the calculation of the TDI that is more stable and reliable than the parametric method when working with distorted data . It is also relatively easy to calculate and less affected by outliers or extremes than the parametric approach. The method is simply to calculate the quantiles of an ordered list of matched 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 bootstrap resample. This seems to be the same as a percentile method first described by Bland and Altman , except that in the case of repeated measurements, we use bootstrap resampling to maintain the upper limit. Although it does not assume a normal distribution, we must always assume that the paired differences are independent and distributed identically. Other non-parametric methods are available [31, 32]. Stevens  also developed a generalization of the probability of agreement based on the moment method, which does not require a distribution assumption for real values.

It has also been proposed in the complete Bayesian versions of the chord limit method, for example schluter`s Bayesian chord method . In addition, Barnhart  and Barnhart et al.  describe an interesting method that uses generalized estimation equations to provide a nonparametric estimate of CP.  proposed a new set of correspondence indices adapted to contexts where there are multiple evaluators and heterogeneous variances. The need for confidence intervals alongside consensus limits is strongly emphasized in the literature, and rightly so. However, we consider it just as important – if not more important – to account for individual components of variance (e.g.B variance between subjects and variance within the subject) and estimates of bias alongside correspondence indices, as these clarify the source of disagreement. In addition, it is important to know that differences between devices, as observed in compliance indices, can mask differences in accuracy and measurement error between devices, and also reflect underlying average biases that cannot be adequately modeled by absolute mean differences. For this reason, it is crucial to look beyond disagreement over the underlying causes in order to critically aid the outcomes of the agreement.

Pan Y, Gao J, Haber M, Barnhart HX. Estimation of individual correspondence coefficients (ACEs) for quantitative and binary data using SAS and R. Comput Prog Biomed methods. 2010;98(2):214–9. Consistent studies examine the distance between readings taken by different devices or observers measuring the same amount. If the values generated by each device are close to each other most of the time, we conclude that the devices match. In the literature, several different matching methods have been described in the mixed linear modeling framework that can be used in repeated time-adjusted measures in subjects. One of the most important ways to classify the different methods is to divide them into those that produce standardized compliance indices that are scaled to be within a certain range (for example, the CCC is scaled between −1 and 1 and the CIA between 0 and 1), and those that allow for direct comparison with the original scale of the data and the indication of a clinically acceptable scale Require a difference ( by. B LoA, CP and TDI methods). These groups of methods are generally referred to as scale or scale methods. non-scaled matching methods , and the latter methods are sometimes referred to as “pure match indices” . In fact, the CCC can be more accurately described as an evaluation of the distinction and not as a correspondence, since it is designed to calculate the proportion of variance of a system explained by the subject-activity effect and does not require the specification of a CAD .

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