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Background  To assess the agreement of continuous measurements between a number of observers, Jones et al. introduced limits of agreement with the mean (LOAM) for multiple observers, representing how much an individual observer can deviate from the mean measurement of all observers. Besides the graphical visualisation of LOAM, suggested by Jones et al., it is desirable to supply LOAM with confidence intervals and to extend the method to the case of multiple measurements per observer.    Methods  We reformulate LOAM under the assumption the measurements follow an additive two-way random effects model. Assuming this model, we provide estimates and confidence intervals for the proposed LOAM. Further, this approach is easily extended to the case of multiple measurements per observer.    Results  The proposed method is applied on two data sets to illustrate its use. Specifically, we consider agreement between measurements regarding tumour size and aortic diameter. For the latter study, three measurement methods are considered.    Conclusions  The proposed LOAM and the associated confidence intervals are useful for assessing agreement between continuous measurements.    Supplementary Information  The online version contains supplementary material available at 10.1186/s12874-020-01182-w.

On Jones et al.’s method for extending Bland-Altman plots to limits of agreement with the mean for multiple observers