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Measuring Agreement In Method Comparison Studies

J Martin Bland, Douglas G Altman

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Agreement between two methods of clinical measurement can be quantified using the differences between observations made using the two methods on the same subjects. The 95% limits of agreement, estimated by mean difference 1.96 standard deviation of the differences, provide an interval within which 95% of differences between measurements by the two methods are expected to lie. We describe how graphical methods can be used to investigate the assumptions of the method and we also give confidence intervals. We extend the basic approach to data where there is a relationship between difference and magnitude, both with a simple logarithmic transformation approach and a new, more general, regression approach. We discuss the importance of the repeatability of each method separately and compare an estimate of this to the limits of agreement. We extend the limits of agreement approach to data with repeated measurements, proposing new estimates for equal numbers of replicates by each method on each subject, for unequal numbers of replicates, and for replicated data collected in pairs, where the underlying value of the quantity being measured is changing. Finally, we describe a nonparametric approach to comparing methods.