Measures of agreement for vectorcardiography data

In this paper, nonparametric methods are proposed for quantifying agreement and disagreement between different measurement methods when the results of the measurements are rotation matrices. First, the expected squared distance between two matrices is used to quantify the measurement agreement. Two choices of such distance are considered-the Frobenius distance and geodesic distance. Second, the notion of 'concordance correlation coefficient', a commonly used measure of agreement, is extended to the space of rotation matrices. Such generalized concordance coefficient can be treated as a normalized expected squared distance. Since no two measurement systems can be expected to be in perfect agreement, it becomes necessary to define a notion of practical agreement. We define such a notion. Moreover, for both proposed methods, the percentile bootstrap procedure is implemented to provide a confidence interval to help make a decision concerning practical agreement/disagreement in real-life applications. The methodology is illustrated using two data sets, one based on an application involving vectorcardiography data (Biometrika 1972; 59:665-676) and the other based on a synthetic data set.