Robust Concordance Rate for A Four-Quadrant Plot

Before new clinical measurement methods are implemented in clinical practice, it must be confirmed whether their results are equivalent to those of existing methods. The agreement between these methods is evaluated using the four-quadrant plot, which describes the trend of change in each difference of the two measurement methods' values in sequential time points, and the plot's concordance rate, which is calculated using the sum of data points that agree with this trend divided by the number of all accepted data points in the plot. However, the conventional concordance rate does not consider the covariance between the data on individuals, which may affect its proper evaluation. Therefore, we proposed a new concordance rate calculated by each individual subject according to the number of agreement. Moreover, to adjust outliers that may exist in clinical data and interfere with the estimation, we adopted the minimum covariance determinant (MCD) estimator, when calculating our proposed approach. A numerical simulation conducted with several factors including the estimation methods indicated that the MCD approach resulted in a more accurate evaluation. We also showed a real data and compared the proposed methods with the conventional approach. Finally, we discussed for the implementation in clinical studies.