Multi-Panel Kendall plot in light of an ROC curve analysis applied to measuring dependence

The Kendall plot (K-plot) is a plot measuring dependence between the components of a bivariate random variable. The K-plot graphs the Kendall distribution function against the distribution function of VU, where V and U are independent uniform [0, 1] random variables. We associate K-plots with the receiver operating characteristic (ROC) curve, a well-accepted graphical tool in biostatistics for evaluating the ability of a biomarker to discriminate between two populations. The most commonly used global index of diagnostic accuracy of biomarkers is the area under the ROC curve (AUC). In parallel with the AUC, we propose a novel strategy to measure association between random variables from a continuous bivariate distribution. First, we discuss why the area under the conventional Kendall curve (AUK) cannot be used as an index of dependence. We then suggest a simple and meaningful extension of the definition of the K-plots, and define an index of dependence that is based on AUK. This measure characterizes a wide range of two-variable relationships, thereby completely detecting the underlying dependence structure. Properties of the proposed index satisfy the mathematical definition of a measure. Finally, simulations and real data examples illustrate the applicability of the proposed method.