An extension and a new interpretation of the rank-based concordance index

In applied research many data sets contain observations from ordinal variables rather than continuous ones. In such situations, the study of dependence relationship among variables represents an interesting issue, since ordinal variables are not specified according to a metric scale. Recently, a novel dependence measure called “Rank-based Concordance Index” (RCI), that can contribute to solve this problem, was introduced. In this paper an extension and a statistical interpretation of this index in terms of dependence relationship between a real-valued dependent variable and a quantitative or ordinal independent one is provided. The adequacy and robustness of RCI in the new context are discussed and validated by a simulation study.