Errata for: Carrington et al. A new concordant partial AUC and partial C statistic for imbalanced data in the evaluation of machine learning algorithms

  1. In the section, "Concordance: the C statistic": Kendall's coefficient of concordance (the W coefficient per the reference) is incorrectly included in a list of terms equivalent to the C statistic. It also measures agreement (concordance) on the same scale but in a substantively different way, with a different meaning and value.

  2. In Table 3 the ranges for the true positive rate (TPR) are incorrect--they should be the same as Table 2. The table was not updated properly.

  3. The formula in Table 1 item 4, and Equation 4, are labelled on the left hand side as the simple partial C statistic (simple cΔ), however on the right hand side the two factors 1/(2JN) and 1/(2PK) normalize the expression, so it defines the normalized version simple c̃Δ, not simple cΔ. Without normalization both factors are 1/(2NP).

    • Normalization (indicated by a tilde) refers to rescaling to the range [0, 1] for comparison with the C statistic or any other normalized partial C statistic.

  4. Similar to the previous point, Equation 7, is labelled on the left hand side as the partial C statistic (cΔ), however on the right hand side it mistakenly shows the normalized version c̃Δ instead of cΔ. The normalized version has the two fractions shown. Without normalization both factors are 1/(2NP).


  • We focus on the C statistic in the case of binary classification and binary diagnostic testing. We list Harrell's C statistic, or the C-index (by Harrell) as "later defined for regression and survival analysis"--but our paper does not cover this version of the C statistic which has multiple time-dependent ROC plots and AUC values for a single prediction model.

  • We do not show the equation for the normalized concordant partial AUC, but it is a simple alteration to Equation 9: instead of the two factors of 1/2, use the factors 1/[2(x2-x1)] and 1/[2(y2-y1)], respectively instead.