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

- 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.
- 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.
- The formula in Table 1 item 4, and Equation 4, are labelled on the left hand side as the simple partial C statistic (simple c
_{Δ}), however on the right hand side the two factors 1/(2JN) and 1/(2PK) normalize the expression, so it defines the normalized version simple c̃_{Δ}, not simple c_{Δ}. 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.

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

# Clarifications:

- 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(x
_{2}-x_{1})] and 1/[2(y_{2}-y_{1})], respectively instead.