PROC HPLOGISTIC is run for a binary fraud classification. The output shows concordance = 0.83, discordance = 0.14, and ties = 0.03. How is the c-statistic (AUC) computed from these values?
Select an answer to reveal the explanation.
Short Explanation
Here's the deal — you compute the c-statistic by taking concordance and adding half of the tied pairs: 0.83 + 0.5(0.03) = 0.845. Tied pairs are split evenly between concordant and discordant, so you multiply them by 0.5.
Full Explanation
The c-statistic (Harrell's C or AUC) from concordance statistics is computed as c = concordance + 0.5 * ties = 0.83 + 0.5(0.03) = 0.845. Tied pairs are split equally between concordant and discordant, hence the 0.5 multiplier. The option that sets the c-statistic equal to concordance alone is wrong because ties are included in the c-statistic. The option that uses (concordance - discordance) divided by the sum of concordance, discordance, and ties describes Somers' D (Gini coefficient). The option that computes concordance - discordance = 0.83 - 0.14 = 0.69 is also a form of Somers' D.