Probabilistic analysis of global performances of diagnostic tests: interpreting the Lorenz curve-based summary measures

Several indices based on the receiver operating characteristic curve (ROC curve) have previously been found to possess probabilistic interpretations. However, these interpretations are based on some unrealistic diagnostic scenarios. In this paper, the author presents a new approach using the Lorenz curve. The author found that the summary indices of the Lorenz curve, that is, the Pietra index and the Gini index, can be interpreted in several ways ('average change in post-test probability', 'per cent maximum prognostic information', and 'probability of correct diagnosis'). These interpretations have a close tie with real-world medical diagnosis, suggesting that these indices are proper measures of test characteristics.