ROC curve analysis and medical decision making: what’s the evidence that matters for evidence-based diagnosis ? Piergiorgio Duca Biometria e Statistica Medica – Dipartimento di Scienze Cliniche Luigi Sacco – Università degli Studi – Via GB Grassi 74 – 20157 MILANO (ITALY)
[email protected] 1) The ROC (Receiver Operating Characteristic) curve and the Area Under the Curve (AUC) The ROC curve is the statistical tool used to analyse the accuracy of a diagnostic test with multiple cut-off points. The test could be based on a continuous diagnostic indicant, such as a serum enzyme level, or just on an ordinal one, such as a classification based on radiological imaging. The ROC curve is based on the probability density distributions, in actually diseased and non diseased patients, of the diagnostician’s confidence in a positive diagnosis, and upon a set of cut-off points to separate “positive” and “negative” test results (Egan, 1968; Bamber, 1975; Swets, Pickett, 1982; Metz, 1986; Zhou et al, 2002). The Sensitivity (SE) – the proportion of diseased turned out to be test positive – and the Specificity (SP) – the proportion of non diseased turned out to be test negative – will depend on the particular confidence threshold the observer applies to partition the continuously distributed perceptions of evidence into positive and negative test results. The ROC curve is the plot of all the pairs of True Positive Rates (TPR = SE), as ordinate, and False Positive Rates (FPR = (1 – SP)), as abscissa, related to all the possible cut-off points. An ROC curve represents all of the compromises between SE and SP can be achieved, changing the confidence threshold.