Receiver operating characteristic curve analysis of clinical risk models

Receiver operating characteristic (ROC) curve analysis is a useful method to measure the ability of a clinical risk model to discriminate between hospital deaths and survivors. Its use in medicine originated as a method for synthesizing the specificity and sensitivity of diagnostic tests across a spectrum of possible cut points. The area under the ROC curve can be interpreted as a probability of correct classification or prediction. We illustrate its use in three steps: first, with a dichotomous variable to introduce specificity and sensitivity; next, with a categorical risk factor (surgical urgency) to produce a primitive ROC curve; and finally, with a continuous risk factor (age) to approximate the usual ROC curve used for clinical risk models.