ROC curves with multiple marker measurements

Properties of receiver operating characteristic (ROC) curves are explored for markers that are measured repeatedly, through space or time, for each subject. The true underlying response, positive or negative, of each subject is assumed to be constant across marker measurements, and is determined from assessment of some "gold standard." A marker-based test is considered positive when at least one of a subject's marker values exceeds a designated cutoff. If subjects with positive and negative underlying responses differ in the number of marker measurements per subject, the ROC curve for a noninformative marker is bowed above or below the diagonal line representing the "null" curve for a marker that is measured just once per subject. If subjects with negative responses tend to have more measurements than those with positive responses, the ROC curve for even an informative marker may lie beneath the curve for the same marker measured once per subject. The form of the ROC curve for a marker used in this way is strongly influenced by the strength of the correlation of measurements within subjects.