Receiver operating characteristic studies and measurement errors

A receiver operating characteristic (ROC) curve expresses the probability of a true positive (PTP) as a function of the probability of a false positive (PFP) for all possible values of the cutoff between cases and controls. 0, the area under the ROC curve, is a measure of the diagnostic ability of the separator variable. The usual nonparametric estimate of 0 is shown to be biased when the separator is measured with error. An expression for the largest-order term of the bias is found. The observed values and the measurement error variance are used to form a kernel estimate of the underlying distribution. These kernel estimates are used to estimate the bias. Monte Carlo simulation indicates that, for several families of distributions, the bias-corrected estimators have much smaller bias and comparable MSE to the usual estimator. An application to the data of Clayton, Moncrieff, and Roberts (1967, British Medical Journal 3, 133-136) illustrates the technique.