The effect of random measurement error on receiver operating characteristic (ROC) curves

In this paper confidence intervals for the area under the ROC curve are adjusted for the presence of measurement error. A parametric normal model is assumed. The ratio of intra-individual to inter-individual variance provides a relative measure of the amount of measurement error. An exact adjusted confidence interval is developed for the equal variance case and an approximation is derived for the unequal variance case. We illustrate, using an example, the effect of ignoring the measurement error on the confidence interval for the area and show that the effect can be substantial on the decision as to the diagnostic effectiveness of the marker. We also examine, by means of a simulation study, the coverage probability of the unadjusted confidence interval and show that it can be far from its nominal value when measurement error is present.