Confidence bounds when the estimated ROC area is 1.0

Rationale and Objectives. In studies with small samples, the authors often encounter data sets in which the estimated area under the receiver operating characteristic (ROC) curve is 1.0. In such cases, neither asymptotic nor resampling methods provide a means of estimating the standard error or constructing a lower confidence bound. The purpose of this study was to develop tables for determining the approximate 95% lower confidence bound when the estimated ROC area is 1.0. Materials and Methods. Using Monte Carlo simulation. the authors generated 10.000 data sets for each specification of sample sizes, ROC curve shape. and data format (continuous and ordinal scale). For each of these combinations the authors determined the 95% lower confidence bound. Results. When the estimated ROC area is 1.0, the 95% lower confidence bounds differ dramatically depending on the shape of the ROC curve and on whether the test results are ordinal or continuous. Four tables of 95% lower confidence bounds are provided, along with guidelines for their use. Conclusion. Given the different shapes of ROC curves and the different formats in which ROC data are collected, it is not feasible to offer one simple method of constructing confidence bounds that works for all ROC curves. The tables provided in this article are useful for interpreting studies with estimated ROC areas of 1.0.