  To evaluate a classification algorithm, it is common practice to plot the ROC
curve using test data. However, the inherent randomness in the test data can
undermine our confidence in the conclusions drawn from the ROC curve,
necessitating uncertainty quantification. In this article, we propose an
algorithm to construct confidence bands for the ROC curve, quantifying the
uncertainty of classification on the test data in terms of sensitivity and
specificity. The algorithm is based on a procedure called conformal prediction,
which constructs individualized confidence intervals for the test set and the
confidence bands for the ROC curve can be obtained by combining the
individualized intervals together. Furthermore, we address both scenarios where
the test data are either iid or non-iid relative to the observed data set and
propose distinct algorithms for each case with valid coverage probability. The
proposed method is validated through both theoretical results and numerical
experiments.
