  The accuracy of a diagnostic test is typically characterised using the
receiver operating characteristic (ROC) curve. Summarising indexes such as the
area under the ROC curve (AUC) are used to compare different tests as well as
to measure the difference between two populations. Often additional information
is available on some of the covariates which are known to influence the
accuracy of such measures. We propose nonparametric methods for covariate
adjustment of the AUC. Models with normal errors and non-normal errors are
discussed and analysed separately. Nonparametric regression is used for
estimating mean and variance functions in both scenarios. In the general noise
case we propose a covariate-adjusted Mann-Whitney estimator for AUC estimation
which effectively uses available data to construct working samples at any
covariate value of interest and is computationally efficient for
implementation. This provides a generalisation of the Mann-Whitney approach for
comparing two populations by taking covariate effects into account. We derive
asymptotic properties for the AUC estimators in both settings, including
asymptotic normality, optimal strong uniform convergence rates and MSE
consistency. The usefulness of the proposed methods is demonstrated through
simulated and real data examples.
