Estimation of the volume under a ROC surface in presence of covariates

A new method to adjust for covariate effects in the estimation of volume under a ROC surface (VUS) is presented. The method is based on the induced-regression methodology, which uses location-scale regression models to explain the relation between the test results and the covariate(s). For the estimation of the models, it is proposed to use a semiparametric generalized estimating equations (GEE) approach if the parametric forms of the mean and variance functions are specified. Alternatively, a nonparametric method is proposed, based on local linear regression (LL). In order to estimate the covariate-specific VUS, a covariate-specific Mann-Whitney representation of VUS is used, and working samples constructed after fitting the location-scale models by the GEE or LL approach. This leads to new MW-GEE and MW-LL covariate-specific VUS estimators. The asymptotic behaviour of the new estimators is investigated. More precisely, their mean squared consistency is proved. Moreover, the performance of the estimators in finite samples is explored through several simulation experiments, and an illustration, based on data from the Alzheimer's Disease Neuroimaging Initiative, is provided.