Multivariate ROC curve models that include an interaction term be- tween biomarker type and false positive rate is important in comparative biomarker studies, because such interaction allows ROC curves of different biomarkers to cross each other. However, there has been limited work in drawing inference for comparing multivariate ROC curves, especially when the interaction terms are present. In this article we derive the asymptotic covariance of three estimators for multivariate ROC models. These covariance estimates have not been readily available in the literature, and bootstrap methods have to be used to obtain co- variance estimates. With the readily available variance estimates, we can easily perform hypothesis testing among ROC curves while bootstrap tests are not so easily performed. The asymptotic results are applied to compare ROC curves and their areas under ROC curves. Moreover, we derive simultaneous confidence bands for multivariate ROC curves. We evaluate and compare the finite sample performance of our asymptotic covariance estimators. We also discuss the ad- vantage of using our asymptotic results over bootstrap procedures. Finally, we illustrate our approach through a well-known pancreatic cancer study.



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