Semiparametic models and estimation procedures for binormal ROC curves with multiple biomarkers

In diagnostic medicine, there is great interest in developing strategies for combining biomarkers in order to optimize classification accuracy. A popular model that has been used for receiver operating characteristic (ROC) curve modelling when one biomarker is available is the binormal model. Extension of the model to accommodate multiple biomarkers has not been considered in this literature. Here, we consider a multivariate binormal framework for combining biomarkers using copula functions that leads to a natural multivariate extension of the binormal model. Estimation in this model will be done using rank-based procedures. We show that the Van der Waerden rank score coefficient estimation procedure can be used for the multivariate binormal model. We also discuss adjustment for covariates in this class of models. We provide a simple two-stage estimation procedure that can be fit using standard software packages. Asymptotic results of the proposed methods are given. The techniques are applied to data from two cancer biomarker studies.