The receiver operating characteristic (ROC) curve and in particular the area under the curve (AUC) is commonly used to examine the discriminatory ability of diagnostic markers. Certain markers while basically continuous and non-negative have a positive probability mass (spike) at the value zero. We discuss a flexible modelling approach to such data and contrast it with the standard non-parametric approach. We show how the modelling approach can be extended to take account of the effect of explanatory variables. We motivate this problem and illustrate the modelling approach using data on the coronary calcium score, measured by electron beam tomography, which is a marker for atherosclerosis. Copyright © 2005 John Wiley & Sons, Ltd.