The binormal ROC curve is a widely used statistical tool in diagnostic accuracy and works by assuming normality on test scores from a healthy and a disease population. Lehmann family ROC model provides an attractive alternative to its binormal counterpart, as it is distribution free and focuses on the relation of diseased and healthy scores. It has been shown that the Lehmann family ROC model can be easily fit by a proportional hazards model and covariate effects can be directly assessed on the ROC curve. However, a Lehmann family ROC curve can be restrictive, as it rises quickly at low false positive rate region. We propose to extend the Lehmann family ROC model to overcome this pitfall. We first consider an ROC model based on Lehmann's alternative. We show that this new proposal is equivalent to a proportional reversed hazards model and that it can be fit easily using existing survival analysis software. We further consider a more flexible framework that is a mixture of Lehmann family and Lehmann's alternative. An EM algorithm is developed to carry out the model estimation. We conduct both simulation and real data analysis to illustrate how these extensions work.