The predictiveness curve shows the population distribution of risk endowed by a marker or risk prediction model. It provides a means for assessing the model's capacity for risk stratification. Methods for making inference about the predictiveness curve have been developed using cross-sectional or cohort data. Here we consider inference based on case-control studies and prior knowledge about prevalence or incidence of the outcome. We exploit the relationship between the ROC curve and the predictiveness curve given disease prevalence. Methods are developed for deriving the predictiveness curve from a parametric ROC model. Estimation of the whole range and of a portion of the curve are both investigated. We apply the methods to prostate cancer data, comparing PSA and PSA velocity as markers for predicting risk of prostate cancer.
Huang, Ying and Pepe, Margaret, "A Parametric ROC Model Based Approach for Evaluating the Predictiveness of Continuous Markers in Case-control Studies" (November 2007). UW Biostatistics Working Paper Series. Working Paper 318.