A Parametric ROC Model‐Based Approach for Evaluating the Predictiveness of Continuous Markers in Case–Control Studies

Summary 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 stratifying the population according to risk. 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, which are far more common in practice. We investigate the relationship between the ROC curve and the predictiveness curve. Insights about their relationship provide alternative ROC interpretations for the predictiveness curve and for a previously proposed summary index of it. Next the relationship motivates ROC based methods for estimating the predictiveness curve. An important advantage of these methods over previously proposed methods is that they are rank invariant. In addition they provide a way of combining information across populations that have similar ROC curves but varying prevalence of the outcome. We apply the methods to prostate‐specific antigen (PSA), a marker for predicting risk of prostate cancer.