Evaluating the predictiveness of a continuous marker

Consider a continuous marker for predicting a binary outcome. For example, the serum concentration of prostate specific antigen may be used to calculate the risk of finding prostate cancer in a biopsy. In this article, we argue that the predictive capacity of a marker has to do with the population distribution of risk given the marker and suggest a graphical tool, the predictiveness curve, that displays this distribution. The display provides a common meaningful scale for comparing markers that may not be comparable on their original scales. Some existing measures of predictiveness are shown to be summary indices derived from the predictiveness curve. We develop methods for making inference about the predictiveness curve, for making pointwise comparisons between two curves, and for evaluating covariate effects. Applications to risk prediction markers in cancer and cystic fibrosis are discussed.