The performance of a well calibrated risk model, Risk(Y)=P(D=1|Y), can be characterized by the population distribution of Risk(Y) and displayed with the predictiveness curve. Better performance is characterized by a wider distribution of Risk(Y), since this corresponds to better risk stratification in the sense that more subjects are identified at low and high risk for the outcome D=1. Although methods have been developed to estimate predictiveness curves from cohort studies, most studies to evaluate novel risk prediction markers employ case-control designs. Here we develop semiparametric and nonparametric methods that accommodate case-control data and assume apriori knowledge of P(D=1). Large and small sample properties are investigated. The semiparametric methods are flexible, substantially more efficient than the nonparametric counterparts and naturally generalize methods previously developed for cohort data. Applications to prostate cancer risk prediction markers illustrate the methods.
Huang, Ying and Pepe, Margaret, "Semiparametric and nonparametric methods for evaluating risk prediction markers in case-control studies" (July 2008). UW Biostatistics Working Paper Series. Working Paper 333.