Doubly robust nonparametric estimators of the predictive value of covariates for survival data

The predictive value of a covariate is often of interest in studies with a survival endpoint. A common situation is that there are some well established predictors and a potential valuable new marker. The challenge is how to judge the potentially added predictive value of this new marker. We propose to use the positive predictive value (PPV) curve based on a nonparametric scoring rule. The estimand of interest is viewed as a single transformation of the underlying data generating probability measure, which allows us to develop a robust nonparametric estimator of the PPV by first calculating the corresponding efficient influence function. We provide asymptotic results and illustrate the approach with numerical studies and with 2 cancer data studies.