Semi-parametric ROC regression analysis with placement values

Abstract

Advances in technology provide new diagnostic tests for early detection of disease. Frequently, these tests have continuous outcomes. One popular method to summarize the accuracy of such a test is the Receiver Operating Characteristic (ROC) curve. Methods for estimating ROC curves have long been available. To examine covariate effects, Pepe (1997, 2000) and Alonzo and Pepe (2002) proposed distribution-free approaches based on a parametric regression model for the ROC curve. Cai and Pepe (2002) extended the parametric ROC regression model by allowing an arbitrary non-parametric baseline function. In this paper, while we follow the same semi-parametric setting as in that paper, we highlight a new estimator that offers several improvements over the earlier work: superior efficiency, the ability to estimate the covariate effects without estimating the non-parametric baseline function and easy implementation with standard software. The methodology is applied to a case control dataset where we evaluate the accuracy of the prostate-specific antigen as a biomarker for early detection of prostate cancer. Simulation studies suggest that the new estimator under the semi-parametric model, while always being more robust, has efficiency that is comparable to or better than the Alonzo and Pepe (2002) estimator from the parametric model.