Binary isotonic regression procedures, with application to cancer biomarkers
There is a lot of interest in the development and characterization of new biomarkers for screening large populations for disease. In much of the literature on diagnostic testing, increased levels of a biomarker correlate with increased disease risk. However, parametric forms are typically used to associate these quantities. In this article, we specify a monotonic relationship between biomarker levels with disease risk. This leads to consideration of a nonparametric regression model for a single biomarker. Estimation results using isotonic regression-type estimators and asymptotic results are given. We also discuss confidence set estimation in this setting and propose three procedures for computing confidence intervals. Methods for estimating the receiver operating characteristic (ROC) curve are also described. The finite-sample properties of the proposed methods are assessed using simulation studies and applied to data from a pancreatic cancer biomarker study.
Debashis Ghosh, Moulinath Banerjee, and Pinaki Biswas. 2004. "Binary isotonic regression procedures, with application to cancer biomarkers" The University of Michigan Department of Biostatistics Working Paper Series
Available at: http://works.bepress.com/debashis_ghosh/18