View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Collection Of Biostatistics Research Archive University of Michigan School of Public Health The University of Michigan Department of Biostatistics Working Paper Series Year 2004 Paper 38 Binary isotonic regression procedures, with application to cancer biomarkers Debashis Ghosh∗ Moulinath Banerjeey Pinaki Biswasz ∗University of Michigan, [email protected] yUniversity of Michigan, [email protected] zUniveristy of Michigan, [email protected] This working paper is hosted by The Berkeley Electronic Press (bepress) and may not be commer- cially reproduced without the permission of the copyright holder. http://biostats.bepress.com/umichbiostat/paper38 Copyright c 2004 by the authors. Binary isotonic regression procedures, with application to cancer biomarkers Debashis Ghosh, Moulinath Banerjee, and Pinaki Biswas Abstract There is a lot of interest in the development and characterization of new biomark- ers for screening large populations for disease. In much of the literature on di- agnostic 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. Meth- ods for estimating the receiver operating characteristic (ROC) curve are also de- scribed. 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