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Biostatistics Advance Access originally published online on August 11, 2006
Biostatistics 2007 8(2):402-413; doi:10.1093/biostatistics/kxl018
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© The Author 2006. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Incorporating monotonicity into the evaluation of a biomarker

Debashis Ghosh*

Department of Biostatistics, University of Michigan, 1420 Washington Heights Ann Arbor, Michigan 48105, USA ghoshd{at}umich.edu

* To whom correspondence should be addressed.

In the assessment of clinical utility of biomarkers, case–control studies are often undertaken based on existing serum samples. A common assumption made in these studies is that higher levels of the biomarker are associated with increased disease risk. In this article, we consider methods of analysis in which monotonicity is incorporated in associating the biomarker and the clinical outcome. We consider the roles of discrimination versus association and assess methods for both goals. In addition, we propose a semiparametric isotonic regression model for binary data and describe a simple estimation procedure as well as attendant inferential procedures. We apply the various methodologies to data from a prostate cancer study involving a serum biomarker.

Keywords: Generalized linear model; Mixed model; Monotone regression; Pooled adjacent violators algorithm; Smoothing spline

Received August 12, 2005; revised February 2, 2006; revised July 9, 2006; revised August 1, 2006; accepted for publication August 9, 2006.


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