Incorporating monotonicity into the evaluation of a biomarker

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.