Selected topics in two and three class ROC analysis
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In traditional ROC analysis, a biomarker is used to discriminate between only two classes: healthy and disease. There is extensive literature on measuring the discriminatory ability of a biomarker and for selecting a diagnostic cut-point in this setting. However, in practice there exist disease processes with three or more classes. For example, in Alzheimer's disease (AD) there is an intermediate stage between healthy patients and those with dementia. While there is extensive literature on overall summary measures for this ordinal three-class setting, there is virtually none on cut-point selection. In this work I propose two new selection methods that provide diagnostic cut-points with low variability and balanced classification rates, while sacrificing little in terms of overall accuracy. The three-classes of disease process are not always ordinal in progression, as was the case of the AD example. For instance, in lung cancer it is essential to identify biomarkers that can discriminate healthy patients from two disease classes (squamous cell and large cell carcinoma). This example refers to umbrella ordering, for which limited literature is presented on the topic and naïve approaches are often used in practice. I propose a ROC framework for summarizing the discriminatory ability of a biomarker under umbrella ordering, while also proposing methods for obtaining diagnostic cut-points and estimating the sensitivity given a fixed specificity. These methods are then applied to an existing lung cancer dataset. Returning to the two-class setting, there is extensive literature on combining multiple markers for improving diagnostic accuracy. However, there has been little focus on how to measure the incremental improvement associated with additional biomarkers, and how to select the diagnostic cut-points for the combined biomarkers. I also propose methods based on generalized inference and bootstrapping to address these issues. The proposed methods are applied to a Duchenne Muscular Dystrophy (DMD) dataset.