Two‐Step Error‐Controlling Classifiers With Application to Cost‐Effective Disease Diagnosis

Accurate classifiers that use novel biomarkers and readily available predictors significantly enhance decision-making in various clinical scenarios, such as assessing the need for biopsies in cancer diagnosis. When classification performance is limited, a decision framework can be applied to rule in or rule out invasive diagnostic procedures while incorporating a neutral zone for indeterminate classifications. Building on this framework, we propose a new family of two-step classifiers that selectively use costly biomarker testing for a targeted subset of individuals undergoing multiple evaluations. The optimal solution expands upon the Neyman-Pearson Lemma, highlighting a vital trade-off between the costs of expensive biomarker measurements and improving classification performance while minimizing uncertainty in the decision process. We demonstrate the practical utility of our approach through a biomarker study focused on prostate cancer diagnosis.