Optimizing Sequential Decision Rules for Prostate Cancer Biopsy Management: A Multi-Objective Statistical Framework

Binary medical decision-making increasingly demands sequential diagnostic strategies that optimize accuracy while minimizing patient burden and healthcare costs. In prostate cancer diagnosis, many patients undergo unnecessary biopsies despite existing biomarkers and imaging tests that already inform risk stratification. Sequential testing, where tests are selectively administered based on prior results, offers a promising approach to balance diagnostic power with procedural efficiency. We propose a novel framework for deriving optimal sequential decision rules using a multi-objective optimization perspective. Specifically, we aim to (1) minimize unnecessary invasive procedures while maintaining sensitivity to underlying disease, and (2) reduce procedural costs by limiting the number of subsequent tests. Rather than collapsing multiple goals into a single weighted score, which forces subjective choices about trade-off weights, we optimize one target while requiring the others to meet prespecified standards. This constrained formulation can be solved efficiently using Lagrange multipliers, yielding a family of optimal sequential rules and a trade-off curve that summarizes the best achievable balance among sensitivity, specificity, and testing burden for clinical protocol design. In the prostate cancer diagnostic data with biomarker and imaging measurements and biopsy-confirmed outcomes, the sequential strategies identify testing pathways that reduce unnecessary procedures while preserving diagnostic quality.