We study the problem of designing optimal targeted mass screening of non-uniform populations. Mass screening is an essential tool that is widely utilized in a variety of settings, for example, preventing infertility through screening programs for sexually transmitted diseases, ensuring a safe blood supply for transfusion, and mitigating the transmission of infectious diseases. The objective of mass screening is to maximize the overall classification accuracy under limited budget. In this paper, we address this problem by proposing a proactive optimization-based framework that factors in population heterogeneity, limited budget, different testing schemes, the availability of multiple assays, and imperfect assays. By analyzing the resulting optimization problem, we take advantage of the structure of the problem as a multi-dimensional fractional knapsack problem and identify an efficient globally convergent threshold-style solution scheme that fully characterizes an optimal solution across the entire budget spectrum. Using real-world data, we conduct a geographic-based nationwide case study on targeted COVID-19 screening in the United States. Our results reveal that the identified screening strategies substantially outperform conventional practices by significantly lowering misclassifications while utilizing the same amount of budget. Moreover, our results provide valuable managerial insights with regard to the distribution of testing schemes, assays, and budget across different geographic regions.

中文翻译：

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通过多种测试和方案在非均匀人群中进行最佳目标大规模筛查

我们研究设计非均匀人群的最佳目标大规模筛查的问题。大规模筛查是一种重要工具，广泛应用于各种环境，例如，通过性传播疾病筛查计划预防不孕、确保输血的安全血液供应以及减少传染病的传播。大规模筛选的目标是在有限的预算下最大化总体分类精度。在本文中，我们通过提出一个基于主动优化的框架来解决这个问题，该框架考虑了群体异质性、有限的预算、不同的测试方案、多种检测的可用性和不完善的检测。通过分析所产生的优化问题，我们利用问题的结构作为多维分数背包问题，并确定了一种有效的全局收敛阈值式解决方案，该方案充分描述了整个预算范围内的最优解决方案。我们利用真实世界的数据，对美国的有针对性的 COVID-19 筛查进行了一项基于地理的全国性案例研究。我们的结果表明，所确定的筛选策略在利用相同预算的情况下显着降低了错误分类，大大优于传统做法。此外，我们的结果为不同地理区域的测试方案、检测和预算的分配提供了宝贵的管理见解。