Pathogenic infections pose a significant threat to global health, affecting millions of people every year and presenting substantial challenges to healthcare systems worldwide. Efficient and timely testing plays a critical role in disease control and transmission prevention. Group testing is a well-established method for reducing the number of tests needed to screen large populations when the disease prevalence is low. However, it does not fully utilize the quantitative information provided by qPCR methods, nor is it able to accommodate a wide range of pathogen loads. To address these issues, we introduce a novel adaptive semi-quantitative group testing (SQGT) scheme to efficiently screen populations via two-stage qPCR testing. The SQGT method quantizes cycle threshold ($Ct$) values into multiple bins, leveraging the information from the first stage of screening to improve the detection sensitivity. Dynamic $Ct$ threshold adjustments mitigate dilution effects and enhance test accuracy. Comparisons with traditional binary outcome GT methods show that SQGT reduces the number of tests by $24$% while maintaining a negligible false negative rate.

翻译：病原体感染对全球健康构成重大威胁，每年影响数百万人，给世界各国的医疗系统带来巨大挑战。高效及时的检测在疾病控制和传播预防中发挥着关键作用。分组检测是一种在疾病流行率较低时减少大规模人群筛查所需检测次数的成熟方法。然而，该方法未能充分利用qPCR方法提供的定量信息，也无法适应宽范围的病原体载量。为解决这些问题，我们提出了一种新型自适应半定量分组检测（SQGT）方案，通过两阶段qPCR检测实现高效人群筛查。SQGT方法将循环阈值（$Ct$值）量化为多个区间，利用第一阶段筛查信息提高检测灵敏度。动态$Ct$阈值调整可减轻稀释效应并提升检测准确性。与传统二元结果GT方法相比，SQGT在保持可忽略的假阴性率的同时，将检测次数减少了$24$%。