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：病原体感染每年影响全球数百万人，给世界各地的医疗系统带来了巨大挑战，对全球健康构成重大威胁。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。混合检测是一种在疾病流行率较低时筛查大规模人群、减少检测次数的经典方法，但它未能充分利用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，我们提出了一种新的自适应半定量混合检测（SQGT）方案，通过两阶段qPCR检测高效筛查人群。SQGT方法将循环阈值（$Ct$）量化为多个分箱，利用第一轮筛查的信息提高检测灵敏度。通过动态调整$Ct$阈值，减轻稀释效应并提升检测准确性。与传统的二元结果混合检测方法相比，SQGT在保持极低假阴性率的同时，将检测次数减少了$24$%。