Population-wide screening is a powerful tool for controlling infectious diseases. Group testing enables such screening despite limited resources. Viral concentration of pooled samples are often positively correlated, either because prevalence and sample collection are influenced by location, or through intentional enhancement via pooling samples according to risk/household. Such correlation is known to improve efficiency under fixed test sensitivity. However, in reality, a test's sensitivity depends on the concentration of the analyte (e.g., viral RNA), as in the so-called dilution effect, where sensitivity decreases for larger pools. We show that concentration-dependent test error alters correlation's effect under the most widely-used group testing procedure, the two-stage Dorfman procedure. We prove that when test sensitivity increases with concentration, pooling correlated samples together (correlated pooling) achieves asymptotically higher sensitivity than independently pooling the samples (naive pooling). In contrast, in the concentration-independent case, correlation does not affect sensitivity. Moreover, with concentration-dependent errors, correlation can degrade test efficiency compared to naive pooling whereas under concentration-independent errors, correlation always improves efficiency. We propose an alternative measure of test resource usage, the number of positives found per test consumed, which we argue is better aligned with infection control, and show that correlated pooling outperforms naive pooling on this measure. In simulation, we show that the effect of correlation under realistic concentration-dependent test error meaningfully differs from correlation's effect assuming fixed sensitivity. Our findings underscore the importance for policy-makers of using models that incorporate naturally-occurring correlation and of considering ways of strengthening this correlation.

翻译：大规模人群筛查是控制传染病的有效手段。群体检测使得在资源有限的情况下仍能实施此类筛查。混合样本的病毒浓度通常呈正相关，这既可能源于地理位置对感染率与样本采集的影响，也可能通过按风险/家庭分组样本的有意增强策略实现。已知在固定检测灵敏度条件下，此类相关性可提升检测效率。然而现实中，检测灵敏度取决于分析物浓度（如病毒RNA），即存在所谓的稀释效应——混合样本规模增大时灵敏度降低。我们证明，在最广泛使用的两阶段Dorfman群体检测流程中，浓度依赖性检测误差会改变相关性的作用机制。我们严格论证：当检测灵敏度随浓度升高而增加时，将相关样本集中混合检测（相关混合法）能获得渐近高于独立样本混合检测（朴素混合法）的灵敏度。相比之下，在浓度无关的场景中，相关性不影响灵敏度。此外，在浓度依赖性误差条件下，相关性可能降低检测效率；而在浓度无关误差条件下，相关性始终提升效率。我们提出一种新的检测资源利用率度量指标——单位消耗检测数对应的阳性检出量，并论证该指标更符合传染病控制需求，同时证明相关混合法在此指标上优于朴素混合法。通过仿真实验，我们揭示在现实浓度依赖性检测误差下相关性的作用效果，与固定灵敏度假设下的作用模式存在显著差异。本研究结论强调：政策制定者需采用包含自然相关性的检测模型，并探索增强相关性的可行路径。