Correlation Improves Group Testing

Population-wide screening to identify and isolate infectious individuals is a powerful tool for controlling COVID-19 and other infectious diseases. Testing an entire population, however, requires significant resources. Group testing can enable large-scale screening, but dilution degrades its sensitivity, reducing its effectiveness as an infection control measure. Analysis of this tradeoff typically assumes pooled samples are independent. Building on recent empirical results in the literature, we argue that this assumption significantly underestimates group testing's true benefits. Indeed, placing samples from a social group into the same pool correlates a pool's samples. Hence, a positive pool likely contains multiple positive samples, increasing a pooled test's sensitivity and also tending to reduce the number of pools requiring follow-up testing. We prove that under a general correlation structure, pooling correlated samples together (called correlated pooling) achieves higher sensitivity and requires fewer tests per positive identified compared to independently pooling the samples (called naive pooling) using the same pool size within the classic two-stage Dorfman procedure. To the best of our knowledge, our work is the first to theoretically characterize correlation's effect on sensitivity and test usage under models of general correlation structure and realistic test errors. Under a 1% starting prevalence, simulation results estimate that correlated pooling requires 12.9% fewer tests than naive pooling to achieve infection control. Thus, we argue that correlation is an important consideration for policy-makers designing infection control interventions: it makes screening more attractive for infection control and it suggests that sample collection should maximize correlation.