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Population-wide screening to identify and isolate infectious individuals is apowerful tool for controlling COVID-19 and other infectious diseases. Grouptesting can enable such screening despite limited testing resources. Samples'viral loads are often positively correlated, either because prevalence andsample collection are both correlated with geography, or through intentionalenhancement, e.g., by pooling samples from people in similar risk groups. Suchcorrelation is known to improve test efficiency in mathematical models withfixed sensitivity. In reality, however, dilution degrades a pooled test'ssensitivity by an amount that varies with the number of positives in the pool.In the presence of this dilution effect, we study the impact of correlation onthe most widely-used group testing procedure, the Dorfman procedure. We showthat correlation's effects are significantly altered by the dilution effect. Weprove that under a general correlation structure, pooling correlated samplestogether (called correlated pooling) achieves higher sensitivity but candegrade test efficiency compared to independently pooling the samples (callednaive pooling) using the same pool size. We identify an alternative measure oftest resource usage, the number of positives found per test consumed, which weargue is better aligned with infection control, and show that correlatedpooling outperforms naive pooling on this measure. We build a realisticagent-based simulation to contextualize our theoretical results within anepidemic control framework. We argue that the dilution effect makes it evenmore important for policy-makers evaluating group testing protocols forlarge-scale screening to incorporate naturally arising correlation and tointentionally maximize correlation.

Correlation Improves Group Testing: Capturing the Dilution Effect