  Population-wide screening to identify and isolate infectious individuals is a
powerful tool for controlling COVID-19 and other infectious diseases. Group
testing can enable such screening despite limited testing resources. Samples'
viral loads are often positively correlated, either because prevalence and
sample collection are both correlated with geography, or through intentional
enhancement, e.g., by pooling samples from people in similar risk groups. Such
correlation is known to improve test efficiency in mathematical models with
fixed sensitivity. In reality, however, dilution degrades a pooled test's
sensitivity 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 on
the most widely-used group testing procedure, the Dorfman procedure. We show
that correlation's effects are significantly altered by the dilution effect. We
prove that under a general correlation structure, pooling correlated samples
together (called correlated pooling) achieves higher sensitivity but can
degrade test efficiency compared to independently pooling the samples (called
naive pooling) using the same pool size. We identify 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. We build a realistic
agent-based simulation to contextualize our theoretical results within an
epidemic control framework. We argue that the dilution effect makes it even
more important for policy-makers evaluating group testing protocols for
large-scale screening to incorporate naturally arising correlation and to
intentionally maximize correlation.
