Correlation Improves Group Testing: Modeling Concentration-Dependent Test Errors

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.