Testing for Dilution Effects in Group Testing

Group testing is widely used to improve screening efficiency in populations with low prevalence, but pooling may reduce assay sensitivity through dilution. Existing statistical work often incorporates this effect as a modeling assumption or design constraint, while the question of whether a dilution effect is present in a specific testing procedure is less often treated as a formal inferential problem. This paper develops a hypothesis testing framework for assessing dilution effects under a binary measurement error model. Dilution is represented by an increase in the group-specific false negative rate as pool size increases, with specificity assumed to remain stable across pool sizes. We derive closed-form estimators and one-sided test statistics for both unknown- and known-prevalence settings, using normal and Poisson approximations together with null-bootstrap critical-value calibration. Simulation studies show that the proposed procedures control type I error reasonably well and gain power as the dilution effect becomes stronger, although detection is more difficult under very low prevalence. Applications to infectious disease screening settings and SARS-CoV-2 pooled NAAT data illustrate how the framework can quantify evidence for reduced sensitivity under pooling.