Clustered and Unclustered Group Testing for Biosecurity

Group testing is an important element of biosecurity operations, designed to efficiently reduce the risk of introducing exotic pests and pathogens with imported agricultural products. Groups of units, such as seeds, are selected from a consignment and tested for contamination, with a positive or negative test returned for each group. These schemes are usually designed such that the probability of detecting contamination is high assuming random mixing and a somewhat arbitrary design prevalence. We propose supplementing this approach with an assessment of the distribution of the number of contaminated units conditional on testing results. We develop beta-binomial models that allow for between-consignment variability in contamination levels, as well as including beta random effects to allow for possible clustering within the groups for testing. The latent beta distributions can be considered as priors and chosen based on expert judgement, or estimated from historical test results. We show that the parameter representing within-group clustering is, unsurprisingly, effectively non-identifiable. Sensitivity analysis can be conducted by investigating the consequences of assuming different values of this parameter. We also demonstrate theoretically and empirically that the estimated probability of a consignment containing contamination and evading detection is almost perfectly robust to mis-specification of the clustering parameter. We apply the new models to large cucurbit seed lots imported into Australia where they provide important new insights on the level of undetected contamination. Supplementary materials accompanying this paper appear on-line.