Estimation and Inference of Contamination using Group Testing

Codes and shiny app for the "Estimation and Inference of Contamination using Group Testing" paper. Group-testing of units is an important element of biosecurity management of imported agricultural products. A number of 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 pathogen is high, assuming random mixing and a somewhat arbitrary design prevalence. We propose supplementing this operating characteristics approach with an assessment of the distribution of the number of contaminated items conditional on testing results from a population. We develop beta-binomial models allowing for between-consignment variability in contamination levels, with a further layer of nesting to allow for possible clustering within the groups for testing. We clarify the relationships between a number of alternative models that have been proposed, showing that in some cases, a binomial model is equivalent to a less tractable hypergeometric model even for small populations. The latent beta distributions can be considered as priors and chosen based on expert judgement, or estimated from historical test results. We demonstrate by simulation that estimation and inference of our models is feasible, except for the parameter controlling clustering within groups, which cannot be directly estimated and must be handled by sensitivity analysis. We apply the approach to large cucurbit seed lots imported into Australia, where it provides important new insights