Inferring leakage in imports of frozen seafood allowing for censoring, testing accuracy and a minimum positive prevalence.

Many countries screen import consignments to guard against the entry of exotic pests, contaminants, and pathogens. A widely used strategy is to pool individual units into groups and test each group for presence or absence of contamination. Consignments are typically rejected if there are any detections. Screening samples are commonly designed to give a high chance of detection assuming a design prevalence. What is less common, however, is to analyze the history of testing outcomes to infer how many accepted consignments contain contaminated units, and the number of contaminated units-jointly referred to as "leakage." We build on existing censored beta-binomial models to answer these questions for the importation of frozen seafood into Australia, allowing for unknown test sensitivity and specificity. We present new theory and empirical results demonstrating that specificity is identifiable from test data in this context, but sensitivity is not. We also develop a new class of models in which consignment propensity is either zero or above a minimum positive prevalence threshold, motivated by our case study but applicable more widely. Past testing data are modeled under multiple scenarios using both hierarchical Bayes and maximum likelihood methods, revealing new insights into the risk of leakage.