Herd-level test performance based on uncertain estimates of individual test performance, individual true prevalence and herd true prevalence.
A generalized model was derived for understanding the performance of herd-testing protocols when there is uncertainty and variability in individual-level sensitivity, specificity, prevalence of infection within infected herds, and prevalence of infected herds in the population. The model uses Monte-Carlo techniques to provide estimates of test performance for a dichotomous classification of herd-disease status. Uncertainty and variability in input assumptions are described using empirical and parametric probability distributions. The model permits both cluster-correlated behavior of inputs and sampling of animals without replacement. Disease due to obligate parasites is modeled differently from that due to organisms that persist for long periods in the environment. Dependence among model outcomes is assessed using Spearman's rank correlation. Model output is suitable for inclusion in risk-assessment models requiring probabilistic estimates of herd-level test performance, such as those developed for food-safety decision making and import-export risk assessment. The model was demonstrated using an example scenario based on Shiga-like toxin (SLT) producing Escherichia coli O157 in Ontario beef-cattle herds. Inputs were derived from the literature and Statistics Canada agricultural census data. Where appropriate, these data were subjected to distribution-fitting techniques. Otherwise, subjective interpretation was used to select input distributions and their parameters. Simulation revealed that the distribution of herd-level sensitivity for detecting herds infected with SLT producing E. coli O157 has a large range (0.003-0.99) and a median of 0.19. Herd-level specificity also had a large range (0.58-1) and a median of 0.94. Distributions of herd-level positive and negative predictive values exhibited similar degrees of uncertainty. In combination with poor likelihood ratios for positive and negative herd tests, results indicate that the testing protocol investigated has limited ability to discriminate between herds infected and not infected with SLT producing E. coli O157.