On the surveillance for animal diseases in small herds

Small herds may present a problem in surveillance for infectious animal diseases because typical levels of a within-herd design prevalence are not directly applicable. We suggest a definition of small herds as those smaller than 2/(within-herd design prevalence) on the basis that such herds would be expected to have less than two (i.e. only one) infected animals. Consequently, the probability of detecting small herds cannot be improved by choosing a larger sample size within the herd. We derive necessary sample sizes of herds and the probability ("confidence") of detecting disease within a stratum of small herds, given the among-herd design prevalence and test diagnostic sensitivity. Both a binomial model and a Poisson model can be used to establish the confidence for a given sample size of herds (and vice versa). The results of a simulation study suggest that the Poisson model provides more conservative (lower) estimates of the confidence for a given sample size and should therefore be preferred.