Analysis of sampling strategies to substantiate freedom from disease in large areas

In this paper, we deal with the strategies of surveys to substantiate freedom from disease for a certain territory. Infection might not be distributed homogeneously. So, a relatively high within-herd prevalence might be observed while the herd-level prevalence is lower. For this situation, we compare various two-stage sample strategies. The calculation of appropriate sample sizes becomes quite complicated. The theoretical generalization of the hypergeometric distribution by Cameron and Baldock [Prev. Vet. Med. 24 (1998) 1] introduces a simple way to evaluate multi-stage sample sizes while regarding real-test properties. We demonstrate the theoretical foundations of these calculations. These principles open up the possibility of optimizing costs or other relevant variables, by choosing the appropriate sample strategy (each of which ensures the same alpha-level for the first stage). In addition, we evaluate the statistical power of the complete strategies under consideration. Furthermore, we apply our theoretical results to a data example of Brucella melitensis. We used the herd-size situation in Germany, characterized by many small sheep holdings and only a few large ones. The consequences of real-test properties on sample sizes and on the applicability of several strategies are discussed.