Cut-off points for aggregate herd testing in the presence of disease clustering and correlation of test errors

In order to test if disease is present in a large herd, an investigator will often subject only a small sample of animals to a fallible diagnostic test. The herd is declared positive for disease if the number of test-positive animals is greater than or equal to a previously chosen cut-off value. Such a test, called an aggregate test, has a sensitivity and specificity that depends on the sample size, the cut-off point and the sensitivity and specificity of the individual test. It also depends on the distribution of the disease among the herds being tested and on the fact that factors such as herd-level seropositivity may cause some herds to be more prone to testing errors than others. In this paper, the beta-binomial distribution is used to model all these factors and thereby calculate the tabulate aggregate test sensitivities and specificities under a variety of conditions. Receiver operating characteristic (ROC) curve methodology permits the choice of optimum sample sizes and cut-off values. The situation in which an investigator may be willing to miss detecting the disease if the prevalance in the herd is low is also examined. A compiled FORTRAN program for the calculation of aggregate test cut-off point properties, including positive and negative predictive values, is available from the authors.