Sense and sensitivity--designing surveys based on an imperfect test.

Designing a survey to detect the presence of a disease is complicated if the test used to detect the disease has non-perfect sensitivity and specificity. This paper gives two new approximations that simplify such a task. The first gives the cumulative probability distribution of the number of apparently diseased animals detected in the survey and the second gives the probability that no diseased animals are detected if the test used has 100% specificity. Both approximations can be used to determine confidence limits for the true prevalence. The main purpose of the approximations is to determine the number of animals that need to be tested to be confident that a herd is free of disease, and then to determine the number of herds that need to be tested to demonstrate area freedom. One approach to such an area survey has been to classify each herd as diseased or not based on the number of reactors found in the herd, and then to use the number of herds classified as diseased to determine the area's status. The paper points out that basing the decision simply on the magnitude of the maximum observed within-herd reactor proportion results in a more accurate survey for the same number of animals and herds tested.