2.1.1.1. Detection of rare events

Epidemiological surveys are often designed to detect (or not detect) relatively rare events in a population. It is often impractical or impossible to prove that a disease or pest organism is not found in a region with 100% certainty. However, a properly designed disease surveillance system can give a set level of confidence that a disease or pest species is not present in a defined population at a predefined prevalence level. These results, by extension, can help to declare a region as free from a particular disease or parasite which may have important implications for policy makers.

In most cases, disease prevalence in individual members (i.e. colonies) will be categorical, that is the disease will either be present or absent (Fosgate, 2009). The number of individuals that would need to be examined (n) in an infinite population (where the number of individuals exceeds 1,000 members) given a minimum disease prevalence (P) is given by equation 2.1.1.1.a (Fosgate, 2009).

Equation 2.1.1.1.a

Where α is the 1-confidence with which one wants to be certain the disease is detected. In finite populations (< 1,000) with a population size of N, the number of individuals that need to be examined (n) to be certain to detect at least one positive case at a defined 1-confidence (α), where the minimum  prevalence of disease in the population (P) is given by equation 2.1.1.1.b.

Equation 2.1.1.1.b

Both of these approaches assume tests which are 100% sensitive, which is often unrealistic. In cases where sensitivity is imperfect but known (S), the number of individuals that would need to be examined

(n) in an infinite population to be 1-confident (α) of detecting at least one diseased case with a disease prevalence of P is given by equation 2.1.1.1.c (Fosgate, 2009).

Equation 2.1.1.1.c

Box 4.

The bump technique is a new method meant to detect the presence of Tropilaelaps mites (Anderson et al., 2013). This test, when applied to colonies that have an average infestation of 4.6 ± 0.06 mites per 100 brood cells, has a sensitivity of 36% (Pettis, Rose, and vanEngelsdorp, unpublished data). How many colonies need to be tested in a region with more than 1,000 colonies in order to detect one infected colony with 95% Confidence, assuming that 5% of colonies are infested?

Box 4 Equation

Thus, 165 randomly selected colonies would need to be tested to be 95% confident of detecting at least one positive colony given a 5% infestation rate.