## Test interpretation at the group level

In aquaculture, diagnostic tests are most frequently used on individual fish (or pooled individuals) to reach conclusions about populations of fish (Thorburn, 1996). Martin et al. (1992) expanded the principles of sensitivity, specificity and predictive values to encompass group- (usually farm-) level testing. Hence, it is possible to assess the impact that diagnostic test errors have on decisions made about groups of fish. Farm-level sensitivity (specificity) is defined as the probability that an infected (non-infected) farm is declared positive (negative), given a specific sampling and diagnostic protocol. Farm-level positive (negative) predictive value is the probability that a farm that is declared positive (negative) is infected (free of infection). Estimates of farm-level sensitivity, specificity and predictive values are critical to the design and interpretation of results from regional disease control and eradication programmes.

The farm-level sensitivity (FSENS), i.e. the probability of observing at least one or more reactors (test-positive fish) in a randomly selected sample of n fish from an infected farm, is calculated as follows:

For instance, if a diagnostic test with 80% sensitivity and 99.9% specificity is used to test 60 fish randomly selected from a farm where the prevalence of infection is 2%:

ap = (0.02 x 0.8) + [(1 - 0.02) x (1 - 0.999)] = 0.016 + 0.001 = 0.017

Hence, there is a 36% chance that an infected farm will not, under these conditions, be declared positive (i.e. that no test-positive fish will be included in the sample).

Farm-level sensitivity increases with increasing diagnostic-test sensitivity, prevalence and numbers of fish sampled. It decreases, however, with increasing diagnostic-test specificity, since there will be a lower probability of non-infected fish falsely testing positive. On an infected farm, a false-positive test result will result in that farm being correctly classified as infected; note, however, that lower test specificity will result in lower farm-level positive predictive value.

The farm-level specificity (FSPEC), i.e. the probability of detecting no reactors in n fish sampled from a non-infected farm, is calculated as follows:

FSPEC = specificity"

For example, if the above diagnostic test with a specificity of 99.9% was used on 60 fish randomly selected from a non-infected farm:

Hence, there is a 6% chance that a non-infected farm will, under these conditions, be falsely declared infected. Farm-level specificity increases with increasing test specificity and decreasing sample size.

If the diagnostic test is less than 100% specific, the farm-level positive predictive value decreases and the farm-level negative predictive value increases, with increasing n and decreasing farm-level prevalence (i.e. proportion of farms that are infected). Refer to Martin et al. (1992) for formulae to calculate farm-level predictive values. Other methodological issues surrounding group testing have been elaborated by Donald et al. (1994) and Carpenter and Gardner (1996). Thorburn (1996) investigated the impact of apparent prevalence assumptions on FSENS and FSPEC in routine surveillance of asymptomatic salmonid populations.

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