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Abstract
Surveys to substantiate freedom from disease are becoming increasingly important.
This is due to the changes in rules governing international trade in animals and animal
products, and to an increase in disease eradication and herd-level accreditation schemes.
To provide the necessary assurances, these surveys must have a sound theoretical basis.
Until now, most surveys have been based on the assumption that the screening test
used was perfect (sensitivity and specificity both equal to one), and/or that the
study population was infinite. Clearly, these assumptions are virtually always invalid.
This paper presents a new formula that calculates the exact probability of detecting
diseased animals, and considers both imperfect tests and finite population size. This
formula is computationally inconvenient, and an approximation that is simpler to calculate
is also presented. The use of these formulae for sample-size calculation and analysis
of survey results is discussed. A computer program, 'FreeCalc', implementing the formulae
is presented along with examples of sample size calculation for two different scenarios.
These formulae and computer program enable the accurate calculation of survey sample-size
requirements, and the precise analysis of survey results. As a result, survey costs
can be minimised, and survey results will reliably provide the required level of proof.