A new probability formula for surveys to substantiate freedom from disease.

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.