1-Stage Freedom analysis

# FreeCalc: Calculate sample size for freedom testing with imperfect tests

This utility calculates the required sample size and cut-point for testing to demonstrate population freedom from disease using imperfect tests and allowing for small populations.

This utility uses the methods described by:

- - Cameron and Baldock (1998): A new probability formula for surveys to substantiate freedom from disease.
*Prev. Vet. Med.***34**:1-17; and - - Cameron (1999):
*Survey Toolbox for Livestock Diseases - A practical manual and software package for active surveillance of livestock diseases in developing countries.*Australian Centre for International Agricultural Research, Canberra, Australia.

### Inputs include:

- - Size of the population sampled;
- - Test sensitivity and specificity;
- - Design prevalence (the hypothetical prevalence to be detected). Design prevalence can be specified as either a fixed number of elements from the population or a proportion of the population;
- - Maximum acceptable Type I (1 - population-sensitivity) and Type II (1 - population-specificity) error values for determining whether to accept/reject the null or alternative hypothesis, assuming a null hypothesis that the population is diseased;
- - Calculation method: hypergeometric (for small populations), or simple binomial (for large populations);
- - The population size threshold, above which the simple binomial method is used regardless of which calculation method has been selected;
- - The maximum upper limit for required sample size (must be < 100,000); and
- - The desired precision of results (number of digits to be displayed after the decimal point).

### The results are presented as:

- - The minimum sample size and corresponding cut-point number of positives to achieve the specified type I and type II errors for the given population, design prevalence and test performance;
- - Achieved Type I and Type II error levels and corresponding population-level sensitivities and specificities;
- - A descriptive interpretation of the results; and
- - An error message if the desired error levels cannot be achieved within the limits of population and/or maximum sample size.

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