1-Stage Freedom analysis

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

Analysis options:

Calculation method:
(these settings can usually be left as default values)

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.