1-Stage Freedom analysis

FreeCalc: Calculate sample size for freedom testing with imperfect tests

Population size

Test sensitivity

Test specificity

Design prevalence (proportion or number of units)

Analysis options:

Desired type I error (1 - minimum population-sensitivity)

Desired type II error (1 - minimum population-specificity)

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

Modified hypergeometric exact

Simple binomial (large population)

Population threshold for binomial method

Maximum limit for sample size

Precision (significant digits)

Submit

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.