FreeCalc: Calculate sample size for freedom testing with imperfect tests

Input Values

Population Size:
Test Sensitivity:
Test Specificity:
Design prevalence:
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):
  

Calculate the required sample size and cut-point for testing to demonstrate population freedom from disease using imperfect tests an 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 popultion 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 populatuon and/or maximum sample size.

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