# Sample size calculation for fixed pool size and perfect tests

## Input Values

This program calculates the approximate numbers of pools required for given values for pool size, estimated prevalence and desired confidence and precision of the estimate, assuming fixed pool sizes and a test with 100% sensitivity and specificity. The required number of pools (m) to estimate pi with a perfect test and fixed pool size (k) can be calculated using the following equation, where e is the desired precision (allowable error) of the estimate and Z is the standard normal variate for the desired level of confidence. See the User Guide or Worlund & Taylor (1983) for more details. See demonstration analysis

m(perfect test) = (Z(1 - pi)/(ek))^2((1 - pi)^-k - 1)

For fixed pool size and perfect tests, the optimum value of m can be calculated that minimises the variance of the estimated prevalence and consequently minimises the number of pools requiring testing to achieve the desired confidence and precision. This optimum value for m depends on the prevalence and is approximately 1.6/pi. This equates to the pool size which results in an expected number of 1.6 infected individuals per pool. See the User Guide or Sacks et al. (1989) for more details. In practice, it is advisable to select a smaller pool size and test a larger number of pools to minimise potential bias in the result.

### Input values

Required inputs are the estimated true prevalence, the desired level of precision (or acceptable error) and the desired level of confidence. For example, you might wish to estimate the prevalence where the true value is assumed to be about 0.01 (1%), and you wish to have 95% (0.95) confidence that the true value is within +/- 0.005 (0.5%) of your estimate. You can also input a suggested pool size if desired, and the program will calculate the corresponding number of pools to be tested for that pool size (in addition to predetermined pool sizes). Suggested pool size is ignored if it is zero.

### Outputs

The program calculates the number of pools required for the input-scenario for a range of pool sizes and presents the results in tabular and graphical formats. The optimum pool size and corresponding number of pools are also calculated.

Estimated true prevalence:
Desired precision (+/-):
Desired confidence level:
Suggested pool size:

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