# Pooled Prevalence Calculator – Demonstration analyses

## Simulate sampling for variable pool size and assumed perfect test

This program simulates sampling and prevalence estimation for a specified (design) prevalence value and level of confidence. The program runs multiple iterations of sampling, pooling and testing from an infinite population with the specified prevalence, estimates true prevalence for each iteration and calculates the mean prevalence and estimated bias across all iterations. It assumes variable pool sizes and a test with 100% sensitivity and specificity. Values for the true sensitivity and specificity that are different to the assumed values of 100% can also be entered if desired to check the importance of the assumption of a perfect test

For this analysis, six alternative pooling strategies were evaluated for the estimation of prevalence in a population with an assumed true prevalence of 0.14 (14%). This is equivalent to the observed prevalence and precision when 162 samples from little red flying foxes in Queensland were tested individually, with 22 positive results. Pool sizes and numbers of pools were used to provide the same total sample size (210 samples) as used for the fixed pool size and perfect test example. The true sensitivity and specificity of the test were both assumed to be 1 (100%), equal to the assumed values for prevalence estimation. Input values, pooling strategies and results are summarised in the tables below:

 Input Value Method Variable pool size & perfect test 0.14 1 1 1 1 0.95 6 1000

 Strategy Pool size 1 Number of pools 1 Pool size 2 Number of pools 2 1 5 42 0 0 2 5 40 1 10 3 5 40 10 1 4 10 21 0 0 5 10 20 1 10 6 20 10 10 1

 Strategy 1 0.14272 0.05293 0.28226 0.00272 0.11136 NaN NaN 0.01909 0.01946 NaN 0.945 2 0.14256 0.05826 0.27087 0.00256 0.11016 NaN NaN 0.01793 0.01826 NaN 0.935 3 0.14161 0.05986 0.25929 0.00161 0.11187 NaN NaN 0.01139 0.01153 NaN 0.97 4 0.15136 0.06262 0.92587 0.01136 0.14941 NaN NaN 0.07507 0.08116 NaN 0.935 5 0.14654 0.06912 0.32703 0.00654 0.1433 NaN NaN 0.0446 0.04669 NaN 0.949 6 0.49031 0.04148 0.89974 0.35031 0.18629 NaN NaN 0.71447 2.50225 NaN 0.49

The standard error of the estimate cannot be calculated using this method, so that and other measures derived from it (Mean sq. error and Bias/MSE) are listed as ‘NaN’ (Not a number).