# Pooled Prevalence Calculator – Demonstration analyses

## Simulate sampling for fixed pool size and test with known sensitivity and specificity

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 assuming known test sensitivity and specificity (using Method 4) for each iteration and calculates the mean prevalence and estimated bias across all iterations. It assumes fixed pool sizes and that the true values of both sensitivity and specificity are known exactly (i.e. that there is no uncertainty about the values). Values for the true sensitivity and specificity that are different to the assumed values can also be entered if desired to check the importance of the assumption of a perfect test

For this analysis, five alternative pooling strategies were evaluated for the estimation of prevalence in a population with an assumed true prevalence of 0.14 (14%). Pool sizes and numbers of pools were previously estimated to provide 95% confidence of estimating a true prevalence of 0.14 with a precision of 0.055 ( see sample size examples). 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 (H. Field, pers com). The sensitivity and specificity of the test were assumed to be 0.9 (90%) and 1 (100%) for prevalence estimation, and the true values were assumed to be the same as the assumed values for prevalence estimation. Input values, pooling strategies and results are summarised in the tables below:

 Input Value Method Fixed pool size and known Se & Sp 0.14 0.9 1 0.9 1 0.95 5 1000

 Strategy Pool size Number of pools 1 2 82 2 3 47 3 4 30 4 5 20 5 10 5

Mean confidence interval widths are greater than the target value of 0.11 (± 0.55) because exact methods were used to calculate confidence limits in these simulations, rather than the asymptotic methods used ti estimate sample size.

 Strategy 1 0.14102 0.05575 0.28432 0.00102 0.12572 0.02788 0.00078 0.0072 0.00725 0.00131 0.964 2 0.14285 0.03257 0.2875 0.00285 0.14582 0.02787 0.00079 0.01995 0.02036 0.01028 0.967 3 0.14153 0.04991 0.26221 0.00153 0.17028 0.02749 0.00076 0.01082 0.01094 0.00308 0.978 4 0.14581 0.03581 0.35561 0.00581 0.21857 0.0275 0.00079 0.03983 0.04149 0.04256 0.98 5 0.1377 0 0.19726 -0.0023 0.83581 0.0252 0.00064 -0.01672 -0.01644 0.00824 0.821