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1 - Fixed pool size and perfect tests

Two methods are provided for fixed pool sizes and perfect tests, one producing asymptotic confidence intervals (Method 1) and the other exact confidence intervals (Method 2). These methods should only be used if you can be confident that the sensitivity and specificity of the test are both close to 100%. If the true prevalence is likely to be close to zero, Method 2 (with exact confidence limits) should be used in preference to Method 1, because Method 1 could produce a negative lower confidence limit.

For this analysis, it was assumed that samples from 210 individual fruit bats were aggregated into 42 pools of 5 samples each, that 22 pools produced a positive test result and that the test sensitivity and specificity were both 100%. Input values and results for this analysis are summarised in the table below.

	Method 1	Method 2
Input values:
Number of pools tested	42	42
Number of pools positive	22	22
Pool size	5	5
Lower CL	0.025	0.025
Upper CL	0.975	0.975
Results:
Estimated Prevalence	0.1379	0.1379
2.5 percentile	0.0866	0.0832
97.5 percentile	0.2038	0.1926
Standard Error	0.0279	0.0279

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Contents
1	Fixed pool size and perfect tests
2	Fixed pool size and tests with known sensitivity and specificity
3	Fixed pool size and tests with uncertain sensitivity and specificity
4	Variable pool size and perfect test
5	Pooled prevalence using a Gibbs sampler
6	Estimated true prevalence using one test (unpooled) with a Gibbs sampler
7	Estimated true prevalence using two tests (unpooled) with a Gibbs sampler
8	Sample size calculation for fixed pool size and perfect tests
9	Sample size calculation for fixed pool size and tests with known sensitivity and specificity
10	Sample size calculation for fixed pool size and tests with uncertain sensitivity and specificity
11	Simulate sampling for fixed pool size and assumed perfect test
12	Simulate sampling for fixed pool size and test with known sensitivity and specificity
13	Simulate sampling for fixed pool size and test with uncertain sensitivity and specificity
14	Simulate sampling for variable pool size and assumed perfect test
15	Demonstration of freedom using pooled testing with tests of known sensitivity and fixed pool size
16	Estimation of alpha and beta Parameters for Prior Beta distributions
17	Estimation of Beta probability distributions for specified alpha and beta parameters