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2 - Fixed pool size and tests with known sensitivity and specificity

Two methods are provided for fixed pool sizes and tests with known sensitivity and specificity, one producing asymptotic confidence intervals (Method 3) and the other exact confidence intervals (Method 4). These methods assume that the true values of both sensitivity and specificity are known exactly (i.e. that there is no uncertainty about the values). They do not allow for additional uncertainty in the prevalence estimate associated with uncertainty about test performance. They should be used if the test is well characterised and you can be confident that the sensitivity and specificity of the test are both close to the estimated values. If the true prevalence is likely to be close to zero, Method 4 (with exact confidence limits) should be used in preference to Method 3, because Method 3 could produce a negative lower confidence limit. Asymptotic confidence intervals (Method 3) can also be substantially narrower than exact intervals (Method 4) in some instances.

For this analysis, it was assumed that samples from 100 individual fruit bats were aggregated into 20 pools of 5 samples each, that 10 pools produced a positive test result and that the test sensitivity was 90% and specificity was 100%. An assumed sensitivity of less than 100% was used to demonstrate the possible effect of dilution on sensitivity of the pooled test. Input values and results for this analysis are summarised in the table below.

  Method 3 Method 4
Input values:    
Number of pools tested 20 20
Number of pools positive 10 10
Pool size 5 5
Sensitivity 0.9 0.9
Specificity 1.0 1.0
Lower CL 0.025 0.025
Upper CL 0.975 0.975
Results:    
Estimated Prevalence 0.1497 0.1497
2.5 percentile 0.0943 0.0694
97.5 percentile 0.2052 0.2818
Standard Error 0.0283 0.0283

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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