# 3 - Fixed pool size and tests with uncertain sensitivity and specificity

This method (Method 5) is for fixed pool sizes and tests with uncertain sensitivity and specificity and produces asymptotic confidence intervals about the estimated prevalence. This method assumes that the true values of both sensitivity and specificity are not known exactly and have been estimated in a limited number of samples. The analysis allows for the additional uncertainty in the prevalence estimate associated with uncertainty about test performance, based on the sample sizes used to estimate sensitivity and specificity values. This method should be used if you are uncertain about the true values of sensitivity and specificity. If the true prevalence is likely to be close to zero, the lower confidence limit could be negative.

For this analysis, it was assumed that samples from 300 individual fruit bats were aggregated into 60 pools of 5 samples each, that 29 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. To allow for uncertainty about the true values of test sensitivity and specificity, it was assumed that sample sizes of 50 and 10,000, respectively, were used to estimate these values. Input values and results for this analysis are summarised in the table below.

Method 5
Input values:
Number of pools tested   60
Number of pools positive   29
Pool size   5
Sensitivity   0.9
Specificity   1.0
Sample size for sensitivity estimate   50
Sample size for specificity estimate   10000
Lower CL   0.025
Upper CL   0.975
Results:
Estimated Prevalence   0.1427
2.5 percentile   0.0876
97.5 percentile   0.1979
Standard Error   0.0282

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

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