# 15 - Demonstration of freedom using pooled testing with tests of known sensitivity and fixed pool size

This program estimates the confidence that a population is free of disease, or of detecting disease at a specified design prevalence, using pooled testing and assuming a fixed pool size, a test of known sensitivity and 100% specificity and that all pools have a negative test result.

For this analysis, it was assumed that 30 pools of 10 were tested using a test with a sensitivity of 0.9 (90%) and perfect specificity. The design prevalence we wish to detect is 0.01 (1%) and we require 95% confidence of detecting one or more positives if the true prevalence is greater than or equal to the design prevalence. Input values and results are summarised below.

### Input values

Pool size Number of pools Sensitivity Confidence level Design prevalence
10 30 0.9 0.95 0.01

### Results

If all pools test negative, there is 95% confidence that the true prevalence is less than 0.0111.

If all pools test negative, there is 93.28% confidence that the true prevalence is less than 0.01.

For a pool size of 10, a minimum of 34 pools must be tested to provide 95% confidence of detecting a prevalence of 0.01.

The table below lists the number of pools required for various pool sizes to provide 95% confidence of detecting a prevalence of 0.01 and assuming a test sensitivity of 0.9 for all pool sizes.

Pool size Number of pools
1 332
2 166
3 111
4 83
5 67
10 34
15 23
20 17
25 14
30 12
40 9
50 7
100 4

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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