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10 - Sample size calculation for fixed pool size and tests with uncertain sensitivity and specificity

This option can be used to calculate the number of pools that need to be tested for various values for pool size, estimated prevalence and desired confidence and precision of the estimate. It assumes fixed pool sizes and that the true values of both sensitivity and specificity are not known exactly and have been estimated in a limited number of samples.

For this analysis, sample size was calculated to provide 95% confidence of estimating a true prevalence of 0.14 (14%) with a precision of 0.055 (5.5%). 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). Test sensitivity was assumed to be 90%, to demonstrate the effect of imperfect test sensitivity on sample size estimates and specificity was assumed to be 100%. 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. For a pool size of five, 59 pools would be sufficient to provide the desired precision and confidence in the estimated prevalence.

Input Value
Prevalence 0.14
Precision 0.055
Confidence 0.95
Sensitivity 0.9
Specificity 1
Sensitivity sample size 50
Specificity sample size 10000
Pool size Number of pools Total number of individual samples
1 183 183
2 102 204
5 59 295
10 67 670
15 238 3570

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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