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.
|Pool size||Number of pools||Sensitivity||Confidence level||Design prevalence|
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||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|