This program calculates the approximate numbers of pools required for a range of pool sizes and specified values for estimated prevalence and desired confidence and precision of the estimate, assuming fixed pool sizes and a test with 100% sensitivity and specificity. See Worlund & Taylor (1983) for more details.
The required number of pools (m) to estimate the true prevalence with the desired precision is
For fixed pool size and perfect tests, the optimum value of m can be calculated that minimises the variance of the estimated prevalence and consequently minimises the number of pools requiring testing to achieve the desired confidence and precision. This optimum value for m depends on the prevalence and is approximately 1.6/pi. This equates to the pool size which results in an expected number of 1.6 infected individuals per pool. See Sacks et al. (1989) for more details. Prevalence estimates may be upwardly biased, particularly as the probability of all pools testing positive increases (high prevalence and/or small numbers of large pools). Therefore, it is advisable to select a lower value for pool size and test a larger number of smaller pools to minimise potential bias in the result.
Required inputs for this analysis are:
For example, you might wish to estimate the prevalence where the true value is assumed to be about 0.01 (1%), and you wish to have 95% (0.95) confidence that the true value is within +/- 0.005 (0.5%) of your estimate. The assumed prevalence, desired precision and level of confidence must all be >0 and <1.
You can also input a suggested pool size if desired, and the program will calculate the corresponding number of pools to be tested for that pool size (in addition to predetermined pool sizes). Suggested pool size is ignored if it is zero.
Output from the analysis is:
|3||Bayesian vs Frequentist methods|
|4||Fixed pool size and perfect tests|
|5||Fixed pool size and known Se & Sp|
|6||Fixed pool size and uncertain Se & Sp|
|7||Variable pool size and perfect tests|
|8||Pooled prevalence using a Gibbs sampler|
|9||True prevalence using one test|
|10||Estimated true prevalence using two tests with a Gibbs sampler|
|11||Estimation of parameters for prior Beta distributions|
|12||Sample size for fixed pool size and perfect test|
|13||Sample size for fixed pool size and known test sensitivity and specificity|
|14||Sample size for fixed pool size and uncertain test sensitivity and specificity|
|15||Simulate sampling for fixed pool size|
|16||Simulate sampling for variable pool sizes|
|18||Pooled prevalence estimates are biased!|