This method uses frequentist approaches to estimate prevalence and confidence limits, assuming a fixed pool size and a test with unknown (uncertain) values for sensitivity and specificity, as described below.
This method (Method 6 from Cowling et al. (1999) assumes fixed pool size but unknown test sensitivity and specificity. Uncertainty associated with the point estimates of test sensitivity and specificity is incorporated through the inclusion of additional variance associated with the sample size used to determine the values used for these parameters. The smaller the sample size, the greater the uncertainty about the true values for sensitivity and/or specificity and hence the greater the uncertainty about the resulting prevalence estimate. Confidence limits are based on a normal approximation and may be <0 for low prevalence values.
Prevalence is estimated as for Method 3:
and the standard error (SE(p)) is estimated as the square root of the variance, given by:
Asymptotic confidence limits are calculated using the normal approximation:
where is the standardised normal variate corresponding to the desired confidence limit.
Required inputs for this method are:
Pool size, number of pools, number of pools positive and sample sizes for estimating sensitivity and specificity must be positive integers and the number of positive pools must be less than the number of pools tested. Sensitivity and specificity must be >0 and <=1 and upper and lower confidence limits must be >0 and <1.
Estimates are only valid if the proportion of positive pools is greater than the false positive rate (1 - Specificity) and less than or equal to the true positive rate (Sensitivity). Invalid results are indicated by NA in the results table.
|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!|