This analysis uses a Bayesian approach and Gibbs sampler to estimate the true animal-level prevalence of infection based on testing of individual (not pooled) samples using a test with imperfect sensitivity and/or specificity. The analysis requires prior estimates of true prevalence, test sensitivity and test specificity as Beta probability distributions, and outputs posterior distributions for prevalence, sensitivity and specificity. See Joseph et al. (1995) for more details.
Required inputs for this analysis are:
The number of samples tested must be a positive integer and the number of positive samples must be an integer >=0 and <= the number of samples tested. Alpha and beta parameters for prevalence, sensitivity and specificity must be >0 and upper and lower confidence limits must be >0 and <1. Starting values for the numbers of true positives and false negatives must be integers >= zero and <= the number of positive samples and the number of negative samples, respectively. The number of iterations and the number discarded must both be positive integers (>0) and the number discarded must be less than the number of iterations.
Prior estimates of the true prevalence and test sensitivity and specificity may be based on expert knowledge or on previous data. These estimates are specified as Beta probability distributions, with parameters alpha and beta. Beta probability distributions are commonly used to express uncertainty about a proportion based on a random sample of individuals. In this situation, if x individuals are positive for a characteristic out of n examined, then the alpha and beta parameters can be calculated as alpha = x + 1 and beta = n - x + 1. Alternatively, alpha and beta can be calculated using the Beta distribution utility, provided estimates of the mode and 5% or 95% confidence limits are available from expert opinion.
Outputs from the Gibbs sampler are posterior probability distributions for:
These distributions are described by their:
Because the Gibbs sampler estimates prevalence iteratively, based on the data and the prior distributions, it may take a number of iterations for the model to converge on the true value. Therefore, a specified number of initial iterations must be discarded (not used for estimation) to allow the model to converge on the true values. This number must be sufficient to allow convergence, and should be at least 2000 - 5000. It is also important to carry out an adequate number of iterations to support inference from the results. Suggested minimum values for the total number of iterations and the number to be discarded are provided, but can be varied if desired.
This analysis may take several minutes to complete, depending on the number of iterations required.
|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!|