Introduction
This method uses a Bayesian approach and Gibbs sampling to estimate the true animallevel
prevalence of infection based on testing of individual (not pooled) samples using two tests with
imperfect sensitivity and/or specificity. The analysis requires prior estimates of true prevalence
ans test sensitivity and test specificity for both tests as Beta probability distributions, and
outputs posterior distributions for prevalence, sensitivity and specificity. The analysis assumes
that the two tests are independent, conditional on disease status. See the
User Guide or
Joseph et al. (1995) for more details.
See demonstration analysis
Input values
Required inputs for this analysis are the number of samples in each cell of the 2x2 table of
comparative test results and alpha and beta parameters for prior Beta distributions for true
prevalence and test sensitivity and specificity for both tests. Additional inputs are the number
of iterations to be simulated in the Gibbs sampler, the number of iterations to be discarded to allow
convergence of the model, the lower and upper probability (confidence) limits for summarising the
output distributions and starting values for the assumed number of truly infected individuals in each
cell of the 2x2 table of results. The Gibbs sampler is then used to estimate the probability
distributions of true prevalence, sensitivity and specificity that best fit the data and prior
distributions provided.
Prior distributions for Prevalence, Se and Sp
The Gibbs sampler requires prior estimates of the true prevalence and test sensitivity and
specificity for both tests, based on expert knowledge or 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 utilities, provided estimates of the mode and 5% or 95% confidence limits
are available from expert opinion.
If there is no prior information on which to base a prior distribution,
alpha = beta = 1 should be used. This results in a uniform (uninformed) distribution, in
which all values between 0 and 1 have equal probability of occurrence.
Outputs
Outputs for this method are posterior probability distributions for prevalence, sensitivity and
specificity. These distributions are described by their minimum,
maximum, upper and lower probability limits specified, median, mean and standard deviation. A histogram
and density chart and a text file of simulation results can also be downloaded for each parameter.
How many iterations?
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. It is
also important to carry out an adequate numebr of iterations to support inference from the results.
suggested default values for the total number of iterations and the number to be discarded are provided,
but can be varied if desired.
Note:
This analysis may take several minutes to complete, depending on the number of iterations required.
