Pooled Prevalence Calculator – Demonstration analyses

Estimated true prevalence using one test (unpooled) with a Gibbs sampler

This method uses a Bayesian approach and Gibbs sampling 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. As for the Bayesian method for pooled sampling, 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. This method is preferable to the conventional (Rogan-Gladen) method for estimating true prevalence, because it allows for uncertainty about the true values for sensitivity and specificity when calculating probability limits for the true prevalence estimate, which are not routinely included in the conventional approach. It also allows incorporation of prior information on the likely true prevalence based on pre-existing estimates or expert opinion.

For this analysis, the original values for stool sampling for Strongyloides infection in Cambodian refugees from Joseph et al. (1996) were used, as listed in the table below, and 95% probability limits were calculated about the estimated prevalence.

 Input Value Number tested 162 Number test +ve 40 1 1 4.44 13.31 71.25 3.75 25000 5000 35 35

The prior Beta distributions defined above are equivalent to:

 Distribution Alpha value Beta value 2.5% percentile Median 97.5% percentile Mean Mode Standard deviation Prevalence 1 1 0.025 0.5 0.975 0.5 0.2887 Sensitivity 4.44 13.31 0.0843 0.2406 0.469 0.2501 0.2184 0.1 Specificity 71.25 3.75 0.8909 0.954 0.9868 0.95 0.9623 0.025

The simulation was run for 25,000 iterations, with 5,000 iterations discarded to allow for convergence. Posterior probability distributions for prevalence, sensitivity, specificity and other parameters from the analysis are summarised below.

 0.171 0.135 0.8 0.197 0.243 1 0.32 7 7 0.393 0.212 0.882 0.665 0.336 2.4 0.54 29 33 0.738 0.307 0.951 0.883 0.538 6.4 0.73 38 82 0.985 0.484 0.986 0.969 0.786 24.4 0.85 40 120 1 0.697 0.998 0.994 0.907 157.8 1 40 122 0.728 0.316 0.948 0.871 0.544 7.5 0.72 38 81 0.165 0.07 0.027 0.08 0.124 6.4 0.08 3 25 20000 20000 20000 20000 20000 20000 20000 20000 20000

Graphs for the posterior distributions for each parameter can be viewed by clicking on the appropriate thumbnail when your results are displayed (not for this example). See below for the graph of the posterior distribution for prevalence for this example. An excel spreadsheet for the results of all iterations for each parameter can also be accessed by clicking on the appropriate table icon.

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It provides a range of epidemiological tools for the use of researchers and epidemiologists, particularly in animal health.