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 animallevel 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 (RoganGladen) 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 preexisting 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.