Pooled Prevalence Calculator – Demonstration analyses
Estimated true prevalence using two tests (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 two independent tests with imperfect sensitivity and/or specificity. The analysis requires prior estimates of true prevalence and test sensitivity and test specificity for both tests, as Beta probability distributions. It outputs posterior distributions for prevalence, sensitivity and specificity of both tests and several other parameters of interest. This method is similar to the onetest method, except that it allows incorporation of data from two tests used concurrently, and finds the best estimate that fits the combination of the prior information and the observed data. It also allows for uncertainty about the true values for sensitivity and specificity when calculating probability limits for the true prevalence estimate and the incorporation of prior information on the likely true prevalence based on preexisting estimates or expert opinion. Because of the use of two tests, this method will often produce narrower probability limits about the prevalence estimate than the onetest method, particularly where there is considerable uncertainty about prior estimates.
For this analysis, the original values for stool sampling and serology 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 
38 

87 

2 

35 

1 

1 

21.96 

5.49 

4.1 

1.76 

4.44 

13.31 

71.25 

3.75 

35 

30 

2 

10 

25000 

5000 
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
(serology) 
21.96 
5.49 
0.6346 
0.8073 
0.9242 
0.8 
0.8236 
0.075 
Specificity
(serology) 
4.1 
1.76 
0.3123 
0.7235 
0.9621 
0.6997 
0.8031 
0.175 
Sensitivity
(stool) 
4.44 
13.31 
0.0843 
0.2406 
0.469 
0.2501 
0.2184 
0.1 
Specificity
(stool) 
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.


0.275 
0.689 
0.129 
0.402 
0.021 
0.135 
0.823 
0.565 
0.292 
26 
16 
0 
0 

0.528 
0.791 
0.376 
0.679 
0.277 
0.222 
0.906 
0.775 
0.389 
34 
45 
0 
2 

0.772 
0.889 
0.695 
0.918 
0.639 
0.305 
0.96 
0.907 
0.519 
38 
77 
2 
10 

0.921 
0.954 
0.955 
0.992 
0.858 
0.425 
0.989 
0.973 
0.705 
38 
87 
2 
25 

0.998 
0.984 
0.999 
1 
0.959 
0.615 
0.998 
0.997 
0.895 
38 
87 
2 
35 

0.761 
0.885 
0.688 
0.9 
0.624 
0.308 
0.958 
0.9 
0.525 
37 
74 
2 
10 

0.099 
0.042 
0.16 
0.084 
0.15 
0.051 
0.021 
0.051 
0.079 
1 
11 
1 
6 

20000 
20000 
20000 
20000 
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.