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

Prior prevalence alpha

1

Prior prevalence beta

1

Prior Se alpha

4.44

Prior Se beta

13.31

Prior Sp alpha

71.25

Prior Sp beta

3.75

Iterations

25000

Discard

5000

True pos start

35

False neg start

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.

 

Prevalence

Sensitivity

Specificity

PPV

NPV

LR for positive

LR for negative

True positives

False negatives

Minimum

0.171

0.135

0.8

0.197

0.243

1

0.32

7

7

0.025

0.393

0.212

0.882

0.665

0.336

2.4

0.54

29

33

Median

0.738

0.307

0.951

0.883

0.538

6.4

0.73

38

82

0.975

0.985

0.484

0.986

0.969

0.786

24.4

0.85

40

120

Maximum

1

0.697

0.998

0.994

0.907

157.8

1

40

122

Mean

0.728

0.316

0.948

0.871

0.544

7.5

0.72

38

81

SD

0.165

0.07

0.027

0.08

0.124

6.4

0.08

3

25

Iterations

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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