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6 - 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

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Contents
1 Fixed pool size and perfect tests
2 Fixed pool size and tests with known sensitivity and specificity
3 Fixed pool size and tests with uncertain sensitivity and specificity
4 Variable pool size and perfect test
5 Pooled prevalence using a Gibbs sampler
6 Estimated true prevalence using one test (unpooled) with a Gibbs sampler
7 Estimated true prevalence using two tests (unpooled) with a Gibbs sampler
8 Sample size calculation for fixed pool size and perfect tests
9 Sample size calculation for fixed pool size and tests with known sensitivity and specificity
10 Sample size calculation for fixed pool size and tests with uncertain sensitivity and specificity
11 Simulate sampling for fixed pool size and assumed perfect test
12 Simulate sampling for fixed pool size and test with known sensitivity and specificity
13 Simulate sampling for fixed pool size and test with uncertain sensitivity and specificity
14 Simulate sampling for variable pool size and assumed perfect test
15 Demonstration of freedom using pooled testing with tests of known sensitivity and fixed pool size
16 Estimation of alpha and beta Parameters for Prior Beta distributions
17 Estimation of Beta probability distributions for specified alpha and beta parameters