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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