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 animal-level 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 one-test 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 pre-existing 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 one-test 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

a (T1+/T2+)

38

b (T1+/T2-)

87

c (T1-/T2+)

2

d (T1-/T2-)

35

P alpha

1

P beta

1

Se 1 alpha

21.96

Se 1 beta

5.49

Sp 1 alpha

4.1

Sp 1 beta

1.76

Se 2 alpha

4.44

Se 2 beta

13.31

Sp 2 alpha

71.25

Sp 2 beta

3.75

Y1 start

35

Y2 start

30

Y3 start

2

Y4 start

10

Iterations

25000

Discard

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.

 

Prevalence

Test 1 Se

Test 1 Sp

Test 1 PPV

Test 1 NPV

Test 2 Se

Test 2 Sp

Test 2 PPV

Test 2 NPV

Y1

Y2

Y3

Y4

Minimum

0.275

0.689

0.129

0.402

0.021

0.135

0.823

0.565

0.292

26

16

0

0

0.025

0.528

0.791

0.376

0.679

0.277

0.222

0.906

0.775

0.389

34

45

0

2

Median

0.772

0.889

0.695

0.918

0.639

0.305

0.96

0.907

0.519

38

77

2

10

0.975

0.921

0.954

0.955

0.992

0.858

0.425

0.989

0.973

0.705

38

87

2

25

Maximum

0.998

0.984

0.999

1

0.959

0.615

0.998

0.997

0.895

38

87

2

35

Mean

0.761

0.885

0.688

0.9

0.624

0.308

0.958

0.9

0.525

37

74

2

10

SD

0.099

0.042

0.16

0.084

0.15

0.051

0.021

0.051

0.079

1

11

1

6

Iterations

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.

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