# 12 - Simulate sampling for fixed pool size and test with known sensitivity and specificity

This program simulates sampling and prevalence estimation for a specified (design) prevalence value and level of confidence. The program runs multiple iterations of sampling, pooling and testing from an infinite population with the specified prevalence, estimates true prevalence assuming known test sensitivity and specificity (using Method 4) for each iteration and calculates the mean prevalence and estimated bias across all iterations. It assumes fixed pool sizes and that the true values of both sensitivity and specificity are known exactly (i.e. that there is no uncertainty about the values). Values for the true sensitivity and specificity that are different to the assumed values can also be entered if desired to check the importance of the assumption of a perfect test.

For this analysis, five alternative pooling strategies were evaluated for the estimation of prevalence in a population with an assumed true prevalence of 0.14 (14%). Pool sizes and numbers of pools were previously estimated to provide 95% confidence of estimating a true prevalence of 0.14 with a precision of 0.055 (see sample size examples). This is equivalent to the observed prevalence and precision when 162 samples from little red flying foxes in Queensland were tested individually, with 22 positive results (H. Field, pers com). The sensitivity and specificity of the test were assumed to be 0.9 (90%) and 1 (100%) for prevalence estimation, and the true values were assumed to be the same as the assumed values for prevalence estimation. Input values, pooling strategies and results are summarised in the tables below.

Input Value
Method Fixed pool size and known Se and Sp
Assumed Prevalence 0.14
Assumed Sensitivity 0.9
Assumed Specificity 1
True Sensitivity 0.9
True Specificity 1
Confidence 0.95
Number of strategies 5
Number of iterations 1000
Strategy Pool size Number of pools
1 2 82
2 3 47
3 4 30
4 5 20
5 10 5

Mean confidence interval widths are greater than the target value of 0.11 (0.55) because exact methods were used to calculate confidence limits in these simulations, rather than the asymptotic methods used to estimate sample size.

Strategy Mean prevalence Minimum prevalence Maximum prevalence Mean bias Mean CI width Mean standard error Mean square error Bias/AP Bias/TP Bias/MSE Proportion valid
1 0.14102 0.05575 0.28432 0.00102 0.12572 0.02788 0.00078 0.0072 0.00725 0.00131 0.964
2 0.14285 0.03257 0.2875 0.00285 0.14582 0.02787 0.00079 0.01995 0.02036 0.01028 0.967
3 0.14153 0.04991 0.26221 0.00153 0.17028 0.02749 0.00076 0.01082 0.01094 0.00308 0.978
4 0.14581 0.03581 0.35561 0.00581 0.21857 0.0275 0.00079 0.03983 0.04149 0.04256 0.98
5 0.1377 0 0.19726 -0.0023 0.83581 0.0252 0.00064 -0.01672 -0.01644 0.00824 0.821

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

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