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7 - Pooled prevalence for variable pool size and perfect tests

This method uses generalised linear modelling to calculate maximum-likelihood estimates of prevalence and confidence limits where multiple different pool sizes are used. The method assumes 100% test sensitivity and specificity. See Williams & Moffitt (2001) for more details. Prevalence estimates can be calculated for sampling strategies with up to 10 different pool sizes used.

Required inputs for this method are:

pool size for each pool size used;
number of pools tested for each pool size used;
number of pools positive for each pool size used; and;
desired level of confidence in the estimate.

The desired confidence level must be a decimal number >0 and <1 (for example, 0.99 = 99% or 0.95 = 95%). Pool sizes and numbers of pools must be positive integers (>0) and the numbers of positive pools must be non-negative integers (>=0). The number of positive pools must be less than or equal to the corresponding number of pools tested.

Outputs include:

a point estimate of animal-level prevalence; and;
upper and lower asymptotic confidence limits for the estimate for the specified level of confidence.

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Contents
1	Introduction
2	Overview
3	Bayesian vs Frequentist methods
4	Fixed pool size and perfect tests
5	Fixed pool size and known Se & Sp
6	Fixed pool size and uncertain Se & Sp
7	Variable pool size and perfect tests
8	Pooled prevalence using a Gibbs sampler
9	True prevalence using one test
10	Estimated true prevalence using two tests with a Gibbs sampler
11	Estimation of parameters for prior Beta distributions
12	Sample size for fixed pool size and perfect test
13	Sample size for fixed pool size and known test sensitivity and specificity
14	Sample size for fixed pool size and uncertain test sensitivity and specificity
15	Simulate sampling for fixed pool size
16	Simulate sampling for variable pool sizes
17	Important Assumptions
18	Pooled prevalence estimates are biased!