# 17 - Important Assumptions

As with conventional methods for estimating prevalence, pooled testing methods and bayesian methods for estimating prevalence depend on a number of important assumptions. Violation of these assumptions will result in biased estimates. Key assumptions are that:

• the outcome is assumed to follow a binomial distribution - clustering or overdispersion of the positive outcome can cause substantial bias in the resulting estimate;
• the health status of each individual is independent of the status of others, both within and between pools;
• sampling of the population is by simple random sampling;
• individual samples are allocated into groups (pools) by random selection;
• sample size is small relative to the population being sampled;
• assumed values for sensitivity and specificity are appropriate;
• dilution of individual samples by pooling has no effect on sensitivity or specificity estimates (or the estimates used take any dilution effects into account);
• samples are assumed to be mixed homogeneously in the pools and any sub-samples taken for testing are equally representative of all of the individuals contributing to each pool;
• all pools represent the same number of individuals (except for the variable pool-size method);
• assumed prior distributions for prevalence, sensitivity and specificity for Bayesian methods are appropriate; and
• assumed true prevalence for sample size calculations and simulations is appropriate.

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!

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