Estimating the prevalence of infectious agents using pooled samples: biometrical considerations

Pooled testing of units is a common approach in the prevalence estimation of infectious agents, which leads to a reduction of total costs of diagnostic testing. We examine how the pool size affects the statistical properties of the prevalence estimator r. Exact formulae are used to determine bias and precision of r. It is shown that with moderate pool sizes the (upward) bias of r is negligible. If there is no diagnostic error, the random error of r increases slightly with higher pool sizes, whereas if sensitivity and specificity are lower than 1, pooling may markedly decrease the random error of r. Another reason why pooling may be beneficial (and even indispensable) is that it greatly reduces the huge bias that can result if the assumed values of the sensitivity and specificity of the diagnostic test are not equal to the true values. The numerical calculations show that, in case of prevalence rates of up to 5% and total sample sizes of n > or = 500, pool sizes of about 10 to 20 are generally satisfactory from a statistical view-point. The methodological advantages and disadvantages of more complicated pooling strategies involving repeated testing of units are discussed.