Frequentist and Bayesian approaches to prevalence estimation using examples from Johne's disease

Although frequentist approaches to prevalence estimation are simple to apply, there are circumstances where it is difficult to satisfy assumptions of asymptotic normality and nonsensical point estimates (greater than 1 or less than 0) may result. This is particularly true when sample sizes are small, test prevalences are low and imperfect sensitivity and specificity of diagnostic tests need to be incorporated into calculations of true prevalence. Bayesian approaches offer several advantages including direct computation of range-respecting interval estimates (e.g. intervals between 0 and 1 for prevalence) without the requirement of transformations or large-sample approximations, direct probabilistic interpretation, and the flexibility to model in a straightforward manner the probability of zero prevalence. In this review, we present frequentist and Bayesian methods for animal- and herd-level true prevalence estimation based on individual and pooled samples. We provide statistical methods for detecting differences between population prevalence and frequentist methods for sample size and power calculations. All examples are motivated using Mycobacterium avium subspecies paratuberculosis infection and we provide WinBUGS code for all examples of Bayesian estimation.