Animal Health Research Reviews

Review Article

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

Locksley L. McV. Messama1, Adam J. Branscuma2, Michael T. Collinsa3 and Ian A. Gardnera1 c1

a1 Department of Medicine and Epidemiology, School of Veterinary Medicine, University of California, One Shields Avenue, Davis, CA, USA

a2 Department of Biostatistics, College of Public Health, University of Kentucky, Lexington, KY, USA

a3 Department of Pathobiological Sciences, School of Veterinary Medicine, University of Wisconsin-Madison, Madison, WI, USA


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. They also allow 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.

(Received July 11 2007)

(Accepted September 27 2007)

(Online publication March 17 2008)


c1 Corresponding author. E-mail: