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

Area of Science:

• Veterinary Epidemiology
• Biostatistics
• Infectious Disease Modeling

Background:

• Frequentist prevalence estimation can yield nonsensical results (e.g., >1 or <0) with small sample sizes or low prevalences.
• Incorporating imperfect diagnostic test sensitivity and specificity complicates traditional frequentist approaches.
• Asymptotic normality assumptions are often unmet in real-world epidemiological scenarios.

Purpose of the Study:

• To review and compare frequentist and Bayesian methods for true prevalence estimation in animal health.
• To highlight the advantages of Bayesian approaches for range-respecting interval estimates and probabilistic interpretation.
• To provide practical statistical methods and computational tools for prevalence estimation and study design.

Main Methods:

• Comparison of frequentist and Bayesian statistical frameworks for prevalence estimation.
• Application to individual and pooled sample data at animal and herd levels.
• Utilizing Mycobacterium avium subspecies paratuberculosis infection as a motivating example.
• Provision of WinBUGS code for Bayesian estimation examples.

Main Results:

• Bayesian methods provide direct, range-respecting interval estimates (0-1) without large-sample approximations.
• Bayesian approaches offer straightforward modeling of zero prevalence and direct probabilistic interpretation.
• Frequentist methods for detecting prevalence differences, sample size, and power calculations are also presented.

Conclusions:

• Bayesian methods are advantageous for accurate true prevalence estimation, particularly in challenging scenarios.
• The presented methods and code facilitate robust epidemiological analyses in animal health.
• This review equips researchers with tools to overcome limitations in traditional prevalence estimation techniques.