Hierarchical Bayesian model for prevalence inferences and determination of a country’s status for an animal pathogen

doi:10.1016/S0167-5877(02)00092-2

Preventive Veterinary Medicine

Volume 55, Issue 3, 15 October 2002, Pages 155-171

https://doi.org/10.1016/S0167-5877(02)00092-2 Get rights and content

Abstract

Certification that a country, region or state is “free” from a pathogen or has a prevalence less than a threshold value has implications for trade in animals and animal products. We develop a Bayesian model for assessment of (i) the probability that a country is “free” of or has an animal pathogen, (ii) the proportion of infected herds in an infected country, and (iii) the within-herd prevalence in infected herds. The model uses test results from animals sampled in a two-stage cluster sample of herds within a country. Model parameters are estimated using modern Markov-chain Monte Carlo methods. We demonstrate our approach using published data from surveys of Newcastle disease and porcine reproductive and respiratory syndrome in Switzerland, and for three simulated data sets.

Introduction

To facilitate animal and animal-products trade, veterinary authorities in a country (region, etc.) might try to provide evidence that livestock populations are free from important infectious agents. Countries might always have been “free” of a specific pathogen based on years of negative surveillance data or might have eradicated the agent recently. Historic evidence of pathogen freedom might be based on criteria such as lack of clinical disease for a specified period of time, cessation of use of vaccines that might mask clinical signs, no positive diagnoses at local diagnostic laboratories, and (often) some test-based survey or surveillance data. Formal incorporation of this evidence into the analysis would be useful for making inferences about a country’s status regarding a particular pathogen. In addition, the risk of pathogen introduction can vary geographically depending on the extent of animal contact and/or movement of animal or animal products within and between neighboring regions or countries. This factor might also warrant consideration when data are analyzed.

To provide the necessary assurance of freedom from infection (or a prevalence below a defined threshold), most countries will conduct a national survey using internationally recognized diagnostic tests on a large sample of animals. These surveys could be based on samples collected at slaughter or on testing of live animals in herds. In the latter case, the testing generally would be performed using a two-stage cluster-sampling scheme with the selection of k herds and then a random sample of n animals (the selection could be age-specific or focused on high-risk groups) from each herd. The sample size (n) is often the same from herd to herd, but it could vary based on formulas designed to adjust for the total herd size.

Serologic tests typically are used in national surveys because they are inexpensive, and are rapid and easy to perform. However, such tests will always be imperfectly sensitive and specific. Thus, a survey that resulted in only a few reactors (positive test results) might not imply infection.

Criteria for assessment of pathogen freedom have been suggested by Baldock (1998) and a frequentist approach to the analysis of two-stage cluster-sampling designs incorporating imperfect test sensitivity and specificity has been developed by Cameron and Baldock (1998). As an alternative analytic approach, Audigé and Beckett (1999) developed a stochastic simulation model that allowed for the incorporation of uncertainty in input parameters through the use of probability distributions. They used the magnitude of the likelihood ratio as an indicator of country-level infection. Recently, Audigé et al. (2001) updated the model to incorporate uncertainty in the likelihood ratio and prior probability of country-level infection.

In this paper, we use a Bayesian approach to model test results from a two-stage cluster sample. Our main objective is to extend the work of Audigé and Beckett (1999) and Audigé et al. (2001) to an all-encompassing model for diagnostic test data from herd-level testing that will be useful for making inferences about infection status at three levels—the country, the herd, and within the herd. The model has been implemented in Fortran90 (Digital Equipment Corporation, 110 Spit Brook Road, mail stop ZKO2-3/N30, Nashua, New Hampshire, 03062-2698) and the prior and posterior analyses are performed in R (Free Software Foundation, Temple Place—Suite 330, Boston, MA 02111-1307, USA). We illustrate this modeling approach using survey data from Switzerland for Newcastle disease (ND) virus and porcine reproductive and respiratory syndrome (PRRS), and for three simulated data sets.

We begin by discussing the formulation of our model for pathogen freedom in Section 2. In our model, we assume individual test results are available for each animal from a two-stage cluster sample and assume an equal sample size (n) within herds. In Section 3, we explain the Bayesian approach to inference. In Section 4, we present results for real survey data and for simulated data examples. Finally, we give our conclusions in Section 5.

Section snippets

Model

Our model assumes that the diagnostic test results from a herd-level cluster sample are available. This sampling scheme is used to produce data by randomly selecting k herds (clusters) from the population of herds in a country, and then, within herd i, n_i animals are selected randomly and tested. We assume the herd size is large relative to n_i. We also assume the diagnostic test used to detect the pathogen in question is not perfect; either the test sensitivity (Se=P(T⁺|I⁺)) or specificity (Sp=P

The Bayesian approach

We require prior distributions for the unknown model parameters and the joint distribution of these parameters in conjunction with the latent data used in the model. Independent beta priors are assumed for the model parameters μ, γ, τ, Se, and Sp, and an independent gamma prior for (α+β). In general, for a generic parameter ν we use the notation ν∼beta(a_ν,b_ν) to specify its beta prior distribution. Suppose ν is a model parameter for which a beta(a_ν,b_ν) is to be selected. For the parameter ν,

Illustrations

In this section, we present results of our Bayesian analysis for two data sets previously evaluated by other authors. We analyze survey data that were collected in Switzerland to assess freedom from ND virus in poultry (Gohm et al., 1999) and PRRS in swine Audigé et al., 1997, Canon et al., 1998. We also present the results of three simulated data sets to demonstrate the utility of our model.

Conclusions

We have developed and presented a purely Bayesian model that is potentially useful for evaluating the status of a country or region with respect to freedom from an animal pathogen. The Bayesian approach incorporates prior knowledge along with the observed data to produce updated posterior inferences. It is the calculation of the posterior distributions that is the main advancement over previous work on the topic of inferences about pathogen freedom in animal populations. Specifically, posterior

Acknowledgements

This study was funded in part by USDA Formula Funds and the USDA NRI Competitive Grants Program, award no. 0102494. We thank Dr. Laurent Audigé for providing values used to construct prior distributions for the ND and PRRS analyses.

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Hierarchical Bayesian model for prevalence inferences and determination of a country’s status for an animal pathogen

Abstract

Introduction

Section snippets

Model

The Bayesian approach

Illustrations

Conclusions

Acknowledgements

Prev. Vet. Med.

Prev. Vet. Med.

Prev. Vet. Med.

Prev. Vet. Med.

What constitutes freedom from disease in livestock

Aust. Vet. J.