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EPIDEMIOLOGY UC Davis

Hierarchical Bayesian Model for Certification of a Country as “Free” From an Animal Disease. Eric A. Suess, Dept. of Statistics, Calif. State Univ., Hayward Ian Gardner, Dept. of Med. and Epi., School of Vet. Med., Univ. of Calif., Davis Wes Johnson, Div. of Statistics, Univ. of Calif., Davis.

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EPIDEMIOLOGY UC Davis

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  1. Hierarchical Bayesian Model for Certification of a Country as “Free” From an Animal Disease Eric A. Suess, Dept. of Statistics, Calif. State Univ., Hayward Ian Gardner, Dept. of Med. and Epi., School of Vet. Med., Univ. of Calif., Davis Wes Johnson, Div. of Statistics, Univ. of Calif., Davis EPIDEMIOLOGY UC Davis

  2. Background • Risk analysis for trade in animal products. • Countries are interested in new trading opportunities and maintaining current trade. • Is the country disease free? • Needed for risk analysis to make policy decisions.

  3. Disease Freedom • “Disease freedom” • requires a perfectly sensitive test • All animals • All negative tests • Level of Disease Freedom may not mean total freedom in all situations. • prevalence < threshold

  4. Quantitative Approach • Model: two-stage cluster sample Country Herd Animal

  5. Latent Data – Unknown Truth (conditional) Country D+ ? Yes No Herd D+ ? All Herd D- No Yes No Animal D+ ? All D- All D- Observed T+ T- T+ T- T+ T-

  6. Quantitative Approach We want to incorporate… • Prior history of the Country • Imperfect Test Sensitivity and Specificity Inferences: • Country • Proportion of diseased herds • Within-herd prevalence

  7. Bayesian Statistics • Bayes’ Rule

  8. Bayesian Approach • Prior, Model, Posterior Analysis • Latent Data (“true” status not observed) • Markov Chain Monte Carlo • Gibbs sampler (a simulation technique) • Adaptive Rejection Sampling

  9. Beta Priors Expert opinion mode and percentiles beta(a,b)

  10. Example: Newcastle Disease Data: • 260 flocks, 30 animals per flock • 0 194 flocks • 1 50 • 2 9 • 3 3 • 10 2 • 14 1 • 22 1

  11. Example: Newcastle Disease Priors on model probabilities: • Country diseased = 0.50 uniform(0,1) • Within herd-level prevalence = 0.30 beta(4.4,9) • Herd-level prevalence = 0.05 beta(17,70) • Allowed to vary within flocks • Sensitivity = 0.995 beta(103,1.5) • Specificity = 0.995 beta(190,1.9)

  12. Gibbs Sampler: assume country diseased Reps = 200,000 Burn In =150,000 Results: Country D Probability the country is diseased: 0.71 BCI: (0.16, 0.99)

  13. Proportion of diseased flocks: 0.02 BCI: (0.01, 0.04)

  14. Average within flock prevalence: 0.32 BCI: (0.21, 0.46)

  15. Sensitivity: 0.987 BCI: (0.956, 0.999) Specificity: 0.995 BCI: (0.988, 0.998)

  16. Conclusions • Bayesian approach. • Uses Prior Knowledge • Latent data • Imperfect test • Variable within herd-level prevalence. • Country/Herd/Animal Inference. • Priors for others risk analysis.

  17. Further Work • Variable sample size within herds. • Application to continuous surveillance.

  18. References • Audigé and Beckett (1999). A quantitative assessment of the validity of animal-health surveys using stochastic modeling. Prev. Vet. Med. 38, 259-276. • Gohm, Thür, Audigé, and Hoffmann (1999). A survey of Newcastle disease in Swiss lay-hen flocks using serological testing and simulation modeling. Prev. Vet. Med. 38, 277-288.

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