Modeling cumulative evidence for freedom from disease with applications to BSE surveillance trials



This investigation deals with the question of when a particular population can be considered to be disease-free. The motivation is the case of BSE where specific birth cohorts may present distinct disease-free subpopulations. The specific objective is to develop a statistical approach suitable for documenting freedom of disease, in particular, freedom from BSE in birth cohorts. The approach is based upon a geometric waiting time distribution for the occurrence of positive surveillance results and formalizes the relationship between design prevalence, cumulative sample size and statistical power. The simple geometric waiting time model is further modified to account for the diagnostic sensitivity and specificity associated with the detection of disease. This is exemplified for BSE using two different models for the diagnostic sensitivity. The model is furthermore modified in such a way that a set of different values for the design prevalence in the surveillance streams can be accommodated (prevalence heterogeneity) and a general expression for the power function is developed. For illustration, numerical results for BSE suggest that currently (data status September 2004) a birth cohort of Danish cattle born after March 1999 is free from BSE with probability (power) of 0.8746 or 0.8509, depending on the choice of a model for the diagnostic sensitivity.

Key Words

Design prevalence heterogeneity Diagnostic accuracy Freedom of disease Geometric waiting time Power function 


  1. Böhning, D. (2000), Computer-Assisted Analysis of Mixtures and Applications, Boca Raton, FL: Chapman & Hall/CRC.MATHGoogle Scholar
  2. Cameron, A. R., Martin, P. A. J., Greiner, M., and Barfod, K. (2003), “The Use of Scenario-Tree Modelling using Multiple Complex Data Sources to Demonstrate Danish Freedom from Classical Swine Fever,” in Electronic Proceedings of the 10th Meeting of the International Society for Veterinary Epidemiology and Economics (ISVEE), Vina del Mar, Chile.Google Scholar
  3. Donnelly, C. A., Santos, R., Ramos, M., Galo, A., and Simas, J. P. (1999), “BSE in Portugal: Anticipating the Decline of an Epidemic,” Journal of Epidemiology Biostatistics, 4, 277–283.Google Scholar
  4. EC (2001), Opinion on Requirements for Statistically Authoritative BSE/TSE Surveys. Adopted by the Scientific Steering Committee (29–30 November 2001). Available online at en.pdf. Google Scholar
  5. EC (2003), Report on the Monitoring and Testing of Ruminants for the Presence of Transmissible Spongiform Encephalopathy (TSE) in 2002. Directorate D — Food Safety: Production and Distribution Chain D2 — Biological Risks. Available online at biosafety/bse/annual_report_2002en.pdf. Google Scholar
  6. EC (2004), Report on the Monitoring and Testing of Ruminants for the Presence of Transmissible Spongiform Encephalopathy (TSE) in the EU in 2003, including the Results of the Survey of Prion Protein Genotypes in Sheep Breeds. Directorate D — Food Safety: production and distribution chain D2 — Biological risks. Available online at tse2003en.pdf. Google Scholar
  7. Ferguson, N. M., Donnelly, C. A., Woolhouse, M. E. J., and Anderson, R. M. (1997), “The Epidemiology of BSE in Cattle Herds in Great Britain. II. Model Construction and Analysis of Transmission Dynamics,” Philosophical Transactions of the Royal Society of London, 352, 803–838.CrossRefGoogle Scholar
  8. Martin, P. A. J., Cameron, A. R., Greiner, M., and Jorgensen, P. H. (2003), “Scenario Tree Modelling of the Danish Diagnostic System to Demonstrate Freedom from Highly Pathogenic Avian Influenza,” in Electronic Proceedings of the 10th Meeting of the International Society for Veterinary Epidemiology and Economics (ISVEE), Vina del Mar, Chile.Google Scholar
  9. Morignat, E. C., Ducrot, C., Roy, P., Baron, T., Vinard, J.L., Biacabe, A. G., Madec, J. Y., Bencsik, A., Debeer, S., Eliazsewicz, M., and Calavas, D. (2002), “Targeted Surveillance to Assess the Prevalence of BSE in High-Risk Populations in Western France and the Associated Risk Factors,” Vet Rec, 151, 73–77.Google Scholar
  10. Muller, K. E., and Benignus, V. A. (1992), “Increasing Scientific Power with Statistical Power,” Neurotoxicology and Teratology, 14, 211–219.CrossRefGoogle Scholar
  11. OIE (2004a), Guidelines for the Establishment or the Regaining of Recognition for Foot and Mouth Disease Free Country or Zone, Appendix 3.8.7.of the International Animal HealthCode. Available online at Google Scholar
  12. OIE (2004b), Highly Pathogenic Avian Influenza, Chapter 2.7.12 of the International Animal HealthCode. Available online at en_chapitre_2.7.12.htm. Google Scholar
  13. OIE (2004c), Surveillance Systems for Bovine Spongiform Encephalopathy, Appendix 3.8.4 of the International Animal HealthCode. Available online at eng/normes/ mcode/en_chapitre_3.8.4.htm. Google Scholar
  14. Ridout, M. S., and Morgan, B. J. T. (1991), “Modelling Digit Preference in Fecundability Studies,” Biometrics, 47, 1423–1433.CrossRefGoogle Scholar
  15. StataCorp (2003), Stata Statistical Software: Release 8. College Station: StataCorp LP.Google Scholar
  16. Wilesmith, J. W., and Morris, R. S. (2004), Development of a Method for Evaluation of National Surveillance Data and Optimization of National Surveillance Strategies for Bovine Spongiform Encephalopathy, European Union TSE Community Reference Laboratory, Veterinary Laboratories Agency, Weybrige, UK.Google Scholar

Copyright information

© International Biometric Society 2006

Authors and Affiliations

  1. 1.Applied Statistics, School of Biological SciencesUniversity of ReadingReadingUK
  2. 2.International EpiLabDanish Institute for Food and Veterinary ResearchDenmark
  3. 3.Federal Institute for Risk Assessment (BfR)BerlinGermany

Personalised recommendations