Sheep Feed and Scrapie, France, Appendix

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Vol. 11, No. 8
August 2005

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•	Description of the Clog-log model
•	References
•	Back to article

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Sheep Feed and Scrapie, France

Sandrine Philippe,* Christian Ducrot,† Pascal Roy,‡ Laurent Remontet,‡ Nathalie Jarrige,* and Didier Calavas*
*Agence Française de Sécurité Sanitaire des Aliments, Lyon, France; †Institut National de la Recherche Agronomique, Theix, France; and ‡Centre Hospitalo-Universitaire Lyon-Sud, Lyon, France

Appendix

Description of the Clog-log model

This appendix provides a description of the statistic model, a generalized linear model for binary outcome with the complementary log-log link function, used to assess the associations between flock status and risk factors. The construction is based on the probability (P) for a sheep flock to be qualified as an "infected scrapie flock," assuming independence and equiprobability for animals of a same flock to be infected by scrapie. This probability is equal to

where k is the flock size and p the probability for an animal of the flock to be diagnosed infected by scrapie. Then, applying the complementary log-log function (Clog-log) on P, the quantity below was obtained.

Therefore, the use of Clog-log as the link function (1) leads to model the probability to be infected at the animal level instead of at the flock level. In this model, flock size is introduced through the offset "Log(k)".

where Xj, j∈{1, …, q} is the vector of covariates. Moreover, if X₁ and X₂ are two exposure variables, then

For values of p smaller than 10%, and are very close. Hence, for small values of p,

The parameters estimated from the complementary log-log model can be interpreted as those from a logistic model. The appropriate coding of exposure (X = 1) and nonexposure (X = 0) provides an easy interpretation of the parameters with OR = exp(β) and IC95% = [exp(β) +/- zα/2 s.e.(β)], zα/2 being issued from the cumulative distribution function of the standard normal distribution, and s.e. (β) being the standard error of parameter β (2,3).

References

McCullagh P, Nelder JA. Generalized linear models. 2nd ed. Boca Raton (FL): Chapman and Hall; 1989.
Allard R. A family of mathematical models to describe the risk of infection by a sexually transmitted agent. Epidemiology. 1990;1:30–3.
Shiboski S, Padian NS. Population- and individual-based approaches to the design and analysis of epidemiologic studies of sexually transmitted disease transmission. J Infect Dis. 1996;174(Suppl 2):S188–200.

Comments to the Authors

Please use the form below to submit correspondence to the authors or contact them at the following address:

Didier Calavas, Agence française de sécurité sanitaire des aliments, 31 av. Tony Garnier, F69364 Lyon Cedex 07, France; fax: 33-4-78-61-91-45; email: d.calavas@lyon.afssa.fr

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