A genetic and spatial Bayesian analysis of mastitis resistanceSolve Sæbøa and Arnoldo Frigessib
a IKBM, Agricultural University of Norway, PO Box 5003, 1432 Ås, Norway
b Section of Medical Statistics, University of Oslo, and Norwegian Computing Center, Oslo, Norway
(Received 3 December 2003; accepted 26 April 2004 )
Abstract - A nationwide health card recording system for dairy cattle was introduced in Norway in 1975 (the Norwegian Cattle Health Services). The data base holds information on mastitis occurrences on an individual cow basis. A reduction in mastitis frequency across the population is desired, and for this purpose risk factors are investigated. In this paper a Bayesian proportional hazards model is used for modelling the time to first veterinary treatment of clinical mastitis, including both genetic and environmental covariates. Sire effects were modelled as shared random components, and veterinary district was included as an environmental effect with prior spatial smoothing. A non-informative smoothing prior was assumed for the baseline hazard, and Markov chain Monte Carlo methods (MCMC) were used for inference. We propose a new measure of quality for sires, in terms of their posterior probability of being among the, say 10% best sires. The probability is an easily interpretable measure that can be directly used to rank sires. Estimating these complex probabilities is straightforward in an MCMC setting. The results indicate considerable differences between sires with regards to their daughters disease resistance. A regional effect was also discovered with the lowest risk of disease in the south-eastern parts of Norway.
Key words: disease resistance / genetic effect / Markov chain Monte Carlo / spatial smoothing / survival analysis
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