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1 Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, N-1432 Ås, Norway
2 Department of Genetics and Biotechnology, Danish Institute of Agricultural Sciences, Research Centre Foulum, DK-8830 Tjele, Denmark
3 Department of Animal Sciences, University of Wisconsin-Madison, Madison 53706
Corresponding author: J. Ødegård; e-mail: jorgen.odegard{at}umb.no.
Mastitis is associated with elevated somatic cell count in milk, inducing a positive correlation between milk somatic cell score (SCS) and the absence or presence of the disease. In most countries, selection against mastitis has focused on selecting parents with genetic evaluations that have low SCS. Univariate or multivariate mixed linear models have been used for statistical description of SCS. However, an observation of SCS can be regarded as drawn from a 2- (or more) component mixture defined by the (usually) unknown health status of a cow at the test-day on which SCS is recorded. A hierarchical 2-component mixture model was developed, assuming that the health status affecting the recorded test-day SCS is completely specified by an underlying liability variable. Based on the observed SCS, inferences can be drawn about disease status and parameters of both SCS and liability to mastitis. The prior probability of putative mastitis was allowed to vary between subgroups (e.g., herds, families), by specifying fixed and random effects affecting both SCS and liability. Using simulation, it was found that a Bayesian model fitted to the data yielded parameter estimates close to their true values. The model provides selection criteria that are more appealing than selection for lower SCS. The proposed model can be extended to handle a wide range of problems related to genetic analyses of mixture traits.
Key Words: Bayesian methods • mastitis • mixture model • somatic cell score
Abbreviation key: IM = standard univariate model for SCS ignoring the mixture, LNM = liability normal mixture, NM = mixture model ignoring the structure of the underlying liability to mastitis.
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