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A comparison of a linear and proportional hazards approach to analyse discrete longevity data in dairy cows

Published online by Cambridge University Press:  18 August 2016

R. Lubbers ,
S. Brotherstone ,
V.P. Ducrocq  and
P.M. Visscher
R. Lubbers
Affiliation:
University of Edinburgh, Institute of Ecology and Resource Management, West Mains Road, Edinburgh EH9 3JG Wageningen Agricultural University, PO Box 338, 6700 AH Wageningen, The Netherlands
S. Brotherstone
Affiliation:
University of Edinburgh, Institute of Cell, Animal and Population Biology, West Mains Road, Edinburgh EH9 3JT
V.P. Ducrocq
Affiliation:
Station de Génétique Quantitative et Appliquée, Institut National de la Recherche Agronomique, 78352 Jouy-en-Josas, France
P.M. Visscher*
Affiliation:
University of Edinburgh, Institute of Ecology and Resource Management, West Mains Road, Edinburgh EH9 3JG
*
† Corresponding author.
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Abstract

The objective of this study was to compare two methods for analysis of longevity in dairy cattle. The first method, currently used for routine genetic evaluation in the UK, uses a linear model to analyse lifespan, i.e. the number of lactations a cow has survived or is expected to survive. The second method was based on the concept of proportional hazard, i.e. modelling the conditional survival probability of a cow as a function of time. Comparisons were based on estimated heritabilities, ranking of estimated breeding values of sires, estimated effects of covariates used in the final models, and the distribution of residuals. The same data set, 21497 observations on the number of lactations cows had survived, was used for both analyses, even in the presence of censored observations. Cows in the data were progeny of 487 sires. Heritability estimates for lifespan or survival were approximately 0·06 for both methods, using the definition of heritability on a logarithmic scale for the proportional hazards model. Correlations between breeding values for sires were high, with absolute values ranging from 0·93 to 0·98, depending on the model fitted. It was concluded that it may be justified to use the standard Weibull model even for discrete time measures such as the number of completed lactations, but that more research is needed in the area of discrete time variates.

Keywords

dairy cattleheritabilitylifespanlongevitysurvival
Type
Breeding and genetics
Information
Animal Science , Volume 70 , Issue 2 , April 2000 , pp. 197 - 206
Copyright
Copyright © British Society of Animal Science 2000

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References

Arendonk, J. A. M. van. 1985. Studies on the replacement policies in dairy cattle. II. Optimum policy and influence of changes in production and prices. Livestock Production Science 13:101–121.CrossRefGoogle Scholar
Brotherstone, S. and Hill, W. G. 1991. Dairy herd life in relation to linear type traits and production. 2. Genetic analyses for pedigree and non-pedigree cows. Animal Production 53: 289–297.Google Scholar
Brotherstone, S. and Hill, W. G. 1994. Estimation of non-additive genetic parameters for lactations 1 to 5 and for survival in Holstein-Friesian dairy cattle. Livestock Production Science 40:115–122.Google Scholar
Brotherstone, S., Veerkamp, R.F. and Hill, W.G. 1997. Genetic parameters for a simple predictor of the lifespan of Holstein-Friesian dairy cattle and its relationship to production. Animal Science 65: 31–37.CrossRefGoogle Scholar
Cox, D. R. 1972. Regression models and life-tables. Journal of the Royal Statistical Society (Series B) 34:187–220.Google Scholar
Cox, D. R. and Snell, E. 1968. A general definition of residuals (with discussion). Journal of the Royal Statistical Society (Series B) 30: 248–275.Google Scholar
Dekkers, J. C. M. and Jairath, L. K. 1994. Requirements and uses of genetic evaluations for conformation and herd life. In Proceedings of the fifth world congress on genetics applied to livestock production, Guelph, vol. 17, pp. 61–64.Google Scholar
Ducrocq, V. P. 1987. An analysis of length of productive life in dairy cattle. Ph.D. thesis, Cornell University, New York.Google Scholar
Ducrocq, V. P. 1994. Statistical analysis of length of productive life for dairy cows of the Normande breed. Journal of Dairy Science 77: 855–866.Google Scholar
Ducrocq, V. P. 1999. Two years of experience with the French genetic evaluation of dairy bulls on production-adjusted longevity of their daughters. Proceedings of the international workshop on EU concerted action for genetic improvement of functional traits in cattle; longevity. Interbull Bulletin 21: 60–67.Google Scholar
Ducrocq, V. P. and Casella, G. 1996. A Bayesian analysis of mixed survival models. Genetics, Selection, Evolution 28: 505–529.Google Scholar
Ducrocq, V. P. and Sölkner, J. 1994. The Survival Kit, a FORTRAN package for the analysis of survival data. Proceedings of the fifth world congress on genetics applied to livestock production, Guelph, vol. 22 pp. 51–55.Google Scholar
Ducrocq, V. P. and Sölkner, J. 1998a. The Survival Kit V3.0, user’s manual, 31 March, 1998. Institut National de la Recherche Agronomique, Paris.Google Scholar
Ducrocq, V. P. and Sölkner, J. 1998b. The Survival Kit V3-0, a package for large analyses of survival data. Proceedings of the sixth world congress on genetics applied to livestock production, Armidale, vol. 27, pp. 447–448.Google Scholar
Ducrocq, V. P., Quaas, R. L., Poliak, E. J. and Casella, G. 1988. Length of productive life for dairy cows. I. Justification of a Weibull model. Journal of Dairy Science 71: 3061–3070.Google Scholar
Famula, T. R. 1981. Exponential stayability model with censoring and covariates. Journal of Dairy Science 64: 538–545.CrossRefGoogle Scholar
Groeneveld, E. 1990. PEST, user’s manual. Institute of Animal Husbandry and Animal Ethology, Federal Agricultural Research Centre, Mariensee, Germany.Google Scholar
Groeneveld, E. 1995. REML VCE — A multivariate multimodel restricted maximum likelihood (co)variance component estimation package, version 3.1. User’s guide. Institute of Animal Husbandry and Animal Ethology, Federal Agricultural Research Centre, Mariensee, Germany.Google Scholar
Gröhn, Y.T., Ducrocq, V. P. and Hertl, J. A. 1997. Modelling the effect of diseases on culling in New York state Holstein dairy cows. Journal of Dairy Science 80: 1755–1766.Google Scholar
Kalbfleisch, J. D. and Prentice, R. L. 1980. The statistical analysis of failure time data. John Wiley and Sons, NY.Google Scholar
Korsgaard, I. R., Andersen, A. H. and Jensen, J. 1999. Discussion of heritability of survival traits. Proceedings of an international workshop on EU concerted action for genetic improvement of functional traits in cattle; longevity. Interbull Bulletin 21: 31–35.Google Scholar
Prentice, R. L. and Gloeckler, L. A. 1978. Regression analysis of grouped survival data with application to breast cancer data. Biometrics 34: 57–67.CrossRefGoogle ScholarPubMed
Rendel, J. M. and Robertson, A. 1950. Some aspects of longevity in dairy cows. Empire Journal of Experimental Agriculture 18: 49–56.Google Scholar
Ringmar-Cederberg, E., Johansson, K., Lundeheim, N. and Rydhmer, L. 1997. Longevity of Large White and Swedish Landrace sows. Proceedings of the 48th annual meeting of the European Association for Animal Production, Vienna, Austria, paper G3.6.Google Scholar
Smith, S. P. and Quaas, R. L. 1984. Productive lifespan of bull progeny groups: failure time analysis. Journal of Dairy Science 67: 2999–3007.Google Scholar
Visscher, P. M., Bowman, P. and Goddard, M. E. 1994. Breeding objectives for pasture based production systems. Livestock Production Science 40:123–137.Google Scholar
Vollema, A. R. and Groen, A. 1998. A comparison of breeding value predictors for longevity using a linear model and survival analysis. Journal of Dairy Science 81: 3315–3320.Google Scholar
Vukasinovic, N. J., Moll, J. and Kiinzi, N. 1997. Analysis of productive life in Swiss Brown cattle. Journal of Dairy Science 80: 2572–2579.Google Scholar
Yazdi, M. H., Rydhmer, L., Ringmar-Cederberg, E., Lundeheim, N. and Johansson, K. 2000. Genetic study of longevity in Swedish Landrace sows. Livestock Production Science In press.Google Scholar