Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-28T05:07:29.778Z Has data issue: false hasContentIssue false
  • English
  • Français

Analysis of censored survival data using random regression models

Published online by Cambridge University Press:  18 August 2016

R. F. Veerkamp ,
S. Brotherstone ,
B. Engel  and
T. H. E. Meuwissen
R. F. Veerkamp
Affiliation:
Institute for Animal Science and Health, ID-Lelystad, PO Box 65, 8200 AB Lelystad, The Netherlands
S. Brotherstone
Affiliation:
Institute of Cell, Animal and Population Biology, University of Edinburgh, West Mains Road, Edinburgh EH9 3JT, UK
B. Engel
Affiliation:
Institute for Animal Science and Health, ID-Lelystad, PO Box 65, 8200 AB Lelystad, The Netherlands
T. H. E. Meuwissen
Affiliation:
Institute for Animal Science and Health, ID-Lelystad, PO Box 65, 8200 AB Lelystad, The Netherlands
Get access

Abstract

Censoring of records is a problem in the prediction of breeding values for longevity, because breeding values are required before actual lifespan is known. In this study we investigated the use of random regression models to analyse survival data, because this method combines some of the advantages of a multitrait approach and the more sophisticated proportional hazards models. A model was derived for the binary representation of survival data and links with proportional hazards models and generalized linear models are shown. Variance components and breeding values were predicted using a linear approximation, including time-dependent fixed effects and random regression coefficients. Production records in lactations 1 to 5 were available on 24741 cows in the UK, all having had the opportunity to survive five lactations. The random regression model contained a linear regression on milk yield within herd (no. = 1417) by lactation number (no. = 4), Holstein percentage and year-month of calving effect (no. = 72). The additive animal genetic effects were modelled using orthogonal polynomials of order 1 to 4 with random coefficients and the error terms were fitted for each lactation separately, either correlated or not. Variance components from the full (i.e. uncensored) data set, were used to predict breeding values for survival in each lactation from both uncensored and randomly censored data. In the uncensored data, estimates of heritabilities for culling probability in each lactation ranged from 0·02 to 0·04. Breeding values for lifespan (calculated from the survival breeding values) had a range of 2·4 to 3·6 lactations and a standard deviation of 0·25. Correlations between predicted breeding values for 129 bulls, each with more than 30 daughters, from the various data sets ranged from 0·81 to 0·99 and were insensitive to the model used. It is concluded that random regression analysis models used for test-day records analysis of milk yield, might also be of use in the analysis of censored survival data.

Keywords

dairy cowsheritabilitylongevitysurvival analysis
Type
Breeding and genetics
Information
Animal Science , Volume 72 , Issue 1 , February 2001 , pp. 1 - 10
Copyright
Copyright © British Society of Animal Science 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Boettcher, P. J., Jairath, L. K. and Dekkers, J. C. W. 1999. Comparison of methods for genetic evaluation of sires for survival of their daughters in the first three lactations. Journal of Dairy Science 82: 1034–1044.Google Scholar
Breslow, N. E. and Clayton, D. G. 1993. Approximate inference in generalized linear mixed models. Journal of the American Statistical Association 88: 9–25.Google Scholar
Breslow, N. E. and Lin, X. 1995. Bias correction in generalized linear mixed models with a single component of dispersion. Biometrika 82: 81–91.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.Google Scholar
Brotherstone, S., Veerkamp, R. F. and Hill, W. G. 1998. Predicting breeding values for herd life of Holstein-Friesian dairy cattle from lifespan and type. Animal Science 67: 405–411.CrossRefGoogle Scholar
Carstensen, B. 1996. Regression models for interval censored survival data: application to HIV infection in Danish homosexual men. Statistics in Medicine 15: 2177–2189.Google Scholar
Cox, D. R. and Oakes, D. 1984. Analysis of survival data. Chapman and Hall, London.Google Scholar
Dekkers, J. C. M. and Jairath, L. K. 1994. Requirements and uses of genetic evaluations for conformation and herd life. Proceedings of the fifth world congress on genetics applied to livestock production, Guelph, 7-12 August, vol. 17, pp. 61–68.Google Scholar
Ducrocq, V. 1999. Topics that may deserve further attention in survival analysis applied to dairy cattle breeding: some suggestions. Proceedings of the GIFT workshop on longevity, Jouy-en Jossas, France. INTERBULL Bulletin 21: 181–189.Google Scholar
Ducrocq, V. P. and Solkner, 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. 51–52.Google Scholar
Engel, B. and Buist, W. 1998. Bias reduction of approximate maximum likelihood estimates for heritability in threshold models. Biometrics 54: 1155–1164.Google Scholar
Engel, B., Buist, W. and Visscher, A. 1995. Inference for threshold models with variance components from the generalized linear mixed model perspective. Genetics, Selection, Evolution 27: 15–32.CrossRefGoogle Scholar
Engel, B. and Keen, A. 1994. A simple approach for the analysis of generalized linear mixed models. Statistica Neerlandica 48: 1–22.Google Scholar
Essl, A. 1998. Longevity in dairy cattle breeding: a review. Livestock Production Science 57: 79–89.CrossRefGoogle Scholar
Foulley, J. L., Im, S., Gianola, D. and Hoeschele, I. 1987. Empirical estimation of parameters for n polygenic binary traits. Genetics, Selection, Evolution 19: 197–224.Google Scholar
Gilmour, A. R., Anderson, R. D. and Rae, A. L. 1985. The analysis of binomial data by a generalized linear mixed model. Biometrika 72: 593–599.CrossRefGoogle Scholar
Gilmour, A. R., Cullis, B. R., Welham, S. J. and Thompson, R. 2000. ASREML reference manual version 2000. New South Wales Agriculture, Orange, Australia.Google Scholar
Jairath, L., Dekkers, J. C. M., Schaeffer, L. R., Liu, Z., Burnside, E. B. and Kolstad, B. 1998. Genetic evaluation for herd life in Canada. Journal of Dairy Science 81: 550–562.CrossRefGoogle ScholarPubMed
Jamrozik, J. and Schaeffer, L. R. 1997. Estimates of genetic parameters for a test day model with random regressions for yield traits of first lactation Holsteins. Journal of Dairy Science 80: 762–770.Google Scholar
Kettunen, A. and Mantysaari, E. A. 1996. Estimation of genetic parameters for test-day milk production at different stages of lactation of Finnish Ayrshire heifers. Agricultural and Food Science in Finland 5: 185–192.CrossRefGoogle Scholar
Kirkpatrick, M., Hill, W. G. and Thompson, R. 1994. Estimating the covariance structure of traits during growth and ageing, illustrated with lactation in dairy cattle. Genetical Research 64: 57–69.Google Scholar
Lee, Y. and Nelder, J. A. 1996. Hierarchical generalized linear models. Journal of the Royal Statistical Society, B 44: 226–233.Google Scholar
Lubbers, R., Brotherstone, S., Ducrocq, V. P. and Visscher, P. M. 2000. A comparison of a linear and proportional hazards approach to analyse discrete longevity data in dairy cows. Animal Science 70: 197–206.Google Scholar
Madgwick, P. A. and Goddard, M. E. 1989. Genetic and phenotypic parameters of longevity in Australian dairy cattle. Journal of Dairy Science 72: 2624–2632.CrossRefGoogle Scholar
Pool, M. H. and Meuwissen, T. H. E. 1999. Prediction of daily milk yields from a limited number of test days using test day models. Journal of Dairy Science 82: 1555–1564.Google Scholar
Pool, M. H. and Meuwissen, T. H. E. 2000. Reduction of the number of parameters needed for a polynomial random regression test day model. Livestock Production Science 64: 133–145.Google Scholar
Rendel, J. M. and Robertson, A. 1950. Some aspects of longevity in dairy cattle. Empire Journal of Experimental Agriculture 18: 49–56.Google Scholar
Schall, R. 1991. Estimation in generalized linear models with random effects. Biometrika 78: 719–728.Google Scholar
VanRaden, P. M. and Klaaskate, E. J. H. 1993. Genetic evaluation of length of productive life including predicted longevity of live cows. Journal of Dairy Science 76: 2758–2764.CrossRefGoogle ScholarPubMed
Veerkamp, R. F., Brotherstone, S. and Meuwissen, T. H. E. 1999. Survival analysis using random regression models. Proceedings of the GIFT workshop on longevity, Jouy-en Jossas, France. INTERBULL Bulletin 21: 36–40.Google Scholar
Veerkamp, R. F., Hill, W. G., Stott, A. W., Brotherstone, S. and Simm, G. 1995. Selection for longevity and yield in dairy cows using transmitting abilities for type and yield. Animal Science 61: 189–197.Google Scholar
Visscher, P. M., Thompson, R., Yazdi, H., Hill, W. G. and Brotherstone, S. 1999. Genetic analysis of longevity in the UK: present practice and considerations for the future. Proceedings of the GIFT workshop on longevity, Jouy-en Jossas, France. INTERBULL Bulletin 21: 16–22.Google Scholar
White, I. M. S., Thompson, R. and Brotherstone, S. 1999. Genetic and environmental smoothing of lactation curves with cubic splines. Journal of Dairy Science 82: 632–638.CrossRefGoogle ScholarPubMed