Skip to main content Accessibility help

Analysis of censored survival data using random regression models

  • R. F. Veerkamp (a1), S. Brotherstone (a2), B. Engel (a1) and T. H. E. Meuwissen (a1)


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.



Hide All
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: 10341044.
Breslow, N. E. and Clayton, D. G. 1993. Approximate inference in generalized linear mixed models. Journal of the American Statistical Association 88: 925.
Breslow, N. E. and Lin, X. 1995. Bias correction in generalized linear mixed models with a single component of dispersion. Biometrika 82: 8191.
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: 3137.
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: 405411.
Carstensen, B. 1996. Regression models for interval censored survival data: application to HIV infection in Danish homosexual men. Statistics in Medicine 15: 21772189.
Cox, D. R. and Oakes, D. 1984. Analysis of survival data. Chapman and Hall, London.
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. 6168.
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: 181189.
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. 5152.
Engel, B. and Buist, W. 1998. Bias reduction of approximate maximum likelihood estimates for heritability in threshold models. Biometrics 54: 11551164.
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: 1532.
Engel, B. and Keen, A. 1994. A simple approach for the analysis of generalized linear mixed models. Statistica Neerlandica 48: 122.
Essl, A. 1998. Longevity in dairy cattle breeding: a review. Livestock Production Science 57: 7989.
Foulley, J. L., Im, S., Gianola, D. and Hoeschele, I. 1987. Empirical estimation of parameters for n polygenic binary traits. Genetics, Selection, Evolution 19: 197224.
Gilmour, A. R., Anderson, R. D. and Rae, A. L. 1985. The analysis of binomial data by a generalized linear mixed model. Biometrika 72: 593599.
Gilmour, A. R., Cullis, B. R., Welham, S. J. and Thompson, R. 2000. ASREML reference manual version 2000. New South Wales Agriculture, Orange, Australia.
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: 550562.
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: 762770.
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: 185192.
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: 5769.
Lee, Y. and Nelder, J. A. 1996. Hierarchical generalized linear models. Journal of the Royal Statistical Society, B 44: 226233.
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: 197206.
Madgwick, P. A. and Goddard, M. E. 1989. Genetic and phenotypic parameters of longevity in Australian dairy cattle. Journal of Dairy Science 72: 26242632.
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: 15551564.
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: 133145.
Rendel, J. M. and Robertson, A. 1950. Some aspects of longevity in dairy cattle. Empire Journal of Experimental Agriculture 18: 4956.
Schall, R. 1991. Estimation in generalized linear models with random effects. Biometrika 78: 719728.
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: 27582764.
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: 3640.
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: 189197.
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: 1622.
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: 632638.


Related content

Powered by UNSILO

Analysis of censored survival data using random regression models

  • R. F. Veerkamp (a1), S. Brotherstone (a2), B. Engel (a1) and T. H. E. Meuwissen (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.