Genetic evaluation of longevity in Brown Swiss dairy cows using survival models with simulated data
Abstract
Abstract: The longevity of Brown Swiss dairy cows was evaluated using the non-parametric Kaplan Meier estimator and the Cox and Weibull proportional hazards models through computer simulation. A dataset comprising 10,000 records was generated to simulate cow longevity, defined as the time until the occurrence of five consecutive calvings (event). Age at first calving, herd, and sire (the cow’s father) were analyzed as covariates. The starting point of the study was set at 2,196 days (72 months of age), and the maximum time to failure was 2,562 days (84 months of age). The Kaplan-Meier survival function was used to estimate the survival and hazard rate curves associated with female longevity, identifying the influence of each covariate on the time until the event. Analyses using the Cox and Weibull models were also performed. All covariates significantly influenced cow longevity, according to the Log-Rank and Wilcoxon tests. The mean and median times until the occurrence of the event were approximately 2,435 days. It was observed that sires with superior breeding values presented a greater risk of having daughters reaching five consecutive calvings until 84 months of age, indicating that the event can occur in a shorter average time. In this case, such sires may be used as fathers of future generations as a strategy to enhance the longevity of their offspring.
Keywords: censored data; cow stayability in the herd; Cox and Weibull models; product-limit estimator.
Downloads
References
1. ABCGPS - Associação Brasileira de Criadores de Gado Pardo-Suíço. Pardo-Suíço: Características [Internet]. 2025
[citado em 30 Jul 2025]. Available from: https://pardo-suico.com.br/?page_id=5732
2. Hu H, Mu T, Ma Y, Wang X, Ma Y. Analysis of longevity traits in Holstein cattle: a review. Front Genet. 2021;12:1-15.
Available from: https://doi.org/10.3389/fgene.2021.695543
3. Jamrozik J, Fatehi J, Schaeffer LR. Comparison of models for genetic evaluation of survival traits in dairy cattle: a
simulation study. J Anim Breed Genet. 2008;125:75-83. Available from: https://doi.org/10.1111/j.1439-0388.2007.00712.x
Ciência Animal Brasileira | Brazilian Animal Science, v.27, 84687E, 2026.
4. Caraviello DZ, Weigel KA, Gianola D. Prediction of Longevity Breeding Values for US Holstein Sires Using Survival
Analysis Methodology. J Dairy Sci. 2004;87(10):3518–3525. Available from: https://doi.org/10.3168/jds.S0022
0302(04)73488-8
5. Han R, Kok A, Mourits M, Hogeveen H. Effects of extending dairy cow longevity by adjusted reproduction management
decisions on partial net return and greenhouse gas emissions: A dynamic stochastic herd simulation study. J Dairy Sci.
2024;107(9):6902-6912. Available from: https://doi.org/10.3168/jds.2023-24089
6. Han R, Mourits M, Hogeveen H. The association of dairy cattle longevity with farm level technical inefficiency. Front
Vet Sci. 2022;9:1001015. Available from: https://doi.org/10.3389/fvets.2022.1001015
7. Grandl F, Furger M, Kreuzer M, Zehetmeier M. Impact of longevity on greenhouse gas emissions and profitability of
individual dairy cows analysed with different system boundaries. Animal. 2019;13(1):198-208. Available from: https://
doi.org/10.1017/S175173111800112X
8. Vredenberg I, Han R, Mourits M, Hogeveen H, Steeneveld W. An Empirical Analysis on the Longevity of Dairy
Cows in Relation to Economic Herd Performance. Front Vet Sci. 2021;8:646672. Available from: https://doi.org/10.3389/
fvets.2021.646672
9. Shrestha B, Paudyal S, Kaniyamattam K, Grohn YT. Graduate Student Literature Review: Organic dairy cattle
longevity and economic implications—Contemporary perspectives. J Dairy Sci. 2025;108(4):3734-3745. Available from:
https://doi.org/10.3168/jds.2024-25767
10. Vukasinovic N, Moll J, Künzi N. Analysis of productive life in Swiss Brown cattle. J Dairy Sci. 1997;80(10):2572-2579.
Available from: https://doi.org/10.3168/jds.S0022-0302(97)76213-1
11. Dallago GM, Wade KM, Cue RI, McClure JT, Lacroix R, Pellerin D, Vasseur E. Keeping Dairy Cows for Longer: A
Critical Literature Review on Dairy Cow Longevity in High Milk-Producing Countries. Animals. 2021;11(3):808. Available
from: https://doi.org/10.3390/ani11030808
12. Grandl F, Amelchanka SL, Furger M, Clauss M, Zeitz JO, Kreuzer M, et al. Biological implications of longevity in dairy
cows: 2. Changes in methane emissions and efficiency with age. J Dairy Sci. 2016;99(5):3472-3485. Available from:
http://dx.doi.org/10.3168/jds.2015-10262
13. Cardoso FF, Rosa GJ, Tempelman RJ, Torres Junior RA. Modelos hierárquicos bayesianos para estimação robusta
e análise de dados censurados em melhoramento animal. R Bras Zootec. 2009;38(spe):72–80. Available from: https://
doi.org/10.1590/S1516-35982009001300009
14. Ducrocq V, Quaas RL, Pollak EJ, Casella G. Length of Productive Life of Dairy Cows. 1. Justification of a Weibull
Model. J Dairy Sci. 1988;71(11):3061-3070. Available from: https://doi.org/10.3168/jds.S0022-0302(88)79906-3
15. Schneider MP, Strandberg E, Ducrocq V, Roth A. Survival analysis applied to genetic evaluation for female fertility in
dairy cattle. J Dairy Sci. 2005; 88(6):2253-2259. Available from: https://doi.org/10.3168/jds.S0022-0302(05)72901-5
16. Grzesiak W, Adamczyk K, Zaborski D, Wójcik J. Estimation of Dairy Cow Survival in the First Three Lactations
for Different Culling Reasons Using the Kaplan–Meier Method. Animals. 2022;12(15):1942. Available from: https://doi.
org/10.3390/ani12151942
17. Djedović R, Vukasinovic N, Stanojević D, Bogdanović V, Ismael H, Janković D, et al. Genetic Parameters for
Functional Longevity, Type Traits, and Production in the Serbian Holstein. Animals. 2023;13(3):534. Available from:
https://doi.org/10.3390/ani13030534
18. Roxström A, Ducrocq V, Strandberg E. Survival analysis of longevity in dairy cattle on a lactation basis. Genet Sel
Evol. 2003;35:305-18. Available from: https://doi.org/10.1186/1297-9686-35-3-305
19. Ducrocq V. An improved model for the French genetic evaluation of dairy bulls on length of productive life of their
daughters. Anim Sci. 2005;80(3):249–256. Available from: https://doi.org/10.1079/ASC41720249
20. Kern EL, Cobuci JA, Costa CN, Ducrocq V. Survival analysis of productive life in Brazilian Holstein using a
piecewise Weibull proportional hazard model. Livest Sci. 2016;185:89-96. Available from: https://doi.org/10.1016/j.
livsci.2016.01.019
21. Kaplan EL, Meier P. Nonparametric estimation from incomplete observation. J Am Stat Assoc. 1958;53(282):457
481. Available from: https://doi.org/10.2307/2281868
22. Allison PD. 2010. Survival Analysis Using SAS: A Practical Guide. 2nd ed. Cary: SAS Institute; 2010. 324 p. Inglês.
23. Wienke A. Frailty models in survival analysis. 1st ed. New York: Chapman & Hall/CR; 2010. 324 p. Available from:
https://doi.org/10.1201/9781420073911
24. Cunha EE, Melo TP. Análise de sobrevivência não-paramétrica da idade ao primeiro parto em fêmeas Nelore: um
estudo de simulação. R Bras Biom. 2012;30(3):305-325. Available from: https://biometria.ufla.br/antigos/fasciculos/v30/
v30_n3/A1_Elisangela.pdf.
25. Ducrocq V, Casella G. A Bayesian analysis of mixed survival models. Genet Sel Evol. 1996;28(6):505-529. Available
from: https://doi.org/10.1186/1297-9686-28-6-505
26. Colosimo EA, Giolo SR. Análise de sobrevivência aplicada. 1st ed. São Paulo: Blücher; 2006. 392p. Português.
27. Ducrocq V; Sölkner J, Mészáros G. The Survival Kit v6.1: User's manual. [S.I.: s.n.]; 2012. 83p. Inglês.
Ciência Animal Brasileira | Brazilian Animal Science, v.27, 84687E, 2026.
28. Guedes DG, Cunha EE, Lima GF. Genetic evaluation of age at first calving from Brown Swiss cows through survival
analysis. Arch de Zootec. 2017;66(254):247-255. Available from: https://www.redalyc.org/pdf/495/49553570013.pdf
29. Sas Institute Inc. SAS/STAT® 9.2 User’s guide [CD-ROM]. 2nd ed. Cary: SAS Institute Inc; 2009. 7886p. Available
from: https://support.sas.com/documentation//cdl/en/statug/63033/HTML/default/viewer.htm#titlepage.htm
30. Caetano SL, Rosa GJ, Savegnago RP, Ramos SB, Bezerra LA, Lôbo RB, et al. Characterization of the variable
cow’s age at last calving as a measurement of longevity by using the Kaplan–Meier estimator and the Cox model.
Animal. 2013;7(4):540-546. Available from: https://doi.org/10.1017/S1751731112001826
31. Chirinos Z, Carabaño MJ, Hernández D. Genetic evaluation of length of productive life in the Spanish Holstein
Friesian population. Model validation and genetic parameters estimation. Livest Sci. 2007;106(2-3):120-131. Available
from: https://doi.org/10.1016/j.livsci.2006.07.006
32. Yazdi MH, Visscher PM, Ducrocq V, Thompson R. Heritability, reliability of genetic evaluations and response to
selection in proportional hazard models. J Dairy Sci. 2002;85(6):1563-1577. Available from: https://doi.org/10.3168/jds.
S0022-0302(02)74226-4
33. M’hamdi N, Aloulou R, Bouallegue M, Brar SK, Hamouda MB. Study on functional longevity of Tunisian Holstein
dairy cattle using a Weibull proportional hazard model. Livest Sci. 2010;132(1-3):173-176. Available from: https://doi.
org/10.1016/j.livsci.2010.05.011
34. Amirpour Najafabadi H, Ansari Mahyari S, Edriss MA, Strapakova E. Genetic analysis of productive life length in
Holstein dairy cows using Weibull proportional risk model. Arch Anim Breed. 2016;59(3):387-393. Available from: https://
doi.org/10.5194/aab-59-387-2016
35. Vukasinovic N, Moll J, Casanova L. Implementation of a routine genetic evaluation for longevity based on survival
analysis techniques in dairy cattle populations in Switzerland. J Dairy Sci. 2001;84(9):2073-2080. Available from: https://
doi.org/10.3168/jds.S0022-0302(01)74652-8
36. De Vries A, Marcondes MI. Review: Overview of factors affecting productive lifespan of dairy cows. Animal.
2020;14(S1):s155–s164. Available from: https://doi.org/10.1017/S1751731119003264
37. Saleh AA, Hassan TG, EL-Hedainy DK, El-Barbary AS, Sharaby MA, Rashad AM. Comprehensive assessment of
lifetime performance traits and their genetic background in Holstein cows under semi-arid conditions. Trop Anim Health
Prod. 2026;58(36):1-20. Available from: https://doi.org/10.1007/s11250-025-04806-9
38. Santos GC, Lira TS, Pereira LS, Lopes FB, Ferreira JL. Efeitos não genéticos sobre características produtivas em
rebanhos Nelore criados na região Norte do Brasil. Acta Vet Bras. 2011;5(4):385-392. Available from: https://periodicos.
ufersa.edu.br/acta/article/view/2356/5028
39. Jenko J, V. Ducrocq, M. Kovač. Comparison of piecewise Weibull baseline survival models for estimation of true
and functional longevity in Brown cattle raised in small herds. Animal. 2013;7(10):1583–91. Available from: https://doi.
org/10.1017/S1751731113001055
40. Ziadi C, Sánchez JP, Sánchez M, Molina A. Risk factors and genetic parameters of longevity in Spanish dairy
goat breeds using a Weibull proportional hazards model. Ital J Anim Sci. 2024;23(1):33–41. Available from: https://doi.
org/10.1080/1828051X.2023.2288624
41. Ziadi C, Sánchez JP, Sánchez M, Morales R, Molina A. Survival analysis of productive life in Florida dairy goats using
a Cox proportional hazards model. J Anim Breed Genet. 2023;140:431–439. Available from: https://doi.org/10.1111/
jbg.12769
42. Carvalho MS, Andreozzi VL, Codeço CT, Campos DP, Barbosa MT, Shimakura SE. Análise de sobrevivência: teoria
e aplicações em saúde. 2nd ed. Rio de Janeiro: Editora Fiocruz. 2011. 432 p. Português.
43. Ducrocq V, Sölkner J. “The Survival Kit - v3.0”, a package for large analysis of survival data. In: Proceedings of
the 6th World Congress on Genetics Applied to Livestock Production; 1998 Jan 11-16; Armidale, Australia. New South
Wales: University of New England, 1998, 447-448.
44. Potočnik K, Gantner V, Krsnik J, Štepec M, Logar B, Gorjanc G. Analysis of longevity in Slovenian Holstein cattle.
Acta Agric Slov. 2011;98(2):93-100. Available from: https://doi.org/10.2478/v10014-011-0025-5
45. Samoré AB, Rizzi R, Rossoni A, Bagnato A. Genetic parameters for functional longevity, type traits, somatic cell
scores, milk flow and production in the Italian Brown Swiss. Ital J Anim Sci. 2010;9(2):145-152. Available from: https://
www.tandfonline.com/doi/epdf/10.4081/ijas.2010.e28
46. Forabosco F, Bozzi R, Filippini F, Boettcher P, Van Arendonk JA, Bijma P. Linear model vs. survival analysis for
genetic evaluation of sires for longevity in Chianina beef cattle. Livest Sci. 2006;101(1-3):191-198. Available from:
https://doi.org/10.1016/j.livprodsci.2005.11.010
47. Van Vleck LD, Pollak EJ, Oltenacu EA. Genetics for the animal sciences. New York: W.H. Freeman. 1987. 391p.
Inglês.
48. Sasaki O, Aihara M, Hagiya K, Nishiura A, Ishii K, Satoh M. Genetic evaluation of the longevity of the Holstein
population in Japan using a Weibull proportional hazard model. Animal Sci J. 2012;83(2):95-102. Available from: https://
doi.org/10.1111/j.1740-0929.2011.00943.x
49. Boettcher PJ, Jairath LK, Dekkers JC. Comparison of Methods for Genetic Evaluation of Sires for Survival of Their
Daughters in the First Three Lactations. J Dairy Sci. 1999;82(5):1034–44. Available from: https://doi.org/10.3168/jds.
S0022-0302(99)75324-5
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Brazilian Animal Science/ Ciência Animal Brasileira
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g. in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
How to Cite
Data statement
-
The research data is available on demand, condition justified in the manuscript
