Avaliação genética da longevidade em vacas leiteiras Pardo-Suíças utilizando modelos de sobrevivência com dados simulados

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Resumo

Resumo: A longevidade de vacas leiteiras da raça Pardo-Suíça foi avaliada utilizando o estimador não-paramétrico de Kaplan-Meier e os modelos de riscos proporcionais de Cox e Weibull, por meio de simulação computacional. O conjunto de dados era composto de 10.000 registros simulados referentes à longevidade das vacas, definida como o tempo até a ocorrência de cinco partos consecutivos (evento). A idade ao primeiro parto, o rebanho e o touro (pai da vaca) foram analisados como covariáveis. O ponto inicial do estudo foi estabelecido em 2.196 dias (72 meses de idade) e o tempo máximo até a falha foi de 2.562 dias (84 meses de idade). A função de sobrevivência de Kaplan-Meier foi utilizada para estimar as curvas de sobrevivência e de taxa de risco associadas à longevidade das fêmeas, identificando a influência de cada covariável sobre o tempo até o evento. Análises utilizando os modelos de Cox e Weibull também foram realizadas. Todas as covariáveis influenciaram significativamente a longevidade das vacas, de acordo com os testes de Log-Rank e Wilcoxon. Os tempos médio e mediano até a ocorrência do evento foram de, aproximadamente, 2.435 dias. Observou-se que touros com valores genéticos mais elevados apresentaram um risco maior de terem filhas que alcançam os cinco partos consecutivos até os 84 meses de idade, indicando que o evento pode ocorrer em um tempo médio mais curto. Nesse caso, tais reprodutores podem ser utilizados como pais de futuras gerações, como estratégia para aumentar a longevidade de suas progênies.
Palavras-chave: dados censurados; estimador produto-limite; modelos de Cox e Weibull; permanência da vaca no rebanho.

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Referências

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

Publicado

2026-06-30

Edição

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ZOOTECNIA

Como Citar

ARAÚJO, D. G. P. G. DE; CUNHA, E. E. Avaliação genética da longevidade em vacas leiteiras Pardo-Suíças utilizando modelos de sobrevivência com dados simulados. Ciência Animal Brasileira / Brazilian Animal Science, v. 27, 30 jun.2026.

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