J Dairy Sci 2002 Jun;85(6):1563-77

University of Edinburgh, Institute of Cell, Animal and Population Biology, UK.

The purposes of this study were 1) to investigate the heritability, reliability, and selection response for survival traits following a Weibull frailty proportional hazard model; and 2) to examine the relationship between genetic parameters from a Weibull model, a discrete proportional hazard model, and a binary data analysis using a linear model. Both analytical methods and Monte Carlo simulations were used to achieve these aims. Data were simulated using the Weibull frailty model with two different shapes of the Weibull distribution. Breeding values of 100 unrelated sires with 50 to 100 progeny (with different levels of censoring) were generated from a normal distribution and two different sire variances. For analysis of longevity data on the discrete scale, simulated data were transformed to a discrete scale using arbitrary ends of discrete intervals of 400, 800, or 1200 d. For binary data analysis, an individual's longevity was either 0 (when longevity was less than the end of interval) or 1 (when longevity was equal or greater than the end of interval). Three different statistical models were investigated in this study: a Weibull model, a discrete-time model (a proportional hazard model assuming that the survival data are measured on a discrete scale with few classes), and a linear model based upon binary data. An alternative derivation using basic expressions of reliabilities in sire models suggests a simple equation for the heritability on the original scale (effective heritability) that is not dependent on the Weibull parameters. The predictions of reliabilities using the proposed formulae in this study are in very good agreement with reliabilities observed from simulations. In general, the estimates of reliability from either the discrete model or the binary data analysis were close to estimates from the Weibull model for a given number of uncensored records in this simplified case of a balanced design. Although selection response from the binary data analysis depends on the end of interval point, there is a relatively good agreement between selection responses in the Weibull model and the binary data analysis. In general, when the underlying survival data is from a Weibull distribution, it appears that the method of analyzing data does not greatly affect the results in terms of sire ranking or response to selection, at least for the simplified context considered in this study.

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http://dx.doi.org/10.3168/jds.S0022-0302(02)74226-4 | DOI Listing |

June 2002

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data analysis

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heritability reliability

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J Dairy Sci 2004 May;87(5):1469-76

Department of Dairy Science, University of Wisconsin, Madison 53706, USA.

Predicted transmitting abilities (PTA) of US Jersey sires for daughter longevity were calculated using a Weibull proportional hazards sire model and compared with predictions from a conventional linear animal model. Culling data from 268,008 Jersey cows with first calving from 1981 to 2000 were used. The proportional hazards model included time-dependent effects of herd-year-season contemporary group and parity by stage of lactation interaction, as well as time-independent effects of sire and age at first calving. Read More

May 2004

J Anim Sci 2006 Jun;84(6):1338-50

Department of Animal Science and Animal Health, Royal Veterinary and Agricultural University, Grønnegårdsvej 2, 1870 Frederiksberg C, Denmark.

The objective of this study was, by means of simulation, to quantify the effect of ignoring individual heterogeneity in Weibull sire frailty models on parameter estimates and to address the consequences for genetic inferences. Three simulation studies were evaluated, which included 3 levels of individual heterogeneity combined with 4 levels of censoring (0, 25, 50, or 75%). Data were simulated according to balanced half-sib designs using Weibull log-normal animal frailty models with a normally distributed residual effect on the log-frailty scale. Read More

June 2006

J Dairy Sci 2004 Oct;87(10):3518-25

Department of Dairy Science, niversity of Wisconsin, Madison 53706, USA.

Breeding values of Holstein sires for daughter longevity in each of 9 geographical regions of the United States were predicted using a Weibull proportional hazards model. Longevity (also commonly referred to as herd life or length of productive life) was defined as the number of days from first calving until culling or censoring. Records from 2,322,389 Holstein cows with first calving from 1990 to 2000 were used. Read More

October 2004

J Dairy Sci 2009 Mar;92(3):1229-39

Department of Genetics and Biotechnology, Faculty of Agricultural Sciences, Aarhus University, Tjele, Denmark.

The objectives of this study were to estimate genetic parameters and evaluate models for genetic evaluation of days from calving to first insemination (ICF) and days open (DO). Data including 509,512 first-parity records of Danish Holstein cows were analyzed using 5 alternative sire models that dealt with censored records in different ways: 1) a conventional linear model (LM) in which a penalty of 21 d was added to censored records; 2) a bivariate threshold-linear model (TLM), which included a threshold model for censoring status (0, 1) of the observations, and a linear model for ICF or DO without any penalty on censored records; 3) a right-censored linear model (CLM); 4) a Weibull proportional hazard model (SMW); and 5) a Cox proportional hazard model (SMC) constructed with piecewise constant baseline hazard function. The variance components for ICF and DO estimated from LM and TLM were similar, whereas CLM gave higher estimates of both additive genetic and residual components. Read More

March 2009