Comparison between linear models and survival analysis for genetic evaluation of clinical mastitis in dairy cattle

Clinical mastitis was analyzed with mixed linear models (LM) and survival analysis (SA) using data from the first 3 lactations of >200,000 Swedish Holstein cows having their first calving between 1995 and 2000. The model for both methods included fixed effects of year-month and age at calving, fixed regressions of proportions of heterosis and North American Holstein genes, and random effects of herd-year at calving and sire. For the LM, clinical mastitis was defined as a binary trait measured from 10 d before to 150 d after calving. For the SA, clinical mastitis was defined either as the time period from 10 d before calving to the day of first treatment or culling because of mastitis (uncensored record) or from 10 d before to the day of next calving, culling for reasons other than mastitis, movement to a new herd, or to lactation d 240 (censored record). The heritability estimates from SA (0.03 to 0.04) were higher than those obtained with the LM (0.01 to 0.03). Consequently, the accuracies of estimated transmitting abilities were also higher for the trait analyzed with SA. The difference between estimates from the 2 methods was greater for later lactations. This study reveals the potential of analyzing clinical mastitis data with SA.     

Genetic evaluation of mastitis in dairy cattle using linear models, threshold models, and survival analysis: a simulation study

The objective was to study, by simulation, whether survival analysis results in a more precise genetic evaluation for mastitis in dairy cattle than cross-sectional linear models and threshold models by using observation periods for mastitis of 2 lengths (the first 150 d of lactation, and the full lactation, respectively). True breeding values for mastitis liability on the underlying scale were simulated for daughters of 400 sires (average daughter group size, 60 or 150), and the possible event of a mastitis case within lactation for each cow was created. For the linear models and the threshold models, mastitis was defined as a binary trait within either the first 150 d of lactation or the full lactation. For the survival analysis, mastitis was defined as the number of days from calving to either the first case of mastitis (uncensored record) or to the day of censoring (i.e., day of culling, lactation d 150 or day of next calving; censored record). Cows could be culled early in lactation (within 10 d after calving) for calving-related reasons or later on because of infertility. The correlation between sire true breeding values for mastitis liability and sire predicted breeding values was greater when using the full lactation data (0.76) than when using data from the first 150 d (0.70) with an average of 150 daughters per sire. The corresponding results were 0.60 and 0.53, respectively, with an average of 60 daughters per sire. Under these simulated conditions, the method used had no effect on accuracy. The higher accuracy of sire breeding values can be translated into a greater genetic gain, unless counteracted by a longer generation interval.     

Detection of different shapes of lactation curve for milk yield in dairy cattle by empirical mathematical models

The study of relationships between mathematical properties of functions used to model lactation curves is usually limited to the evaluation of the goodness of fit. Problems related to the existence of different lactation curve shapes are usually neglected or solved drastically by considering shapes markedly different from the standard as biologically atypical. A deeper investigation could yield useful indications for developing technical tools aimed at modifying the lactation curve in a desirable fashion. Relationships between mathematical properties and lactation curve shapes were analyzed by fitting several common functions (Wood incomplete gamma, Wilmink's exponential, Ali and Schaeffer's polynomial regression, and fifth-order Legendre polynomials) to 229,518 test-day records belonging to 27,837 lactations of Italian Simmental cows. Among the best fits (adjusted r(2) higher than 0.75), the 3-parameter models (Wood and Wilmink) were able to detect 2 main groups of curve shape: standard and atypical. Five-parameter models (Ali and Schaeffer function and the Legendre polynomials) were able to recognize a larger number of curve shapes. The higher flexibility of 5-parameter models was accompanied by increased sensitivity to local random variation as evidenced by the bias in estimated test-day yields at the beginning and end of lactation (border effect). Meaning of parameters, range of their values and of their (co) variances are clearly different among groups of curves. Our results suggest that analysis based on comparisons between parameter values and (co)variances should be done carefully. Comparisons among parameter values and (co)variances could yield more robust, reliable, and easy to interpret results if performed within groups based on curve shape.     

Survival analysis applied to genetic evaluation for female fertility in dairy cattle

The objective of this research was to study whether survival analysis results in a more accurate genetic evaluation for female fertility traits compared with the usual methodology based on linear models. The fertility trait studied was interval between calving and last insemination. A stochastic simulation describing the reproductive cycle of first-parity cows was done, in which true breeding values for conception rate were created. A model containing effects of sire and herd was used both with survival analysis and with mixed linear model analysis to predict sire breeding values. Correlations between true breeding values for conception rate and breeding values for calving to last insemination predicted by the best survival analysis model or the best linear model were 0.77 and 0.68, respectively. The results showed that when pregnancy status is known, survival analysis is a better method than linear models for genetic evaluation of conception rate when using observations on the interval between calving and last insemination.     

Comparison of different models for genetic analysis of clinical mastitis in Austrian Fleckvieh dual-purpose cows

The performance of different models for genetic analyses of clinical mastitis in Austrian Fleckvieh dual-purpose cows was evaluated. The main objective was to compare threshold sire models (probit and logit) with linear sire and linear animal models using REML algorithm. For comparison, data were also analyzed using a Bayesian threshold sire model. The models were evaluated with respect to ranking of sires and their predictive ability in cross-validation. Only minor differences were observed in estimated variance components and heritability from Bayesian and REML probit models. Heritabilities for probit and logit models were 0.06 and 0.08, respectively, whereas heritabilities for linear sire and linear animal models were lower (0.02). Correlations among ranking of sires from threshold and linear sire models were high (>0.99), whereas correlations between any sire model (threshold or linear) and the linear animal model were slightly lower (0.96). The worst sires were ranked very similar across all models, whereas for the best sires some reranking occurred. Further, models were evaluated based on their ability to predict future data, which is one of the main concerns of animal breeders. The predictive ability of each model was determined by using 2 criteria: mean squared error and Pearson correlation between predicted and observed value. Overall, the 5 models did not differ in predictive ability. In contrast to expectations, sire models had the same predictive ability as animal models. Linear models were found to be robust toward departures from normality and performed equally well as threshold models.     

Genetic analysis of mastitis data with different models

The aim of this study was to analyze different mastitis data sets with different statistical models and compare results. Data recording took place on 3 commercial milk farms with an average herd size of 3,200 German Holstein cows. Recording started in February 1998 and was completed in December 2005. During this period, 63,540 treatments for clinical mastitis were recorded. Five different data sets were analyzed and the number of cows varied between 12,972 and 13,618, depending on the data set. Data collection periods contained either the first 50 or the first 300 d of lactation. When the data-recording period ended after 50 d of lactation, data sets were analyzed with a lactation threshold model (LTM), a multiple threshold lactation model (MTLM), and a test-day threshold model (TDTM). In the LTM analysis, mastitis was treated as a binary trait coded as 0 (no mastitis) or 1 (mastitis), whereas in MTLM mastitis, codes were between 0 and 4, depending on the number of estimated days with mastitis. The TDTM treated each day as a single observation coded similarly to that of the LTM. When the data collection period included the first 300 d of lactation, data sets were analyzed with the LTM or MTLM only, because the TDTM was computationally infeasible. Mastitis frequencies in LTM data sets were 25.8 and 39.2%, and 26.9 and 39.2% in MTLM data sets, when data recording ended after 50 and 300 d of lactation, respectively. The mastitis frequency in the TDTM data set was 5.2%. Respective heritability estimates of liability to clinical mastitis were 0.08 and 0.09 using the LTM, and 0.08 and 0.11 using the MTLM. When the TDTM was used, the estimated heritability was 0.15. Rank correlation between breeding values of the different data sets ranged between 0.40 and 0.97. Rank correlation between the LTM and MTLM were higher (0.78 to 0.97) than those between these 2 models and the TDTM (0.40 to 0.59).The MTLM combined the positive effects of both the LTM, with respect to the size of the data sets, and the TDTM, with respect to the lack of information.     

Genotype x environment interaction for protein yield in Dutch dairy cattle as quantified by different models

Variance components and breeding values for protein yield were estimated with REML without and with correction for heterogeneity of variances. Three different sire models were applied, which all accounted for genotype x environment (G x E) interaction. The first model included a sire x herd-year-season subclass (HYS) interaction. The second model divided all records in four different types of management groups, based on estimated HYS subclass effect. The third model, the reaction norm model, performed a random linear regression on the estimated HYS effect. For comparison, a standard model that did not take G x E interaction into account was also applied. Data consisted of 102,899 305-d first-lactation protein records of Holstein Friesians of 1,000 ofthe largest Dutch dairy herds. All animals calved in 1997, 1998, or 1999. Estimated breeding values (EBV) for 2,150 bulls with at least five daughters were calculated. The interaction model detected an interaction variance of 2.5% of the phenotypic variance. The EBV showed a correlation of 1.00 with those of the standard model without interaction. The model with the division in groups showed correlations between groups ranging from 0.73 to 0.86. The EBV showed correlations from 0.84 to 0.91 with the EBV of the standard model. The reaction norm model calculated EBV that had a correlation of 1.00 with the EBV of the standard model. The reaction norm model was not able to detect significant variance of the slope for the protein data corrected for heterogeneity of variances.     

Genetic analysis of somatic cell score in Norwegian cattle using random regression test-day models

The dataset used in this analysis contained a total of 341,736 test-day observations of somatic cell scores from 77,110 primiparous daughters of 1965 Norwegian Cattle sires. Initial analyses, using simple random regression models without genetic effects, indicated that use of homogeneous residual variance was appropriate. Further analyses were carried out by use of a repeatability model and 12 random regression sire models. Legendre polynomials of varying order were used to model both permanent environmental and sire effects, as did the Wilmink function, the Lidauer-M?ntysaari function, and the Ali-Schaeffer function. For all these models, heritability estimates were lowest at the beginning (0.05 to 0.07) and higher at the end (0.09 to 0.12) of lactation. Genetic correlations between somatic cell scores early and late in lactation were moderate to high (0.38 to 0.71), whereas genetic correlations for adjacent DIM were near unity. Models were compared based on likelihood ratio tests, Bayesian information criterion, Akaike information criterion, residual variance, and predictive ability. Based on prediction of randomly excluded observations, models with 4 coefficients for permanent environmental effect were preferred over simpler models. More highly parameterized models did not substantially increase predictive ability. Evaluation of the different model selection criteria indicated that a reduced order of fit for sire effects was desireable. Models with zeroth- or first-order of fit for sire effects and higher order of fit for permanent environmental effects probably underestimated sire variance. The chosen model had Legendre polynomials with 3 coefficients for sire, and 4 coefficients for permanent environmental effects. For this model, trajectories of sire variance and heritability were similar assuming either homogeneous or heterogeneous residual variance structure.     

Short communication: Optimal random regression models for milk production in dairy cattle

Legendre polynomials of orders 3 to 8 in random regression models (RRM) for first-lactation milk production in Canadian Holsteins were compared statistically to determine the best model. Twenty-six RRM were compared using LP of order 5 for the phenotypic age-season groupings. Variance components of RRM were estimated using Bayesian estimation via Gibbs sampling. Several statistical criteria for model comparison were used including the total residual variance, the log likelihood function, Akaike's information criterion, the Bayesian information criterion, Bayes factors, an information-theoretic measure of model complexity, and the percentage relative reduction in complexity. The residual variance always picks the model with the most parameters. The log likelihood and information-theoretic measure picked the model with order 5 for additive genetic effects and order 7 for permanent environmental effects. The currently used model in Canada (order 5 for both additive and permanent environmental effects) was not the best for any single criterion, but was optimal when considering all criteria.     

Evaluation of different feed intake models for dairy cows

The objective of the current study was to evaluate feed intake prediction models of varying complexity using individual observations of lactating cows subjected to experimental dietary treatments in periodic sequences (i.e., change-over trials). Observed or previous period animal data were combined with the current period feed data in the evaluations of the different feed intake prediction models. This would illustrate the situation and amount of available data when formulating rations for dairy cows in practice and test the robustness of the models when milk yield is used in feed intake predictions. The models to be evaluated in the current study were chosen based on the input data required in the models and the applicability to Nordic conditions. A data set comprising 2,161 total individual observations was constructed from 24 trials conducted at research barns in Denmark, Finland, Norway, and Sweden. Prediction models were evaluated by residual analysis using mixed and simple model regression. Great variation in animal and feed factors was observed in the data set, with ranges in total dry matter intake (DMI) from 10.4 to 30.8 kg/d, forage DMI from 4.1 to 23.0 kg/d, and milk yield from 8.4 to 51.1 kg/d. The mean biases of DMI predictions for the National Research Council, the Cornell Net Carbohydrate and Protein System, the British, Finnish, and Scandinavian models were −1.71, 0.67, 2.80, 0.83, −0.60 kg/d with prediction errors of 2.33, 1.71, 3.19, 1.62, and 2.03 kg/d, respectively, when observed milk yield was used in the predictions. The performance of the models were ranked the same, using either mixed or simple model regression analysis, but generally the random contribution to the prediction error increased with simple rather than mixed model regression analysis. The prediction error of all models was generally greater when using previous period data compared with the observed milk yield. When the average milk yield over all periods was used in the predictions of feed intake, the increase in prediction error of all models was generally less than when compared with previous period animal data combined with current feed data. Milk yield as a model input in intake predictions can be substantially affected by current dietary factors. Milk yield can be used as model input when formulating rations aiming to sustain a given milk yield, but can generate large errors in estimates of future feed intake and milk production if the economically optimal diet deviates from the current diet.     

草鱼鱼糜中沙门氏菌生长预测模型的建立

为建立鱼糜中沙门氏菌生长预测模型,选用新鲜草鱼鱼糜和鼠伤寒沙门氏菌作为研究对象,比较了4、10、20、28、37℃条件下鱼糜中鼠伤寒沙门氏菌的生长情况,分别采用Huang模型,Baranyi模型和修正的Gompertz模型进行拟合,建立鱼糜中鼠伤寒沙门氏菌一级生长动力学模型。并用平方根模型方程描述温度与比生长速率和延滞期的关系,得到鼠伤寒沙门氏菌生长二级模型。使用判定系数R2,准确因子(Af),偏差因子(Bf)和均方误差(MSE)对一级和二级模型可靠性进行评价,结果表明修正的Gompertz模型更适合于描述4~37℃条件下鱼糜中鼠伤寒沙门氏菌的生长变化,二级平方根模型可用于描述鱼糜中鼠伤寒沙门氏菌的生长参数,能够为鱼糜中沙门氏菌的监测提供一定的参考依据。      

Estimating microbial survival parameters from dynamic survival data using Microsoft Excel

Reliable survival parameter estimation is an essential part of building predictive models for microbial survival. It has been demonstrated that these parameters can be accurately identified using a one‐step regression approach that fits a survival model to multiple dynamic data sets at once. However, the existing methods are not quite user‐friendly because their application requires relatively high computer skills. In this study, a recursive equation for the Weibull model was used to construct microbial survival curves under dynamic conditions. Based on this, a procedure was developed to estimate survival parameters by fitting the equation to dynamic survival data sets using the built‐in functions and Solver of Microsoft Excel. The results showed that the method provided an easy and accurate way for estimating microbial survival parameters.     

Calculating microbial survival parameters and predicting survival curves from non-isothermal inactivation data

Irrespective of whether the isothermal semi-logarithmic survival curves of heat inactivated microbial cells or spores are linear or nonlinear, it is theoretically possible to numerically calculate their survival parameters from inactivation data obtained under non-isothermal conditions. A method to do the calculation, when the temperature history ('profile') is expressed algebraically, is demonstrated with simulated survival curves. It has been tested with the published survival data of Salmonella, whose nonlinear semi-logarithmic isothermal survival curves can be described by a power law model. The reported survival ratios of Salmonella, determined during non-isothermal heat treatments in a broth and in ground chicken breast, were used to estimate its isothermal survival parameters in the two media and their temperature dependence. These, in turn, were used to predict the cells' survival curves under different temperature 'profiles.' There was a good agreement between the predicted and the reported experimental survival curves in the broth case and reasonable agreement in the ground chicken breasts, where the database was considerably smaller The development of a mathematical method to calculate survival parameters from non-isothermal inactivation data will eliminate the need to determine these parameters under isothermal conditions, which can only be approximated and are technically difficult to perform. In many cases, the proposed method will also enable the determination of the survival parameters in the actual food or medium of interest, which may contain particles, or is too viscous to be heated and cooled effectively using the currently available experimental procedures. In principle, the described mathematical method can also be used to assess organisms' survival parameters in nonthermal inactivation processes, such as exposure to a dissipating chemical agent or the application of ultra high-pressure.     

Genetic parameters for functional traits in dairy cattle from daily random regression models

The objective of the research was to estimate genetic parameters, such as heritabilities and genetic correlations, using daily test day data for milk yield (MY), milking speed (MS), dry matter intake (DMI), and body weight (BW) using random regression methodology. Data were from first lactation dairy cows (n = 320) from the Chamau research farm of the Swiss Federal Institute of Technology, Switzerland over the period from April 1994 to 2004. All traits were recorded daily using automated machines. Estimated heritabilities (h²) varied from 0.18 to 0.30 (mean h² = 0.24) for MY, 0.003 to 0.098 (mean h² = 0.03) for MS, 0.22 to 0.53 (mean h² = 0.43) for BW, and 0.12 to 0.34 (mean h² = 0.23) for DMI. A permanent environmental effect was included in both the univariate and bivariate models, but was assumed constant in estimating some genetic correlations because of convergence problems. Estimated genetic correlations varied from 0.31 to 0.41 between MY and MS, from −0.47 to 0.29 between MY and DMI, from −0.60 to 0.54 between MY and BW, from 0.17 to 0.26 between MS and DMI, from −0.18 to 0.25 between MS and BW, and from −0.89 to 0.29 between DMI and BW. Genetic correlations for MY, MS, DMI, and BW from calving to midlactation decreased similarly to 0.40, 0.36, 0.14, and 0.36 and, at the end of the lactation, decreased to −0.06, 0.23, −0.07, and 0.09, respectively. Daily genetic variance-covariance of many functional traits are reported for the first time and will be useful when constructing selection indexes for more than one trait based on longitudinal genetic parameters.     

Genetic analysis of cow survival in the Israeli dairy cattle population.

The linear model method of VanRaden and Klaaskate for analyzing herd life was expanded. Information on conception and protein yield was included in the estimation of predicted herd life of Israeli Holsteins. Variance components were estimated by a multitrait animal model. Heritability was slightly higher for herd life than for number of parities, but genetic correlations were close to unity. Animal model heritability estimates of herd life were higher than were sire model estimates. The expected herd life of pregnant cows was 420 d greater than for open cows. Each kilogram of increase in protein yield increased expected herd life by 9.5 d. Heritability of expected herd life increased from 0.11 for cows 6 mo after first calving to 0.14 for cows 3 yr from first calving. The genetic correlation of expected and actual herd life increased from 0.87 for records cut after 6 mo to 0.99 for records cut 3 yr after first calving. Phenotypic correlations increased from 0.61 to 0.94. Sire genetic evaluations based on predicted herd life of live cows were strongly biased if all records were weighted equally, and evaluations derived by weighting incomplete records to account for the effects of current herd life on variance components were nearly unbiased.     

Comparison between sire-maternal grandsire and animal models for genetic evaluation of longevity in a dairy cattle population with small herds

Survival analysis techniques for sire-maternal grandsire (MGS) and animal models were used to test the genetic evaluation of longevity in a Slovenian Brown cattle population characterized by small herds. Three genetic models were compared: a sire-MGS model for bulls and an approximate animal model based on estimated breeding values (EBV) from the sire-MGS model for cows, an animal model, and an animal model based on the estimated variance components from the sire-MGS model. In addition, modeling the contemporary group effect was defined as either a herd or a herd-year (HY) effect. With various restrictions on the minimum HY group size (from 1 to 10 cows per HY), changes in estimates of variance components, and consequently also in EBV, were observed for the sire-MGS and animal models. Variance of contemporary group effects decreased when an HY effect was fitted instead of a herd effect. In the case of a sire-MGS model, estimates of additive genetic variance were mostly robust to changes in minimum HY group size or fitting herd or HY effect, whereas they increased in the animal model when HY instead of herd effects was fitted, possibly revealing some confounding between cow EBV and contemporary group effect. Estimated heritabilities from sire-MGS models were between 0.091 and 0.119 and were mainly influenced by the restriction on the HY group size. Estimated heritabilities from animal models were higher: between 0.125 and 0.160 when herd effect was fitted and between 0.171 and 0.210 when HY effect was fitted. Rank correlations between the animal model and the approximate animal model based on EBV from the sire-MGS model were high: 0.94 for cows and 0.93 for sires when a herd effect was fitted and 0.90 for cows and 0.93 for sires when an HY effect was fitted. Validation performed on the independent validation data set revealed that the correlation between sire EBV and daughter survival were slightly higher with the approximate animal model based on EBV from the sire-MGS model compared with the animal model. The correlations between the sire EBV and daughter survival were higher when the model included an HY effect instead of a herd effect. To avoid confounding and reduce computational requirements, it is suggested that the approximate animal model based on EBV from the sire-MGS model and HY as a contemporary group effect is an interesting compromise for practical applications of genetic evaluation of longevity in cattle populations.     

预测微生物模型的评价方法

在预测微生物模型构建过程中,模型验证是必不可少的步骤,其可靠性和适用性得到合理评价后才具有应用价值。本文综述预测微生物模型的常用评价方法及对应的参数,着重归纳总结相关评价参数的基本概念及意义,并结合前期工作的论文数据阐述演示各常用评价参数的应用方法及评价依据。     

盐水鸭中单核细胞增生李斯特菌生长预测模型的建立

为研究盐水鸭中单核细胞增生李斯特菌(Listeriamonocytogenes,Lm)的生长规律,通过测定4、10、16、25℃条件下的生长数据,选用4种常用的一级模型(Gompertz、Logistic、Richards及MMF模型)对数据进行拟合,比较各模型决定系数R^2和均方误差(MSE),确定最适一级模型,根据一级模型得到的最大比生长速率(μmax)和迟滞期(λ)建立与温度相关的二级模型。结果表明:Gompertz模型拟合的生长曲线R^2均达到0.99以上,为最适一级模型,在25℃条件下,Lm经0.78 h后即进入对数期,从4℃提高到10℃时,生长速率从0.02 1g(cfu/g)·h^-1增至0.05 1g(cfu/g)·h^-1,说明温度对盐水鸭中Lm的生长影响较大。选用Ratkowsky平方根模型建立的温度与μmax关系的二级模型R^2为0.98,偏差因子(Bf)、准确因子(Af)分别为0.99、1.01,二次多项式模型建立的温度与λ关系的R^2为0.99,Bf、Af分别为1.01、1.08,表明所建两种模型均能较好地描述盐水鸭中Lm的生长情况。本研究建立的生长模型可为监控盐水鸭的食品安全和风险评估提供参考。     

Genetic analysis of fertility in dairy cattle using negative binomial mixed models.

Two negative binomial mixed models with different dispersion specifications were compared for analysis of dairy reproduction count data. The first model was developed previously and had heterogeneous overdispersion in an associated logarithmic scale, assigning greater uncertainty to observations with smaller conditional expectations. The second model postulated homogeneous overdispersion across all data. A simulation study was used to compare marginal modal estimates of additive genetic variance, based on these two negative binomial models, with analogous estimates computed by an overdispersed Poisson mixed model. Estimators from the second negative binomial and overdispersed Poisson models had better frequentist properties than did those from the first negative binomial model. Nevertheless, application to a data set of number of artificial inseminations until conception in Holstein heifers suggested a slightly better fit of the first negative binomial model. A marginal likelihood ratio test indicated that the additive genetic variance was significant. Cross-validation analyses suggested that the two negative binomial mixed models had slightly better predictive ability than a linear mixed model.