Vazquez A I, Gianola D, Bates D, Weigel K A, Heringstad B
Department of Dairy Science, University of Wisconsin, Madison 53706, USA.
J Dairy Sci. 2009 Feb;92(2):739-48. doi: 10.3168/jds.2008-1325.
Clinical mastitis is typically coded as presence/absence during some period of exposure, and records are analyzed with linear or binary data models. Because presence includes cows with multiple episodes, there is loss of information when a count is treated as a binary response. The Poisson model is designed for counting random variables, and although it is used extensively in epidemiology of mastitis, it has rarely been used for studying the genetics of mastitis. Many models have been proposed for genetic analysis of mastitis, but they have not been formally compared. The main goal of this study was to compare linear (Gaussian), Bernoulli (with logit link), and Poisson models for the purpose of genetic evaluation of sires for mastitis in dairy cattle. The response variables were clinical mastitis (CM; 0, 1) and number of CM cases (NCM; 0, 1, 2, ..). Data consisted of records on 36,178 first-lactation daughters of 245 Norwegian Red sires distributed over 5,286 herds. Predictive ability of models was assessed via a 3-fold cross-validation using mean squared error of prediction (MSEP) as the end-point. Between-sire variance estimates for NCM were 0.065 in Poisson and 0.007 in the linear model. For CM the between-sire variance was 0.093 in logit and 0.003 in the linear model. The ratio between herd and sire variances for the models with NCM response was 4.6 and 3.5 for Poisson and linear, respectively, and for model for CM was 3.7 in both logit and linear models. The MSEP for all cows was similar. However, within healthy animals, MSEP was 0.085 (Poisson), 0.090 (linear for NCM), 0.053 (logit), and 0.056 (linear for CM). For mastitic animals the MSEP values were 1.206 (Poisson), 1.185 (linear for NCM response), 1.333 (logit), and 1.319 (linear for CM response). The models for count variables had a better performance when predicting diseased animals and also had a similar performance between them. Logit and linear models for CM had better predictive ability for healthy cows and had a similar performance between them.
临床型乳腺炎通常编码为在某个暴露时间段内是否存在，记录通过线性或二元数据模型进行分析。由于存在情况包括有多次发病的奶牛，将计数视为二元反应时会有信息损失。泊松模型是为计数随机变量设计的，尽管它在乳腺炎流行病学中被广泛使用，但很少用于研究乳腺炎的遗传学。已经提出了许多用于乳腺炎遗传分析的模型，但它们尚未进行正式比较。本研究的主要目标是比较线性（高斯）、伯努利（带logit连接）和泊松模型，以用于奶牛乳腺炎种公牛的遗传评估。反应变量为临床型乳腺炎（CM；0, 1）和CM病例数（NCM；0, 1, 2, ..）。数据包括分布在5286个牛群中的245头挪威红牛种公牛的36178头头胎女儿的记录。通过使用预测均方误差（MSEP）作为终点的3折交叉验证来评估模型的预测能力。NCM的种公牛间方差估计在泊松模型中为0.065，在线性模型中为0.007。对于CM，种公牛间方差在logit模型中为0.093，在线性模型中为0.003。对于以NCM为反应变量的模型，牛群方差与种公牛方差之比在泊松模型和线性模型中分别为4.6和3.5，对于CM模型，logit模型和线性模型均为3.7。所有奶牛的MSEP相似。然而，在健康动物中，MSEP分别为0.085（泊松）、0.090（NCM的线性模型）、0.053（logit）和0.056（CM的线性模型）。对于患乳腺炎的动物，MSEP值分别为1.206（泊松）、1.185（NCM反应的线性模型）、1.333（logit）和1.319（CM反应的线性模型）。计数变量模型在预测患病动物时表现更好，且它们之间的表现相似。CM的logit和线性模型对健康奶牛具有更好的预测能力，且它们之间的表现相似。
