Elghafghuf Adel, Dufour Simon, Reyher Kristen, Dohoo Ian, Stryhn Henrik
Centre for Veterinary Epidemiological Research, University of Prince Edward Island, Charlottetown, PEI C1A 4P3, Canada; Department of Statistics, Faculty of Science, University of Misurata, P.O. Box 2478, Misurata, Libya.
Department of Pathology and Microbiology, Faculty of Veterinary Medicine, University of Montreal, C.P. 5000, St-Hyacinthe, Quebec J2S 7C6, Canada.
Prev Vet Med. 2014 Dec 1;117(3-4):456-68. doi: 10.1016/j.prevetmed.2014.09.013. Epub 2014 Oct 5.
Mastitis is a complex disease affecting dairy cows and is considered to be the most costly disease of dairy herds. The hazard of mastitis is a function of many factors, both managerial and environmental, making its control a difficult issue to milk producers. Observational studies of clinical mastitis (CM) often generate datasets with a number of characteristics which influence the analysis of those data: the outcome of interest may be the time to occurrence of a case of mastitis, predictors may change over time (time-dependent predictors), the effects of factors may change over time (time-dependent effects), there are usually multiple hierarchical levels, and datasets may be very large. Analysis of such data often requires expansion of the data into the counting-process format - leading to larger datasets - thus complicating the analysis and requiring excessive computing time. In this study, a nested frailty Cox model with time-dependent predictors and effects was applied to Canadian Bovine Mastitis Research Network data in which 10,831 lactations of 8035 cows from 69 herds were followed through lactation until the first occurrence of CM. The model was fit to the data as a Poisson model with nested normally distributed random effects at the cow and herd levels. Risk factors associated with the hazard of CM during the lactation were identified, such as parity, calving season, herd somatic cell score, pasture access, fore-stripping, and proportion of treated cases of CM in a herd. The analysis showed that most of the predictors had a strong effect early in lactation and also demonstrated substantial variation in the baseline hazard among cows and between herds. A small simulation study for a setting similar to the real data was conducted to evaluate the Poisson maximum likelihood estimation approach with both Gaussian quadrature method and Laplace approximation. Further, the performance of the two methods was compared with the performance of a widely used estimation approach for frailty Cox models based on the penalized partial likelihood. The simulation study showed good performance for the Poisson maximum likelihood approach with Gaussian quadrature and biased variance component estimates for both the Poisson maximum likelihood with Laplace approximation and penalized partial likelihood approaches.
乳腺炎是一种影响奶牛的复杂疾病，被认为是奶牛群中成本最高的疾病。乳腺炎的风险是许多管理和环境因素共同作用的结果，这使得奶农很难控制这种疾病。对临床乳腺炎（CM）的观察性研究通常会生成具有许多影响数据分析特征的数据集：感兴趣的结果可能是乳腺炎病例发生的时间，预测因素可能随时间变化（时间依赖性预测因素），因素的影响可能随时间变化（时间依赖性影响），通常存在多个层次水平，并且数据集可能非常大。对这类数据的分析通常需要将数据扩展为计数过程格式——从而导致数据集更大——因此分析变得复杂，需要大量的计算时间。在本研究中，将具有时间依赖性预测因素和影响的嵌套脆弱性Cox模型应用于加拿大牛乳腺炎研究网络的数据，该数据跟踪了来自69个牛群的8035头奶牛的10831次泌乳，直至首次发生CM。该模型以泊松模型拟合数据，在奶牛和牛群水平上具有嵌套的正态分布随机效应。确定了与泌乳期间CM风险相关的风险因素，如胎次、产犊季节、牛群体细胞评分、牧场使用情况、预挤奶以及牛群中CM治疗病例的比例。分析表明，大多数预测因素在泌乳早期有很强的影响，并且还表明奶牛之间和牛群之间的基线风险存在很大差异。针对与实际数据类似的情况进行了一项小型模拟研究，以评估采用高斯求积法和拉普拉斯近似法的泊松最大似然估计方法。此外，将这两种方法的性能与基于惩罚偏似然的广泛使用的脆弱性Cox模型估计方法的性能进行了比较。模拟研究表明，采用高斯求积法的泊松最大似然方法性能良好，而采用拉普拉斯近似法的泊松最大似然方法和惩罚偏似然方法的方差分量估计存在偏差。
