Gonçalves M A D, Bello N M, Dritz S S, Tokach M D, DeRouchey J M, Woodworth J C, Goodband R D
J Anim Sci. 2016 May;94(5):1940-50. doi: 10.2527/jas.2015-0106.
Advanced methods for dose-response assessments are used to estimate the minimum concentrations of a nutrient that maximizes a given outcome of interest, thereby determining nutritional requirements for optimal performance. Contrary to standard modeling assumptions, experimental data often present a design structure that includes correlations between observations (i.e., blocking, nesting, etc.) as well as heterogeneity of error variances; either can mislead inference if disregarded. Our objective is to demonstrate practical implementation of linear and nonlinear mixed models for dose-response relationships accounting for correlated data structure and heterogeneous error variances. To illustrate, we modeled data from a randomized complete block design study to evaluate the standardized ileal digestible (SID) Trp:Lys ratio dose-response on G:F of nursery pigs. A base linear mixed model was fitted to explore the functional form of G:F relative to Trp:Lys ratios and assess model assumptions. Next, we fitted 3 competing dose-response mixed models to G:F, namely a quadratic polynomial (QP) model, a broken-line linear (BLL) ascending model, and a broken-line quadratic (BLQ) ascending model, all of which included heteroskedastic specifications, as dictated by the base model. The GLIMMIX procedure of SAS (version 9.4) was used to fit the base and QP models and the NLMIXED procedure was used to fit the BLL and BLQ models. We further illustrated the use of a grid search of initial parameter values to facilitate convergence and parameter estimation in nonlinear mixed models. Fit between competing dose-response models was compared using a maximum likelihood-based Bayesian information criterion (BIC). The QP, BLL, and BLQ models fitted on G:F of nursery pigs yielded BIC values of 353.7, 343.4, and 345.2, respectively, thus indicating a better fit of the BLL model. The BLL breakpoint estimate of the SID Trp:Lys ratio was 16.5% (95% confidence interval [16.1, 17.0]). Problems with the estimation process rendered results from the BLQ model questionable. Importantly, accounting for heterogeneous variance enhanced inferential precision as the breadth of the confidence interval for the mean breakpoint decreased by approximately 44%. In summary, the article illustrates the use of linear and nonlinear mixed models for dose-response relationships accounting for heterogeneous residual variances, discusses important diagnostics and their implications for inference, and provides practical recommendations for computational troubleshooting.
剂量反应评估的先进方法用于估计营养素的最低浓度，该浓度可使给定的感兴趣结果最大化，从而确定最佳性能的营养需求。与标准建模假设相反，实验数据通常呈现出一种设计结构，其中包括观测值之间的相关性（即区组、嵌套等）以及误差方差的异质性；如果忽略其中任何一个，都可能误导推断。我们的目标是展示线性和非线性混合模型在剂量反应关系中的实际应用，同时考虑相关数据结构和异质误差方差。为了说明这一点，我们对来自随机完全区组设计研究的数据进行建模，以评估标准化回肠可消化（SID）色氨酸：赖氨酸比例对保育猪生长育肥比（G:F）的剂量反应。拟合了一个基础线性混合模型，以探索G:F相对于色氨酸：赖氨酸比例的函数形式，并评估模型假设。接下来，我们对G:F拟合了3个相互竞争的剂量反应混合模型，即二次多项式（QP）模型、折线线性（BLL）上升模型和折线二次（BLQ）上升模型，所有这些模型都包括由基础模型决定的异方差规范。使用SAS（版本9.4）的GLIMMIX过程拟合基础模型和QP模型，使用NLMIXED过程拟合BLL模型和BLQ模型。我们进一步说明了使用初始参数值的网格搜索来促进非线性混合模型中的收敛和参数估计。使用基于最大似然的贝叶斯信息准则（BIC）比较相互竞争的剂量反应模型之间的拟合度。对保育猪G:F拟合的QP、BLL和BLQ模型的BIC值分别为353.7、343.4和345.2，因此表明BLL模型的拟合度更好。SID色氨酸：赖氨酸比例的BLL断点估计值为16.5%（95%置信区间[16.1, 17.0]）。估计过程中的问题使得BLQ模型的结果值得怀疑。重要的是，考虑异方差提高了推断精度，因为平均断点置信区间的宽度减少了约44%。总之，本文说明了线性和非线性混合模型在考虑异质残差方差的剂量反应关系中的应用，讨论了重要的诊断方法及其对推断的影响，并为计算故障排除提供了实际建议。
