Jaffrézic F, Venot E, Laloë D, Vinet A, Renand G
INRA Quantitative and Applied Genetics, 78352 Jouy-en-Josas Cedex, France.
J Anim Sci. 2004 Dec;82(12):3465-73. doi: 10.2527/2004.82123465x.
Growth curve analysis is an important issue for many agricultural and laboratory species, for both phenotypic and genetic studies. The aim of this paper is to present the use of a novel statistical approach, namely the structured antedependence (SAD) models, to deal with this issue. The basic idea of these models is that an observation at time t can be explained by the previous observations. These models are especially appropriate to deal with cumulative traits such as growth, as BW at age t clearly depends on BW measures at ages (t -1), (t -2), etc. These models were applied on an INRA experimental Charolais herd data set. The data comprised BW records for 560 cows born over an 11-yr period (from 1988 to 1998) from 60 sires and 369 dams. The proposed SAD models were compared with the well-known random regression (RR) models that are already widely used in various areas of longitudinal data analysis. It was found that the SAD models fit the growth process better with far fewer parameters than the RR models (9 instead of 16 covariance parameters for the phenotypic analysis, and 14 instead of 21 for the genetic analysis). Despite this smaller number of covariance parameters, the likelihood value was found to be much higher with the SAD vs. the RR models, with a difference of 262.9 for the phenotypic analysis with a quartic polynomial for the RR and 751.5 for the genetic analysis with a cubic polynomial for both the genetic and environmental parts of the RR model. The SAD models also proved to be better able to interpolate missing values. Heritability, genetic, and environmental correlation coefficients were estimated for weights from birth to adulthood. The structured antedependence models proved, in this study, to be very appropriate to model growth data in a parsimonious and flexible way.
生长曲线分析对于许多农业和实验室物种而言，无论是在表型研究还是遗传研究中，都是一个重要问题。本文旨在介绍一种新型统计方法即结构化自相关（SAD）模型的应用，以处理这一问题。这些模型的基本思想是，时间t处的观测值可以由先前的观测值来解释。这些模型特别适用于处理诸如生长等累积性状，因为t龄时的体重（BW）显然取决于（t - 1）龄、（t - 2）龄等时的BW测量值。这些模型应用于法国国家农业研究院（INRA）的夏洛来实验牛群数据集。数据包括1988年至1998年11年间出生的560头母牛的BW记录，这些母牛来自60头公牛和369头母牛。将提出的SAD模型与在纵向数据分析的各个领域中已广泛使用的著名随机回归（RR）模型进行了比较。结果发现，SAD模型比RR模型能以少得多的参数更好地拟合生长过程（表型分析中协方差参数为9个而非16个，遗传分析中为14个而非21个）。尽管协方差参数数量较少，但发现SAD模型的似然值比RR模型高得多，RR模型的四次多项式表型分析相差262.9，RR模型的遗传和环境部分均为三次多项式的遗传分析相差751.5。SAD模型还被证明更能插值缺失值。估计了从出生到成年体重的遗传力、遗传和环境相关系数。在本研究中，结构化自相关模型被证明以一种简约且灵活的方式对生长数据建模非常合适。
