Miok Viktorian, Wilting Saskia M, van Wieringen Wessel N
Department of Epidemiology and Biostatistics, VU University Medical Center, 1007, MB, Amsterdam, The Netherlands.
Department of Pathology, VU University Medical Center, 1007, MB, Amsterdam, The Netherlands.
Biom J. 2017 Jan;59(1):172-191. doi: 10.1002/bimj.201500269. Epub 2016 Nov 7.
Omics experiments endowed with a time-course design may enable us to uncover the dynamic interplay among genes of cellular processes. Multivariate techniques (like VAR(1) models describing the temporal and contemporaneous relations among variates) that may facilitate this goal are hampered by the high-dimensionality of the resulting data. This is resolved by the presented ridge regularized maximum likelihood estimation procedure for the VAR(1) model. Information on the absence of temporal and contemporaneous relations may be incorporated in this procedure. Its computational efficient implemention is discussed. The estimation procedure is accompanied with an LOOCV scheme to determine the associated penalty parameters. Downstream exploitation of the estimated VAR(1) model is outlined: an empirical Bayes procedure to identify the interesting temporal and contemporaneous relationships, impulse response analysis, mutual information analysis, and covariance decomposition into the (graphical) relations among variates. In a simulation study the presented ridge estimation procedure outperformed a sparse competitor in terms of Frobenius loss of the estimates, while their selection properties are on par. The proposed machinery is illustrated in the reconstruction of the p53 signaling pathway during HPV-induced cellular transformation. The methodology is implemented in the ragt2ridges R-package available from CRAN.
具有时间进程设计的组学实验或许能使我们揭示细胞过程中基因间的动态相互作用。多元技术（如描述变量间时间和同期关系的VAR(1)模型）虽有助于实现这一目标，但所得数据的高维度给其带来了阻碍。本文提出的VAR(1)模型的岭正则化最大似然估计程序解决了这一问题。该程序可纳入关于不存在时间和同期关系的信息。文中讨论了其计算高效的实现方式。估计程序配有留一法交叉验证（LOOCV）方案以确定相关惩罚参数。概述了对估计的VAR(1)模型的下游利用：一种用于识别有趣的时间和同期关系的经验贝叶斯程序、脉冲响应分析、互信息分析以及将协方差分解为变量间的（图形）关系。在一项模拟研究中，就估计的弗罗贝尼乌斯损失而言，本文提出的岭估计程序优于一个稀疏竞争方法，而它们的选择特性相当。在人乳头瘤病毒（HPV）诱导的细胞转化过程中p53信号通路的重建中展示了所提出的方法机制。该方法在可从综合R存档网络（CRAN）获取的ragt2ridges R包中得以实现。
