Ridge estimation of the VAR(1) model and its time series chain graph from multivariate time-course omics data

Globaltest confidence regions and their application to ridge regression

We construct confidence regions in high dimensions by inverting the globaltest statistics, and use them to choose the tuning parameter for penalized regression. The selected model corresponds to the point in the confidence region of the parameters that minimizes the penalty, making it the least complex model that still has acceptable fit according to the test that defines the confidence region. As the globaltest is particularly powerful in the presence of many weak predictors, it connects well to ridge regression, and we thus focus on ridge penalties in this paper. The confidence region method is quick to calculate, intuitive, and gives decent predictive potential. As a tuning parameter selection method it may even outperform classical methods such as cross‐validation in terms of mean squared error of prediction, especially when the signal is weak. We illustrate the method for linear models in simulation study and for Cox models in real gene expression data of breast cancer samples.

Identification of Deregulated Pathways, Key Regulators, and Novel miRNA-mRNA Interactions in HPV-Mediated Transformation

Next to a persistent infection with high-risk human papillomavirus (HPV), molecular changes are required for the development of cervical cancer. To identify which molecular alterations drive carcinogenesis, we performed a comprehensive and longitudinal molecular characterization of HPV-transformed keratinocyte cell lines. Comparative genomic hybridization, mRNA, and miRNA expression analysis of four HPV-containing keratinocyte cell lines at eight different time points was performed. Data was analyzed using unsupervised hierarchical clustering, integrated longitudinal expression analysis, and pathway enrichment analysis. Biological relevance of identified key regulatory genes was evaluated in vitro and dual-luciferase assays were used to confirm predicted miRNA-mRNA interactions. We show that the acquisition of anchorage independence of HPV-containing keratinocyte cell lines is particularly associated with copy number alterations. Approximately one third of differentially expressed mRNAs and miRNAs was directly attributable to copy number alterations. Focal adhesion, TGF-beta signaling, and mTOR signaling pathways were enriched among these genes. PITX2 was identified as key regulator of TGF-beta signaling and inhibited cell growth in vitro, most likely by inducing cell cycle arrest and apoptosis. Predicted miRNA-mRNA interactions miR-221-3p_BRWD3, miR-221-3p_FOS, and miR-138-5p_PLXNB2 were confirmed in vitro. Integrated longitudinal analysis of our HPV-induced carcinogenesis model pinpointed relevant interconnected molecular changes and crucial signaling pathways in HPV-mediated transformation.

Ridge estimation of network models from time-course omics data

Time-course omics experiments enable the reconstruction of the dynamics of the cellular regulatory network. Here, we describe the means for this reconstruction and the downstream exploitation of the inferred network. It is assumed that one of the various vector-autoregressive models (VAR) models presented here serves as a reasonably accurate description of the time-course omics data. The models are estimated through ridge penalized likelihood maximization, accompanied by functionality for the determination of optimal penalty paramaters. Prior knowledge on the network topology is accommodated by the estimation procedures. Various routes that translate the fitted models into more tangible implications for the medical researcher are described. The network is inferred from the-nonsparse-ridge estimates through empirical Bayes probabilistic thresholding. The influence of a (trait of a) molecular entity at the current time on those at future time points is assessed by mutual information, impulse response analysis, and path decomposition of the covariance. The presented methodology is applied to the omics data from the p53 signaling pathway during HPV-induced cellular transformation. All methodology is implemented in the ragt2ridges package, freely available from the Comprehensive R Archive Network.

Reconstruction of molecular network evolution from cross-sectional omics data

Cross-sectional studies may shed light on the evolution of a disease like cancer through the comparison of patient traits among disease stages. This problem is especially challenging when a gene-gene interaction network needs to be reconstructed from omics data, and, in addition, the patients of each stage need not form a homogeneous group. Here, the problem is operationalized as the estimation of stage-wise mixtures of Gaussian graphical models (GGMs) from high-dimensional data. These mixtures are fitted by a (fused) ridge penalized EM algorithm. The fused ridge penalty shrinks GGMs of contiguous stages. The (fused) ridge penalty parameters are chosen through cross-validation. The proposed estimation procedures are shown to be consistent and their performance in other respects is studied in simulation. The down-stream exploitation of the fitted GGMs is outlined. In a data illustration the methodology is employed to identify gene-gene interaction network changes in the transition from normal to cancer prostate tissue.