Large-scale studies of gene expression are commonly influenced by biological and technical sources of expression variation, including batch effects, sample characteristics, and environmental impacts. Learning the causal relationships between observable variables may be challenging in the presence of unobserved confounders. Furthermore, many high-dimensional regression techniques may perform worse. In fact, controlling for unobserved confounding variables is essential, and many deconfounding methods have been suggested for application in a variety of situations. The main contribution of this article is the development of a two-stage deconfounding procedure based on Bow-free Acyclic Paths (BAP) search developed into the framework of Structural Equation Models (SEM), called SEMbap(). In the first stage, an exhaustive search of missing edges with significant covariance is performed via Shipley d-separation tests; then, in the second stage, a Constrained Gaussian Graphical Model (CGGM) is fitted or a low dimensional representation of bow-free edges structure is obtained via Graph Laplacian Principal Component Analysis (gLPCA). We compare four popular deconfounding methods to BAP search approach with applications on simulated and observed expression data. In the former, different structures of the hidden covariance matrix have been replicated. Compared to existing methods, BAP search algorithm is able to correctly identify hidden confounding whilst controlling false positive rate and achieving good fitting and perturbation metrics.

MOTIVATION: With the exponential growth of expression and protein-protein interaction (PPI) data, the identification of functional modules in PPI networks that show striking changes in molecular activity or phenotypic signatures becomes of particular interest to reveal process-specific information that is correlated with cellular or disease states. This requires both the identification of network nodes with reliability scores and the availability of an efficient technique to locate the network regions with the highest scores. In the literature, a number of heuristic methods have been suggested. We propose SEMtree(), a set of tree-based structure discovery algorithms, combining graph and statistically interpretable parameters together with a user-friendly R package based on structural equation models framework. RESULTS: Condition-specific changes from differential expression and gene-gene co-expression are recovered with statistical testing of node, directed edge, and directed path difference between groups. In the end, from a list of seed (i.e. disease) genes or gene P-values, the perturbed modules with undirected edges are generated with five state-of-the-art active subnetwork detection methods. The latter are supplied to causal additive trees based on Chu-Liu-Edmonds' algorithm (Chow and Liu, Approximating discrete probability distributions with dependence trees. IEEE Trans Inform Theory 1968;14:462-7) in SEMtree() to be converted in directed trees. This conversion allows to compare the methods in terms of directed active subnetworks. We applied SEMtree() to both Coronavirus disease (COVID-19) RNA-seq dataset (GEO accession: GSE172114) and simulated datasets with various differential expression patterns. Compared to existing methods, SEMtree() is able to capture biologically relevant subnetworks with simple visualization of directed paths, good perturbation extraction, and classifier performance. AVAILABILITY AND IMPLEMENTATION: SEMtree() function is implemented in the R package SEMgraph, easily available at https://CRAN.R-project.org/package=SEMgraph.

MOTIVATION: With the advent of high-throughput sequencing in molecular biology and medicine, the need for scalable statistical solutions for modeling complex biological systems has become of critical importance. The increasing number of platforms and possible experimental scenarios raised the problem of integrating large amounts of new heterogeneous data and current knowledge, to test novel hypotheses and improve our comprehension of physiological processes and diseases. RESULTS: Combining network analysis and causal inference within the framework of structural equation modeling (SEM), we developed the R package SEMgraph. It provides a fully automated toolkit, managing complex biological systems as multivariate networks, ensuring robustness and reproducibility through data-driven evaluation of model architecture and perturbation, which is readily interpretable in terms of causal effects among system components. AVAILABILITY AND IMPLEMENTATION: SEMgraph package is available at https://cran.r-project.org/web/packages/SEMgraph. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Pathway enrichment analysis is extensively used in high-throughput experimental studies to gain insight into the functional roles of pre-defined subsets of genes, proteins and metabolites. Methods that leverages information on the topology of the underlying pathways outperform simpler methods that only consider pathway membership, leading to improved performance. Among all the proposed software tools, there's the need to combine high statistical power together with a user-friendly framework, making it difficult to choose the best method for a particular experimental environment. RESULTS: We propose SEMgsa, a topology-based algorithm developed into the framework of structural equation models. SEMgsa combine the SEM p values regarding node-specific group effect estimates in terms of activation or inhibition, after statistically controlling biological relations among genes within pathways. We used SEMgsa to identify biologically relevant results in a Coronavirus disease (COVID-19) RNA-seq dataset (GEO accession: GSE172114) together with a frontotemporal dementia (FTD) DNA methylation dataset (GEO accession: GSE53740) and compared its performance with some existing methods. SEMgsa is highly sensitive to the pathways designed for the specific disease, showing low p values ([Formula: see text]) and ranking in high positions, outperforming existing software tools. Three pathway dysregulation mechanisms were used to generate simulated expression data and evaluate the performance of methods in terms of type I error followed by their statistical power. Simulation results confirm best overall performance of SEMgsa. CONCLUSIONS: SEMgsa is a novel yet powerful method for identifying enrichment with regard to gene expression data. It takes into account topological information and exploits pathway perturbation statistics to reveal biological information. SEMgsa is implemented in the R package SEMgraph, easily available at https://CRAN.R-project.org/package=SEMgraph .