Integrative Sufficient Dimension Reduction Methods for Multi-Omics Data Analysis

During the past two decades, computational analysis has become paramount for biological research. Advancements in high-throughput methods and computational tools resulted in the generation of large amounts of data from different omics fields (multi-omics), such as genomics, epigenomics, transcriptomics, and metabolomics. This plethora of large scale and diverse omics data is being driven by the understanding that a single-omic type does not provide adequate information and integrative analysis of multi-omics data is optimal to gain sufficiently meaningful insights into the actual biological mechanisms. Although various open-source tools have been developed for this purpose, multi-omics data integration and analysis are still beset by a number of problems, including software compatibility, complex parameter selection and creation of functional pipelines with multiple steps of analyses. In this work we present GenOptics, a novel visual analytics platform that aims to facilitate the integration and subsequent analysis of diverse multi-omics datasets as well as meta-data (e.g., clinical data), through a fully interactive environment. The platform comprises of two separate parts. The first incorporates asynchronous analyses of Next-Generation Sequencing raw data, including RNA-, Whole exome-, and ChIP-Seq, using workflows implemented with the Common Workflow Language (doi:10.6084/m9.figshare.3115156.v2) and Docker containers to automate software installation and confer cross-platform portability. The second part constitutes the analytical platform itself, designed to facilitate the execution of robust bioinformatics analyses by life scientists with minimal or no knowledge of programming. GenOptics constitutes an open source (https://genoptics.github.io/), computational biology platform for novel pattern and biomarker detection.

Sliced average third‐moment estimation (SATME) is a typical method for sufficient dimension reduction (SDR) based on high‐order conditional moment. It is useful, particularly in the scenarios of regression mixtures. However, as SATME uses the third‐order conditional moment of the predictors given the response, it may not as robust as some other SDR methods that use lower order moments, say, sliced inverse regression (SIR) and slice average variance estimation (SAVE). Based on the space displacement function, a local influence analysis framework of SATME is constructed including a statistic of influence assessment for the observations. Furthermore, a data‐trimming strategy is suggested based on the above influence assessment. The proposed methodologies solve a typical issue that also exists in some other SDR methods. A real‐data analysis and simulations are presented.

With the development and improvement of high-throughput sequencing technologies, the acquisition and processing approaches of various biological omics data on different levels are becoming more mature. Despite several new disease-associated factors have been discovered based on single omics data analysis, identification of disease targets by integrative analysis of multi-omics data is still growing. Since life is a complex regulatory system in which the regulation of gene mutations, epigenetic alterations, abnormal gene expression as well as anomalous variations in signal pathway are related with the occurrence and development of diseases, it is obvious that finding therapeutic factors using single omics data analysis has its limitation. Systematical studies of clinical and pathological mechanisms and identification of optimal therapeutic targets through integrative analysis of multi-omics data from different levels and resources have become an important research direction of precision medicine, which would provide innovative perspectives on disease study and new theoretical basis for early diagnosis, personalized treatment and medicine guide. In this review, we introduce new technologies and research progresses in screening therapeutic targets using systematic omics such as genomics, transcriptomics and epigenomics, and also discusse new strategies and advantages of integrative analysis among them.

Recent technology has made it possible to simultaneously perform multi-platform genomic profiling (e.g. DNA methylation (DM) and gene expression (GE)) of biological samples, resulting in so-called ‘multi-dimensional genomic data’. Such data provide unique opportunities to study the coordination between regulatory mechanisms on multiple levels. However, integrative analysis of multi-dimensional genomics data for the discovery of combinatorial patterns is currently lacking. Here, we adopt a joint matrix factorization technique to address this challenge. This method projects multiple types of genomic data onto a common coordinate system, in which heterogeneous variables weighted highly in the same projected direction form a multi-dimensional module (md-module). Genomic variables in such modules are characterized by significant correlations and likely functional associations. We applied this method to the DM, GE, and microRNA expression data of 385 ovarian cancer samples from the The Cancer Genome Atlas project. These md-modules revealed perturbed pathways that would have been overlooked with only a single type of data, uncovered associations between different layers of cellular activities and allowed the identification of clinically distinct patient subgroups. Our study provides an useful protocol for uncovering hidden patterns and their biological implications in multi-dimensional ‘omic’ data.

In this work, we address the longstanding puzzle that Sliced Inverse Regression (SIR) often performs poorly for sufficient dimension reduction when the structural dimension d (the dimension of the central space) exceeds 4. We first show that in the multiple index model Y=f(PX)+ϵ where X is a p-standard normal vector, ϵ is an independent noise, and P is a projection operator from Rp to Rd, if the link function f follows the law of a Gaussian process. Then with high probability, the dth eigenvalue λd of Cov[E(X|Y)] satisfies λd≤Ce−θd for some positive constants C and θ. We then focus on the low signal regime where λd can be arbitrarily small and not larger than d−8.1, and prove that the minimax risk of estimating the central space is lower bounded by dp nλd. Combining these two results, we provide a convincing explanation for the poor performance of SIR when d is large, a phenomenon that has perplexed researchers for nearly three decades. The technical tools developed here may be of independent interest for studying other sufficient dimension reduction methods.

Sufficient dimension reduction (SDR) is a popular framework for supervised dimension reduction, aiming at reducing the dimensionality of input data while information on output data is maximally maintained. On the other hand, in many recent supervised classification learning tasks, it is conceivable that the balance of samples in each class varies between the training and testing phases. Such a phenomenon, referred to as class-prior change, causes existing SDR methods to perform undesirably particularly when the training data is highly imbalanced. In this paper, we extend the state-of-the-art SDR method called leastsquares gradients for dimension reduction (LSGDR) to be able to cope with such class-prior change under the semi-supervised learning setup where unlabeled test data are available in addition to labeled training data. Through experiments, we demonstrate the usefulness of our proposed method.

Colorectal cancer (CRC) exhibits substantial heterogeneity in molecular subtypes and clinical outcomes. We performed an integrative analysis of multi-omics data from 274 CRC patients to investigate the impact of gut microbiota composition on prognosis, identify novel subtypes, and develop a machine learning-based prognostic model. Our microbiome analysis revealed significant differences between CRC and normal tissues. Multi-omics clustering identified two major CRC subtypes, CS1 and CS2, with distinct molecular characteristics and survival outcomes. We developed the Multi-Omics Integrative Clustering and Machine Learning Score (MCMLS) model, which demonstrated strong prognostic value in predicting patient survival and outperformed existing models. The MCMLS low-score group exhibited higher immune cell infiltration, increased metabolic pathway activity, and potentially better immunotherapy response. In contrast, the MCMLS high-score group showed higher mutation burden, fibroblast infiltration, and enrichment of cell adhesion and migration pathways. Bacterial analysis revealed differentially abundant bacteria associated with prognosis. Importantly, MCMLS consistently predicted immunotherapy response across six independent datasets. Our findings highlight the complex interplay between the gut microbiome, tumor microenvironment, and immune landscape in CRC, providing valuable insights for improving patient stratification and personalized treatment strategies.

The recent development of high-throughput technology has allowed us to accumulate vast amounts of multi-omics data. Because even single omics data have a large number of variables, integrated analysis of multi-omics data suffers from problems such as computational instability and variable redundancy. Most multi-omics data analyses apply single supervised analysis, repeatedly, for dimensional reduction and variable selection. However, these approaches cannot avoid the problems of redundancy and collinearity of variables. In this study, we propose a novel approach using blockwise component analysis. This would solve the limitations of current methods by applying variable clustering and sparse principal component (sPC) analysis. Our approach consists of two stages. The first stage identifies homogeneous variable blocks, and then extracts sPCs, for each omics dataset. The second stage merges sPCs from each omics dataset, and then constructs a prediction model. We also propose a graphical method showing the results of sparse PCA and model fitting, simultaneously. We applied the proposed methodology to glioblastoma multiforme data from The Cancer Genome Atlas. The comparison with other existing approaches showed that our proposed methodology is more easily interpretable than other approaches, and has comparable predictive power, with a much smaller number of variables.

BackgroundCharacterizing cancer molecular subtypes is crucial for improving prognosis and individualized treatment. Integrative analysis of multi-omics data has become an important approach for disease subtyping, yielding better understanding of the complex biology. Current multi-omics integration tools and methods for cancer subtyping often suffer challenges of high computational efficiency as well as the problem of weight assignment on data types.ResultsHere, we present an efficient multi-omics integration via weighted affinity and self-diffusion (MOSD) to dissect cancer heterogeneity. MOSD first construct local scaling affinity on each data type and then integrate all affinities by weighted linear combination, followed by the self-diffusion to further improve the patients’ similarities for the downstream clustering analysis. To demonstrate the effectiveness and usefulness for cancer subtyping, we apply MOSD across ten cancer types with three measurements (Gene expression, DNA methylation, miRNA).ConclusionsOur approach exhibits more significant differences in patient survival and computationally efficient benchmarking against several state-of-art integration methods and the identified molecular subtypes reveal strongly biological interpretability. The code as well as its implementation are available in GitHub: https://github.com/DXCODEE/MOSD.

Robust sufficient dimension reduction via ball covariance

Sufficient dimension reduction (SDR) continues to be an active field of research. When estimating the central subspace (CS), inverse regression based SDR methods involve solving a generalized eigenvalue problem, which can be problematic under the large-p-small-n situation. In recent years, new techniques have emerged in numerical linear algebra, called randomized algorithms or random sketching, for high-dimensional and large scale problems. To overcome the large-p-small-n SDR problem, we combine the idea of statistical inference with random sketching to propose a new SDR method, called integrated random-partition SDR (iRP-SDR). Our method consists of the following three steps: (i)Randomly partition the covariates into subsets to construct an envelope subspace with low dimension. (ii)Obtain a sketch of the CS by applying a conventional SDR method within the constructed envelope subspace. (iii)Repeat the above two steps many times and integrate these multiple sketches to form the final estimate of the CS. After describing the details of these steps, the asymptotic properties of iRP-SDR are established. Unlike existing methods, iRP-SDR does not involve the determination of the structural dimension until the last stage, which makes it more adaptive to a high-dimensional setting. The advantageous performance of iRP-SDR is demonstrated via simulation studies and a practical example analyzing EEG data.

The complexity of biological systems and the limitations of analyzing individual omics studies for biomarker discovery have raised the need for a holistic approach by multi-omics integration. By integrating data from multiple layers, researchers can gain insights into the entire system rather than just individual components. Also, integrative analysis can help identify molecular signatures that are more accurate in predicting disease onset, progression, and response to treatment, leading to better-targeted therapies and personalized medicine. In this paper, we explored statistical and deep learning methods for integrative analysis of metabolomics, lipidomics, peptidomics, proteomics, and glycoproteomics data acquired by LC-MS/MS analysis of serum samples from 20 hepatocellular carcinoma (HCC) cases and 20 patients with liver cirrhosis (CIRR). The goal is to identify a panel of multi-omics features that distinguish HCC cases from cirrhotic controls. A pathway analysis using these features identified biological pathways such as LXR/RXR Activation and Acute Response signaling as significantly enriched in our multi-omics datasets.

With the rapid development of high-throughput experimental technologies, bioinformatics and computational modeling has been a rapid evolving science field concerned with the development of various analysis methods and tools for investigating these large biological data efficiently and rigorously. There are many methods and tools available for the analysis of single omics dataset. It is a great challenge that biological systems are being further investigated by integrating multiple heterogeneous and large omics data. Many powerful methods and algorithmic techniques have been developed to answer important biomedical questions through integrative analysis. In this chapter, in order to help the bench biologist analyze omics data, we introduced various methods from classical statistical techniques for single marker association and multivariate analysis to more recent advances from gene network analysis and integrative analysis of multi-omics data.

Several neural decoding algorithms have successfully converted brain signals into commands to control a computer cursor and prosthetic devices. A majority of decoding methods, such as population vector algorithms (PVA), optimal linear estimators (OLE), and neural networks (NN), are effective in predicting movement kinematics, including movement direction, speed and trajectory but usually require a large number of neurons to achieve desirable performance. This study proposed a novel decoding algorithm even with signals obtained from a smaller numbers of neurons. We adopted sliced inverse regression (SIR) to predict forelimb movement from single-unit activities recorded in the rat primary motor (M1) cortex in a water-reward lever-pressing task. SIR performed weighted principal component analysis (PCA) to achieve effective dimension reduction for nonlinear regression. To demonstrate the decoding performance, SIR was compared to PVA, OLE, and NN. Furthermore, PCA and sequential feature selection (SFS) which are popular feature selection techniques were implemented for comparison of feature selection effectiveness. Among SIR, PVA, OLE, PCA, SFS, and NN decoding methods, the trajectories predicted by SIR (with a root mean square error, RMSE, of 8.47 ± 1.32 mm) was closer to the actual trajectories compared with those predicted by PVA (30.41 ± 11.73 mm), OLE (20.17 ± 6.43 mm), PCA (19.13 ± 0.75 mm), SFS (22.75 ± 2.01 mm), and NN (16.75 ± 2.02 mm). The superiority of SIR was most obvious when the sample size of neurons was small. We concluded that SIR sorted the input data to obtain the effective transform matrices for movement prediction, making it a robust decoding method for conditions with sparse neuronal information.

On permutation tests for predictor contribution in sufficient dimension reduction