Identification of influential observations in high-dimensional cancer survival data through the rank product test

Enhancing Prognostic Signatures in Glioblastoma with Feature Selection and Regularised Cox Regression

BACKGROUND

Glioblastoma is a highly aggressive brain tumour with poor survival outcomes, highlighting the need for reliable prognostic models. Developing robust and interpretable prognostic signatures is critical for improving patient stratification and guiding therapy. This study explored the integration of machine learning feature selection with regularised Cox regression to construct prognostic gene signatures for glioblastoma patients.

METHODS

We combined the Boruta algorithm and Random Survival Forests (RSFs) with regularised Cox regression, along with network-based regularisation techniques (HubCox and OrphanCox), to develop interpretable prognostic signatures for stratifying high- and low-risk glioblastoma patients. Using mRNA-seq and survival data from The Cancer Genome Atlas (TCGA), we developed predictive models following WHO-2021 glioma guidelines.

RESULTS

Integrating Boruta or RSF with regularised Cox regression improved the performance and interpretability. Boruta increased the concordance indexes (C-indexes) by 0.030 and 0.013 for LASSO and Elastic Net, respectively, while significantly reducing the feature numbers. RSF similarly enhanced the performance and feature reduction. The genes Lysyl Oxidase Like 1 (LOXL1) and Insulin Like Growth Factor Binding Protein 6 (IGFBP6) were consistently selected and linked to glioma survival, emphasising their clinical significance. The network-based methods demonstrated superior survival probability prediction (lower Integrated Brier Score), although with lower C-index values, highlighting limitations in ranking the survival times. To evaluate the generalisability, external validation using the Chinese Glioma Genome Atlas (CGGA) confirmed that a multigene signature derived from the most consistently selected genes significantly stratified the patients by risk.

CONCLUSIONS

This study underscored the utility of combining machine learning feature selection with survival analysis to enhance prognostic modelling while balancing predictive performance and interpretability.

Robust variable selection methods with Cox model-a selective practical benchmark study

With the advancement of biological and medical techniques, we can now obtain large amounts of high-dimensional omics data with censored survival information. This presents challenges in method development across various domains, particularly in variable selection. Given the inherently skewed distribution of the survival time outcome variable, robust variable selection methods offer potential solutions. Recently, there has been a focus on extending robust variable selection methods from linear regression models to survival models. However, despite these developments, robust methods are currently rarely used in practical applications, possibly due to a limited appreciation of their overall good performance. To address this gap, we conduct a selective review comparing the variable selection performance of twelve robust and non-robust penalised Cox models. Our study reveals the intricate relationship among covariates, survival outcomes, and modeling approaches, demonstrating how subtle variations can significantly impact the performance of methods considered. Based on our empirical research, we recommend the use of robust Cox models for variable selection in practice based on their superior performance in presence of outliers while maintaining good efficiency and accuracy when there are no outliers. This study provides valuable insights for method development and application, contributing to a better understanding of the relationship between correlated covariates and censored outcomes.

Statistical analysis of high-dimensional biomedical data: a gentle introduction to analytical goals, common approaches and challenges

BACKGROUND

In high-dimensional data (HDD) settings, the number of variables associated with each observation is very large. Prominent examples of HDD in biomedical research include omics data with a large number of variables such as many measurements across the genome, proteome, or metabolome, as well as electronic health records data that have large numbers of variables recorded for each patient. The statistical analysis of such data requires knowledge and experience, sometimes of complex methods adapted to the respective research questions.

METHODS

Advances in statistical methodology and machine learning methods offer new opportunities for innovative analyses of HDD, but at the same time require a deeper understanding of some fundamental statistical concepts. Topic group TG9 "High-dimensional data" of the STRATOS (STRengthening Analytical Thinking for Observational Studies) initiative provides guidance for the analysis of observational studies, addressing particular statistical challenges and opportunities for the analysis of studies involving HDD. In this overview, we discuss key aspects of HDD analysis to provide a gentle introduction for non-statisticians and for classically trained statisticians with little experience specific to HDD.

RESULTS

The paper is organized with respect to subtopics that are most relevant for the analysis of HDD, in particular initial data analysis, exploratory data analysis, multiple testing, and prediction. For each subtopic, main analytical goals in HDD settings are outlined. For each of these goals, basic explanations for some commonly used analysis methods are provided. Situations are identified where traditional statistical methods cannot, or should not, be used in the HDD setting, or where adequate analytic tools are still lacking. Many key references are provided.

CONCLUSIONS

This review aims to provide a solid statistical foundation for researchers, including statisticians and non-statisticians, who are new to research with HDD or simply want to better evaluate and understand the results of HDD analyses.

Identification of influential observations in high-dimensional survival data through robust penalized Cox regression based on trimming

Penalized Cox regression can efficiently be used for the determination of biomarkers in high-dimensional genomic data related to disease prognosis. However, results of Penalized Cox regression is influenced by the heterogeneity of the samples who have different dependent structure between survival time and covariates from most individuals. These observations are called influential observations or outliers. A robust penalized Cox model (Reweighted Elastic Net-type maximum trimmed partial likelihood estimator, Rwt MTPL-EN) is proposed to improve the prediction accuracy and identify influential observations. A new algorithm AR-Cstep to solve Rwt MTPL-EN model is also proposed. This method has been validated by simulation study and application to glioma microarray expression data. When there were no outliers, the results of Rwt MTPL-EN were close to the Elastic Net (EN). When outliers existed, the results of EN were impacted by outliers. And whenever the censored rate was large or low, the robust Rwt MTPL-EN performed better than EN. and could resist the outliers in both predictors and response. In terms of outliers detection accuracy, Rwt MTPL-EN was much higher than EN. The outliers who "lived too long" made EN perform worse, but were accurately detected by Rwt MTPL-EN. Through the analysis of glioma gene expression data, most of the outliers identified by EN were those "failed too early", but most of them were not obvious outliers according to risk estimated from omics data or clinical variables. Most of the outliers identified by Rwt MTPL-EN were those who "lived too long", and most of them were obvious outliers according to risk estimated from omics data or clinical variables. Rwt MTPL-EN can be adopted to detect influential observations in high-dimensional survival data.

Mining subgraph coverage patterns from graph transactions

Pattern mining from graph transactional data (GTD) is an active area of research with applications in the domains of bioinformatics, chemical informatics and social networks. Existing works address the problem of mining frequent subgraphs from GTD. However, the knowledge concerning the coverage aspect of a set of subgraphs is also valuable for improving the performance of several applications. In this regard, we introduce the notion of subgraph coverage patterns (SCPs). Given a GTD, a subgraph coverage pattern is a set of subgraphs subject to relative frequency, coverage and overlap constraints provided by the user. We propose the Subgraph ID-based Flat Transactional (SIFT) framework for the efficient extraction of SCPs from a given GTD. Our performance evaluation using three real datasets demonstrates that our proposed SIFT framework is indeed capable of efficiently extracting SCPs from GTD. Furthermore, we demonstrate the effectiveness of SIFT through a case study in computer-aided drug design.