Including network knowledge into Cox regression models for biomarker signature discovery

Structured sparsity regularization for analyzing high-dimensional omics data

The development of new molecular and cell technologies is having a significant impact on the quantity of data generated nowadays. The growth of omics databases is creating a considerable potential for knowledge discovery and, concomitantly, is bringing new challenges to statistical learning and computational biology for health applications. Indeed, the high dimensionality of these data may hamper the use of traditional regression methods and parameter estimation algorithms due to the intrinsic non-identifiability of the inherent optimization problem. Regularized optimization has been rising as a promising and useful strategy to solve these ill-posed problems by imposing additional constraints in the solution parameter space. In particular, the field of statistical learning with sparsity has been significantly contributing to building accurate models that also bring interpretability to biological observations and phenomena. Beyond the now-classic elastic net, one of the best-known methods that combine lasso with ridge penalizations, we briefly overview recent literature on structured regularizers and penalty functions that have been applied in biomedical data to build parsimonious models in a variety of underlying contexts, from survival to generalized linear models. These methods include functions of $\ell _k$-norms and network-based penalties that take into account the inherent relationships between the features. The successful application to omics data illustrates the potential of sparse structured regularization for identifying disease's molecular signatures and for creating high-performance clinical decision support systems towards more personalized healthcare. Supplementary information: Supplementary data are available at Briefings in Bioinformatics online.

State of the art in selection of variables and functional forms in multivariable analysis-outstanding issues

BACKGROUND

How to select variables and identify functional forms for continuous variables is a key concern when creating a multivariable model. Ad hoc 'traditional' approaches to variable selection have been in use for at least 50 years. Similarly, methods for determining functional forms for continuous variables were first suggested many years ago. More recently, many alternative approaches to address these two challenges have been proposed, but knowledge of their properties and meaningful comparisons between them are scarce. To define a state of the art and to provide evidence-supported guidance to researchers who have only a basic level of statistical knowledge, many outstanding issues in multivariable modelling remain. Our main aims are to identify and illustrate such gaps in the literature and present them at a moderate technical level to the wide community of practitioners, researchers and students of statistics.

METHODS

We briefly discuss general issues in building descriptive regression models, strategies for variable selection, different ways of choosing functional forms for continuous variables and methods for combining the selection of variables and functions. We discuss two examples, taken from the medical literature, to illustrate problems in the practice of modelling.

RESULTS

Our overview revealed that there is not yet enough evidence on which to base recommendations for the selection of variables and functional forms in multivariable analysis. Such evidence may come from comparisons between alternative methods. In particular, we highlight seven important topics that require further investigation and make suggestions for the direction of further research.

CONCLUSIONS

Selection of variables and of functional forms are important topics in multivariable analysis. To define a state of the art and to provide evidence-supported guidance to researchers who have only a basic level of statistical knowledge, further comparative research is required.

The Impact of Pathway Database Choice on Statistical Enrichment Analysis and Predictive Modeling

Pathway-centric approaches are widely used to interpret and contextualize -omics data. However, databases contain different representations of the same biological pathway, which may lead to different results of statistical enrichment analysis and predictive models in the context of precision medicine. We have performed an in-depth benchmarking of the impact of pathway database choice on statistical enrichment analysis and predictive modeling. We analyzed five cancer datasets using three major pathway databases and developed an approach to merge several databases into a single integrative one: MPath. Our results show that equivalent pathways from different databases yield disparate results in statistical enrichment analysis. Moreover, we observed a significant dataset-dependent impact on the performance of machine learning models on different prediction tasks. In some cases, MPath significantly improved prediction performance and also reduced the variance of prediction performances. Furthermore, MPath yielded more consistent and biologically plausible results in statistical enrichment analyses. In summary, this benchmarking study demonstrates that pathway database choice can influence the results of statistical enrichment analysis and predictive modeling. Therefore, we recommend the use of multiple pathway databases or integrative ones.

The Impact of Pathway Database Choice on Statistical Enrichment Analysis and Predictive Modeling

Pathway-centric approaches are widely used to interpret and contextualize -omics data. However, databases contain different representations of the same biological pathway, which may lead to different results of statistical enrichment analysis and predictive models in the context of precision medicine. We have performed an in-depth benchmarking of the impact of pathway database choice on statistical enrichment analysis and predictive modeling. We analyzed five cancer datasets using three major pathway databases and developed an approach to merge several databases into a single integrative one: MPath. Our results show that equivalent pathways from different databases yield disparate results in statistical enrichment analysis. Moreover, we observed a significant dataset-dependent impact on the performance of machine learning models on different prediction tasks. In some cases, MPath significantly improved prediction performance and also reduced the variance of prediction performances. Furthermore, MPath yielded more consistent and biologically plausible results in statistical enrichment analyses. In summary, this benchmarking study demonstrates that pathway database choice can influence the results of statistical enrichment analysis and predictive modeling. Therefore, we recommend the use of multiple pathway databases or integrative ones.

Inference of Genome-Scale Gene Regulatory Networks: Are There Differences in Biological and Clinical Validations?

Causal networks, e.g., gene regulatory networks (GRNs) inferred from gene expression data, contain a wealth of information but are defying simple, straightforward and low-budget experimental validations. In this paper, we elaborate on this problem and discuss distinctions between biological and clinical validations. As a result, validation differences for GRNs reflect known differences between basic biological and clinical research questions making the validations context specific. Hence, the meaning of biologically and clinically meaningful GRNs can be very different. For a concerted approach to a problem of this size, we suggest the establishment of the HUMAN GENE REGULATORY NETWORK PROJECT which provides the information required for biological and clinical validations alike.

Combining Pathway Identification and Breast Cancer Survival Prediction via Screening-Network Methods

Breast cancer is one of the most common invasive tumors causing high mortality among women. It is characterized by high heterogeneity regarding its biological and clinical characteristics. Several high-throughput assays have been used to collect genome-wide information for many patients in large collaborative studies. This knowledge has improved our understanding of its biology and led to new methods of diagnosing and treating the disease. In particular, system biology has become a valid approach to obtain better insights into breast cancer biological mechanisms. A crucial component of current research lies in identifying novel biomarkers that can be predictive for breast cancer patient prognosis on the basis of the molecular signature of the tumor sample. However, the high dimension and low sample size of data greatly increase the difficulty of cancer survival analysis demanding for the development of ad-hoc statistical methods. In this work, we propose novel screening-network methods that predict patient survival outcome by screening key survival-related genes and we assess the capability of the proposed approaches using METABRIC dataset. In particular, we first identify a subset of genes by using variable screening techniques on gene expression data. Then, we perform Cox regression analysis by incorporating network information associated with the selected subset of genes. The novelty of this work consists in the improved prediction of survival responses due to the different types of screenings (i.e., a biomedical-driven, data-driven and a combination of the two) before building the network-penalized model. Indeed, the combination of the two screening approaches allows us to use the available biological knowledge on breast cancer and complement it with additional information emerging from the data used for the analysis. Moreover, we also illustrate how to extend the proposed approaches to integrate an additional omic layer, such as copy number aberrations, and we show that such strategies can further improve our prediction capabilities. In conclusion, our approaches allow to discriminate patients in high-and low-risk groups using few potential biomarkers and therefore, can help clinicians to provide more precise prognoses and to facilitate the subsequent clinical management of patients at risk of disease.

Cancer Progression Prediction Using Gene Interaction Regularized Elastic Net

Different types of genomic aberration may simultaneously contribute to tumorigenesis. To obtain a more accurate prognostic assessment to guide therapeutic regimen choice for cancer patients, the heterogeneous multi-omics data should be integrated harmoniously, which can often be difficult. For this purpose, we propose a Gene Interaction Regularized Elastic Net (GIREN) model that predicts clinical outcome by integrating multiple data types. GIREN conveniently embraces both gene measurements and gene-gene interaction information under an elastic net formulation, enforcing structure sparsity, and the "grouping effect" in solution to select the discriminate features with prognostic value. An iterative gradient descent algorithm is also developed to solve the model with regularized optimization. GIREN was applied to human ovarian cancer and breast cancer datasets obtained from The Cancer Genome Atlas, respectively. Result shows that, the proposed GIREN algorithm obtained more accurate and robust performance over competing algorithms (LASSO, Elastic Net, and Semi-supervised PCA, with or without average pathway expression features) in predicting cancer progression on both two datasets in terms of median area under curve (AUC) and interquartile range (IQR), suggesting a promising direction for more effective integration of gene measurement and gene interaction information.

Cancer Markers Selection Using Network-Based Cox Regression: A Methodological and Computational Practice

International initiatives such as the Cancer Genome Atlas (TCGA) and the International Cancer Genome Consortium (ICGC) are collecting multiple datasets at different genome-scales with the aim of identifying novel cancer biomarkers and predicting survival of patients. To analyze such data, several statistical methods have been applied, among them Cox regression models. Although these models provide a good statistical framework to analyze omic data, there is still a lack of studies that illustrate advantages and drawbacks in integrating biological information and selecting groups of biomarkers. In fact, classical Cox regression algorithms focus on the selection of a single biomarker, without taking into account the strong correlation between genes. Even though network-based Cox regression algorithms overcome such drawbacks, such network-based approaches are less widely used within the life science community. In this article, we aim to provide a clear methodological framework on the use of such approaches in order to turn cancer research results into clinical applications. Therefore, we first discuss the rationale and the practical usage of three recently proposed network-based Cox regression algorithms (i.e., Net-Cox, AdaLnet, and fastcox). Then, we show how to combine existing biological knowledge and available data with such algorithms to identify networks of cancer biomarkers and to estimate survival of patients. Finally, we describe in detail a new permutation-based approach to better validate the significance of the selection in terms of cancer gene signatures and pathway/networks identification. We illustrate the proposed methodology by means of both simulations and real case studies. Overall, the aim of our work is two-fold. Firstly, to show how network-based Cox regression models can be used to integrate biological knowledge (e.g., multi-omics data) for the analysis of survival data. Secondly, to provide a clear methodological and computational approach for investigating cancers regulatory networks.

Identifying the gene signatures from gene-pathway bipartite network guarantees the robust model performance on predicting the cancer prognosis

For the purpose of improving the prediction of cancer prognosis in the clinical researches, various algorithms have been developed to construct the predictive models with the gene signatures detected by DNA microarrays. Due to the heterogeneity of the clinical samples, the list of differentially expressed genes (DEGs) generated by the statistical methods or the machine learning algorithms often involves a number of false positive genes, which are not associated with the phenotypic differences between the compared clinical conditions, and subsequently impacts the reliability of the predictive models. In this study, we proposed a strategy, which combined the statistical algorithm with the gene-pathway bipartite networks, to generate the reliable lists of cancer-related DEGs and constructed the models by using support vector machine for predicting the prognosis of three types of cancers, namely, breast cancer, acute myeloma leukemia, and glioblastoma. Our results demonstrated that, combined with the gene-pathway bipartite networks, our proposed strategy can efficiently generate the reliable cancer-related DEG lists for constructing the predictive models. In addition, the model performance in the swap analysis was similar to that in the original analysis, indicating the robustness of the models in predicting the cancer outcomes.