Survival analysis is a statistical technique widely used in many fields of science, in particular in the medical area, and which studies the time until an event of interest occurs. Outlier detection in this context has gained great importance due to the fact that the identification of long or short-term survivors may lead to the detection of new prognostic factors. However, the results obtained using different outlier detection methods and residuals are seldom the same and are strongly dependent of the specific Cox proportional hazards model selected. In particular, when the inherent data have a high number of covariates, dimensionality reduction becomes a key challenge, usually addressed through regularized optimization, e.g. using Lasso, Ridge or Elastic Net regression. In the case of transcriptomics studies, this is an ubiquitous problem, since each observation has a very high number of associated covariates (genes). In order to solve this issue, we propose to use the Rank Product test, a non-parametric technique, as a method to identify discrepant observations independently of the selection method and deviance considered. An example based on the The Cancer Genome Atlas (TCGA) ovarian cancer dataset is presented, where the covariates are patients’ gene expressions. Three sub-models were considered, and, for each one, different outliers were obtained. Additionally, a resampling strategy was conducted to demonstrate the methods’ consistency and robustness. The Rank Product worked as a consensus method to identify observations that can be influential under survival models, thus potential outliers in the high-dimensional space. The proposed technique allows us to combine the different results obtained by each sub-model and find which observations are systematically ranked as putative outliers to be explored further from a clinical point of view.

Learning accurate models from ‘omics data is bringing many challenges due to their inherent high-dimensionality, e.g. the number of gene expression variables, and comparatively lower sample sizes, which leads to ill-posed inverse problems. Furthermore, the presence of outliers, either experimental errors or interesting abnormal clinical cases, may severely hamper a correct classification of patients and the identification of reliable biomarkers for a particular disease. We propose to address this problem through an ensemble classification setting based on distinct feature selection and modeling strategies, including logistic regression with elastic net regularization, Sparse Partial Least Squares - Discriminant Analysis (SPLS-DA) and Sparse Generalized PLS (SGPLS), coupled with an evaluation of the individuals’ outlierness based on the Cook’s distance. The consensus is achieved with the Rank Product statistics corrected for multiple testing, which gives a final list of sorted observations by their outlierness level. We applied this strategy for the classification of Triple-Negative Breast Cancer (TNBC) RNA-Seq and clinical data from the Cancer Genome Atlas (TCGA). The detected 24 outliers were identified as putative mislabeled samples, corresponding to individuals with discrepant clinical labels for the HER2 receptor, but also individuals with abnormal expression values of ER, PR and HER2, contradictory with the corresponding clinical labels, which may invalidate the initial TNBC label. Moreover, the model consensus approach leads to the selection of a set of genes that may be linked to the disease. These results are robust to a resampling approach, either by selecting a subset of patients or a subset of genes, with a significant overlap of the outlier patients identified. The proposed ensemble outlier detection approach constitutes a robust procedure to identify abnormal cases and consensus covariates, which may improve biomarker selection for precision medicine applications. The method can also be easily extended to other regression models and datasets.

Data availability by modern sequencing technologies represents a major challenge in oncological survival analysis, as the increasing amount of molecular data hampers the generation of models that are both accurate and interpretable. To tackle this problem, this work evaluates the introduction of graph centrality measures in classical sparse survival models such as the elastic net. We explore the use of network information as part of the regularization applied to the inverse problem, obtained both by external knowledge on the features evaluated and the data themselves. A sparse solution is obtained either promoting features that are isolated from the network or, alternatively, hubs, i.e. , features that are highly connected within the network. We show that introducing the degree information of the features when inferring survival models consistently improves the model predictive performance in breast invasive carcinoma (BRCA) transcriptomic TCGA data while enhancing model interpretability. Preliminary clinical validation is performed using the Cancer Hallmarks Analytics Tool API and the String database. These case studies are included in the recently released glmSparseNet R package ¹ , a flexible tool to explore the potential of sparse network-based regularizers in generalized linear models for the analysis of omics data.

High-dimensional omics data integration has emerged as a prominent avenue within the healthcare industry, presenting substantial potential to improve predictive models. However, the data integration process faces several challenges, including data heterogeneity, priority sequence in which data blocks are prioritized for rendering predictive information contained in multiple blocks, assessing the flow of information from one omics level to the other and multicollinearity. We propose the Priority-Elastic net algorithm, a hierarchical regression method extending Priority-Lasso for the binary logistic regression model by incorporating a priority order for blocks of variables while fitting Elastic-net models sequentially for each block. The fitted values from each step are then used as an offset in the subsequent step. Additionally, we considered the adaptive elastic-net penalty within our priority framework to compare the results. The Priority-Elastic net and Priority-Adaptive Elastic net algorithms were evaluated on a brain tumor dataset available from The Cancer Genome Atlas (TCGA), accounting for transcriptomics, proteomics, and clinical information measured over two glioma types: Lower-grade glioma (LGG) and glioblastoma (GBM). Our findings suggest that the Priority-Elastic net is a highly advantageous choice for a wide range of applications. It offers moderate computational complexity, flexibility in integrating prior knowledge while introducing a hierarchical modeling perspective, and, importantly, improved stability and accuracy in predictions, making it superior to the other methods discussed. This evolution marks a significant step forward in predictive modeling, offering a sophisticated tool for navigating the complexities of multi-omics datasets in pursuit of precision medicine’s ultimate goal: personalized treatment optimization based on a comprehensive array of patient-specific data. This framework can be generalized to time-to-event, Cox proportional hazards regression and multicategorical outcomes. A practical implementation of this method is available upon request in R script, complete with an example to facilitate its application.

Survival analysis is a well known technique in the medical field. The identification of individuals whose survival time is too short or to long given their profile, assumes great importance for the detection of new prognostic factors. The study of these outlying observations have gained increasing relevancy with the availability of high-throughput molecular and clinical data for large cohorts of patients. Several methods for outlier detection in survival data have been proposed, which include the analysis of the residuals, the measurement of the concordance c-index, and methods based on quantile regression for censored data. However, different results are obtained depending on the type of method used. In order to solve the disparity of results we proposed to apply the Rank Product test. A simulated dataset, and two clinical datasets were used to illustrate our proposed consensus outlier detection method, one from myeloma disease and the other from The Cancer Genome Atlas (TCGA) ovarian cancer. Finally, the Rank Product with multiple testing corrections was performed in order to identify which observations have the highest rank amongst the methods considered. Our results illustrate the potential of this consensus approach for the automated retrieval of outliers and also the identification of biomarkers associated with survival in large datasets.