Accounting for grouped predictor variables or pathways in high-dimensional penalized Cox regression models

Abstract

Background: The standard lasso penalty and its extensions are commonly used to develop a regularized regression model while selecting candidate predictor variables on a time-to-event outcome in high-dimensional data. However, these selection methods focus on a homogeneous set of variables and do not take into account the case of predictors belonging to functional groups; typically, genomic data can be grouped according to biological pathways or to different types of collected data. Another challenge is that the standard lasso penalisation is known to have a high false discovery rate. Results: We evaluated different penalizations in a Cox model to select grouped variables in order to further penalize variables that, in addition to having a low effect, belong to a group with a low overall effect; and to favor the selection of variables that, in addition to having a large effect, belong to a group with a large overall effect. We considered the case of prespecified and disjoint groups and proposed diverse weights for the adaptive lasso method. In particular we proposed the product Max Single Wald by Single Wald weighting (MSW*SW) which takes into account the information of the group to which it belongs and of this biomarker. Through simulations, we compared the selection and prediction ability of our approach with the standard lasso, the composite Minimax Concave Penalty (cMCP), the group exponential lasso (gel), the Integrative L1-Penalized Regression with Penalty Factors (IPF-Lasso), and the Sparse Group Lasso (SGL) methods. In addition, we illustrated the methods using gene expression data of 614 breast cancer patients. Conclusions: The adaptive lasso with the MSW*SW weighting method incorporates both the information in the grouping structure and the individual variable. It outperformed the competitors by reducing the false discovery rate without severely increasing the false negative rate.

Complex Disease Individual Molecular Characterization Using Infinite Sparse Graphical Independent Component Analysis

“…The remaining 1689 probes were standardized and then filtered with the package jetset 29 to retain a single probe by gene, resulting in a final dataset including the expression of 1063 genes. As in Belhechmi et al, 30 we mapped to probes to 3 molecular signatures with a prognostic effect in early breast cancer (Immune System, Proliferation, and Stroma invasion 31 ) and one without (SRC activation signature 31 ), all the other probes were categorized as “Others”.…”

“…The proliferation-based signature, immune-system signature, and stroma-related signature seemed to be related to the components 2/5, 4/7/8/15, and 3, respectively. The SRC, which was picked as a “negative control” signature in Belhechmi et al, 30 was not straightforward to map to a particular molecular component.…”

Prognosis of lasso-like penalized Cox models with tumor profiling improves prediction over clinical data alone and benefits from bi-dimensional pre-screening

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Favoring the hierarchical constraint in penalized survival models for randomized trials in precision medicine

“…Single Wald (SW) weighting is inspired by our previous work [18], where we showed that weighting strategies based on the Wald statistic gives good results for biomarker selection in the case of biomarkers grouped by pathways. The SW weighting strategy assigns the same weight to the biomarker and its interaction with treatment.…”