Abstract
ABSTRACTThe growing role of targeted medicine has led to an increased focus on the development of actionable biomarkers. Current penalized selection methods that are used to identify biomarker panels for classification in high-dimensional data, however, often result in highly complex panels that need careful pruning for practical use. In the framework of regularization methods, a penalty that is a weighted sum of the L1 and L0 norm has been proposed to account for the complexity of the resulting model. In practice, the limitation of this penalty is that the objective function is non-convex, non-smooth, the optimization is computationally intensive and the application to high-dimensional settings is challenging. In this paper, we propose a stepwise forward variable selection method which combines the L0 with L1 or L2 norms. The penalized likelihood criterion that is used in the stepwise selection procedure results in more parsimonious models, keeping only the most relevant features. Simulation results and a real application show that our approach exhibits a comparable performance with common selection methods with respect to the prediction performance while minimizing the number of variables in the selected model resulting in a more parsimonious model as desired.
Highlights
The high costs and long duration of clinical development, paired with high levels of attrition, require the quantification of the risk when moving from early to late stage clinical development, and biomarkers may play an important role in this quantification
The results showed that their method achieved sparser solutions than Least Absolute Shrinkage and Selection Operator (Lasso) and more stable solutions that the LL0 regularization
We propose a method for variable selection that penalizes the likelihood function with a linear combination of LL0 with LL1 or LL2 penalties (CL, CL2) in a stepwise forward variable selection procedure
Summary
The high costs and long duration of clinical development, paired with high levels of attrition, require the quantification of the risk when moving from early to late stage clinical development, and biomarkers may play an important role in this quantification. Only rarely the number of variables (biomarkers) in the resulting panel plays an active role in selection procedures. Variable selection is an important aspect in the determination of such panels in the framework of high-dimensional statistical modeling. Keeping only the relevant variables in the model makes interpretation easier and may increase the predictability of the resulting model. In the framework of regularization methods, various penalty functions are used to perform variable selection. Ββdd ) ∈ Rdd. When qq ≤ 1 the penalty performs variable selection
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