Problem
Research questions and friction points this paper is trying to address.
Variable Selection
False Discovery Rate
Generalized Linear Models
Cox Regression
Virtual Dummies
FDR-Controlled Variable Selection for Generalized Linear Models and Cox Regression with Virtual Dummies
🤖 AI Summary
This study addresses the lack of scalable and effective methods for high-dimensional nonlinear variable selection in generalized linear models and Cox regression that simultaneously control the false discovery rate (FDR). To this end, this work extends the T-Rex selector to these modeling frameworks for the first time. By integrating a dummy variable technique into a score-based forward selection algorithm within a terminating random experiments framework, the proposed approach achieves memory-efficient computation while preserving distributional equivalence to ensure theoretical rigor. Simulation studies demonstrate that the method maintains strict FDR control with high statistical power. Furthermore, its practical utility is validated through applications to genotype data and cancer survival analysis, confirming its effectiveness in real-world high-dimensional settings.
📝 Abstract
In genomics, imaging and clinical studies, only a few of many candidate predictors are often nonlinearly associated with a response that may be, e.g. binary, categorical, a count or a censored event time. The Terminating-Random Experiments (T-Rex) selector is a scalable variable selection method that controls the false discovery rate (FDR) by letting synthetic null variables (dummies) compete with the real predictors. While the FDR control theory embraces more general settings, to date, the T-Rex selector has been specified only for linear models. We propose a memory-efficient selection procedure with FDR control for generalized linear models and Cox regression by extending the recently developed virtual dummy construction to score-based forward selection for Bernoulli, Poisson, multinomial and Cox responses. The virtual-dummy-based selection path remains equal in distribution to explicit augmentation, so FDR control carries over under the same assumptions. Simulations confirm this equivalence and the power gained by correct model specification. Real-world applicability is illustrated on simulated genotypes and on cancer survival data.
Innovation
Methods, ideas, or system contributions that make the work stand out.
FDR control
Virtual dummies
Generalized linear models
Cox regression
Variable selection
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