GR-SAFS: A Graph-Regularized Stacking Framework with Adaptive Feature Selection for High-Dimensional Prognostic Biomarker Discovery

Identifying prognostic biomarkers from high-dimensional transcriptomic data poses a triple challenge: achieving sparsity, preserving biological network topology, and integrating complementary nonlinear signals. Existing methods typically ignore network structure, miss nonlinear interactions, or lack a principled mechanism to fuse heterogeneous model outputs. We introduce GR-SAFS (Graph-Regularized Stacking with Adaptive Feature Selection), a framework with three modules: a Graph-Lasso engine embedding gene co-expression network Laplacian priors, run in parallel with a Random Forest engine; an empirical cumulative distribution function (eCDF) alignment layer that places sparse and dense importances on a common percentile scale; and a diversity-penalized quadratic programming router whose strict convexity yields a unique global optimum. On the TCGA-LUAD cohort, GR-SAFS identifies a 20-gene signature with a training concordance index of 0.700. Across two independent cross-platform microarray cohorts, GR-SAFS is the only method whose frozen signature retains statistically significant risk stratification in every cohort, where stronger-C-index baselines lose significance on at least one external cohort. Functional enrichment anchors the signature to a coherent Wnt/ β -catenin axis. An open-source implementation is released for full reproducibility.