Regularized Cox Models Versus Deep Survival Networks in Low Events-per-Variable Regimes: A Benchmark Across Censoring Levels

Abstract

Survival analysis on biomedical data has seen quick methodological growth, but practitioners face limited guidance on which family of methods to prefer when censoring rates are high or the ratio of predictors to events is unsuitable. This paper presents a systematic benchmark of six survival models-the classical Cox model, lasso-penalized Cox, the Bayesian elastic net Cox model (BEN-Cox), random survival forests, DeepSurv, and Cox-Time-across three publicly available datasets (METABRIC, SUPPORT, and TCGA-BRCA) under controlled censoring regimes. The experimental grid scans events-per-variable (EPV) ratios from 0.6 to 7.6 and censoring rates from 33% to 86%. Performance is evaluated using Harrell's concordance index, time-dependent concordance, the integrated Brier score, and the calibration slope, with statistical comparisons carried out by paired Wilcoxon signed-rank tests with Holm correction. Three main findings are obtained. First, BEN-Cox, lasso-Cox, and random survival forests form a narrow top tier in discrimination, with pooled C -index values within 0.003 of each other, while DeepSurv and Cox-Time do not reach this tier in any configuration. Second, calibration separates models that discrimination does not: BEN-Cox achieves the lowest integrated Brier score in all six configurations, while lasso-Cox produces calibration slopes closest to one on the high-dimensional datasets; deep models and the unpenalized Cox model are systematically overconfident. Third, increasing censoring widens the gap between the regularized top tier and the deep architectures without changing which model family is preferred. An empirical partition of the (c, EPV) plane summarizes these observations. Because the entire grid falls below the classical EPV threshold of ten, the partition documents the low-EPV regime in which regularized models dominate but does not identify the boundary at which deep models may become competitive.