Nested Elastic-Net Cox Modeling for Post-Recurrence Survival Risk Stratification in Hepatocellular Carcinoma: Development and Internal Validation

Post-recurrence survival (PRS) after hepatocellular carcinoma (HCC) recurrence is heterogeneous and may reflect the combined effects of tumor burden, liver reserve, treatment characteristics, and routine laboratory measures. This secondary analysis aimed to develop and internally validate a penalized Cox model for PRS risk stratification. A total of 431 patients with recurrent HCC from a previously reported prospective cohort were analyzed using 30 baseline candidate predictors. A nested five-fold elastic-net Cox framework was applied, with inner cross-validation for lambda selection and outer cross-validation for strictly out-of-fold (OOF) prediction. The mixing parameter was fixed at alpha = 0.5; missing values were imputed using training-fold medians or modes, and tied event times were handled with the Breslow approximation. Among 431 patients, 183 experienced the predefined death event and 248 were censored. Eight predictors were retained in at least four of five outer folds: ablative modality, tumor number, gamma-glutamyl transferase, albumin, Child-Pugh class, drinking, smoking, and tumor size. The OOF C-index was 0.5576, with 1-, 3-, and 5-year AUCs of 0.5560, 0.5745, and 0.5934. Median OOF risk score stratification separated 216 low-risk and 215 high-risk patients, with median PRS of 44.07 versus 24.03 months (HR = 1.500, 95% CI 1.120-2.009; log-rank P = 0.00622). The framework provided significant risk stratification but limited discrimination and calibration, supporting its interpretation as an exploratory internally validated model rather than a stand-alone clinical prediction tool.