Spline-Enhanced survival modelling of treatment effect heterogeneity in breast Cancer

Abstract

This study investigates breast cancer prognosis using the Rotterdam dataset by integrating traditional and advanced modelling approaches to examine treatment heterogeneity and non-linear predictor effects. Linear regression revealed tumor size (>50 mm) and hormonal therapy were strongly associated with higher nodal counts, the latter likely indicative of treatment selection bias. Logistic regression provided superior predictive performance for recurrence (AUC = 0.71) compared with linear models (AUC = 0.61). Cubic spline functions were applied to Cox proportional hazards models to capture non-linear relationships, uncovering a U-shaped effect of age on recurrence risk and a pronounced hazard increase (HR = 38.3) for patients with 1–3 positive nodes, indicating a strong threshold effect. While chemotherapy showed a modest overall benefit (HR = 0.89), its interaction with nodal status was not significant (p = 0.78). Key predictors, including tumor size and grade, violated the proportional hazards assumption, indicating time-varying effects. Methodologically, logistic regression offered strong predictive performance, whereas spline-based Cox models provided deeper clinical insight into complex risk patterns. These findings underscore the value of flexible, non-linear modelling in oncology and suggest that risk stratification based solely on linear assumptions or nodal thresholds may require refinement.