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