Estimation of Baseline Hazard Function with B-Spline in Additive Hazard Model

Survival analysis is a branch of statistics that studies the time until the occurrence of an event, such as death or disease recurrence. One of the main challenges is handling censored data, especially right censoring. The Cox Proportional Hazards (Cox PH) model is often used, but it has limitations if the proportional hazards assumption is not met. As an alternative, the Additive Hazard model offers flexibility without requiring assumptions. This study estimates the baseline hazard function in the Additive Hazard model using the maximum penalized likelihood (MPL) approach with a B-spline basis. This method allows controlling the smoothness of the hazard function and guarantees non-negative estimates, while reducing the risk of overfitting through penalties on the model. The model was applied to data of breast cancer patients at West Nusa Tenggara Provincial Hospital, with the independent variables being stage and surgery status. The results indicate that both variables have a significant impact on patient survival time, with the baseline hazard curve increasing over time. These findings suggest that the B-spline-based Additive Hazard model with MPL is a reliable alternative in survival analysis, particularly when the proportional hazards assumption is not met.