Subgroup detection in the heterogeneous partially linear additive Cox model

In the analysis of survival data, it is crucial to consider individual heterogeneities related to therapy, gender, and genetics as they can impact the validity of conclusions. The heterogeneous partially linear additive Cox model offers a versatile and useful approach for addressing these variations by incorporating both heterogeneous linear components and homogeneous additive components. We propose a subgroup detection method for this model under right-censoring using B-spline smoothing technique to approximate the additive functions. Without imposing any specific subgroup structure, we generate an objective function by combining a log partial likelihood function with a fusion penalty. To estimate parameters and detect subgroups simultaneously, we employ a majorized alternating direction method of multipliers (ADMM) algorithm. Furthermore, we establish oracle properties and model selection consistency for the proposed penalised estimator. Simulation studies and real data analysis on breast cancer demonstrate the performance of our method.