Segmented time-dependent effect Cox model and landmark time breakpoint estimation

Background This study addresses the challenge of modeling time-dependent effects in the Cox model by proposing a novel approach, the segmented time-dependent effect Cox model, and introducing the landmark time breakpoint (LTB). The aim is to overcome limitations in existing methods and provide valuable insights through a Systolic Blood Pressure Intervention Trial (SPRINT) case study. Methods A two-step procedure is presented to implement the segmented linear time-dependent effect Cox model. In the first step, LTB is estimated using segmented linear regression with weighted Schoenfeld residuals. The second step involves piecewise linear regression for time-dependent effect estimation, addressing biases identified in simulation results. Results Application of the proposed method to the SPRINT case study reveals nuanced insights into time-dependent effects. Despite biases identified in the simulation, the proposed method offers advantages over existing techniques in terms of estimation efficiency and interpretability. The SPRINT case study demonstrates the practical significance of LTB (LTB, 2.66, [95% CI, (1.76, 3.57)]), capturing temporal patterns in hazard ratio trends. Conclusion This study introduces the segmented time-dependent effect Cox model and the LTB for survival analysis, providing a deeper understanding of hazard ratio trends through a SPRINT case study. Future research may benefit from integrating segmented regression and breakpoint estimation directly into the Cox model for a more streamlined one-step estimation process.