Survival analysis with a random change-point.

Area of Science:

• Biostatistics
• Survival Analysis
• Epidemiology

Background:

• Traditional change-point survival models assume a single change-point for all individuals.
• This assumption is inadequate for phenomena like individual menopausal age affecting disease-free survival.
• Maximum likelihood estimation for fixed change-points is computationally complex, often requiring bootstrap methods.

Purpose of the Study:

• To propose a novel proportional hazards model incorporating a random change-point.
• To address the limitations of fixed change-point models in scenarios with individual-specific change-points.
• To develop a robust statistical framework for analyzing survival data influenced by unobserved, variable factors.

Main Methods:

• Developed a nonparametric maximum likelihood estimation approach.
• Devised a stable expectation-maximization algorithm for computing estimators.
• Utilized conventional likelihood theory for inference, leveraging asymptotic normality and profile-likelihood for variance estimation.

Main Results:

• Simulation studies confirmed the proposed methods' satisfactory finite-sample performance.
• The methods demonstrated small bias and proper coverage probabilities in simulations.
• The novel model was successfully applied to a breast cancer study analyzing disease-free survival.

Conclusions:

• The proposed random change-point survival model provides a more accurate and flexible alternative to fixed change-point models.
• The developed estimation and inference procedures are computationally stable and statistically sound.
• This approach enhances the analysis of survival data where change-points are inherently individual-specific, as seen in breast cancer studies.