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Efficient estimation of Cox model with random change point.

Xuerong Chen1, Yalu Ping1, Jianguo Sun2

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This study introduces new statistical models for analyzing disease risk changes over time, accounting for individual patient differences. The method effectively identifies subject-specific change points in clinical data, improving risk prediction.

Keywords:
Cox modelrandom change pointsieve maximum likelihood approach

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Area of Science:

  • Biostatistics
  • Clinical Epidemiology
  • Survival Analysis

Background:

  • Disease risk can change significantly at specific biological thresholds.
  • Individual patient characteristics (physical, psychological) can influence these thresholds, leading to subject-specific change points.
  • Existing methods often assume a single, fixed change point for all subjects, limiting applicability.

Purpose of the Study:

  • To develop statistical models that incorporate subject-specific change points in failure time data.
  • To provide a framework for subgroup analysis within these models.
  • To address limitations of current methods that assume uniform change points.

Main Methods:

  • Proposed two Cox-type regression models to handle subject-specific change points.
  • Developed a sieve maximum likelihood estimation procedure for parameter inference.
  • Established asymptotic properties for the proposed estimators.

Main Results:

  • The proposed models successfully identify individual-specific thresholds where disease risk changes.
  • Simulation studies confirmed the empirical performance and practicality of the method.
  • The approach was validated using breast cancer patient data.

Conclusions:

  • The developed statistical framework effectively models subject-specific change points in clinical studies.
  • This approach enhances the analysis of failure time data by accommodating individual variability.
  • The findings have implications for personalized medicine and subgroup analysis in disease research.