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A Cox-type regression model with change-points in the covariates.
Uwe Jensen1, Constanze Lütkebohmert
1Institut für Angewandte Mathematik und Statistik, Universität Hohenheim, 70593 Stuttgart, Germany. Prof.Uwe.Jensen@uni-hohenheim.de
Lifetime Data Analysis
|January 29, 2008
Summary
This study introduces a Cox-type regression model with covariate change-points, demonstrating that both change-point and regression parameter estimates are square root n-consistent. This finding contrasts previous conjectures and offers improved statistical modeling for complex data.
Area of Science:
- Biostatistics
- Survival Analysis
- Statistical Modeling
Background:
- Cox-type regression models are widely used for survival data analysis.
- Identifying shifts in covariate influence is crucial for accurate modeling.
- Existing methods may have limitations in estimating change-point locations.
Purpose of the Study:
- To develop and analyze a Cox-type regression model incorporating change-points in covariates.
- To investigate the estimation properties of change-points and regression parameters.
- To provide a robust statistical framework for data with smooth covariate influence shifts.
Main Methods:
- Development of a Cox-type regression model with smooth covariate change-points.
- Derivation of estimators for change-point locations and regression parameters.
- Asymptotic analysis using M-estimator theory to establish consistency and normality.
Main Results:
- Estimates for both regression parameters and change-points are shown to be square root n-consistent.
- Asymptotic normality of the estimators is demonstrated.
- The model is successfully applied to actuarial (PBC dataset) and engineering (electric motors) data.
Conclusions:
- The proposed model effectively handles change-points in covariates within a Cox-type regression framework.
- The square root n-consistency of change-point estimates is a significant finding, challenging prior assumptions.
- The model's applicability across diverse datasets highlights its practical utility in biostatistics and beyond.
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