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A general framework for random effects survival analysis in the Cox proportional hazards setting
1Division of Biostatistics, Mayo Clinic, Rochester, Minnesota 55905, USA. sargent@mayo.edu
Biometrics
|January 12, 1999
Summary
This study introduces a new hierarchical Cox model for analyzing survival data with random effects. This flexible approach avoids assumptions on hazard functions and random effect distributions, offering a more complete data analysis.
Area of Science:
- Biostatistics
- Statistical Modeling
- Survival Analysis
Background:
- Random effects modeling is increasingly used in statistics.
- Application in survival analysis has been limited by restrictive assumptions.
- Previous methods required specific hazard function forms or model classes.
Purpose of the Study:
- To develop a flexible random effects model for survival data.
- To extend Cox's formulation without specifying the baseline hazard function.
- To allow arbitrary distributions for random effects.
Main Methods:
- Developed the hierarchical Cox model.
- Utilized Markov chain Monte Carlo (MCMC) methods.
- Applied within a Bayesian statistical framework.
Main Results:
- The hierarchical Cox model accommodates unspecified baseline hazard functions.
- It allows for arbitrary distributions of random effects.
- Demonstrated utility with a dataset on multiple mammary tumor occurrences in rats.
Conclusions:
- The proposed method provides a more satisfying analysis of survival data with multiple events.
- It overcomes limitations of standard approaches like analyzing only the first event or assuming independence.
- This approach fully utilizes available data for more precise estimations.