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Estimation of a change point in a hazard function based on censored data.
1Université Catholique de Louvain, Belgium. gijbels@stat.ucl.ac.be
Lifetime Data Analysis
|March 6, 2004
Summary
This study introduces a new method to detect changes in failure rates (hazard function) in survival data, even with censored observations. The proposed least squares approach is less biased but has higher variance than existing methods.
Area of Science:
- Statistics
- Reliability Engineering
- Survival Analysis
Background:
- The hazard function is crucial in reliability and survival studies, indicating instantaneous failure risk.
- Real-world data often shows abrupt changes in hazard functions due to maintenance or operational events.
Purpose of the Study:
- To estimate a single change point in a piecewise constant hazard function.
- To assess the magnitude of change in the hazard function.
- To handle randomly censored data.
Main Methods:
- Developed a novel estimation procedure using structural properties and least squares.
- Conducted a simulation study to compare performance against existing estimators.
- Evaluated estimators based on Nelson-Aalen functional and maximum likelihood.
Main Results:
- The proposed least squares estimator demonstrated reduced bias compared to other methods.
- The least squares estimator exhibited a larger variance.
- The method was successfully applied to real-world datasets.
Conclusions:
- The least squares method offers a viable alternative for change point estimation in piecewise constant hazard functions with censoring.
- Trade-offs between bias and variance should be considered when selecting an estimator.