Assessing influence in regression analysis with censored data

Area of Science:

• Statistics
• Biostatistics
• Survival Analysis

Background:

• Maximum likelihood estimation is crucial for analyzing censored survival data.
• Understanding the impact of perturbations is vital for robust statistical modeling.
• Traditional influence statistics have limitations in complex models.

Purpose of the Study:

• To develop and present methods for evaluating the influence of perturbations on maximum likelihood estimates in censored survival data.
• To extend the application of these methods to other nonlinear estimation problems.
• To offer new interpretations and extensions of local influence statistics.

Main Methods:

• Utilizing log-likelihood displacement and local influence methods.
• Developing new interpretations for local influence statistics.
• Comparing these statistics with traditional case deletion influence statistics.

Main Results:

• The proposed statistics effectively identify individual and combinations of cases that significantly influence parameter estimates.
• Demonstrated the utility of these methods on the Stanford Heart Transplant data using a parametric regression model.
• Showcased how local influence statistics complement traditional methods.

Conclusions:

• The developed methods provide a robust framework for assessing the impact of perturbations in censored survival data.
• These techniques enhance the reliability and interpretability of statistical models.
• The study offers valuable tools for data scientists and biostatisticians working with survival data.