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Model choice and influential cases for survival studies.

W H Wei¹, J S Su

¹Institute of Statistics, Academia Sinica, Taiwan, ROC. wenwei@stat.sinica.edu.tw

|April 21, 2001

Summary

New deletion diagnostics identify influential observations in failure time data regression models. These diagnostics help ensure robust statistical analysis by revealing how data points impact model parameters.

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Area of Science:

Biostatistics
Survival Analysis
Statistical Modeling

Background:

Accurate estimation of regression and mixture parameters is crucial for relative risk functions in failure time data analysis.
Identifying influential observations is essential for robust statistical modeling and reliable inference.
Existing diagnostic measures may not fully capture the influence of observations on complex survival models.

Purpose of the Study:

To develop novel deletion diagnostics for assessing the influence of individual observations on regression and mixture parameter estimates.
To generalize existing influence measures, including martingale residuals, Schoenfeld's partial residuals, and score residuals.
To investigate the impact of observation deletion on model selection in survival analysis.

Main Methods:

Development of generalized deletion diagnostics based on extensions of established residual types.
Application of diagnostics to a specific family of relative risk functions proposed by Guerrero and Johnson (1982).
Illustrative example demonstrating the practical utility of the developed diagnostics.

Main Results:

The proposed diagnostics effectively identify observations that significantly influence regression and mixture parameter estimates.
Generalizations of martingale, Schoenfeld's partial, and score residuals provide valuable insights into observation influence.
The influence of certain observations can be highly sensitive to changes in the mixture parameter, potentially altering model choice.

Conclusions:

The developed deletion diagnostics are valuable tools for robust analysis of failure time data.
These diagnostics enhance the reliability of regression and mixture parameter estimation in survival models.
Careful consideration of observation influence is necessary, as it can impact model selection and interpretation.

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