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Graphical generalized residuals in fitting distributions: applications to epidemiological follow-up data
R C Elandt-Johnson1, F B Smith
1Department of Biostatistics-CSCC, University of North Carolina, Chapel Hill 27599.
Statistics in Medicine
|June 1, 1989
Summary
Generalized residuals aid in assessing parametric distribution fits but are less reliable for Cox
Area of Science:
- Biostatistics
- Survival Analysis
- Statistical Modeling
Background:
- Generalized residuals derived from probability integral transformation are commonly used for goodness-of-fit testing.
- Their utility in parametric distribution fitting is established, but their application to Cox's proportional hazard rate (PHR) models requires careful consideration.
Purpose of the Study:
- To evaluate the effectiveness of generalized residuals in goodness-of-fit testing for Cox's PHR models.
- To explore alternative methods for risk factor selection and model building in PHR analysis.
Main Methods:
- Definition and discussion of three types of generalized residuals based on probability integral transformation.
- Analysis of the impact of PHR model characteristics (non-parametric nature, censoring) on residual interpretation.
- Introduction of non-parametric stratified residual plots for risk factor selection.
- Proposal for discretizing continuous variables in preliminary PHR models.
Main Results:
- Generalized residuals often suggest a good fit for PHR models due to inherent model properties and data characteristics, potentially limiting their inferential meaning for overall fit.
- Residuals remain valuable for exploratory analysis in PHR models.
- Non-parametric stratified residual plots offer a method for risk factor selection, equivalent to comparing empirical survival functions across strata.
- Discretizing continuous variables can aid in analytically assessing covariate contributions.
Conclusions:
- The apparent good fit from generalized residuals in PHR models should be interpreted cautiously due to methodological factors.
- Generalized residuals are more useful for exploratory purposes than for definitive goodness-of-fit assessment in PHR models.
- Non-parametric stratified plots and variable discretization are recommended for robust risk factor identification and model specification in PHR analysis.