Martingale-based residuals for survival models

Terry M. Therneau; Patricia M. Grambsch; Thomas R. Fleming

doi:10.1093/biomet/77.1.147

Martingale-based residuals for survival models

Terry M. Therneau, Patricia M. Grambsch, Thomas R. Fleming

Quantitative Health Sciences

Research output: Contribution to journal › Article › peer-review

698 Scopus citations

Abstract

Graphical methods based on the analysis of residuals are considered for the setting of the highly-used Cox (1972) regression model and for the Andersen-Gill (1982) generalization of that model. We start with a class of martingale-based residuals as proposed by Barlow & Prentice (1988). These residuals and/or their transforms are useful for investigating the functional form of a covariate, the proportional hazards assumption, the leverage of each subject upon the estimates of ß, and the lack of model fit to a given subject.

Original language	English (US)
Pages (from-to)	147-160
Number of pages	14
Journal	Biometrika
Volume	77
Issue number	1
DOIs	https://doi.org/10.1093/biomet/77.1.147
State	Published - Mar 1990

Keywords

Cox regression
Deviance
Influence function
Martingale
Outlier detection
Proportional hazards
Regression diagnostic
Residual

ASJC Scopus subject areas

Statistics and Probability
Mathematics(all)
Agricultural and Biological Sciences (miscellaneous)
Agricultural and Biological Sciences(all)
Statistics, Probability and Uncertainty
Applied Mathematics

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abstract = "Graphical methods based on the analysis of residuals are considered for the setting of the highly-used Cox (1972) regression model and for the Andersen-Gill (1982) generalization of that model. We start with a class of martingale-based residuals as proposed by Barlow & Prentice (1988). These residuals and/or their transforms are useful for investigating the functional form of a covariate, the proportional hazards assumption, the leverage of each subject upon the estimates of {\ss}, and the lack of model fit to a given subject.",

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year = "1990",

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AU - Grambsch, Patricia M.

AU - Fleming, Thomas R.

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AB - Graphical methods based on the analysis of residuals are considered for the setting of the highly-used Cox (1972) regression model and for the Andersen-Gill (1982) generalization of that model. We start with a class of martingale-based residuals as proposed by Barlow & Prentice (1988). These residuals and/or their transforms are useful for investigating the functional form of a covariate, the proportional hazards assumption, the leverage of each subject upon the estimates of ß, and the lack of model fit to a given subject.

KW - Cox regression

KW - Deviance

KW - Influence function

KW - Martingale

KW - Outlier detection

KW - Proportional hazards

KW - Regression diagnostic

KW - Residual

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JO - Biometrika

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Martingale-based residuals for survival models

Abstract

Keywords

ASJC Scopus subject areas

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