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Biometrika 1990 77(1):147-160; doi:10.1093/biomet/77.1.147
© 1990 by Biometrika Trust
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Martingale-based residuals for survival models

TERRY M. THERNEAU, PATRICIA M. GRAMBSCH and THOMAS R. FLEMING

Division of Biostatistics, Mayo Clinic Rochester, Minnesota 55905, U.S.A.
Department of Biostatistics, University of Washington Seattle, Washington 98195, U.S.A.

Received for publication 1 April 1988. Revision received 1 April 1989.
  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 β, and the lack of model fit to a given subject.

Key Words: Cox regression • Deviance • Influence function • Martingale • Outlier detection • Proportional hazards • Regression diagnostic • Residual


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