© 1993 by Biometrika Trust
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Checking the Cox model with cumulative sums of martingale-based residuals
1 Department of Biostatistics, SC-32, University of Washington Seattle, Washington 98195, U.S.A.
2 Department of Biostatistics, Harvard University 677 Huntington Ave., Boston, Massachusetts 02115, U.S.A.
3 Department of Statistics, 101 Illini Hall, University of Illinois Champaign, Illinois 61820, U.S.A.
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Abstract |
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This paper presents a new class of graphical and numerical methods for checking the adequacy of the Cox regression model. The procedures are derived from cumulative sums of martingale-based residuals over follow-up time and/or covariate values. The distributions of these stochastic processes under the assumed model can be approximated by zero-mean Gaussian processes. Each observed process can then be compared, both visually and analytically, with a number of simulated realizations from the approximate null distribution. These comparisons enable the data analyst to assess objectively how unusual the observed residual patterns are. Special attention is given to checking the functional form of a covariate, the form of the link function, and the validity of the proportional hazards assumption. An omnibus test, consistent against any model misspecification, is also studied. The proposed techniques are illustrated with two real data sets.
Key Words: Censoring • Goodness of fit • Link function • Omnibus test • Proportional hazards • Regression diagnostic • Residual plot • Survival data
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|
|
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|
|
|
|
|
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|
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|
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|
|
|
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