© 1994 by Biometrika Trust
Articles |
Proportional hazards tests and diagnostics based on weighted residuals
1 Division of Biostatistics, School of Public Health, University of Minnesota Minneapolis, Minnesota 55455, U.S.A.
2 Department of Health Science Research Mayo Clinic, Rochester, Minnesota 55905, U.S.A.
Received for publication 1 March 1993.
Revision received 1 January 1994.
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Abstract |
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Nonproportional hazards can often be expressed by extending the Cox model to include time varying coefficients; e.g., for a single covariate, the hazard function for subject i is modelled as exp {β(t)Zi(t)}. A common example is a treatment effect that decreases with time. We show that the function βi(t) can be directly visualized by smoothing an appropriate residual plot. Also, many tests of proportional hazards, including those of Cox (1972), Gill & Schumacher (1987), Harrell (1986), Lin (1991), Moreau, O'Quigley & Mesbah (1985), Nagelkerke, Oosting & Hart (1984), O'Quigley & Pessione (1989), Schoenfeld (1980) and Wei (1984) are related to time-weighted score tests of the proportional hazards hypothesis, and can be visualized as a weighted least-squares line fitted to the residual plot.
Key Words: Cox model • Loess • Schoenfeld residuals • Weighted regression
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