Abstract
SUMMARY 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 { fl(t)Zi(t)}. A common example is a treatment effect that decreases with time. We show that the function /3(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.
Keywords
MathematicsStatisticsEconometrics
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Publication Info
- Year
- 1994
- Type
- article
- Volume
- 81
- Issue
- 3
- Pages
- 515-526
- Citations
- 5332
- Access
- Closed
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Cite This
Patricia M. Grambsch,
Terry M. Therneau
(1994).
Proportional hazards tests and diagnostics based on weighted residuals.
Biometrika
, 81
(3)
, 515-526.
https://doi.org/10.1093/biomet/81.3.515
Identifiers
- DOI
- 10.1093/biomet/81.3.515