Proportional hazards tests and diagnostics based on weighted residuals
1994/01/01 by PATRICIA M. GRAMBSCH, Patricia M. Grambsch, Terry M. Therneau +1 · 5,666 citations
Mathematics · #Advanced Causal Inference Techniques #Advanced Statistical Methods and Models #Econometrics #Mathematics #Statistical Methods and Inference #Statistics
paper · doi:10.1093/biomet/81.3.515
published in Biometrika 81(3), 515-526 (Oxford University Press)
openalex publication_date 1994/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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.
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