Proportional hazards tests and diagnostics based on weighted residuals
数学
统计
计量经济学
作者
Patricia M. Grambsch,Terry M. Therneau
出处
期刊:Biometrika [Oxford University Press] 日期:1994-01-01卷期号:81 (3): 515-526被引量:4821
标识
DOI:10.1093/biomet/81.3.515
摘要
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.