PROPORTIONAL HAZARDS TESTS AND DIAGNOSTICS BASED ON WEIGHTED RESIDUALS

• 成果类型: Article
• 署名作者: GRAMBSCH, PM; THERNEAU, TM
• 署名单位: Mayo Clinic
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• 发表日期: 1994
• 页码: 515526
• 关键词: partial likelihood; REGRESSION-MODEL; survival analysis; GOODNESS; fit

摘要

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{beta(t)Z(i)(t)}. A common example is a treatment effect that decreases with time. We show that the function beta(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 and Mesbah (1985), Nagelkerke, Oosting and Hart (1984), O'Quigley and 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.