PROPORTIONAL HAZARDS TESTS AND DIAGNOSTICS BASED ON WEIGHTED RESIDUALS

Nonproportional hazards can often be expressed by extending the Cox mo del 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 hazard s, including those of Cox (1972), Gill & Schumacher (1987), Harrell (1 986), Lin (1991), Moreau, O'Quigley and Mesbah (1985), Nagelkerke, Oos ting and Hart (1984), O'Quigley and Pessione (1989), Schoenfeld (1980) and Wei (1984) are related to time-weighted score tests of the propor tional hazards hypothesis, and can be visualized as a weighted least-s quares line fitted to the residual plot.