Proportional hazards tests and diagnostics based on weighted residuals. (English) Zbl 0810.62096

Grambsch, Patricia M.; Therneau, Terry M.

Biometrika 81, No. 3, 515-526 (1994).

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 \(\exp\{ \beta(t) Z_ i(t)\}\). 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 test of proportional hazards, including those of Cox (1972), Gill and 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.

MSC:

62P10	Applications of statistics to biology and medical sciences; meta analysis
62G10	Nonparametric hypothesis testing
62J12	Generalized linear models (logistic models)
62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F03	Parametric hypothesis testing

Keywords:

nonproportional hazards; Schoenfeld residuals; weighted regression; Cox model; time varying coefficients; residual plot; test of proportional hazards; time-weighted score tests; proportional hazards hypothesis; weighted least-squares