Residuals for relative risk regression. (English) Zbl 0632.62102

Barlow, William E.; Prentice, Ross L.

Biometrika 75, No. 1, 65-74 (1988).

Several possible definitions of residuals are given for relative risk regression with time-varying covariates. Each such residual has a representation as an estimator of a stochastic integral with respect to the martingale arising from a subject’s failure time counting process. Previously proposed residuals for individual study subjects and for specific time points are shown to be special cases of this definition, as are previously derived regression diagnostics. An illustration and various generalizations are also given.

MSC:

62P10	Applications of statistics to biology and medical sciences; meta analysis
62M99	Inference from stochastic processes
62N05	Reliability and life testing

Keywords:

case-control study; censoring; influence function; proportional hazards; definitions of residuals; relative risk regression; time-varying covariates; estimator of a stochastic integral; martingale; failure time counting process; regression diagnostics