A residual bootstrap for regression parameters in proportional hazards models

Abstract

A resampling plan is introduced for bootstrapping regression parameter estimators for the Cox (1972) proportional hazards regression model when explanatory variables are nonrandom constants fixed by the design of the experiment. The plan is an analog to the residual-resampling method for regression introduced by Efron (1979) and is related to the resampling method proposed by Hjort (1985) for the Coxmodel. The resampled quantities are a form of generalized residuals which have a distribution that is independent of the explanatory variables. Hence, unlike some methods, this approach does not require resampling of explanatory variables, which would be contrary to the assumption that they are nonrandom. An invariance property of the Cox likelihood allows these residuals to be transformed into a convenientscale for generating a likelihood. Also, the method can incorporate many forms of censoring. A simuation study of the proposed procedure shows that it can be used to improve upon the usual estimation procedures for regression parameters in the Cox model.