On functional misspecification of covariates in the Cox regression model

Model misspecification is discussed for the analysis of censored survival d ata with the Cox regression model. The maximum partial likelihood estimator for covariate effects has an asymptotic normal distribution under model mi sspecification (Lin & Wei, 1989). Situations where the assumed functional f orm for covariates is wrong are considered in a general framework in which we also derive the limit of Breslow's (1972) estimator. Furthermore, we giv e explicit expressions for the asymptotic variance of the maximum partial l ikelihood estimator. Numerical values for the errors of the maximum partial likelihood estimator and of the usual variance estimator are obtained for functional misspecification of a single relevant covariate and looking at t he effect of a first factor, representing treatment or something similar, f or functional wrong incorporation of auxiliary covariate measurements. In t he latter situations we analyse the impact of dependence between the covari ates.