On functional misspecification of covariates in the Cox regression model

Model misspecification is discussed for the analysis of censored survival data with the Cox regression model. The maximum partial likelihood estimator for covariate effects has an asymptotic normal distribution under model misspecification (Lin & Wei, 1989). Situations where the assumed functional form for covariates is wrong are considered in a general framework in which we also derive the limit of Breslow's (1972) estimator. Furthermore, we give explicit expressions for the asymptotic variance of the maximum partial likelihood 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 the effect of a first factor, representing treatment or something similar, for functional wrong incorporation of auxiliary covariate measurements. In the latter situations we analyse the impact of dependence between the covariates.