Estimating the Parameters in the Cox Model when Covariate Variables are Measured with Error

Abstract

The Cox proportional hazards model is commonly used to evaluate the effects of treatment and prognostic factors on survival. However, prognostic factors are often measured with error. If we use the traditional partial likelihood method to estimate the parameters without taking into account the effect of measurement errors of covariates, we risk estimating parameters which will be biased towards the null. An alternative strategy is to take into account the error in measurement, which may be carried out for the Cox model in a number of ways. I examine several different approaches for estimating the parameters in the Cox model when covariates are measured with error, including techniques making different assumptions on the distribution of the true covariates. We introduce a likelihood-based approach, which we refer to as the semiparametric method. In this method, we do not make parametric assumptions on the unobservable true covariates X, while we assume that the densities of X belong to a class of smooth and less restrictive densities. We show that this method is an appealing alternative to other methods.