Likelihood-based methods for missing covariates in the Cox proportional hazards model

Problems associated with missing covariate data are well known but often ignored. We present a method for estimating the parameters in the Cox proportional hazards model when the missing data are missing at random (MAR) and censoring is noninformative. Due to the computational burden of this method, we introduce an approximation that allows us to use a weighted expectation-maximization (EM) algorithm to estimate the parameters more easily. When the missing covariates are continuous rather than categorical, we implement a Monte Carlo version of the Ehl algorithm along with the Gibbs sampler to obtain parameter estimates. We also give the asymptotic distribution of these estimates. The primary advantage of this method over complete case analysis is that it produces more efficient parameter estimates and corrects for bias in the MAR setting. To motivate the methodology, we present an analysis of a phase III melanoma clinical trial conducted by the Eastern Cooperative Oncology Group.