  We consider the situation of estimating Cox regression in which some
covariates are subject to missing, and there exists additional information
(including observed event time, censoring indicator and fully observed
covariates) which may be predictive of the missing covariates. We propose to
use two working regression models: one for predicting the missing covariates
and the other for predicting the missing probabilities. For each missing
covariate observation, these two working models are used to define a nearest
neighbor imputing set. This set is then used to nonparametrically impute
covariate values for the missing observation. Upon the completion of
imputation, Cox regression is performed on the multiply imputed datasets to
estimate the regression coefficients. In a simulation study, we compare the
nonparametric multiple imputation approach with the augmented inverse
probability weighted (AIPW) method, which directly incorporates the two working
models into estimation of Cox regression. We show that all approaches can
reduce bias due to non-ignorable missing mechanism. The proposed nonparametric
imputation method is robust to mis-specification of either one of the two
working models and robust to mis-specification of the link function of the two
working models. In contrast, the AIPW method is not robust to mis-specification
of the link function of the two working models and is sensitive to the
selection probability. We apply the approaches to a breast cancer dataset from
Surveillance, Epidemiology and End Results (SEER) Program .
