Cox regression model with mismeasured covariates or missing covariate data

In this article we present a new method to estimate the regression coefficient beta and the baseline cumulative hazard function Lambda(0)(t) in the Cox regression model, where some covariates are measured with non-differential error or some covariate data are missing at random. The basic idea of the proposed method is to combine the EM algorithm with the profile likelihood theory. At the E-step, the conditional expectation of the log-likelihood function based on the complete data is computed. At the M-step, new estimate of beta is obtained through the profile likelihood and new estimate of Lambda(0)(t) through the Nelson-Aalen estimator, as in the original Cox regression. This method preserves the semiparametric property of the original Cox regression and achieves consistent estimation of beta and Lambda(0)(t) simultaneously. We have proved the convergence of the EM algorithm and the consistency of <(beta)over cap> and <(Lambda)over cap>(0)(t) by the von Mises method and the martingale theory. The asymptotic distribution of <(beta)over cap> is derived directly from the profile likelihood function. Comparisons with other existing estimators through simulations show that when beta is moderate or large, the proposed estimator outstands from all the existing estimators for its unbiasedness, its lowest mean-square-error, and its best probability coverage of a confidence interval.