<p>This research develops a general semiparametric maximum likelihood (ML) method for Cox proportional hazards models with nonmonotone missing at random covariates, where the covariates can be a combination of continuous and discrete variables. It describes an EM algorithm with closed form expressions for both the E-step and the M-step to compute semiparametric ML estimates of the parameters in the model and the corresponding asymptotic variances. It’s computationally convenient and can be easily implemented in standard software. Furthermore, it investigates the curse of dimensionality problem in the likelihood model and proposes using standard classification techniques in the semiparametric model to further improve its efficiency. The method is robust against covariate model misspecification while at the same time avoiding modeling the missing data mechanism. Extensive simulation studies are provided to examine the performance of the new method and demonstrate that it can yield a more efficient estimator than the multiple imputation method. Data from a clinical study on early breast cancer are analyzed for illustration.</p>