Maximum Likelihood Inference for the Cox Regression Model with Applications to Missing Covariates.
In this paper, we carry out an in-depth theoretical investigation for existence of maximum likelihood estimates for the Cox model (Cox, 1972, 1975) both in the full data setting as well as in the presence of missing covariate data. The main motivation for this work arises from missing data problems, where models can easily become difficult to estimate with certain missing data configurations or large missing data fractions. We establish necessary and sufficient conditions for existence of the maximum partial likelihood estimate (MPLE) for completely observed data (i.e., no missing data) settings as well as sufficient conditions for existence of the maximum likelihood estimate (MLE) for survival data with missing covariates via a profile likelihood method. Several theorems are given to establish these conditions. A real dataset from a cancer clinical trial is presented to further illustrate the proposed methodology.
Ming-Hui Chen is Professor, Department of Statistics, University of Connecticut, 215 Glenbrook Road, U-4120, Storrs, CT 06269-4120, Email:  mhchen@merlot.stat.uconn.edu . Joseph G. Ibrahim is Professor, Department of Biostatistics, University of North Carolina, McGavran-Greenberg Hall, Chapel Hill, NC 27599, Email:  ibrahim@bios.unc.edu . Qi-Man Shao is Professor, Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, Email:  maqmshao@ust.hk.
Ming-Hui
MH
Chen
Joseph G
JG
Ibrahim
Qi-Man
QM
Shao