Full likelihood inferences in the Cox model: an empirical likelihood approach.

For the regression parameter β in the Cox model, there have been several estimators constructed based on various types of approximated likelihood, but none of them has demonstrated small-sample advantage over Cox's partial likelihood estimator. In this article, we derive the full likelihood function for ( β, F), where F is the baseline distribution in the Cox model. Using the empirical likelihood parameterization, we explicitly profile out nuisance parameter F to obtain the full-profile likelihood function for β and the maximum likelihood estimator (MLE) for ( β, F). The relation between the MLE and Cox's partial likelihood estimator for β is made clear by showing that Taylor's expansion gives Cox's partial likelihood estimating function as the leading term of the full-profile likelihood estimating function. We show that the log full-likelihood ratio has an asymptotic chi-squared distribution, while the simulation studies indicate that for small or moderate sample sizes, the MLE performs favorably over Cox's partial likelihood estimator. In a real dataset example, our full likelihood ratio test and Cox's partial likelihood ratio test lead to statistically different conclusions. [ABSTRACT FROM AUTHOR]