Full likelihood inferences in the Cox model: an empirical likelihood approach
Abbreviated Journal Title
Ann. Inst. Stat. Math.
Right censored data; Empirical likelihood; Maximum likelihood estimator; Partial likelihood; Profile likelihood; CENSORED SURVIVAL DATA; REGRESSION-MODELS; LARGE SAMPLE; EFFICIENCY; ESTIMATORS; Statistics & Probability
For the regression parameter beta (0) 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 (beta (0), F (0)), where F (0) is the baseline distribution in the Cox model. Using the empirical likelihood parameterization, we explicitly profile out nuisance parameter F (0) to obtain the full-profile likelihood function for beta (0) and the maximum likelihood estimator (MLE) for (beta (0), F (0)). The relation between the MLE and Cox's partial likelihood estimator for beta (0) 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.
Annals of the Institute of Statistical Mathematics
"Full likelihood inferences in the Cox model: an empirical likelihood approach" (2011). Faculty Bibliography 2010s. 1812.