On the Bartlett Adjustment for the Partial Likelihood Ratio Test in the Cox Regression Model

Abstract

The Bartlett adjustment for the partial likelihood ratio test in Cox regression model is established under one-dimensional parameter. If the baseline hazard is unspecified, the adjustment factor can be estimated from the data. The procedure give more accurate probability than the normal approximation to the log-rank test. Abbreviated Title. Bartlett's Adjustment for Partial Likelihood. AMS 1980 subject classification. Primary 62E20, 62G05; Secondary 62P10. Key Words and Phrases. Adjustment, Asymptotic Expansion, Partial likelihood, Cox regression model, Survival data. 1. Introduction and result. In parametric inference, the likelihood ratio test is one of the most popular statistics for inference. One reason for its popularity is the Bartlett (1937) adjustment to the likelihood ratio statistics. When the sample size is small, this adjustment may have a significant improvement over the ordinary asymptotic theory. For a detailed account and the proof, see Barndoff-Nielsen and Cox (1..