Abstract: We consider a likelihood ratio method for testing whether a monotone baseline hazard function in the Cox model has a particular value at a fixed point. We derive the asymptotic distribution of the likelihood ratio statistic, which is identical for a nondecreasing and a nonincreasing baseline hazard. The asymptotic distribution of the likelihood ratio test enables, via inversion, the construction of pointwise confidence intervals. Simulations show that these confidence intervals exhibit comparable coverage probabilities but shorter length, on average, than the confidence intervals based on the asymptotic distribution of the nonparametric maximum likelihood estimator of a monotone baseline hazard function.

Key words and phrases: Cox model, likelihood ratio test, nonparametric maximum likelihood estimation, shape constrained estimators.