  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. The
characterization of the estimators involved is provided both in the
nondecreasing and the nonincreasing setting. These characterizations facilitate
the derivation of the asymptotic distribution of the likelihood ratio test,
which is identical in the nondecreasing and in the nonincreasing case. 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 with the
confidence intervals based on the asymptotic distribution of the nonparametric
maximum likelihood estimator of a monotone baseline hazard function.
