Isotonized smooth estimators of a monotone baseline hazard in the Cox model

•The Cox regression model with a monotone baseline hazard is considered.•Two isotonized smooth estimators of the baseline hazard are proposed.•These estimators are shown to be asymptotically normal.•They exhibit the same asymptotic variance but different biases.•Numerical results on pointwise confidence intervals are provided.

We consider two isotonic smooth estimators for a monotone baseline hazard in the Cox model, a maximum smooth likelihood estimator and a Grenander-type estimator based on the smoothed Breslow estimator for the cumulative baseline hazard. We show that they are both asymptotically normal at rate nm∕(2m+1), where m≥2 denotes the level of smoothness considered, and we relate their limit behavior to kernel smoothed isotonic estimators studied in Lopuhaä and Musta (2016). It turns out that the Grenander-type estimator is asymptotically equivalent to the kernel smoothed isotonic estimators, while the maximum smoothed likelihood estimator exhibits the same asymptotic variance but a different bias. Finally, we present numerical results on pointwise confidence intervals that illustrate the comparable behavior of the two methods.