Estimation of hazard functions with shape restrictions using regression splines

In the estimation of distributions with time-to-event data, it is often natural to impose shape and smoothness constraints on the hazard function. Systems that fail because of wearing out might be assumed to have monotone hazard, or perhaps monotone-convex. Organ transplant failures are often assumed to have convex or bathtub-shaped hazard function. In this paper we present estimates that maximize the likelihood over a set of shape-restricted regression splines. Right censoring is a simple extension. The methods are applied to real and simulated data sets to illustrate their properties and to compare with existing nonparametric estimators.