  The proportional hazards model represents the most commonly assumed hazard
structure when analysing time to event data using regression models. We study a
general hazard structure which contains, as particular cases, proportional
hazards, accelerated hazards, and accelerated failure time structures, as well
as combinations of these. We propose an approach to apply these different
hazard structures, based on a flexible parametric distribution (Exponentiated
Weibull) for the baseline hazard. This distribution allows us to cover the
basic hazard shapes of interest in practice: constant, bathtub, increasing,
decreasing, and unimodal. In an extensive simulation study, we evaluate our
approach in the context of excess hazard modelling, which is the main quantity
of interest in descriptive cancer epidemiology. This study exhibits good
inferential properties of the proposed model, as well as good performance when
using the Akaike Information Criterion for selecting the hazard structure. An
application on lung cancer data illustrates the usefulness of the proposed
model.
