  In epidemiological or demographic studies, with variable age at onset, a
typical quantity of interest is the incidence of a disease (for example the
cancer incidence). In these studies, the individuals are usually highly
heterogeneous in terms of dates of birth (the cohort) and with respect to the
calendar time (the period) and appropriate estimation methods are needed. In
this article a new estimation method is presented which extends classical
age-period-cohort analysis by allowing interactions between age, period and
cohort effects. This paper introduces a bidimensional regularized estimate of
the hazard rate where a penalty is introduced on the likelihood of the model.
This penalty can be designed either to smooth the hazard rate or to enforce
consecutive values of the hazard to be equal, leading to a parsimonious
representation of the hazard rate. In the latter case, we make use of an
iterative penalized likelihood scheme to approximate the L0 norm, which makes
the computation tractable. The method is evaluated on simulated data and
applied on breast cancer survival data from the SEER program.
