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 data are usually reported in the form of registers which contain the number of observed cases and the number of individuals at risk to contract the disease. These data 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. In order to take into account possible overfitting issues, 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 hazards to be equal, leading to a parsimonious representation of the hazard rate. The method is evaluated on simulated data and applied on the E3N cohort data of breast cancer.