Regularized Bidimensional Estimation of the Hazard Rate

Vivien Goepp (1, 2, 3) , Jean-Christophe Thalabard (1, 2, 4, 5, 6, 7) , Grégory Nuel (8) , Olivier Bouaziz (1, 2, 3, 9)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 UPD5 - Université Paris Descartes - Paris 5
3 UPD5 Mathématiques Informatique - Université Paris Descartes - UFR de Mathématiques et Informatique
4 USPC - Université Sorbonne Paris Cité
5 Hôpital Cochin [AP-HP]
6 Service de gynécologie et d'endocrinologie [CHU Cochin]
7 UPD5 Médecine - Université Paris Descartes - Faculté de Médecine
8 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
9 IUT - Paris Descartes - Institut Universitaire de Technologie Paris Descartes

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 L$_0$ norm, which makes the computation tractable. The method is evaluated on simulated data and applied on breast cancer survival data from the SEER program.

Mots clés: Age-Period-Cohort Analysis; Penalized Likelihood; Survival Analysis; Adaptive Ridge Procedure; Piecewise Constant Hazard

Domaines: Applications [stat.AP]

Vivien Goepp, Jean-Christophe Thalabard, Grégory Nuel, Olivier Bouaziz. Regularized Bidimensional Estimation of the Hazard Rate. 2020. ⟨hal-01662197v4⟩