Regularized Bidimensional Estimation of the Hazard Rate

TL;DR

This paper introduces a novel bidimensional regularized estimation method for hazard rates in epidemiological studies, extending age-period-cohort analysis by incorporating interaction effects and penalization techniques.

Contribution

The paper presents a new estimation approach that allows for interactions between age, period, and cohort effects with regularization, improving hazard rate modeling in heterogeneous populations.

Findings

Method effectively estimates hazard rates in simulated data.

Application to breast cancer data demonstrates practical utility.

Regularization improves model interpretability and smoothness.

Abstract

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.