# On models for the estimation of the excess mortality hazard in case of insufficiently stratified life tables

## TL;DR

This paper introduces two parametric correction methods for excess mortality hazard models to address biases caused by insufficiently stratified life tables in cancer epidemiology, demonstrating their effectiveness through simulations and real data.

## Contribution

It proposes novel parametric correction techniques, including a frailty model, to improve excess hazard estimation when life tables lack detailed stratification.

## Key findings

- Proposed methods reduce bias in excess hazard estimates.
- Simulation studies show good statistical performance.
- Application to lung cancer data demonstrates practical utility.

## Abstract

In cancer epidemiology using population-based data, regression models for the excess mortality hazard is a useful method to estimate cancer survival and to describe the association between prognosis factors and excess mortality. This method requires expected mortality rates from general population life tables: each cancer patient is assigned an expected (background) mortality rate obtained from the life tables, typically at least according to their age and sex, from the population they belong to. However, those life tables may be insufficiently stratified, as some characteristics such as deprivation, ethnicity, and comorbidities, are not available in the life tables for a number of countries. This may affect the background mortality rate allocated to each patient, and it has been shown that not including relevant information for assigning an expected mortality rate to each patient induces a bias in the estimation of the regression parameters of the excess hazard model. We propose two parametric corrections in excess hazard regression models, including a single-parameter or a random effect (frailty), to account for possible mismatches in the life table and thus misspecification of the background mortality rate. In an extensive simulation study, the good statistical performance of the proposed approach is demonstrated, and we illustrate their use on real population-based data of lung cancer patients. We present conditions and limitations of these methods, and provide some recommendations for their use in practice.