Individual frailty excess hazard models in cancer epidemiology

TL;DR

This paper introduces a new frailty model for excess hazard in cancer survival analysis, accounting for unobserved heterogeneity, with a flexible structure and practical implementation in R, improving survival estimates.

Contribution

It extends frailty modeling to the relative survival framework with closed-form solutions, enabling better interpretation and inference in cancer epidemiology.

Findings

The proposed model accurately captures unobserved heterogeneity in simulations.

Application to lung cancer data shows impact on survival estimates.

Model implementation available in R package IFNS.

Abstract

Unobserved individual heterogeneity is a common challenge in population cancer survival studies. This heterogeneity is usually associated with the combination of model misspecification and the failure to record truly relevant variables. We investigate the effects of unobserved individual heterogeneity in the context of excess hazard models, one of the main tools in cancer epidemiology. We propose an individual excess hazard frailty model to account for individual heterogeneity. This represents an extension of frailty modelling to the relative survival framework. In order to facilitate the inference on the parameters of the proposed model, we select frailty distributions which produce closed-form expressions of the marginal hazard and survival functions. The resulting model allows for an intuitive interpretation, in which the frailties induce a selection of the healthier individuals among survivors. We model the excess hazard using a flexible parametric model with a general hazard structure which facilitates the inclusion of time-dependent effects. We illustrate the performance of the proposed methodology through a simulation study. We present a real-data example using data from lung cancer patients diagnosed in England, and discuss the impact of not accounting for unobserved heterogeneity on the estimation of net survival. The methodology is implemented in the R package IFNS.