Non-parametric estimation of net survival under dependence between death causes

TL;DR

This paper introduces a generalized non-parametric estimator for net survival in competing risks models that accounts for dependence between causes of death, relaxing the traditional independence assumption and providing new theoretical insights.

Contribution

It extends the Pohar Perme estimator to handle dependent death causes using stochastic processes and martingales, with formal asymptotic analysis and practical applications.

Findings

The new estimator accommodates dependence structures between causes of death.

Simulation studies show the impact of dependence assumptions on survival estimates.

Application to colorectal cancer data demonstrates practical utility.

Abstract

Relative survival methodology deals with a competing risks survival model where the cause of death is unknown. This lack of information occurs regularly in population-based cancer studies. Non-parametric estimation of the net survival is possible through the Pohar Perme estimator. Derived similarly to Kaplan-Meier, it nevertheless relies on an untestable independence assumption. We propose here to relax this assumption and provide a generalized non-parametric estimator that works for other dependence structures, by leveraging the underlying stochastic processes and martingales. We formally derive asymptotics of this estimator, providing variance estimation and log-rank-type tests. Our approach provides a new perspective on the Pohar Perme estimator and the acceptability of the underlying independence assumption. We highlight the impact of this dependence structure assumption on simulation studies, and illustrate them through an application on registry data relative to colorectal cancer, before discussing potential extensions of our methodology.