Integrating relative survival in multi-state models -- a non-parametric approach

TL;DR

This paper introduces a non-parametric method to incorporate relative survival into multi-state models, enabling the separation of disease-related and non-disease mortality without requiring cause of death data.

Contribution

It extends multi-state models by integrating population mortality tables, providing a non-parametric approach to estimate transition hazards and probabilities considering relative survival.

Findings

Method effectively separates disease and non-disease mortality.

Simulation studies demonstrate accurate variance estimation and confidence intervals.

Application to stem cell transplant data illustrates practical utility.

Abstract

Multi-state models provide an extension of the usual survival/event-history analysis setting. In the medical domain, multi-state models give the possibility of further investigating intermediate events such as relapse and remission. In this work, a further extension is proposed using relative survival, where mortality due to population causes (i.e. non-disease-related mortality) is evaluated. The objective is to split all mortality in disease and non-disease-related mortality, with and without intermediate events, in datasets where cause of death is not recorded or is uncertain. To this end, population mortality tables are integrated into the estimation process, while using the basic relative survival idea that the overall mortality hazard can be written as a sum of a population and an excess part. Hence, we propose an upgraded non-parametric approach to estimation, where population mortality is taken into account. Precise definitions and suitable estimators are given for both the transition hazards and probabilities. Variance estimating techniques and confidence intervals are introduced and the behaviour of the new method is investigated through simulations. The newly developed methodology is illustrated by the analysis of a cohort of patients followed after an allogeneic hematopoietic stem cell transplantation. The work is also implemented in the R package mstate.