  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.
