Multi-state models for the analysis of time-to-event data

TLDR

Multi‑state models represent patient trajectories with multiple intermediate states, enabling estimation of progression rates, risk‑factor effects, survival, and prognostic forecasting. This article reviews modelling approaches and software for multi‑state models, emphasizing estimation of transition and survival probabilities. The authors compare methodological differences, discuss advantages and disadvantages, and introduce a new R library for fitting such models. Illustrations using Stanford heart‑transplant and Galician breast‑cancer data demonstrate the application of the reviewed methods and software.

Abstract

The experience of a patient in a survival study may be modelled as a process with two states and one possible transition from an “alive” state to a “dead” state. In some studies, however, the “alive” state may be partitioned into two or more intermediate (transient) states, each of which corresponding to a particular stage of the illness. In such studies, multi-state models can be used to model the movement of patients among the various states. In these models issues, of interest include the estimation of progression rates, assessing the effects of individual risk factors, survival rates or prognostic forecasting. In this article, we review modelling approaches for multi-state models, and we focus on the estimation of quantities such as the transition probabilities and survival probabilities. Differences between these approaches are discussed, focussing on possible advantages and disadvantages for each method. We also review the existing software currently available to fit the various models and present new software developed in the form of an R library to analyse such models. Different approaches and software are illustrated using data from the Stanford heart transplant study and data from a study on breast cancer conducted in Galicia, Spain.