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

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.

Assessing Markov and Time Homogeneity Assumptions in Multi-state Models: Application in Patients with Gastric Cancer Undergoing Surgery in the Iran Cancer Institute

“…In cases where Markov assumption is not held, using non-Markov and semi-Markov models (Chen and Tien, 2004;Ruiz-Castro and Pérez-Ocón, 2004;Kang and Lagakos, 2007;MeiraMachado et al, 2009;Foucher et al, 2010;Titman and Sharples, 2010b;Titman, 2012), and in cases where time homogeneity assumption is not held, constructing models of transition rates as time-dependent, based on parametric models; or constructing models based on piecewise constant models have been proposed as alternatives (Omar et al, 1995;Pérez-Ocón et al, 2001;Hsieh et al, 2002;Mathieu et al, 2005;Ocañ-Riola, 2005;Meira-Machado et al, 2009;Titman, 2011). But, generally, using each of these generalizations requires assessing Markov and time homogeneity assumptions because if these assumptions are held, it will be inappropriate to use more complicated models.…”

Parametric hazard rate models for long-term sickness absence

“…To each of the possible transitions covariates can be linked. In multi-state models assumptions can be made about the dependence of hazard rates on time (Putter et al 2007;Meira-Machado et al 2008;Lie et al 2008).…”

Regional variation in hospitalisation and mortality in heart failure: comparison of England and Lombardy using multistate modelling

“…The msm package allows for an informal check of the Markovian assumption via the plot.prevalence.msm function, and the resulting plots showed good agreement between the observed and predicted outcomes for each state. More formally, we tested the association between the time spent in the previous state and the probability of transition from the current state as per Section 4.1.2 of [19] via hazard ratios and their 95% confidence intervals from the hazard.msm function. For example, in the three-state models we tested whether the number of days spent as an inpatient was associated with the transition from the community to death or with the transition from the community back to the hospital.…”