Multi-state modelling: a brief introduction

Written by Chris Morton | PhD Student

Multi-state modelling, a flexible framework which describes complex clinical processes over time, is often overlooked by the more favourable survival and longitudinal models. In this blog, I hope to provide an accessible introduction to multi-state modelling, drawing on my recent dissertation for my MSc at Lancaster, whilst also introducing my current research.

What is a multi-state model?

The concepts of multi-state models may be more familiar to researchers than they realise.

In a multi-state model, an individual/patient falls under one of several ‘states’, and may transition between those states over the course of their lifetime.

So in a 3-state illness-death model, a healthy patient is in state 1, they transition to stage 2 if they become diseased and stage 3 reflects death. Traditional survival analysis can be considered a 2-state (alive or deceased) model.

Health researchers are often interested though, in the effect of covariates (e.g. treatment regime) on the risk of an event at each instant of time. For a general multi-site model, the event is the transition from one state to another, and it is possible for separate baseline risk and covariate effects to be associated with each transition.

Why use multi-site models in primary care?

Multi-state models are commonly applied to clinical conditions where there is an increasing state of disease severity which precedes eventual death. Only using this approach though, it unnecessarily limiting — there are a wide range of potential applications of multi-site models in a primary care setting (e.g. mental health conditions and patient habits such as smoking and alcohol consumption).

The biggest advantage of using a multi-site approach is the insight you can gain about every aspect of a process. For example, we can separately measure the factors affecting a smoker’s decision to quit and those affecting a relapse into smoking.

For my dissertation, the illness-death model is used to describe the progress of intact dental veneers (state 1), which may at first become discoloured (state 2) before eventually fracturing (state 3). My methodology focuses on the methodology rather than this particular application, but the example illustrates the diversity of potential uses for a multi-state approach.

What are the key steps in model building?

1) Representing clinical processes

The first step for a researcher is deciding how to represent a clinical process in terms of a discrete state and the permitted transitions between them — which isn’t always straightforward.

For example, when following the habits of a smoker, do two states (‘current smoker’ and ‘current abstinence’) adequately capture their behaviour? Or, do we want at least three — ‘habitual smoker’, ‘withdrawal phase’ and ‘long-term abstinence’ (see paper).

2) Matching covariates with state transitions

Consider which covariates act on each state transition and whether their effect should be constrained to be equal amongst transitions (due to a biological rationale, or to simplify model calculation).

3) Model Fitting

A natural starting point for model fitting is using freely available packages in R software: ‘mstate’ and ‘msm’. Mstate’ can be used if state transitions are observed at an exact date, such as when a patient dies. ‘Msm’ can handle panel data, such as when a patient is known only to have changed state at a time since their previous clinical observation.

Beyond the functionality of the above packages, lies potential complications which were the focus of my dissertation. I analysed panel data with a clear dependence structure (multiple veneers in the same patient) and showing evidence of time-inhomogeneity (the instantaneous risk of a state transition changes over time).

Unfortunately though, some of these more complicated models remain inaccessible to many researchers, largely due to a lack of software availability.

What next?

Fresh from a MSc in Statistics at Lancaster University, I now face the trials and tribulations of a PhD at the Research Institute for Primary Care and Health Sciences at Keele. My research investigates the treatment and symptom patterns of patients with polymyalgia rheumatica (PMR) and what factors predict these.

Patients go from being treated with steroids to a state of remission, which may be followed by future relapses, again bringing to mind a multi-state framework. It is still too early to say whether such methods will provide me with an informative perspective, and research trajectories don’t always run so smoothly.

Regardless, multi-state modelling, together with longitudinal methods learned at Lancaster will always be a welcome tool to have in my future career as a primary care researcher, and I hope this blog has you already considering further applications for this interesting and useful area of methodology.