Multi-state modelling
Many questions are about pathways rather than a single event: patients who relapse, recover or die, who reach remission and then relapse, or who have repeated events while other events compete. Multi-state models describe those transitions, and what they imply for the chance of being in each state over time. We design, fit and interpret them for clinical, register and health-economic data, and explain what they show.
Built by the people who wrote the methods and the software. merlin, our own framework, fits multi-state and competing-risks models in R and Stata.
Four kinds of question
The model has to follow the question, not the other way round. These are the questions we are asked most.
Patients who move between states
Multi-state models extend survival analysis to settings where individuals move between several states over time, capturing complex disease pathways and the transitions between them.
Events that compete
A patient who has one event may no longer be able to have another. Competing risks are the simplest multi-state model, and the risk of each event depends on the rates of all of them.
Events that repeat
Recurrent events occur many times for the same person, and people may also face competing events that change what can happen next. Ignoring either misleads.
An answer a clinician can use
Transition probabilities, the chance of lasting remission, and clinically useful measures of the difference between treatments, rather than coefficients alone.
An illness–death model and its transition rates
and the chance of being in each state it implies
From the model to what it means
Most engagements are one of these, or a few of them together.
Design the model around the question
Which states and transitions, whether the clock restarts in each state, and which time scale: chosen from the clinical question and the data you have.
Fit it with the software we wrote
Transition-specific models, parametric or semi-parametric, fitted in the merlin family in R and Stata, and turned into state probabilities and length of stay.
Predict and explain
State probabilities, cumulative incidence and expected time in each state, with the uncertainty around them. Try the multi-state and competing-risks explorer.
Simulate to check a design
Simulating from competing-risks and general multi-state models to see what a design can and cannot show before a study.
Health-economic models
Multi-state structures for the cost-effectiveness model, with the transition hazards estimated in one coherent framework. See our HTA survival modelling.
Teaching your team
The methods taught hands-on, in our open courses on multi-state survival analysis and competing risks, or as bespoke in-house training.
Multi-state methods we have developed
Nine peer-reviewed papers on multi-state, competing-risks and recurrent-event models, each with Michael Crowther as an author, published between 2014 and 2025. Where a method became software, the software paper is listed too.
- 2025Parametric estimation of the mean number of events in the presence of competing risks. Biometrical Journal 2025;67(1):e70038. View →
- 2024Multiple imputation strategies for missing event times in a multi-state model analysis. Statistics in Medicine 2024;43(6):1238-1255. View →
- 2023Exploring different research questions via complex multi-state models when using registry-based repeated prescriptions of antidepressants in women with breast cancer and a matched comparison group. BMC Medical Research Methodology 2023;23(1):87. View →
- 2022On the choice of timescale for other cause mortality in a competing risk setting using flexible parametric survival models. Biometrical Journal 2022;64(7):1161-1177. View →
- 2021A multistate model incorporating estimation of excess hazards and multiple time scales. Statistics in Medicine 2021;40(9):2139-2154. View →
- 2021Relaxing the assumption of constant transition rates in a multi-state model in hospital epidemiology. BMC Medical Research Methodology 2021;21(1):16. View →
- 2017Parametric multi-state survival models: flexible modelling allowing transition-specific distributions with application to estimating clinically useful measures of effect differences. Statistics in Medicine 2017;36(29):4719-4742. View →
- 2017Flexible parametric modelling of the cause-specific cumulative incidence function. Statistics in Medicine 2017;36(9):1429-1446. View →
- 2014Multilevel mixed effects parametric survival models using adaptive Gauss-Hermite quadrature with application to recurrent events and individual participant data meta-analysis. Statistics in Medicine 2014;33(22):3844-3858. View →
The software papers
- 2022Simulating time-to-event data from parametric distributions, custom distributions, competing-risks models, and general multistate models. The Stata Journal: Promoting communications on statistics and Stata 2022;22(1):3-24. View →
- 2021Development of a dynamic interactive web tool to enhance understanding of multi-state model analyses: MSMplus. BMC Medical Research Methodology 2021;21(1):262. View →
- 2020
Published work
The question, the approach, and what it showed.
Mapping the path to lasting remission in lymphoma
RDA's Sara Ekberg and Michael Crowther used multi-state modelling — built on the Stata merlin and multistate packages — to estimate the real-world chance of lasting remission after diffuse large B-cell lymphoma in 2,941 Swedish patients. Published in British Journal of Cancer.
Read the case study →Counting recurrent events when death gets in the way
RDA-led methods development (Entrop & Crowther): a new parametric model that estimates the mean number of recurrent events — hospitalisations, infections, recurrences — over time while correctly accounting for competing events such as death. Published in Biometrical Journal.
Read the case study →The people who wrote the methods and the software
The expertise behind this work is published and open to inspection.
merlin
Our framework for survival, joint, multi-state and competing-risks models, maintained in R and Stata.
pendragon
Multi-state and competing-risks models built on the merlin engine, with transition probabilities and length of stay. In development for R and Stata.
The explorer
Choose a model structure, set the intensity of each transition, and watch state-occupancy probabilities, cumulative incidence and restricted mean time-in-state update live.
Specialises in survival analysis and joint longitudinal–survival models, is the author of the merlin framework, and teaches advanced courses with an emphasis on joint modelling and multi-state survival analysis.
View profile →
Research focused on cancer survival and survivorship, and lead author of the published multi-state model of patient trajectories after lymphoma (British Journal of Cancer, 2022).
View profile →Engagements that fit the problem
Expert advisory
Hours to days. A focused conversation or short review: a second opinion on a model, a sanity check on an approach, or direction before you commit to an analysis.
Project engagement
Weeks to months. Scoped to a defined deliverable, such as the multi-state analysis for a study or a paper, with a named expert team, an agreed scope and milestones, and reproducible code and documentation.
Ongoing support
Continuous access across several studies a year, where the relationship compounds.
The method, in the open
Primers, worked examples and a tool on the problems above. Nothing needs an account.
What is a multi-state model?
Transition hazards, the illness–death model, state probabilities, length of stay, clock forward or reset, and the data set-up.
What are competing risks?
Why one minus Kaplan–Meier overstates the risk, cause-specific hazards versus cumulative incidence, the methods, and what to report.
What is the cumulative incidence function?
How the Aalen–Johansen estimator builds it from a small example, how to compare groups and what to report.
Competing risks in merlin
Two cause-specific models in one command, and the arithmetic that shows they are the same two models you would have fitted separately.
Semi-parametric multi-state modelling
Multi-state models with a Cox model for every transition, fitted with merlin and turned into transition probabilities and length of stay.
Multi-state & competing-risks explorer
Set the states and the transitions between them, and see where patients actually end up, with length of stay.