Multi-State Survival Model
Also known as: illness-death model, multi-state transition model, Çok Durumlu Model (Multi-State / Illness-Death)
The multi-state model is a generalised survival framework, formalised in the work of Andersen and Keiding and brought to wide biostatistical practice by Putter, Fiocco and Geskus (2007), that models individuals moving through multiple distinct health states — for example, healthy, ill and dead — over time. A separate hazard function is estimated for each possible transition, and transition probabilities are recovered via the product-integral of the cumulative transition intensities.
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When to use it
Use a multi-state model when individuals can occupy more than two states over the course of follow-up and the transitions between states are themselves of scientific interest, not merely intermediate nuisances. Typical examples are the illness-death model (healthy → diseased → dead), staging models in oncology, and organ-transplant wait-list models (waiting → transplanted → dead or relapsed). The method requires at minimum around 100 subjects with sufficient events on each transition to estimate separate hazard functions reliably. The key modelling assumption is that, given the current state, the future trajectory depends only on the current state (Markov) or on the time already spent in it (semi-Markov), not on the full earlier history. Non-informative censoring is required for all transitions jointly. When the sample is too small for separate transition estimation, Cox regression on the composite endpoint is the pragmatic fallback.
Strengths & limitations
- Models the full trajectory through multiple disease states rather than reducing the outcome to a single endpoint.
- Produces transition probabilities that directly answer clinical questions such as 'what is the probability of being disease-free and alive at five years given current state?'.
- Competing risks are naturally embedded: each state can have multiple outgoing transitions, eliminating the need for a separate competing-risks analysis.
- Compatible with the Cox proportional-hazards framework, so familiar estimation and inference tools apply to each transition.
- Requires adequate event counts on every transition; rare transitions produce wide uncertainty in their estimated hazards and probabilities.
- The Markov assumption must be checked; when history beyond the current state matters, a semi-Markov or stratified approach is needed.
- Data preparation is substantially more complex than standard survival analysis, requiring a multi-row-per-person counting-process format.
- Minimum recommended sample size of 100 limits use in small-cohort studies.
Frequently asked
How is a multi-state model different from competing-risks analysis?
Competing-risks analysis focuses on the first of several possible events from a single origin state and estimates the cumulative incidence of each event type. A multi-state model extends this by allowing individuals to continue making further transitions after the first event — for example, moving from illness to recovery or from recovery to death. Competing risks are a special case of multi-state models with only one transient state.
What is the Markov assumption and how do I check it?
The Markov assumption states that the future trajectory of an individual depends only on their current state, not on how they arrived there. You can check it by testing whether the time spent in the current state (sojourn time) or the history of previous states predicts the current transition hazard. Graphical checks, such as comparing transition hazards stratified by prior state, are also informative. If the assumption fails, a semi-Markov model — where the hazard also depends on time in the current state — is more appropriate.
What is the minimum sample size needed?
Each transition in the model needs enough events to estimate its hazard reliably. The rule of thumb inherited from Cox regression is roughly 10–15 events per covariate per transition. With a total minimum of 100 subjects, multi-state models can become unstable if several transitions are rare. When transition counts are too small, collapsing states or using a simpler composite endpoint with standard Cox regression is advisable.
What outputs does a multi-state model produce?
The primary outputs are transition-specific hazard ratios (for covariates) and transition probability curves — the probability of being in each state at each future time given a starting state. These probability curves, obtained via the Aalen-Johansen estimator, are the most interpretable summary for clinicians and policy makers. Length of stay in each state (sojourn time) can also be derived by integrating the state occupation probabilities.
Sources
- Putter, H., Fiocco, M. & Geskus, R.B. (2007). Tutorial in Biostatistics: Competing Risks and Multi-State Models. Statistics in Medicine, 26(11), 2389–2430. DOI: 10.1002/sim.2712 ↗
- Jackson, C.H. (2011). Multi-State Models for Panel Data: The msm Package for R. Journal of Statistical Software, 38(8), 1–28. DOI: 10.18637/jss.v038.i08 ↗
How to cite this page
ScholarGate. (2026, June 1). Multi-State Survival Model. ScholarGate. https://scholargate.app/en/survival/multi-state-model
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Competing Risks AnalysisSurvival↔ compare
- Frailty ModelSurvival↔ compare
- Kaplan-MeierSurvival↔ compare
- Royston-Parmar ModelSurvival↔ compare