Markov Model — Probabilistic State-Transition Modeling
Markov Chain Model · Also known as: Markov Chain, Discrete-Time Markov Chain, DTMC, Markov Process
A Markov Model represents a system as a finite set of states and specifies the probability of moving from one state to another at each time step. By capturing only the current state — not the full history — it enables tractable analysis of complex dynamic processes across health economics, engineering reliability, operations research, and social-science modeling.
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When to use it
Use a Markov Model when: (1) a process can be described as transitions among a small number of distinct states; (2) the memoryless assumption is defensible — future transitions depend only on the current state; (3) you need long-run or expected-value summaries (steady-state proportions, expected costs, expected quality-adjusted life years). It is particularly standard in health-technology assessment (HTA) and reliability engineering. Do NOT use when: history strongly affects future transitions (use higher-order chains or semi-Markov models instead); the number of states explodes with problem complexity (consider simulation instead); data for reliable transition-probability estimation are unavailable; or the process involves continuous state spaces without natural discretization.
Strengths & limitations
- Transparent and auditable: the transition matrix fully specifies the model and can be inspected, validated, and communicated to non-technical stakeholders.
- Analytically tractable: closed-form solutions exist for steady-state distributions, mean passage times, and absorption probabilities.
- Widely accepted in regulatory contexts, especially health-technology assessment (NICE, CADTH guidelines recognize Markov cohort models).
- Flexible time horizon: supports both short-run transient analysis and long-run steady-state queries with the same model.
- Easily extended to Markov Decision Processes (MDPs) when control or policy optimization is needed.
- The memoryless (Markov) assumption is often violated in practice — sojourn times that follow non-exponential distributions require semi-Markov or phase-type extensions.
- State-space explosion: adding detail to represent history or heterogeneity multiplies the number of states, rapidly increasing model complexity and data requirements.
- Transition probabilities must be estimated from data; sparse data lead to wide uncertainty intervals that can dominate model conclusions.
- Homogeneity assumption: standard Markov chains assume transition probabilities are constant over time, which may be unrealistic for aging cohorts or evolving systems.
Frequently asked
How many states should a Markov model have?
Use the fewest states that preserve clinically or operationally meaningful distinctions. More states improve realism but increase data requirements and verification burden. A practical starting point is 3-8 states; beyond 15-20, individual simulation approaches often become preferable.
What if my data suggest transition probabilities change over time?
A time-homogeneous Markov chain assumes constant transition probabilities. If probabilities vary with time or age, use a time-inhomogeneous chain (different P matrix per cycle), a semi-Markov model (sojourn-time-dependent transitions), or individual-level microsimulation.
How do I handle parameter uncertainty?
Fit Dirichlet distributions to each row of the transition matrix using observed counts, then sample from these distributions in a probabilistic sensitivity analysis (PSA). Report results as cost-effectiveness acceptability curves or credible intervals rather than point estimates.
What is the difference between a Markov model and a Markov Decision Process?
A Markov model describes a system passively — transitions are governed by fixed probabilities. A Markov Decision Process (MDP) extends this by adding actions and rewards, enabling optimization of decisions or policies over time.
When should I use a cohort Markov model versus individual-level microsimulation?
Cohort models track proportions across states and are computationally cheap and transparent; prefer them when the Markov assumption holds and heterogeneity is limited. Microsimulation tracks individual histories, making it suitable when memory effects, individual variability, or interaction between individuals matter, at the cost of greater computational and data demands.
Sources
- Norris, J. R. (1997). Markov Chains. Cambridge University Press, Cambridge. ISBN: 9780521633963
- Markov chain. Wikipedia. link ↗
How to cite this page
ScholarGate. (2026, June 3). Markov Chain Model. ScholarGate. https://scholargate.app/en/simulation/markov-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.
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