Concept Architecture
Concept
Theoretically, Cohort Simulation is a population-based modelling approach in which a cohort of individuals is represented by proportions occupying mutually exclusive health states over successive time periods. Rather than simulating individual patients, the model follows the expected movement of the cohort through predefined states using average transition probabilities. In health economics, cohort simulation is the standard implementation of state-transition (Markov) models for evaluating long-term costs, health outcomes and cost-effectiveness.
Mathematically, cohort simulation is represented by repeated multiplication of a cohort state vector by a transition probability matrix. The mathematical framework estimates the expected distribution of the cohort across health states at each cycle, allowing calculation of accumulated costs, life years and quality-adjusted life years over the model horizon.
In practice, cohort simulations are constructed by defining health states, cycle length, transition probabilities, costs and health utilities. Transition probabilities are estimated from clinical trials, epidemiological studies or survival analyses, and model outputs are validated through internal consistency checks, calibration and sensitivity analyses before being used in health technology assessment.
Purpose
Used to estimate the long-term movement of patient cohorts through health states, calculate expected costs and health outcomes, and evaluate the cost-effectiveness of healthcare interventions.
Mathematical Formulae
Primary Formula
Cohort state update:
????? = ?????
where:
- ??? = cohort state vector at cycle t
- ?? = transition probability matrix
Supporting Formulae
State occupancy after n cycles:
??? = ?????�
Expected total cost:
C = ????? ?????
Expected total health outcome:
E = ????? ?????
where:
- ?? = vector of state-specific costs
- ?? = vector of state-specific health outcomes (for example, utilities or QALYs)
Related Mathematical Methods
- Markov modelling
- Matrix algebra
- State-transition modelling
- Transition probability estimation
- Survival analysis
- Probabilistic sensitivity analysis
Example
A cohort of 1,000 patients begins entirely in a stable disease state:
??? = [1, 0, 0]
with transition matrix
?? =
?0.85 0.10 0.05?
?0.00 0.80 0.20?
?0.00 0.00 1.00?
After one cycle:
??? = ????? = [0.85, 0.10, 0.05]
Thus, 85% of the cohort remains stable, 10% progresses to the next health state and 5% enters the absorbing death state. Costs and quality-adjusted life years are calculated by applying state-specific values to the cohort distribution during each cycle.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| MMULT | =MMULT(StateVector,TransitionMatrix) | Calculate cohort distribution after each cycle |
| SUMPRODUCT | =SUMPRODUCT(StateVector,CostVector) | Calculate expected cost per cycle |
| SUMPRODUCT | =SUMPRODUCT(StateVector,UtilityVector) | Calculate expected QALYs per cycle |
| TRANSPOSE | =TRANSPOSE(StateVector) | Prepare vectors for matrix calculations |
| MUNIT | =MUNIT(States) | Create identity matrices for model development |
VBA (Optional)
Automate repeated cohort simulations across multiple strategies, time horizons and probabilistic sensitivity analysis iterations.
Sources
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press; 2006.
- Sonnenberg FA, Beck JR. Markov models in medical decision making: a practical guide. Medical Decision Making. 1993;13(4):322?338.
- Siebert U, Alagoz O, Bayoumi AM, et al. State-transition modeling: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force-3. Medical Decision Making. 2012;32(5):690?700.
- NICE. Health Technology Evaluation Manual.
- Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press.
Related Concepts (3)
Library
Publications
1
An Introduction to Markov Modelling for Economic Evaluation — Briggs & Sculpher, Vol. 13, No. 4 ed., 1998 (PharmacoEconomics)
The foundational tutorial paper introducing Markov (state-transition) models for health economic evaluation, covering health states, cycle length, transition probabilities and the calculation of expected costs and outcomes. Widely cited as the standard entry point to Markov modelling.
Journal ArticleView source →
Frequently Asked Questions (6)
What is cohort simulation?
The process of running a Markov model by tracking the proportion of a hypothetical cohort in each health state over cycles, not individual patients.
Source: Sonnenberg FA, Beck JR. Markov models in medical decision making: a practical guide. Medical Decision Making. 1993;13(4):322-338. doi:10.1177/0272989X9301300409.
How does cohort simulation move a group through health states?
Cohort simulation starts with a whole hypothetical group placed in their initial health states and, at each cycle, moves a fixed proportion of those in each state to others according to the transition probabilities. Rather than following any single patient, it records how the group is spread across the states as the cycles pass. The proportions in each state, multiplied by the values attached to them, give the cohort's total cost and health. It is the standard way of running a Markov cohort model. Briggs and colleagues (2006) describe this process.
Source: Briggs et al. 2006
How does cohort simulation work?
Cohort simulation works by starting with the cohort distributed across the health states, then, at each cycle, applying the transition probabilities to move proportions of the cohort between states, updating the distribution. Costs and health effects are accrued according to the proportions in each state each cycle. This is repeated over the model's cycles, and the accumulated costs and effects give the cohort's expected outcomes. The method tracks the shares of the cohort in each state over time rather than simulating individuals.
Source: Sonnenberg & Beck 1993
How does cohort simulation differ from individual simulation?
Cohort simulation tracks the proportions of a group in each state using average transition probabilities, following the cohort as a whole, whereas individual, or microsimulation, follows patients one at a time, each with their own characteristics and history. Cohort simulation is simpler, faster, and deterministic given the inputs, but it cannot capture individual heterogeneity or history beyond the current state. Individual simulation captures these but is more demanding. The choice depends on whether individual-level detail materially affects the results.
Source: Sonnenberg & Beck 1993
What are the advantages of cohort simulation?
Cohort simulation is simple, transparent, and computationally efficient, since it tracks proportions using average transition probabilities rather than simulating many individuals, and it gives a deterministic result for given inputs, avoiding the random variation of individual simulation. It is easy to build, check, and communicate, and it supports extensive sensitivity analysis quickly. For problems where outcomes depend on average effects and individual heterogeneity and history do not much matter, cohort simulation provides valid results efficiently, which is why it is widely used.
Source: Sonnenberg & Beck 1993
What are the limitations of cohort simulation?
Cohort simulation cannot easily represent individual heterogeneity, patient history beyond the current state, or interactions between individuals, because it follows the cohort by average rates and the standard Markov model has no memory. Where future risks depend on past events, capturing this requires adding states, which can multiply their number. Where such individual-level features materially affect outcomes, an individual simulation is needed instead. The limitations arise from tracking proportions rather than individuals, which is the source of the method's simplicity.
Source: Sonnenberg & Beck 1993
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 7 Oct 2025
Content version: 1.0.0
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