Concept Architecture
Concept
Theoretically, State Occupancy is the probability or proportion of individuals occupying a particular health state at a specified point in time within a state-transition model. It represents the evolving distribution of a cohort or simulated population across mutually exclusive health states and provides the basis for calculating expected clinical and economic outcomes. In health economics, state occupancy is a fundamental quantity in Markov models, cohort simulations and microsimulation models.
Mathematically, state occupancy is represented by the state probability vector obtained by repeated application of the transition probability matrix. Each element of the vector gives the probability or proportion of the cohort occupying a specific health state during a model cycle. State occupancy is subsequently combined with state-specific costs, utilities and other outcomes to estimate cumulative economic and health consequences.
In practice, state occupancy is calculated automatically during each simulation cycle using estimated transition probabilities derived from clinical trials, observational studies or survival analyses. The resulting state occupancy distributions are used to estimate life years, quality-adjusted life years, healthcare costs and resource utilisation, and to validate that the model behaves consistently over the selected time horizon.
Purpose
Used to quantify the distribution of individuals across health states during model simulation, enabling calculation of expected costs, health outcomes and resource use over time.
Mathematical Formulae
Primary Formula
State occupancy vector:
????? = ?????
where:
- ??? = state occupancy vector at cycle t
- ?? = transition probability matrix
The occupancy of state j at cycle t is the j-th element of ???.
Supporting Formulae
State occupancy after n cycles:
??? = ?????�
Expected cycle cost:
C? = ?????
Expected cycle health outcome:
E? = ?????
where:
- ?? = vector of state-specific costs
- ?? = vector of state-specific health outcomes
Related Mathematical Methods
- Markov chains
- Matrix algebra
- State-transition modelling
- Cohort simulation
- Cohort trace
- Probabilistic sensitivity analysis
Example
A Markov model contains three health states: Stable Disease, Progressive Disease and Death.
After five annual cycles, the state occupancy vector is:
??? = [0.58, 0.27, 0.15]
This indicates that 58% of the cohort remains in the stable disease state, 27% has progressed and 15% has died. Multiplying these occupancies by state-specific annual costs and utility values produces the expected costs and quality-adjusted life years for cycle five.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| MMULT | =MMULT(StateVector,TransitionMatrix) | Calculate state occupancy after each cycle |
| SUMPRODUCT | =SUMPRODUCT(StateVector,CostVector) | Estimate expected cycle costs |
| SUMPRODUCT | =SUMPRODUCT(StateVector,UtilityVector) | Estimate expected QALYs for each cycle |
| INDEX | =INDEX(StateVector,StateNumber) | Retrieve occupancy for a specific health state |
| SUM | =SUM(StateVector) | Verify that state occupancies sum to one |
VBA (Optional)
Automate calculation of state occupancy vectors across all cycles and summarise cumulative health and economic outcomes.
Sources
- 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.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press; 2006.
- 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 state occupancy?
The amount of time, typically in cycles, that a patient or cohort proportion spends within a given health state in a Markov model.
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.
What does state occupancy measure over a model run?
State occupancy measures how much time a patient, or a proportion of the cohort, spends in each health state across the whole run, usually counted in cycles. Summed over the horizon, it gives the total time the cohort accumulates in every state, which is the quantity the model finally values. Because cost and health are earned per unit of time in a state, the pattern of occupancy across states largely determines the results. It is what the cohort trace records cycle by cycle. Briggs and colleagues (2006) describe this quantity.
Source: Briggs et al. 2006
How is state occupancy calculated?
State occupancy is calculated by summing, over the cycles of the model, the proportion of the cohort, or the time an individual, spends in a state. In a cohort model, the occupancy of a state is the sum across cycles of the proportion in that state, giving the expected time the cohort spends there. Multiplying occupancy by the state's per-cycle cost and utility, and summing across states, yields the total costs and effects, so occupancy is the quantity that translates the cohort trace into outcomes.
Source: Sonnenberg & Beck 1993
Why is state occupancy important?
State occupancy is important because costs and health effects in a Markov model are typically accrued for each cycle a patient occupies a state, so the total time spent in each state, weighted by its cost and utility, determines the model's outcomes. States occupied longer contribute more to the totals. Occupancy of a good-quality state adds quality-adjusted life years, while occupancy of a costly state adds cost. Thus state occupancy is the link between the cohort's movement through states and the estimated costs and effects.
Source: Sonnenberg & Beck 1993
How does state occupancy drive costs and effects?
State occupancy drives costs and effects because each state carries a per-cycle cost and a per-cycle health value, or reward, and these are accrued for each cycle of occupancy. The total cost from a state is its per-cycle cost times its occupancy, and similarly for health effects, so summing across states gives the model's total costs and quality-adjusted life years. Because outcomes accrue with time in states, the pattern of state occupancy over the horizon determines the results the model produces.
Source: Sonnenberg & Beck 1993
How does state occupancy relate to the cohort trace?
State occupancy relates to the cohort trace as its accumulation over time: the cohort trace records the proportion in each state at every cycle, and the occupancy of a state is the sum of those proportions across cycles. The trace shows membership cycle by cycle, while occupancy totals the time spent in each state. Occupancy is thus derived from the trace, and multiplying occupancies by state values gives the outcomes, so the trace provides the detail from which occupancy and results are computed.
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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