Concept Architecture
Concept
Theoretically, Cohort Trace is the sequence of cohort state distributions generated during a cohort simulation, showing the proportion of the cohort occupying each health state at every model cycle. It provides a complete description of how the cohort evolves over time within a state-transition model and forms the basis for calculating accumulated costs, life years and quality-adjusted life years. In health economics, the cohort trace is a fundamental output of cohort-based Markov models.
Mathematically, the cohort trace is obtained by successive multiplication of the initial cohort state vector by the transition probability matrix. Each row of the trace represents the expected state occupancy of the cohort at a given cycle, allowing estimation of cumulative health and economic outcomes across the model time horizon.
In practice, cohort traces are generated automatically during cohort simulation. The resulting state occupancy matrix is combined with state-specific costs, utilities and other outcomes to calculate expected costs and health benefits. Cohort traces are routinely examined to validate model behaviour, confirm conservation of cohort membership and identify implausible transition patterns.
Purpose
Used to describe the distribution of a cohort across health states over time, supporting the calculation, validation and interpretation of long-term health and economic outcomes in cohort-based state-transition models.
Mathematical Formulae
Primary Formula
For cycle t:
??? = ??????
where:
- ??? = initial cohort state vector
- ?? = transition probability matrix
- ??? = cohort state distribution at cycle t
Supporting Formulae
Cohort trace matrix:
?? = [???; ???; ?; ???]
Cycle-specific expected cost:
C? = ?????
Cycle-specific expected health outcome:
E? = ?????
where:
- ?? = vector of state-specific costs
- ?? = vector of state-specific health outcomes
Related Mathematical Methods
- Matrix algebra
- Markov modelling
- State-transition modelling
- Cohort simulation
- Transition probability estimation
Example
A three-state Markov model begins with all patients in the healthy state:
??? = [1, 0, 0]
After successive applications of the transition matrix, the cohort trace is:
| Cycle | Healthy | Diseased | Dead |
|---|---|---|---|
| 0 | 1.00 | 0.00 | 0.00 |
| 1 | 0.85 | 0.10 | 0.05 |
| 2 | 0.72 | 0.16 | 0.12 |
| 3 | 0.61 | 0.19 | 0.20 |
The cohort trace is then multiplied by state-specific costs and utilities at each cycle to estimate cumulative costs and quality-adjusted life years.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| MMULT | =MMULT(CurrentState,TransitionMatrix) | Calculate the next row of the cohort trace |
| SUMPRODUCT | =SUMPRODUCT(StateVector,CostVector) | Calculate expected cost for each cycle |
| SUMPRODUCT | =SUMPRODUCT(StateVector,UtilityVector) | Calculate expected QALYs for each cycle |
| INDEX | =INDEX(TraceTable,Cycle,State) | Retrieve state occupancy at a specified cycle |
| OFFSET | =OFFSET(B2,1,0) | Reference successive rows of the cohort trace |
VBA (Optional)
Automate generation of complete cohort traces and calculation of cumulative costs and health outcomes across all simulation cycles.
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
State-Transition Modeling: A Report of the ISPOR-SMDM Modeling Good Research Practices Task Force-3 — Siebert, Alagoz, Bayoumi, Jahn, Owens, Cohen & Kuntz, Task Force Report 3 ed., 2012 (Value in Health / Medical Decision Making)
Best-practice guidance for cohort and individual-based state-transition (Markov) models, covering development, analysis, validation and reporting.
Journal ArticleView source →
Frequently Asked Questions (6)
What is a cohort trace?
The complete record of the proportion of a modelled cohort occupying each health state at every cycle, produced by a Markov cohort 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 inspecting a cohort trace reveal?
A cohort trace lays out the proportion of the group in every health state at each cycle, so reading down it shows how the cohort redistributes over time. Inspecting it can reveal errors that summary results hide, such as a proportion that fails to add to one, patients appearing in a state they should not reach, or an implausibly fast drift into death. Because it exposes the model's inner workings cycle by cycle, it is a standard verification tool. Briggs and colleagues (2006) recommend examining it.
Source: Briggs et al. 2006
What does a cohort trace show?
A cohort trace shows, for each cycle of the model, the proportion of the cohort in each health state, so it depicts how patients move through the states over time, such as the shares remaining well, progressing, or having died at each point. It reveals the trajectory of the cohort, including how proportions accumulate in absorbing states like death. By laying out the state distribution over the whole horizon, the cohort trace gives a full picture of the modelled experience.
Source: Sonnenberg & Beck 1993
How is a cohort trace used?
A cohort trace is used to calculate the model's outcomes and to check its behaviour. Costs and health effects are computed by applying the values for each state to the proportions in the trace at each cycle and summing over time. The trace is also examined to verify the model, checking that proportions sum to one, that patients accumulate in absorbing states, and that the trajectory is clinically plausible. It thus serves both as the basis for the results and as a tool for validating the model.
Source: Sonnenberg & Beck 1993
How does a cohort trace help verify a model?
A cohort trace helps verify a model by making its behaviour visible cycle by cycle, allowing checks that the proportions across states sum to one at every cycle, that the cohort accumulates appropriately in absorbing states such as death over the horizon, and that the trajectory of the states is clinically plausible. Implausible patterns, such as too many patients in a state or proportions not summing correctly, signal errors. Inspecting the trace is therefore a standard step in checking that a Markov model behaves as intended.
Source: Sonnenberg & Beck 1993
How does a cohort trace relate to model outcomes?
A cohort trace relates to model outcomes as the record from which they are computed: the costs and health effects of the model are obtained by weighting the proportions in each state, at each cycle in the trace, by the state's cost and utility, and summing over the cycles. The trace thus contains the distribution of the cohort over time that, combined with state values, yields the expected costs and quality-adjusted life years. The outcomes are a summary of the detailed information the cohort trace provides.
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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