Concept Architecture
Concept
Theoretically, Discrete Event Model is a stochastic simulation modelling approach in which the state of a system changes only when discrete events occur. It represents individual entities moving through a sequence of events over continuous time, allowing each entity to possess unique characteristics, histories and interactions. In health economics, discrete event models are used to evaluate complex clinical pathways, competing risks, resource constraints and treatment sequences that cannot be adequately represented using cohort-based state-transition models.
Mathematically, a discrete event model is represented by a stochastic event scheduling framework in which event occurrence times are generated from probability distributions and processed in chronological order. The model estimates patient trajectories, resource utilisation, costs and health outcomes by repeatedly simulating individual patient histories. There is no universally recognised canonical mathematical formula.
In practice, discrete event models are implemented by defining entities, attributes, events, resources, queues and event scheduling rules. Event-time distributions are estimated from clinical trials, observational studies or registry data using recognised statistical methods. Model outputs are generated through Monte Carlo simulation, with uncertainty evaluated using probabilistic sensitivity analysis and model validation against observed clinical and operational data.
Purpose
Used to evaluate complex healthcare systems involving individual patient pathways, competing events, constrained resources, waiting times, treatment sequencing and operational processes where event timing influences health and economic outcomes.
Mathematical Formulae
Primary Formula
There is no universally recognised canonical mathematical formula.
Supporting Formulae
Future event time generated from an event-time distribution:
T = t + �
where:
- t = current simulation time
- � = randomly sampled time until the next event
Related Mathematical Methods
- Discrete-event simulation
- Monte Carlo simulation
- Event scheduling algorithms
- Probability distributions
- Survival analysis
- Queueing theory
- Maximum likelihood estimation
- Probabilistic sensitivity analysis
Example
A hospital compares two treatment pathways for patients requiring cardiac surgery. Individual patients are simulated through referral, diagnostic assessment, surgery, recovery and discharge. Surgical waiting time follows a Weibull distribution, operating theatre capacity is limited to four procedures per day, and postoperative complications occur probabilistically. After 10,000 simulated patients, the intervention reduces average waiting time from 28 to 19 days, decreases mean treatment cost from �18,450 to �17,980 per patient, and increases mean quality-adjusted life years by 0.08.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| RAND | =RAND() | Generate random numbers for stochastic event simulation |
| NORM.INV | =NORM.INV(RAND(),Mean,SD) | Sample event times from a Normal distribution |
| WEIBULL.INV | =WEIBULL.INV(RAND(),Alpha,Beta) | Sample survival or waiting times from a Weibull distribution |
| MIN | =MIN(Event1,Event2,Event3) | Identify the next event to occur |
| SORT | =SORT(EventTable,EventTime,1) | Maintain the chronological event list |
VBA (Optional)
Automate repeated patient-level simulations, event scheduling and summary reporting across multiple intervention scenarios.
Sources
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press; 2006.
- Karnon J, Stahl J, Brennan A, et al. Modeling using discrete event simulation: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force-4. Medical Decision Making. 2012;32(5):701?711.
- Banks J, Carson JS, Nelson BL, Nicol DM. Discrete-Event System Simulation. 5th ed. Pearson.
- Law AM. Simulation Modeling and Analysis. 5th ed. McGraw-Hill.
- 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 (4)
Library
Tools & Resources
1
hesim — Health Economic Simulation Modeling and Decision Analysis (R package) — Devin Incerti & Jeroen P. Jansen, R package ed., 2024 (CRAN)
A modular, computationally efficient R package for building and analysing health economic simulation models — cohort state-transition, partitioned survival, and individual-level continuous-time models — with fast individual-patient simulation and PSA via C++.
Software (R package)View source →
Frequently Asked Questions (6)
What is a discrete event model?
A simulation model representing a system as a sequence of distinct events at specific times, with the system's state changing only at each event.
Source: Law & Kelton 2000
Why does a discrete event model only update at events?
A discrete event model assumes that the system's state stays unchanged between events and jumps only when an event occurs, such as a patient arriving, a treatment finishing, or a bed freeing. Because nothing of interest happens in the gaps, the model can skip over them, advancing its clock straight to the time of the next scheduled event rather than ticking through every moment. This event-to-event stepping makes it efficient for systems where change is occasional rather than continuous. Pidd (2004) describes this design.
Source: Pidd 2004
How does a discrete event model represent a system?
A discrete event model represents a system through its entities, their attributes, the resources they use, and the events that change the system's state, such as an arrival, the start or end of a service, or a departure. The state changes only when an event occurs, and between events it is constant. The model maintains a list of scheduled future events and processes them in time order, updating the state and scheduling new events at each, so the system evolves as a sequence of discrete changes.
Source: Law & Kelton 2000
How does a discrete event model differ from a continuous model?
A discrete event model changes state only at distinct events occurring at specific times, with the state constant between them, whereas a continuous model represents change as occurring smoothly at every instant, usually through differential equations. Discrete event models suit systems where change happens at identifiable moments, such as arrivals and service completions, and they advance from event to event. Continuous models suit smoothly varying quantities. The choice depends on whether the system's changes are naturally discrete or continuous.
Source: Law & Kelton 2000
What systems suit a discrete event model?
Discrete event models suit systems where entities flow through processes and events occur at identifiable moments, such as patients arriving, waiting, being served by staff or equipment, and leaving. They are well suited to representing queues, resource contention, and waiting times in health services, such as clinics, emergency departments, and operating theatres. Where the quantities of interest, such as waiting times and resource use, arise from discrete events involving individual entities, a discrete event model captures them naturally.
Source: Law & Kelton 2000
What are the advantages of a discrete event model?
A discrete event model advances directly from one event to the next, skipping the inactive intervals between, which makes it computationally efficient for systems where events are sparse relative to time. It represents individual entities, their attributes, queues, and resources naturally, capturing waiting and contention that aggregate models miss. This makes it well suited to modelling patient flow and resource use in health services, where the detailed timing of events and the competition for limited resources determine the performance measures of interest.
Source: Law & Kelton 2000
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 6 Oct 2025
Content version: 1.0.0
Canonical Identity
- Term code
- HE-EM-DES-005
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