Concept Architecture
Concept
Theoretically, Event Probability is the probability that a specified event will occur within a defined population and time period. It represents the likelihood of clinical outcomes such as disease progression, adverse events, treatment response or death and forms a fundamental component of probability theory and decision analysis. In health economics, event probabilities determine patient movement through decision trees, state-transition models, microsimulation and dynamic transmission models.
Mathematically, Event Probability is represented as a value between 0 and 1 describing the chance that an event occurs. It may be estimated directly from observed frequencies, derived from rates or hazards, or predicted using statistical models. Event probabilities are frequently converted from continuous-time hazards to cycle-specific probabilities for implementation in discrete-time health economic models.
In practice, Event Probability is estimated using clinical trials, observational studies, disease registries, epidemiological studies or meta-analyses. Health economic models apply event probabilities to simulate disease progression, treatment outcomes, adverse events and mortality. The probabilities may vary according to patient characteristics, treatment allocation or elapsed time and are often incorporated into probabilistic sensitivity analyses.
Purpose
Used to quantify the likelihood of clinical events occurring within health economic models, enabling estimation of expected costs, health outcomes and cost effectiveness.
Mathematical Formulae
Primary Formula
Probability of an event:
P(A) = Number of occurrences of A / Total number of possible outcomes
where:
- P(A) is the probability of event A.
Supporting Formulae
Conversion of a hazard rate to a cycle probability:
p = 1 ? e???
Expected value:
E(X) = ????� p?x?
where:
- p? is the probability of outcome i
- x? is the corresponding outcome value.
Related Mathematical Methods
- Probability theory
- Survival analysis
- Decision tree analysis
- Markov modelling
- Monte Carlo simulation
- Bayesian inference
- Probabilistic sensitivity analysis
Example
A clinical trial reports that 18 of 120 patients receiving standard treatment experience a myocardial infarction within one year.
The event probability is:
P(Myocardial infarction) = 18 / 120 = 0.15
or 15%.
This probability is assigned to the myocardial infarction branch of a decision tree to estimate expected healthcare costs and quality-adjusted life-years (QALYs) associated with alternative treatments.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| COUNTIF | =COUNTIF(B2:B121,""Event"")/COUNTA(B2:B121) | Estimate event probability from observed data. |
| EXP | =1-EXP(-A2*B2) | Convert hazard rates into cycle-specific event probabilities. |
| SUMPRODUCT | =SUMPRODUCT(Probabilities,Outcomes) | Calculate expected costs or health outcomes using event probabilities. |
| IF | =IF(RAND()<Probability,1,0) | Simulate event occurrence in patient-level models. |
| XLOOKUP | =XLOOKUP(State,Table[State],Table[EventProbability]) | Retrieve state-specific event probabilities from model inputs. |
VBA (Optional)
Automate simulation of clinical events by sampling event probabilities across repeated model cycles or Monte Carlo iterations.
Sources
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press; 2006.
- Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press; 2015.
- Ross SM. Introduction to Probability Models. 12th ed. Academic Press; 2019.
- Briggs AH, Weinstein MC, Fenwick EAL, et al. Model parameter estimation and uncertainty analysis: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force Working Group-6. Value in Health. 2012;15(6):835?842.
- National Institute for Health and Care Excellence (NICE). Health Technology Evaluation Manual. Latest edition.
Related Concepts (3)
Library
Publications
1
Decision Modelling for Health Economic Evaluation — Briggs, Claxton & Sculpher, 1st Edition ed., 2006 (Oxford University Press)
Foundational textbook on decision-analytic modelling for economic evaluation, covering decision trees, Markov models, handling parameter and structural uncertainty, probabilistic sensitivity analysis, and value of information. Volume 1 in the Handbooks in Health Economic Evaluation series.
BookView source →
Frequently Asked Questions (6)
What is event probability?
The likelihood that a specific clinical or economic event will occur within a defined period, used as an input across decision-analytic models.
Source: Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press; 2006. doi:10.1093/oso/9780198526629.001.0001.
Why is an event probability tied to a time period?
A probability of an event has no meaning without a period over which it applies, since the chance of an event happening is greater the longer the window considered. A yearly probability of a complication is larger than a monthly one for the same underlying hazard, so the two cannot be used interchangeably. Converting a probability from one period to another requires the underlying rate and a formula relating them, not simple scaling. Stating the period is therefore part of stating the probability. Briggs and colleagues (2006) explain this dependence.
Source: Briggs et al. 2006
How are event probabilities estimated?
Event probabilities are estimated from data on how often the event occurred in a relevant population over a period, drawn from trials, cohort studies, registries, or routine data. The observed proportion experiencing the event gives the probability for that period. Where the data cover a different period than the model's cycle, the probability is converted appropriately, and where it comes from a different population, it may be adjusted. The estimate should reflect the decision population and the period of interest.
Source: Briggs, Claxton & Sculpher 2006
How does the time period affect event probability?
The time period affects event probability because a probability applies to a specific interval, so the chance of an event over a longer period is greater than over a shorter one. A probability estimated over one period cannot be used directly for a different one; it must be converted, which is done correctly by working through the underlying rate, since probabilities do not scale linearly with time. Matching the event probability to the model's cycle length is therefore important for accurate results.
Source: Miller & Homan 1994
How does event probability relate to rate?
Event probability relates to rate in that a rate is the instantaneous frequency of an event per unit time, while a probability is the chance of the event over a specific interval. A rate can be converted to a probability for a given period using an exponential relationship, and this conversion is needed because probabilities do not add or scale linearly across time periods. Understanding the distinction ensures that event probabilities are derived correctly from rates and applied to the right period in a model.
Source: Miller & Homan 1994
Why are event probabilities important in models?
Event probabilities are important because they drive the movement of patients through a model and the occurrence of costly or beneficial events, so they largely determine the estimated costs and outcomes. As transition or branch probabilities, they govern how the cohort progresses and how often events happen. Because the results are sensitive to these probabilities, they are estimated from the best available evidence, matched to the model's time period and population, and their uncertainty is examined in sensitivity analysis.
Source: Briggs, Claxton & Sculpher 2006
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 9 Oct 2025
Content version: 1.0.0
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- Term code
- HE-EM-MP-012
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