Concept Architecture
Concept
Theoretically, Probabilistic Analysis is an analytical framework that explicitly incorporates uncertainty by representing uncertain model inputs as probability distributions rather than fixed values. It recognises that parameters estimated from empirical data are inherently uncertain and that this uncertainty propagates through mathematical models to influence predicted outcomes. In health economics, probabilistic analysis provides the foundation for decision-making under uncertainty by quantifying the probability that an intervention is cost-effective.
Mathematically, probabilistic analysis assigns an appropriate probability distribution to each uncertain parameter and repeatedly samples from these distributions using Monte Carlo simulation. Each simulation produces one possible set of model outcomes, and the complete collection of simulations approximates the joint distribution of costs, health effects and decision statistics. The resulting distributions permit estimation of expected values, confidence intervals and probabilities of cost-effectiveness.
In practice, probabilistic analysis is routinely applied within cost-effectiveness models, budget impact analyses and decision-analytic models. Analysts specify distributions for costs, probabilities, utilities and treatment effects, perform thousands of simulations and summarise results using cost-effectiveness planes, cost-effectiveness acceptability curves, expected net monetary benefit and expected value of information analyses.
Purpose
Used to quantify the impact of parameter uncertainty on health economic outcomes by propagating uncertainty through decision models and estimating the probability that an intervention is cost-effective.
Mathematical Formulae
Primary Formula
Y = f(?)
where:
- ? = vector of uncertain model parameters
- ? ~ D
- Y = model outcome
Supporting Formulae
Expected outcome:
E(Y) � (1/N) ? ?Y?
Incremental Net Monetary Benefit:
INMB = ? ? ?E ? ?C
Probability of cost-effectiveness:
P(INMB > 0)
Monte Carlo standard error:
MCSE = s / �N
Related Mathematical Methods
- Probabilistic Sensitivity Analysis
- Monte Carlo Simulation
- Bayesian Analysis
- Expected Value of Information
- Cost-Effectiveness Acceptability Curve
- Parameter Uncertainty
Example
A cost-effectiveness model assigns:
- Treatment success probability ~ Beta(45,15)
- Annual treatment cost ~ Gamma(18,�520)
- Utility value ~ Beta(82,18)
Using 10,000 Monte Carlo simulations, the model estimates:
- Mean incremental cost = �2,350
- Mean incremental QALYs = 0.11
- Mean ICER = �21,364 per QALY
- Probability of cost-effectiveness at �30,000 per QALY = 0.89
The probabilistic analysis demonstrates substantial decision confidence despite uncertainty in individual parameters.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| RAND | =RAND() | Generate random numbers for Monte Carlo simulation |
| NORM.INV | =NORM.INV(RAND(),Mean,SD) | Sample normally distributed parameters |
| BETA.INV | =BETA.INV(RAND(),Alpha,Beta) | Sample probabilities and utilities |
| GAMMA.INV | =GAMMA.INV(RAND(),Shape,Scale) | Sample healthcare costs |
| AVERAGE | =AVERAGE(ResultRange) | Estimate expected costs and health outcomes across simulations |
VBA (Optional)
A VBA procedure can automate thousands of Monte Carlo simulations, recalculate the decision model and generate probabilistic summaries including cost-effectiveness acceptability curves.
Sources
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
- Drummond MF, et al. Methods for the Economic Evaluation of Health Care Programmes.
- ISPOR-SMDM Modeling Good Research Practices Task Force Reports.
- NICE. Health Technology Evaluation Manual.
- Fenwick E, Claxton K, Sculpher M. Representing Uncertainty: The Role of Cost-Effectiveness Acceptability Curves.
Related Concepts (3)
Library
Tools & Resources
1
SAVI — Sheffield Accelerated Value of Information — Mark Strong, Jeremy Oakley & Penny Breeze (University of Sheffield), Web application ed., 2024 (University of Sheffield)
A free, open-access web calculator that computes value-of-information measures (EVPI, partial EVPI/EVPPI and EVSI) directly from a model’s probabilistic sensitivity analysis output — no need to re-run the model. Also reports payer strategy-specific and uncertainty burden.
Web Tool (R Shiny)View source →
Frequently Asked Questions (6)
What is probabilistic analysis?
An analysis in which uncertain inputs are represented by probability distributions rather than fixed values, and the model runs repeatedly with sampled values.
Source: Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press; 2006. doi:10.1093/oso/9780198526629.001.0001.
How does probabilistic analysis carry input uncertainty through to the result?
Probabilistic analysis assigns each uncertain input a probability distribution rather than a single value, then runs the model many times, each run drawing a fresh set of values from those distributions. The spread of results across the runs shows how the combined uncertainty in all the inputs translates into uncertainty in the output. This propagates uncertainty through the model as a whole, capturing joint effects and correlations that varying inputs one at a time cannot. The output is a distribution of results, not a point. Briggs and colleagues (2006) describe this.
Source: Briggs et al. 2006
How is probabilistic analysis conducted?
Probabilistic analysis is conducted by assigning each uncertain input a probability distribution reflecting its uncertainty, then running the model many times, each iteration drawing a fresh set of values from the distributions, and collecting the results across iterations. Correlated parameters are sampled jointly. The resulting distribution of outputs, such as incremental costs and effects, characterises the combined parameter uncertainty. Enough iterations are run for the estimates to stabilise. Summaries such as cost-effectiveness acceptability curves are then derived to convey the uncertainty in the decision.
Source: Briggs, Claxton & Sculpher 2006
How does probabilistic analysis differ from deterministic analysis?
Probabilistic analysis represents inputs by distributions and samples them repeatedly to produce a distribution of results reflecting combined parameter uncertainty, whereas deterministic analysis fixes inputs at single values and produces one result. Deterministic analysis gives a central estimate and, through one-way and multi-way variation, shows individual sensitivities, but it does not capture the joint effect of all uncertainties, which probabilistic analysis does. The two are complementary, with deterministic analysis giving the point result and transparent individual sensitivities and probabilistic analysis characterising overall uncertainty.
Source: Drummond et al. 2015
What does probabilistic analysis produce?
Probabilistic analysis produces a distribution of results reflecting parameter uncertainty, from which summaries are derived: the mean costs and effects, the joint distribution of incremental cost and effect shown as a scatter on the cost-effectiveness plane, and cost-effectiveness acceptability curves giving the probability that an intervention is cost-effective at different thresholds. These outputs convey how likely each conclusion is, given the uncertainty in the inputs. Probabilistic analysis thus provides both central estimates and a characterisation of the uncertainty around them for decision making.
Source: Briggs, Claxton & Sculpher 2006
What are the limitations of probabilistic analysis?
Probabilistic analysis depends on the distributions assigned to the inputs, so poorly chosen distributions or correlations can misrepresent uncertainty, and it captures parameter uncertainty but not, by itself, structural or methodological uncertainty, which need scenario analysis. It can be computationally demanding, and it requires enough iterations to control Monte Carlo error. These limitations mean probabilistic analysis is conducted with carefully justified distributions, complemented by scenario analysis for structural choices, and checked for convergence, so that its characterisation of uncertainty is credible.
Source: Briggs, Claxton & Sculpher 2006
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 29 Oct 2025
Content version: 1.0.0
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