A method characterising overall model uncertainty by assigning probability distributions to inputs and running the model repeatedly with randomly 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.

Why is PSA regarded as the preferred way to handle uncertainty?

Probabilistic sensitivity analysis is generally preferred for characterising uncertainty because it varies all uncertain inputs together, according to their distributions, rather than one at a time, so it reflects their joint effect and relative plausibility. Its results can be summarised in ways decision-makers use directly, such as the probability that an option is cost-effective at a given threshold. Guidance from bodies such as NICE expects it as the main uncertainty analysis. It captures overall uncertainty in a decision-relevant form. Briggs and colleagues (2006) explain this. Source: Briggs et al. 2006

How is PSA carried out?

PSA is carried out by assigning each uncertain input a probability distribution reflecting its uncertainty, sampling a set of values from these distributions, running the model to obtain a result, and repeating this over many iterations, with correlated parameters sampled jointly. The collected results form a distribution characterising the combined parameter uncertainty. Enough iterations are run for the estimates to stabilise and Monte Carlo error to be small. Outputs such as scatter plots on the cost-effectiveness plane and acceptability curves are then produced to summarise the uncertainty. Source: Briggs, Claxton & Sculpher 2006

What outputs does PSA produce?

PSA produces a distribution of results from which several outputs are derived: the mean incremental costs and effects; a scatter of the sampled incremental cost-effect pairs on the cost-effectiveness plane, showing the joint uncertainty; and cost-effectiveness acceptability curves giving the probability that an intervention is cost-effective across a range of thresholds. These summaries convey how likely each conclusion is under the parameter uncertainty. PSA thus turns the assigned input distributions into a characterisation of the uncertainty in the decision for the analysis. Source: O'Brien 1996

Why is PSA important?

PSA is important because it characterises the combined effect of parameter uncertainty on a model's results, which deterministic analysis cannot, giving decision makers the probability that an intervention is cost-effective and showing where uncertainty is greatest. This informs both the decision and whether further research is worthwhile, through value-of-information analysis built on the PSA. Many guidance bodies expect PSA in submissions. By conveying uncertainty rather than a single figure, PSA supports more informed and honest decision making under the limited evidence typical of economic evaluation. Source: Drummond et al. 2015

What are the limitations of PSA?

PSA depends on the probability distributions assigned to the inputs, so unjustified distributions or omitted correlations can misrepresent the uncertainty, and it captures parameter uncertainty but not structural or methodological uncertainty, which require scenario analysis. It can be computationally intensive and needs enough iterations to control Monte Carlo error. Its outputs can be misinterpreted if the assumptions are not understood. These limitations mean PSA is conducted with carefully justified distributions, complemented by scenario analysis, checked for convergence, and interpreted in light of its assumptions. Source: Briggs, Claxton & Sculpher 2006

Probabilistic Sensitivity Analysis | HealthEconomics.wiki

Concept Architecture

Concept

Theoretically, Probabilistic Sensitivity Analysis is a stochastic uncertainty analysis that evaluates the combined effect of uncertainty in all model input parameters simultaneously. It is founded on probability theory and Monte Carlo simulation and represents uncertain parameters using probability distributions rather than fixed values. In health economics, probabilistic sensitivity analysis is regarded as the standard approach for quantifying parameter uncertainty and informing reimbursement and health technology assessment decisions.

Mathematically, probabilistic sensitivity analysis repeatedly samples values from the joint probability distributions assigned to uncertain model parameters and recalculates model outcomes for each simulation. The resulting empirical distributions of costs, health outcomes and cost-effectiveness estimates characterise the overall uncertainty arising from parameter variation. Correlations between parameters are preserved where appropriate through multivariate sampling methods such as Cholesky decomposition.

In practice, probability distributions are assigned to uncertain model parameters using evidence from clinical trials, observational studies, meta-analyses or expert elicitation. Thousands of Monte Carlo simulations are then performed to estimate the distributions of costs, QALYs, incremental cost-effectiveness ratios and net monetary benefit. Results are commonly presented using cost-effectiveness planes, cost-effectiveness acceptability curves and expected value of perfect information analyses.

Purpose

Used to quantify overall parameter uncertainty, estimate the probability that an intervention is cost-effective and support evidence-based reimbursement decisions in health economic evaluations.

Mathematical Formulae

Primary Formula

There is no universally recognised canonical mathematical formula.

Supporting Formulae

Net monetary benefit:

NMB = ?E ? C

Incremental net monetary benefit:

INMB = ??E ? ?C

Expected value:

E(Y) � (1/n) ? ?Y?

Monte Carlo standard error:

SE = s / �n

Related Mathematical Methods

Monte Carlo Simulation
Parameter Distribution
Beta Distribution
Gamma Distribution
Normal Distribution
Cholesky Decomposition
Latin Hypercube Sampling
Cost-Effectiveness Acceptability Curve
Expected Value of Perfect Information

Example

A cost-effectiveness model assigns beta distributions to transition probabilities, gamma distributions to costs and normal distributions to treatment effects. A probabilistic sensitivity analysis performs 10,000 Monte Carlo simulations. The intervention is estimated to be cost-effective in 8,200 simulations at a willingness-to-pay threshold of �30,000 per QALY, corresponding to an estimated probability of cost-effectiveness of 82%.

Excel Implementation

Function	Example Formula	Health Economics Application
RAND	=RAND()	Generate random values for Monte Carlo simulation.
NORM.INV	=NORM.INV(RAND(),Mean,SD)	Sample normally distributed uncertain parameters.
BETA.INV	=BETA.INV(RAND(),Alpha,Beta)	Sample probabilities and utility values.
GAMMA.INV	=GAMMA.INV(RAND(),Alpha,Beta)	Sample positively skewed cost parameters.
AVERAGE	=AVERAGE(ResultRange)	Estimate expected model outcomes across all simulations.

VBA (Optional)

VBA can automate large-scale probabilistic sensitivity analyses by repeatedly sampling parameter distributions, executing the economic model and exporting cost-effectiveness outputs and acceptability curves.

Sources

Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. Oxford University Press.
Briggs AH, Weinstein MC, Fenwick EAL, Karnon J, Sculpher MJ, Paltiel AD. Model parameter estimation and uncertainty analysis: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force. Medical Decision Making. 2012;32(5):722?732.
NICE. NICE Health Technology Evaluations: The Manual.
ISPOR-SMDM Modeling Good Research Practices Task Force Reports.

Institutional Perspectives (4)

NICE
PSA Preferred in the Reference Case
Probabilistic sensitivity analysis is preferred in the reference case, characterising parameter uncertainty through assigned distributions so it is reflected simultaneously in results; NICE has required PSA in cost-effectiveness models since 2004, with results typically shown via cost-effectiveness acceptability curves.
NICE Health Technology Evaluations: The Manual (PMG36), Section 4 (Economic Evaluation)View source →
ZIN
Probabilistic Analysis Required; EVPI/EVPPI Mandatory
Probabilistic analysis forms the basis of the reference-case uncertainty assessment; in the 2024 guideline the estimation and reporting of value-of-information measures (EVPI and EVPPI), which build on the probabilistic analysis, became mandatory parts of the reference case.
Zorginstituut Nederland, Guideline for Economic Evaluations in Healthcare (2024)View source →
PBAC
Stepped Deterministic Base Case With Sensitivity Analyses
The base-case economic evaluation is presented using a stepped, deterministic approach, with sensitivity analyses (including probabilistic where appropriate) focused on the steps and assumptions that most influence the ICER, such as extrapolation.
Pharmaceutical Benefits Advisory Committee, Guidelines for Preparing a Submission to the PBAC, Section 3A.8View source →
ICER
Deterministic and Probabilistic Sensitivity Analyses Required
The reference case requires both deterministic and probabilistic sensitivity analyses to characterise uncertainty, with particular attention to inputs whose variation moves the result across the $100,000–$150,000 per QALY/evLYG threshold range.
Institute for Clinical and Economic Review, ICER Reference Case (2025)View source →

Library

Publications

BookFeatured
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 →
Book
Bayesian Methods in Health Economics — Gianluca Baio, 1st Edition ed., 2012 (Chapman & Hall / CRC Press)
An overview of Bayesian statistical methods for the analysis of health economic data, covering economic evaluation concepts, statistical cost-effectiveness analysis, Bayesian computation and MCMC, and applied health economic evaluation.
BookView source →
Book
Cost Effectiveness Modelling for Health Technology Assessment: A Practical Course — Edlin, McCabe, Hulme, Hall & Wright, 1st Edition ed., 2015 (Springer (Adis))
A practical, course-based introduction to decision-analytic cost-effectiveness modelling, guiding the reader through building decision trees and Markov models and interpreting results to meet the methodological standards of HTA organisations. Thirteen chapters covering theory and hands-on methods.
BookView source →
Book
Bayesian Cost-Effectiveness Analysis with the R package BCEA — Baio, Berardi & Heath, 1st Edition ed., 2017 (Springer)
A guide to health economic evaluation and cost-effectiveness modelling from a Bayesian statistical perspective, showing how to post-process model results, run probabilistic sensitivity analysis and value-of-information analysis using the BCEA R package and its web interface. Part of the Use R! series.
BookView source →
Journal article
Parameter Estimation and Uncertainty: A Report of the ISPOR-SMDM Modeling Good Research Practices Task Force-6 — Briggs, Weinstein, Fenwick, Karnon, Sculpher & Paltiel, Task Force Report 6 ed., 2012 (Value in Health / Medical Decision Making)
Best-practice guidance on parameter estimation and the characterisation of uncertainty in decision models, covering probabilistic sensitivity analysis, distributional choices, and correlation between parameters.
Journal ArticleView source →

Media

Media
Examples of Graphs Used in Cost-Effectiveness and Value-of-Information Analyses — (NCBI Bookshelf — Institute of Medicine), Open access ed., 2011 (National Center for Biotechnology Information (NCBI))
An open-access figure set illustrating the three core visual outputs of a probabilistic cost-effectiveness analysis: the cost-effectiveness plane scatter, the acceptability curve (CEAC), and the acceptability frontier with an EVPI graph.
PDF / Web (Open Access)View source →
Media
Using and Interpreting Cost-Effectiveness Acceptability Curves (AFFIRM Example) — Fenwick, Marshall, Levy & Nichol, Open access ed., 2006 (BMC Health Services Research (Open Access))
An open-access tutorial article with annotated diagrams walking through the incremental cost-effectiveness plane and the construction and interpretation of cost-effectiveness acceptability curves, using atrial fibrillation trial data.
Web (Open Access)View source →
MediaFeatured
heemod: Markov Models for Health Economic Evaluations (Package Tutorials) — Antoine Filipovic-Pierucci, Kevin Zarca & Isabelle Durand-Zaleski, Package documentation ed., 2023 (heemod / GitHub Pages)
The official tutorial site for the heemod R package, with worked walkthroughs for building Markov models, running PSA and DSA, computing EVPI and performing budget-impact analysis — mirroring the standard decision-modelling textbook workflow.
Tutorial (Web)View source →
Media
BCEA: Bayesian Cost-Effectiveness Analysis with R (Tutorials) — Gianluca Baio, Andrea Berardi & Anna Heath, Package documentation ed., 2023 (BCEA project)
Tutorials for the BCEA R package, demonstrating Bayesian post-processing of probabilistic cost-effectiveness models — acceptability curves, EVPI/EVPPI and standardised value-of-information graphics.
Tutorial (Web)View source →
Media
Making Health Economic Models Shiny: A Tutorial — Robert Smith & Paul Schneider, Open access ed., 2020 (Wellcome Open Research)
An open-access tutorial showing how to wrap a health-economic decision model in an interactive R Shiny web application, making cost-effectiveness models transparent and explorable for decision-makers.
Tutorial (Web)View source →

Tools & Resources

OtherFeatured
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 →
Other
BCEAweb — Bayesian Cost-Effectiveness Analysis Web Interface — Gianluca Baio, Andrea Berardi & Anna Heath, Web application ed., 2023 (University College London)
A user-friendly web front-end to the BCEA R package: users upload probabilistic model output and obtain standardised cost-effectiveness summaries — cost-effectiveness planes, acceptability curves, EVPI and EVPPI — without writing R code.
Web Tool (R Shiny)View source →
OtherFeatured
heemod — Markov Models for Health Economic Evaluations (R package) — Antoine Filipovic-Pierucci, Kevin Zarca & Isabelle Durand-Zaleski, R package ed., 2023 (CRAN)
An R package for building Markov models for health economic evaluation, implementing the modelling and reporting features of standard reference textbooks: PSA, DSA, heterogeneity analysis, semi-Markov and non-homogeneous models, EVPI and budget-impact features.
Software (R package)View source →
Other
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 →
Other
BCEA — Bayesian Cost-Effectiveness Analysis (R package) — Gianluca Baio, Andrea Berardi & Anna Heath, R package ed., 2023 (CRAN)
An R package for post-processing the output of a probabilistic cost-effectiveness model in a Bayesian framework — producing acceptability curves, EVPI/EVPPI, expected incremental benefit and standardised value-of-information graphics.
Software (R package)View source →
Other
dampack — Decision-Analytic Modeling Package (R package) — Fernando Alarid-Escudero, Greg Knowlton, Caleb Easterly & Eva Enns, R package ed., 2023 (CRAN)
An R package of tools for analysing and visualising the output of decision-analytic models — cost-effectiveness analysis, one- and two-way sensitivity analysis, probabilistic sensitivity analysis, and value-of-information analysis.
Software (R package)View source →
Other
TreeAge Pro — Decision Analysis & Modeling Software — TreeAge Software, LLC, Commercial software ed., 2024 (TreeAge Software)
A widely used commercial visual modelling platform for building decision trees, Markov and microsimulation models for cost-effectiveness analysis, with built-in sensitivity and value-of-information analysis — a long-standing industry standard in HTA modelling.
Software (Desktop, Commercial)View source →

Frequently Asked Questions (6)

What is PSA?
A method characterising overall model uncertainty by assigning probability distributions to inputs and running the model repeatedly with randomly 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.
Why is PSA regarded as the preferred way to handle uncertainty?
Probabilistic sensitivity analysis is generally preferred for characterising uncertainty because it varies all uncertain inputs together, according to their distributions, rather than one at a time, so it reflects their joint effect and relative plausibility. Its results can be summarised in ways decision-makers use directly, such as the probability that an option is cost-effective at a given threshold. Guidance from bodies such as NICE expects it as the main uncertainty analysis. It captures overall uncertainty in a decision-relevant form. Briggs and colleagues (2006) explain this.

Source: Briggs et al. 2006
How is PSA carried out?
PSA is carried out by assigning each uncertain input a probability distribution reflecting its uncertainty, sampling a set of values from these distributions, running the model to obtain a result, and repeating this over many iterations, with correlated parameters sampled jointly. The collected results form a distribution characterising the combined parameter uncertainty. Enough iterations are run for the estimates to stabilise and Monte Carlo error to be small. Outputs such as scatter plots on the cost-effectiveness plane and acceptability curves are then produced to summarise the uncertainty.

Source: Briggs, Claxton & Sculpher 2006
What outputs does PSA produce?
PSA produces a distribution of results from which several outputs are derived: the mean incremental costs and effects; a scatter of the sampled incremental cost-effect pairs on the cost-effectiveness plane, showing the joint uncertainty; and cost-effectiveness acceptability curves giving the probability that an intervention is cost-effective across a range of thresholds. These summaries convey how likely each conclusion is under the parameter uncertainty. PSA thus turns the assigned input distributions into a characterisation of the uncertainty in the decision for the analysis.

Source: O'Brien 1996
Why is PSA important?
PSA is important because it characterises the combined effect of parameter uncertainty on a model's results, which deterministic analysis cannot, giving decision makers the probability that an intervention is cost-effective and showing where uncertainty is greatest. This informs both the decision and whether further research is worthwhile, through value-of-information analysis built on the PSA. Many guidance bodies expect PSA in submissions. By conveying uncertainty rather than a single figure, PSA supports more informed and honest decision making under the limited evidence typical of economic evaluation.

Source: Drummond et al. 2015
What are the limitations of PSA?
PSA depends on the probability distributions assigned to the inputs, so unjustified distributions or omitted correlations can misrepresent the uncertainty, and it captures parameter uncertainty but not structural or methodological uncertainty, which require scenario analysis. It can be computationally intensive and needs enough iterations to control Monte Carlo error. Its outputs can be misinterpreted if the assumptions are not understood. These limitations mean PSA is conducted with carefully justified distributions, complemented by scenario analysis, checked for convergence, and interpreted in light of its assumptions.

Source: Briggs, Claxton & Sculpher 2006

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Verified by Dr Darrin Baines

British health economist

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Verification date: 29 Oct 2025

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Persistent URI: https://healtheconomics.wiki/concept/psa
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Probabilistic Sensitivity Analysis