Concept Architecture
Concept
Theoretically, Calibration is the process of estimating unknown model parameters so that model outputs reproduce observed empirical data or predefined calibration targets. Calibration is required when parameters cannot be measured directly or when several parameter combinations are capable of generating similar model behaviour. In health economics, calibration is widely used for decision-analytic models, dynamic transmission models, disease progression models and microsimulation models to ensure that simulated outcomes are consistent with observed epidemiological or clinical evidence.
Mathematically, calibration is formulated as an optimisation or statistical estimation problem in which model outputs are compared with observed data through an objective function. The parameter values that minimise prediction error or maximise agreement between simulated and observed outcomes are selected as the calibrated estimates. Depending on the calibration framework, optimisation may be deterministic, stochastic or Bayesian, with uncertainty characterised through posterior parameter distributions or multiple acceptable parameter sets.
In practice, calibration is performed by defining calibration targets, selecting unknown parameters, specifying an objective function, applying an optimisation or sampling algorithm, and evaluating convergence. Health economic models are commonly calibrated to disease prevalence, incidence, survival, mortality, healthcare utilisation or biomarker trajectories using optimisation methods, Bayesian calibration or sequential Monte Carlo approaches. Calibrated parameter sets are subsequently propagated through probabilistic sensitivity analysis.
Purpose
Used to estimate unknown model parameters so that simulated outcomes reproduce observed data, improving the validity and credibility of health economic models.
Mathematical Formulae
Primary Formula
A commonly used least-squares objective function is
?? = arg min??? �???� w?(y? ? ??(?))�
where:
- ?? = calibrated parameter vector
- y? = observed calibration target
- ??(?) = model prediction
- w? = calibration weight
Supporting Formulae
Maximum likelihood calibration:
?? = arg max??? L(? | y)
Bayesian calibration:
P(? | y) ? P(y | ?)P(?)
Root mean squared error:
RMSE = �[(1/n) �???� (y? ? ??)�]
Related Mathematical Methods
- Optimisation
- Maximum likelihood estimation
- Bayesian calibration
- Markov Chain Monte Carlo
- Sequential Monte Carlo
- Particle filtering
- Simulated annealing
- Genetic algorithms
- Bayesian optimisation
- Least-squares estimation
Example
A dynamic hepatitis C transmission model contains three unknown transmission parameters.
Observed prevalence targets are:
| Year | Observed prevalence |
|---|---|
| 2020 | 2.6% |
| 2025 | 2.1% |
| 2030 | 1.7% |
An optimisation algorithm repeatedly updates the unknown parameters until the model predicts prevalences of 2.58%, 2.09% and 1.72%, minimising the weighted sum of squared errors. The calibrated parameter values are then used to estimate the long-term costs and QALYs associated with alternative screening programmes.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| SUMXMY2 | =SUMXMY2(B2:B11,C2:C11) | Calculate the sum of squared calibration errors |
| SQRT | =SQRT(SUMXMY2(B2:B11,C2:C11)/COUNT(B2:B11)) | Calculate the root mean squared calibration error |
| SUMPRODUCT | =SUMPRODUCT(D2:D11,(B2:B11-C2:C11)^2) | Calculate a weighted calibration objective function |
| ABS | =ABS(B2-C2) | Calculate absolute prediction error |
| Solver | Objective: Minimise calibration objective by changing parameter cells | Estimate unknown model parameters that best reproduce observed calibration targets |
VBA (Optional)
Automate iterative parameter calibration, convergence monitoring and export of calibrated parameter sets for health economic modelling.
Sources
- Briggs AH, Claxton K, Sculpher MJ. Decision Modelling for Health Economic Evaluation. Oxford University Press; 2006.
- Stout NK, Knudsen AB, Kong CY, et al. Calibration Methods Used in Cancer Simulation Models and Suggested Reporting Guidelines. Pharmacoeconomics. 2009;27(7):533-545.
- Vanni T, Karnon J, Madan J, et al. Calibrating Models in Economic Evaluation: A Seven-Step Approach. Pharmacoeconomics. 2011;29(1):35-49.
- ISPOR-SMDM Modeling Good Research Practices Task Force. Model Calibration.
- NICE. Health Technology Evaluation Manual.
Related Concepts (3)
Library
Publications
1
Model Transparency and Validation: A Report of the ISPOR-SMDM Modeling Good Research Practices Task Force-7 — Eddy, Hollingworth, Caro, Tsevat, McDonald & Wong, Task Force Report 7 ed., 2012 (Value in Health / Medical Decision Making)
Best-practice guidance on model transparency and validation, defining face, internal, external and predictive validation and setting out how models should be documented for scrutiny.
Journal ArticleView source →
Frequently Asked Questions (6)
What is calibration in modelling?
The process of adjusting a model's unobserved or uncertain parameters so its predicted outputs match observed real-world data as closely as possible.
Source: Eddy DM, Hollingworth W, Caro JJ, et al. Model transparency and validation: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force-7. Value in Health. 2012;15(6):843-850. doi:10.1016/j.jval.2012.04.012.
When is calibration used to set a model parameter?
Some quantities a model needs cannot be observed or measured directly, such as an underlying progression rate that only reveals itself through its downstream effects. Calibration infers these hidden parameters by adjusting them until the model reproduces outcomes that can be observed, such as recorded survival or prevalence. It is used when direct evidence for a parameter is missing but its consequences are visible in real data. The observable data act as targets the model is tuned to hit. Vanni and colleagues (2011) describe this use.
Source: Vanni et al. 2011
How is calibration performed?
Calibration is performed by identifying calibration targets, observed data the model should reproduce, then searching for values of the uncertain parameters that make the model's outputs match those targets, using a measure of goodness of fit. This search may use optimisation or systematic exploration of the parameter space, accepting parameter sets that fit the targets well. The result is one or more calibrated parameter sets under which the model reproduces the observed data, so calibration effectively fits the model to the targets.
Source: Eddy et al. 2012
Why is calibration used?
Calibration is used when some model parameters cannot be estimated directly from available data but the model should be consistent with observed outcomes, so their values are inferred by making the model reproduce those outcomes. It also improves confidence that the model reflects reality by ensuring it matches known data. Calibration thus provides values for otherwise unobservable parameters and aligns the model with observed evidence, which is common in complex models where not all inputs can be measured but relevant outputs are known.
Source: Eddy et al. 2012
What are the challenges of calibration?
Calibration faces challenges of identifiability and uncertainty: different parameter combinations may fit the targets equally well, so calibration may not give a unique answer, and the calibrated parameters carry uncertainty that should be reflected in the results. The choice of targets and fit measure affects the outcome, and the search can be computationally demanding. Because calibration fits the model to data, it risks overfitting if not done carefully. These challenges mean calibrated parameters and their uncertainty are examined rather than treated as exact.
Source: Eddy et al. 2012
How does calibration relate to model validation?
Calibration relates to validation but is distinct from it. Calibration adjusts parameters so the model matches specified target data, effectively fitting the model, while validation checks whether the model's outputs agree with data, ideally data not used in fitting. A model calibrated to some data may still be validated against other, independent data. Using the same data to calibrate and then claim validation is circular, so genuine validation requires independent comparison, and calibration is best seen as a fitting step whose result is then validated where possible.
Source: Briggs, Claxton & Sculpher 2006
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 13 Oct 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/calibration
- Term code
- HE-EM-MV-006
Stable URI · Machine-readable · Resolvable · CC BY 4.0