Concept Architecture
Concept
Theoretically, Akaike Information Criterion (AIC) is an information-theoretic model selection criterion that estimates the relative quality of competing statistical models fitted to the same dataset. Developed from information theory by Hirotugu Akaike, the criterion balances model goodness of fit against model complexity by penalising the number of estimated parameters. In health economics, AIC is widely used for selecting regression models, survival models and statistical models that provide inputs to decision-analytic models.
Mathematically, AIC is derived as an estimator of the expected Kullback-Leibler information loss between a fitted model and the unknown true data-generating process. The criterion combines the maximised likelihood with a penalty proportional to the number of free parameters. Lower AIC values indicate models expected to lose less information and are therefore preferred when comparing models fitted to identical datasets.
In practice, AIC is calculated after fitting competing statistical models using maximum likelihood estimation. Models are ranked according to their AIC values, with differences in AIC used to assess the relative support for alternative specifications. In health economics, AIC is commonly applied when selecting parametric survival models, regression models for costs or utilities, and epidemiological models used to parameterise economic evaluations.
Purpose
Used to compare competing statistical models by balancing goodness of fit with model complexity, supporting evidence-based model selection in health economic analyses.
Mathematical Formulae
Primary Formula
AIC = 2k ? 2ln(L?)
where:
- k = number of estimated model parameters
- L? = maximised likelihood of the fitted model
Supporting Formulae
Difference in AIC:
?? = AIC? ? AIC???
Akaike weight:
w? = exp(???/2) / �???? exp(???/2)
Related Mathematical Methods
- Maximum likelihood estimation
- Kullback-Leibler divergence
- Model selection
- Regression analysis
- Survival analysis
- Parametric survival modelling
- Bayesian Information Criterion
Example
Three parametric survival models are fitted to overall survival data for patients with advanced cancer.
| Model | Parameters (k) | Log-likelihood |
|---|---|---|
| Exponential | 2 | -320 |
| Weibull | 3 | -312 |
| Gompertz | 3 | -315 |
The Weibull model has
AIC = 2(3) ? 2(?312) = 630
The exponential model has
AIC = 2(2) ? 2(?320) = 644
Because the Weibull model has the lowest AIC, it is selected as the preferred survival model for extrapolation within the cost-effectiveness analysis.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| LN | =2*B2-2*LN(C2) | Calculate AIC from the number of parameters and maximised likelihood |
| MIN | =MIN(D2:D6) | Identify the lowest AIC among competing models |
| ABS | =D2-$D$7 | Calculate the difference in AIC relative to the best-fitting model |
| EXP | =EXP(-(E2/2)) | Calculate the numerator of the Akaike weight |
| SUM | =SUM(F2:F6) | Normalise Akaike weights across competing models |
VBA (Optional)
Automate calculation of AIC values for competing statistical models and rank models according to information-theoretic performance.
Sources
- Akaike H. A New Look at the Statistical Model Identification. IEEE Transactions on Automatic Control. 1974;19(6):716-723.
- Burnham KP, Anderson DR. Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach. 2nd ed. Springer; 2002.
- Claeskens G, Hjort NL. Model Selection and Model Averaging. Cambridge University Press; 2008.
- Briggs AH, Claxton K, Sculpher MJ. Decision Modelling for Health Economic Evaluation. Oxford University Press; 2006.
- NICE. Health Technology Evaluation Manual.
Related Concepts (3)
Library
Publications
1
Modeling Good Research Practices — Overview: A Report of the ISPOR-SMDM Modeling Good Research Practices Task Force-1 — Caro, Briggs, Siebert & Kuntz, Task Force Report 1 ed., 2012 (Value in Health / Medical Decision Making)
The overview paper of the seven-part ISPOR-SMDM modelling good-practice series, setting out best-practice recommendations across model design, technique selection, implementation, validation, parameterisation, uncertainty and use in decision making.
Journal ArticleView source →
Frequently Asked Questions (6)
What is the Akaike information criterion?
A statistic comparing the relative quality of candidate statistical models fitted to the same data, penalising those with more parameters.
Source: Akaike 1974
What does the Akaike information criterion balance?
When comparing candidate statistical models, a more complex one with more parameters can always fit the observed data more closely, but it risks capturing noise rather than the true pattern. The Akaike information criterion balances goodness of fit against the number of parameters, rewarding close fit but penalising added complexity, so the model with the lowest value is preferred. This guards against choosing an over-elaborate model that would predict new data poorly. Burnham and Anderson (2002) set out the criterion.
Source: Burnham & Anderson 2002
How is the Akaike information criterion calculated?
The Akaike information criterion is calculated from the model's maximised likelihood and its number of parameters: it equals twice the number of parameters minus twice the log-likelihood, so a better fit lowers it and more parameters raise it. Lower values indicate a better balance of fit and parsimony. The criterion is computed for each candidate model fitted to the same data, and the models are compared by their values, with the lowest indicating the preferred model on this measure.
Source: Akaike 1974
Why does the Akaike information criterion penalise complexity?
The Akaike information criterion penalises complexity because a model with more parameters can always fit the data at least as well, so fit alone would favour the most complex model, risking overfitting, where the model captures noise rather than the underlying pattern and predicts poorly for new data. By adding a penalty for the number of parameters, the criterion favours models that fit well without unnecessary complexity, aiming for one that generalises rather than merely fitting the observed data closely.
Source: Akaike 1974
How is the Akaike information criterion used?
The Akaike information criterion is used to compare candidate models fitted to the same data and to select among them, choosing the model with the lowest value as the best balance of fit and parsimony. It is applied, for instance, in choosing among survival models for extrapolation in health economic modelling, where the fit and complexity of alternative distributions are compared. Because it ranks models by relative quality, it guides model selection, though it is used alongside judgement and other considerations.
Source: Akaike 1974
How does the Akaike information criterion differ from the Bayesian information criterion?
The Akaike and Bayesian information criteria both compare models by balancing fit against complexity, but they differ in the penalty for parameters. The Akaike criterion penalises each parameter by a fixed amount, while the Bayesian criterion's penalty grows with the sample size, penalising complexity more heavily in large samples. As a result, the Bayesian criterion tends to favour simpler models than the Akaike criterion, especially with much data. The two can select different models, so both may be considered.
Source: Schwarz 1978
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 13 Oct 2025
Content version: 1.0.0
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