Concept Architecture
Concept
Theoretically, Parameter Estimation is the process of using observed data to determine numerical values for unknown parameters within a statistical or mathematical model. Parameters quantify characteristics such as probabilities, rates, risks, costs, utilities, treatment effects and transition intensities that define model behaviour. In health economics, parameter estimation provides the empirical basis for populating decision-analytic models and ensuring that model inputs are supported by available evidence.
Mathematically, parameter estimation seeks values that best represent the underlying population according to a specified estimation criterion. Depending on the modelling framework, parameters may be estimated using methods such as maximum likelihood estimation, least squares estimation or Bayesian inference. The resulting estimates may be expressed as point estimates together with measures of statistical uncertainty, including standard errors, confidence intervals or posterior distributions.
In practice, parameter estimation combines evidence from clinical trials, observational studies, disease registries, routine healthcare data and published literature. Estimated parameters are incorporated into decision trees, Markov models, microsimulation models and transmission models. Parameter uncertainty is subsequently characterised using confidence intervals or posterior distributions and propagated through probabilistic sensitivity analysis.
Purpose
Used to estimate numerical values for model parameters from empirical data, quantify uncertainty, and provide evidence-based inputs for health economic evaluation and decision modelling.
Mathematical Formulae
Primary Formula
For maximum likelihood estimation,
?? = arg max??? L(? | y)
where:
- ?? = estimated parameter
- L(? | y) = likelihood function
- y = observed data
Supporting Formulae
Likelihood function:
L(? | y) = ????� f(y? | ?)
Bayesian parameter estimation:
�(? | y) ? L(y | ?)�(?)
Least squares estimation:
?? = arg min??? �???� (y? ? ??)�
Related Mathematical Methods
- Maximum likelihood estimation
- Bayesian inference
- Least squares estimation
- Markov Chain Monte Carlo
- Regression analysis
- Survival analysis
- Meta-analysis
- Network meta-analysis
Example
A clinical trial reports that 84 of 120 patients respond to a treatment.
The response probability is estimated as
p? = 84/120 = 0.70
This estimated probability is entered into a decision-analytic model as the treatment response parameter. The associated confidence interval is used to define the probability distribution for probabilistic sensitivity analysis.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| AVERAGE | =AVERAGE(B2:B201) | Estimate the mean value of a parameter from observed data |
| COUNT | =COUNT(B2:B201) | Determine the sample size used for estimation |
| STDEV.S | =STDEV.S(B2:B201) | Estimate sampling variability |
| LINEST | =LINEST(B2:B201,A2:A201,TRUE,TRUE) | Estimate regression model parameters |
| LOGEST | =LOGEST(B2:B201,A2:A201,TRUE,TRUE) | Estimate parameters for exponential relationships |
VBA (Optional)
Automate estimation of model parameters from imported datasets and populate health economic model input tables with the resulting estimates and uncertainty measures.
Sources
- Briggs AH, Claxton K, Sculpher MJ. 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.
- Casella G, Berger RL. Statistical Inference. 2nd ed. Duxbury Press; 2002.
- Pawitan Y. In All Likelihood: Statistical Modelling and Inference Using Likelihood. Oxford University Press; 2001.
- ISPOR-SMDM Modeling Good Research Practices Task Force. Model Parameter Estimation and Uncertainty Analysis.
Related Concepts (2)
Library
Publications
1
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 →
Frequently Asked Questions (6)
What is parameter estimation?
The statistical process of using observed data to determine the most likely values for a model's unknown parameters.
Source: Fisher 1922
What does parameter estimation use data to find?
Parameter estimation uses observed data to work out the values of the unknown quantities in a statistical model, such as the average effect of a treatment or the rate of an event. Rather than assuming these values, it infers them from what the data reveal, choosing the values that best fit the observations under the model. Because data are limited, the estimate carries uncertainty, which is quantified alongside it. The estimated parameters then populate the models that use them. Cox and Hinkley (1974) set out the theory.
Source: Cox & Hinkley 1974
What is maximum likelihood estimation?
Maximum likelihood estimation, developed by Fisher, estimates a model's parameters by finding the values that make the observed data most probable under the model, that is, that maximise the likelihood function. The likelihood expresses how probable the data are for given parameter values, and the maximum likelihood estimates are those maximising it. This method has desirable statistical properties and is a standard approach to parameter estimation, providing estimates that best explain the observed data according to the model.
Source: Fisher 1922
Why is parameter estimation important?
Parameter estimation is important because models require values for their parameters to make predictions or inferences, and these values must be obtained from data rather than assumed. Estimation provides the best-supported values and, with them, measures of their uncertainty. In health economics, the parameters populating a model, such as effects, probabilities, and costs, are estimated from evidence, so parameter estimation underlies the inputs of models and statistical analyses. The quality of estimation affects the reliability of everything derived from the parameters.
Source: Fisher 1922
How is uncertainty in parameter estimates expressed?
Uncertainty in parameter estimates is expressed through measures such as standard errors and confidence intervals, which indicate how precisely the parameters are known given the data. A point estimate is accompanied by an interval showing the range of plausible values, reflecting sampling variability. In Bayesian estimation, uncertainty is expressed by the posterior distribution and credible intervals. Conveying this uncertainty is important, since estimates from limited data are imprecise, and the uncertainty in parameters propagates into any conclusions drawn from the model.
Source: Neyman 1937
How does parameter estimation feed into modelling?
Parameter estimation feeds into modelling by providing the values, and the uncertainty around them, for the parameters that populate a model, such as transition probabilities, treatment effects, costs, and utilities. These estimates, drawn from data, become the inputs the model uses to compute outcomes. The uncertainty in the estimates is carried into probabilistic sensitivity analysis, where parameters are represented by distributions reflecting their estimation uncertainty. Sound parameter estimation thus underlies both the point estimates and the uncertainty analysis of a model.
Source: Briggs, Claxton & Sculpher 2006
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 10 Oct 2025
Content version: 1.0.0
Canonical Identity
- Term code
- HE-EM-MP-026
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