Concept Architecture
Concept
Theoretically, Interval Estimate is a range of plausible values for an unknown population parameter derived from sample data. Unlike a point estimate, which provides a single numerical value, an interval estimate quantifies statistical uncertainty by specifying upper and lower limits within which the true parameter is expected to lie with a stated level of confidence or credibility. In health economics, interval estimates are used to communicate uncertainty surrounding treatment effects, costs, utilities, transition probabilities and incremental cost-effectiveness measures.
Mathematically, Interval Estimate is represented by an interval constructed around a point estimate using the estimated sampling variability of the parameter. Frequentist interval estimates are typically expressed as confidence intervals, whereas Bayesian analyses produce credible intervals derived from the posterior distribution. The interval width reflects the precision of the estimate and depends on sample size, variability and the chosen confidence or credibility level.
In practice, Interval Estimate is obtained from clinical trials, observational studies, meta-analyses and Bayesian models. Health economic evaluations use interval estimates to quantify parameter uncertainty, assess statistical precision and inform probabilistic sensitivity analysis. Reporting interval estimates is recommended in economic evaluations because they provide information about the reliability of estimated costs, health outcomes and cost-effectiveness results.
Purpose
Used to quantify the uncertainty surrounding estimated model parameters by providing a plausible range of values rather than a single point estimate.
Mathematical Formulae
Primary Formula
Confidence interval for a population mean:
?? � z??? ? SE(??)
where:
- ?? is the point estimate
- SE(??) is the standard error of the estimate
- z??? is the critical value from the standard normal distribution.
Supporting Formulae
Standard error of the sample mean:
SE = s/�n
Confidence interval using the Student's t-distribution:
?? � t???,??? ? SE(??)
Related Mathematical Methods
- Confidence interval estimation
- Bayesian credible intervals
- Maximum likelihood estimation
- Hypothesis testing
- Bootstrap methods
- Meta-analysis
- Probabilistic sensitivity analysis
Example
A clinical trial estimates an incremental quality-adjusted life-year (QALY) gain of 0.18 with a standard error of 0.04.
Using a 95% confidence interval:
0.18 � 1.96 ? 0.04
0.18 � 0.0784
The interval estimate is:
(0.102, 0.258)
This interval indicates the precision of the estimated treatment benefit and can be incorporated into the uncertainty analysis of a health economic model.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| CONFIDENCE.NORM | =CONFIDENCE.NORM(0.05,0.04,250) | Calculate the margin of error for a confidence interval using the normal distribution. |
| CONFIDENCE.T | =CONFIDENCE.T(0.05,0.04,25) | Calculate the margin of error using the Student's t-distribution. |
| AVERAGE | =AVERAGE(B2:B251) | Calculate the point estimate. |
| STDEV.S | =STDEV.S(B2:B251) | Estimate sample variability. |
| COUNT | =COUNT(B2:B251) | Determine the sample size used in interval estimation. |
VBA (Optional)
Automate calculation and reporting of confidence or credible intervals for model parameters and economic outcomes across multiple analyses.
Sources
- 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.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press; 2006.
- Altman DG, Bland JM. Statistics notes: confidence intervals. BMJ. 2011.
- Casella G, Berger RL. Statistical Inference. 2nd ed. Duxbury Press; 2002.
- National Institute for Health and Care Excellence (NICE). Health Technology Evaluation Manual. Latest edition.
Related Concepts (2)
Library
Publications
1
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 →
Frequently Asked Questions (6)
What is an interval estimate?
A range of values, such as a confidence interval, calculated to convey the uncertainty surrounding a point estimate of a parameter.
Source: Neyman 1937
What does an interval estimate convey that a single figure does not?
A single estimated value gives no sense of how firmly it is known, whereas an interval estimate reports a range within which the true value is judged likely to lie, conveying the precision of the estimate. A wide interval signals that the data leave the quantity uncertain, and a narrow one that it is well pinned down. Presenting the range alongside the estimate lets a reader weigh how much confidence to place in it. This is why results are reported with intervals rather than as bare numbers. Altman and colleagues (2000) explain their use.
Source: Altman et al. 2000
What is a confidence interval?
A confidence interval is an interval estimate constructed so that, over repeated sampling, a stated proportion of such intervals, such as 95 per cent, would contain the true parameter value. It gives a range of plausible values for the parameter, with the confidence level indicating the reliability of the procedure. A 95 per cent confidence interval, for example, is produced by a method that captures the true value 95 per cent of the time. Confidence intervals, formalised by Neyman, are the standard frequentist interval estimate.
Source: Neyman 1937
Why are interval estimates important?
Interval estimates are important because they convey the uncertainty in an estimate, which a single point value hides, allowing the precision of a finding to be judged. A narrow interval indicates a precise estimate, a wide one considerable uncertainty. In research and decision making, knowing the range of plausible values matters, since conclusions may differ across that range. Interval estimates thus provide necessary information about how reliable an estimate is, supporting proper interpretation and cautious use of uncertain quantities.
Source: Neyman 1937
How are interval estimates used in health economics?
In health economics, interval estimates convey the uncertainty in parameters such as treatment effects, costs, and cost-effectiveness results, so that decisions can account for imprecision. Confidence intervals around estimates, and analogous intervals around cost-effectiveness ratios, show the range of plausible values. This uncertainty feeds into probabilistic sensitivity analysis, where the distributions of parameters, related to their interval estimates, are propagated to the results. Interval estimates thus support the assessment of how confident a cost-effectiveness conclusion is.
Source: Briggs, Claxton & Sculpher 2006
How does a confidence interval differ from a credible interval?
A confidence interval is a frequentist interval estimate defined by the long-run proportion of such intervals that would contain the true value, and it does not give the probability that the parameter lies in a particular interval. A credible interval, from Bayesian analysis, is an interval within which the parameter lies with a stated probability given the data and prior. The two answer different questions: the confidence interval concerns the procedure's reliability, the credible interval a direct probability statement about the parameter.
Source: Neyman 1937
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Verified by Dr Darrin Baines
British health economist
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Verification date: 9 Oct 2025
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