Concept Architecture
Concept
Theoretically, the Efficiency Index is a quantitative performance measure that compares observed efficiency with a predefined benchmark, target or optimal level of performance. It provides a dimensionless indicator of how effectively resources are converted into outputs or outcomes and is widely applied in operational research, productivity analysis and health economics. The concept is founded on efficiency measurement theory and enables comparison across organisations, services or time periods.
Mathematically, the Efficiency Index is expressed as the ratio of observed performance to reference performance. Depending on the application, the reference value may represent best practice, a target, an efficiency frontier or an expected level of performance. An index equal to 1 (or 100%) indicates that the benchmark has been achieved, values below the benchmark indicate lower efficiency and values above the benchmark indicate superior performance where appropriate.
In practice, Efficiency Indices are used to evaluate hospitals, health systems, clinical services and healthcare programmes. Health economists apply the measure to assess operational efficiency, monitor productivity, benchmark providers and evaluate the impact of quality improvement initiatives and resource allocation decisions.
Purpose
Used to quantify relative efficiency, benchmark organisational performance, monitor productivity, evaluate resource utilisation and support operational and health economic decision-making.
Mathematical Formulae
Primary Formula
Efficiency Index = Observed Efficiency � Reference Efficiency
Supporting Formulae
Efficiency Index (%) = (Observed Efficiency � Reference Efficiency) ? 100
Technical Efficiency
TE = Observed Output � Frontier Output
Productivity Ratio
Productivity = Output � Input
Related Mathematical Methods
- Technical efficiency
- Data Envelopment Analysis
- Stochastic frontier analysis
- Productivity analysis
- Benchmarking
- Efficiency frontier analysis
Example
A hospital achieves an operational efficiency score of 0.88, while the benchmark efficiency score is 0.95.
Efficiency Index
= 0.88 � 0.95
= 0.926
The hospital therefore has an Efficiency Index of 0.93, indicating that it is operating at approximately 93% of the benchmark level of efficiency.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| Division | =A2/B2 | Calculate the Efficiency Index. |
| Formula | =(A2/B2)*100 | Express the Efficiency Index as a percentage. |
| IF | =IF(C2>=1,"Benchmark Achieved","Below Benchmark") | Compare efficiency with target performance. |
| AVERAGE | =AVERAGE(C2:C13) | Calculate the average Efficiency Index across reporting periods. |
| RANK | =RANK(C2,$C$2:$C$101,0) | Rank providers by Efficiency Index. |
VBA (Optional)
Automate calculation of Efficiency Indices across hospitals, departments and reporting periods while generating benchmarking reports, operational dashboards and productivity analyses.
Sources
- Farrell MJ. The Measurement of Productive Efficiency. Journal of the Royal Statistical Society. 1957.
- Cooper WW, Seiford LM, Tone K. Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software.
- Thanassoulis E. Introduction to the Theory and Application of Data Envelopment Analysis.
- Hollingsworth B. The Measurement of Efficiency and Productivity of Health Care Delivery.
- Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
Related Concepts (2)
Library
Publications
1
Productivity Growth in the English National Health Service from 1998/1999 to 2013/2014 — Bojke, Castelli, Grašič, Howdon & Street, Vol. 26, No. 5 ed., 2017 (Health Economics)
The York Centre for Health Economics measurement of NHS productivity growth as a chained index of outputs over inputs across 15 years, the standard methodological reference for English NHS productivity analysis.
Journal ArticleView source →
Frequently Asked Questions (6)
What is an efficiency index?
A summary statistic quantifying a provider's relative efficiency at converting inputs into outputs, commonly derived from data envelopment analysis.
Source: Charnes, Cooper & Rhodes 1978
What relative efficiency does an efficiency index quantify?
An efficiency index is a summary statistic quantifying a provider's relative efficiency. It quantifies how well a provider converts inputs into outputs compared with others, boiling efficiency down to one figure. It is commonly derived from data envelopment analysis, the method that measures relative efficiency against a best-practice frontier. It is a summary statistic, a single comparable number rather than a detailed breakdown. It is closely related to productivity, the ratio of output to input that efficiency reflects. A provider's efficiency in one figure is what it quantifies. Charnes, Cooper and Rhodes (1978) set this out.
Source: Charnes, Cooper & Rhodes 1978
What does an efficiency index quantify?
An efficiency index quantifies a provider's relative efficiency at converting inputs into outputs, so it puts a number on how efficiently a provider turns inputs into outputs relative to others, commonly derived from data envelopment analysis. This quantification of relative efficiency defines it. So an efficiency index is a summary statistic quantifying a provider's relative efficiency at converting inputs into outputs, commonly derived from data envelopment analysis.
Source: Charnes, Cooper & Rhodes 1978
What is an efficiency index commonly derived from?
An efficiency index is commonly derived from data envelopment analysis, so the summary statistic of a provider's relative efficiency at converting inputs into outputs is often produced by that method. This derivation from data envelopment analysis defines a feature. So an efficiency index is a summary statistic quantifying a provider's relative efficiency at converting inputs into outputs, commonly derived from data envelopment analysis This character as a summary statistic is what makes an efficiency index a single figure for a provider's efficiency.
Source: Charnes, Cooper & Rhodes 1978
What kind of statistic is an efficiency index?
An efficiency index is a summary statistic, so it is a single figure quantifying a provider's relative efficiency at converting inputs into outputs, commonly derived from data envelopment analysis. This character as a summary statistic defines it. So an efficiency index is a summary statistic quantifying a provider's relative efficiency at converting inputs into outputs, commonly derived from data envelopment analysis This relationship is what makes an efficiency index a summary of a provider's productivity relative to others.
Source: Charnes, Cooper & Rhodes 1978
How does an efficiency index relate to productivity?
An efficiency index relates to productivity as a summary of it: productivity is a measure of output produced relative to inputs consumed, and an efficiency index is a summary statistic quantifying a provider's relative efficiency at converting inputs into outputs. So an efficiency index summarises productivity relative to others, connected in that both concern how well inputs are turned into outputs This relationship is what makes an efficiency index a summary of a provider's productivity relative to others.
Source: Charnes, Cooper & Rhodes 1978
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 30 Mar 2026
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/efficiency-index
- Term code
- HS-NHS-PM-008
Stable URI · Machine-readable · Resolvable · CC BY 4.0