Signature
TE_O = y / y_max
| Inputs | Definition | Unit |
|---|---|---|
y | Output the unit produced in the period, such as consultations or case-mix adjusted episodes | units of output per period |
y_max | Output on the estimated frontier for the unit's observed inputs, greater than zero | units of output per period |
TE_O | Observed output as a share of the maximum feasible output from the same inputs | score from 0 to 1 |
|---|
Function
Frontier efficiency measurement function
Maps a decision-making unit's observed inputs, outputs and costs, and a production or cost frontier estimated for comparable units, to efficiency scores between 0 and 1. A score of 1 places the unit on the estimated frontier. The frontier itself is usually estimated by data envelopment analysis, a linear programming method, or by stochastic frontier analysis, a parametric method that separates inefficiency from random noise.
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Implementations
Excel
Technical efficiency score from frontier output
With observed output in ObservedOutput and frontier output in FrontierOutput, Excel returns the score.
=ObservedOutput/FrontierOutput
Assumptions
Frontier estimated from comparable units
y_max comes from a frontier estimated for units with comparable case mix, quality and technology. It is the best performance observed in the data under the model, not an absolute maximum.
Output measured consistently
Outputs are defined and adjusted in the same way for every unit, so that a higher count reflects more of the same service and not easier patients or lower quality.
Worked examples
Outpatient clinic below its frontier
A clinic delivers 10,000 consultations a year, and the frontier estimated from comparable clinics puts the maximum from its staff and budget at 12,500. Output-oriented technical efficiency is 0.8. The figures are illustrative.
y = 10000; y_max = 12500; TE_O = 0.8
Common errors
Reading a productivity ratio as technical efficiency
Consultations per pound compares output with input but not with the maximum feasible output, so a higher ratio can reflect easier patients, lower quality or omitted inputs rather than less waste.
Sources
Definitions of technical efficiency in health care
Palmer S, Torgerson DJ. Economic notes: definitions of efficiency. BMJ. 1999;318(7191):1136. Technical efficiency as the maximum possible improvement in outcome from a set of resource inputs; productive and allocative efficiency defined in health outcome terms.
Farrell measures of efficiency
Farrell MJ. The measurement of productive efficiency. Journal of the Royal Statistical Society, Series A (General). 1957;120(3):253-290. Technical efficiency measured against an efficient frontier estimated from observed units.
Canonical Identity
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