Activity versus value
The simplified quality-adjusted activity measure multiplies consultations by the outcome/quality index. It is illustrative and is not a validated hospital-performance measure.
Comparison
Key takeaway: A higher consultation rate per pound is a productivity finding. Calling it efficiency requires appropriate outcomes, quality, case mix and a feasible comparator.
Position a provider
Maximum feasible output—
Output-oriented TE—
Potential output gain—
Illustrative production frontier
Key takeaway: A frontier score is relative to the specified production technology. It does not prove that the service mix is allocatively efficient or equitable.
Allocate a fixed budget
The remainder goes to treatment. Both services are assumed to operate technically efficiently; the question is whether the mix maximises the stated outcome.
Allocation result
Total health—
Health-maximising share—
Health opportunity gap—
Key takeaway: This optimum follows one stated objective: maximise the synthetic health total. A real decision may also consider equity, severity, access, resilience and implementation.
How to interpret the activities
The explorer uses synthetic values and deliberately simplified relationships. The equations are shown so the calculations can be understood and checked.
- Raw activity per £1 million equals consultations divided by cost in £ millions.
- Quality-adjusted activity per £1 million equals consultations multiplied by the simplified quality index, divided by cost in £ millions.
- The illustrative production frontier is maximum output = 190 × √(resource input).
- Output-oriented technical efficiency equals observed output divided by maximum feasible output and is capped at 100% when a selected point exceeds the illustrative frontier.
- Illustrative prevention health equals 110 × √(prevention share).
- Illustrative treatment health equals 95 × √(treatment share), where treatment share is 100 minus the prevention share.
Productivity is an observed output-to-input relationship. Efficiency requires a feasible or desirable reference. Technical efficiency asks whether output could increase without additional input, while allocative efficiency asks whether resources are distributed in the way that best advances the stated objective.
All values and production relationships are synthetic. They illustrate concepts and must not be used to rank real hospitals or prescribe resource allocation.