Efficiency

Efficiency

A measure of how well a system converts inputs into desired outputs, covering both technical efficiency and allocative efficiency.

In health economics, efficiency concerns how limited healthcare resources are used to produce health, services and other valued outcomes. An efficient health system seeks to avoid unnecessary resource use and allocate available resources to activities that best advance its objectives.

Efficiency does not mean minimising expenditure regardless of consequences. Spending less while reducing valuable health outcomes, quality or access is not necessarily more efficient.

What efficiency means

Efficiency compares what is produced with the resources used and the alternatives available.

An efficiency assessment requires the analyst to specify:

• the decision-making unit;
• the inputs being used;
• the outputs or outcomes being produced;
• the relevant objectives;
• the feasible alternatives;
• the time period;
• the population served;
• quality and case-mix differences; and
• the constraints under which production or allocation occurs.

Without these elements, a claim that one intervention, provider or health system is more efficient than another may be misleading.

Inputs, outputs and outcomes

An input is a resource used to deliver healthcare or produce health.

Inputs may include:

• expenditure;
• staff time;
• medicines;
• equipment;
• beds;
• facilities;
• diagnostic capacity;
• information systems;
• patient and caregiver time; and
• managerial or implementation capacity.

An output is a service or activity produced from those inputs.

Outputs may include:

• consultations;
• procedures;
• diagnostic tests;
• admissions;
• vaccinations;
• treatment courses; and
• completed episodes of care.

An outcome is a consequence of care that matters to patients, populations or decision-makers.

Outcomes may include:

• survival;
• symptoms;
• functional ability;
• quality-adjusted life years;
• complications avoided;
• patient experience;
• access;
• equity; and
• financial protection.

Producing more outputs does not necessarily produce better outcomes. Additional consultations, tests or procedures may have limited value when they are unnecessary, ineffective or poorly targeted.

A simple output-to-input ratio

A basic productivity ratio can be written as:

$$ \text{Output-to-input ratio}

\frac{\text{Output}}{\text{Input}} $$

For example, consultations per staff hour or procedures per £1 million can describe how intensively resources are converted into measured services.

This ratio is not a complete measure of efficiency. It may ignore:

• quality;
• patient outcomes;
• case mix;
• inappropriate activity;
• multiple inputs;
• multiple outputs;
• uncertainty; and
• whether a different allocation would produce greater value.

A higher output-to-input ratio should therefore not automatically be labelled more efficient.

Technical efficiency

Technical efficiency concerns whether a decision-making unit produces the maximum feasible output from a given set of inputs, or uses the minimum feasible inputs to produce a given level of output.

An output-oriented technical-efficiency measure can be represented as:

$$ TE_{\text{output}}

\frac{\text{Observed output}} {\text{Maximum feasible output from the same inputs}} $$

An input-oriented technical-efficiency measure can be represented as:

$$ TE_{\text{input}}

\frac{\text{Minimum feasible input for the observed output}} {\text{Observed input}} $$

A technically efficient provider lies on the estimated production frontier. A technically inefficient provider lies below or inside that frontier because another feasible combination produces more output from the same inputs or the same output from fewer inputs.

Technical efficiency is normally bounded between 0 and 1 under these representations, with 1 indicating a position on the estimated frontier.

Reaching the frontier does not establish that the provider is producing the correct services or that the overall allocation is socially desirable.

Allocative efficiency

Allocative efficiency concerns whether resources are distributed among activities in a way that best advances the decision-maker’s objectives.

In healthcare, an allocatively efficient distribution may seek to maximise population health, welfare or another explicitly stated objective subject to available resources and other constraints.

A simplified allocation problem can be represented as:

$$ \max \sum_{i=1}^{n} V_i(x_i) $$

subject to:

$$ \sum_{i=1}^{n} C_i(x_i) \leq B $$

where:

• (x_i) is the level of activity allocated to programme (i);
• (V_i(x_i)) is the value produced by that activity;
• (C_i(x_i)) is its resource requirement; and
• (B) is the available budget or resource constraint.

Allocative efficiency requires comparison across alternative uses of resources. A programme can be technically efficient but allocatively inefficient if the same resources could produce greater value elsewhere.

Marginal benefit and marginal cost

In a simplified economic model, an allocatively efficient quantity may occur where marginal benefit equals marginal cost:

$$ MB = MC $$

where:

• (MB) is the additional benefit produced by one more unit of activity; and
• (MC) is the additional cost of producing that unit.

This condition depends on the objective, perspective, prices, constraints and assumptions of the model. It should not be treated as a universal operational rule for healthcare.

Healthcare decisions may involve:

• fixed budgets;
• non-market prices;
• capacity constraints;
• uncertain outcomes;
• external effects;
• unequal access;
• ethical obligations; and
• multiple objectives.

These features can make a simple marginal-benefit-equals-marginal-cost rule incomplete.

Productive efficiency

Productive efficiency concerns producing a given output at the lowest possible cost, given available technologies and input prices.

It combines:

• technical efficiency, which concerns avoiding unnecessary input use; and
• appropriate input selection, which concerns choosing the least-cost combination of inputs.

A provider may be technically efficient but not productively efficient if it uses an unnecessarily expensive mix of labour, equipment or facilities.

For example, a service may produce the maximum feasible number of consultations from its current staff mix but still use a more costly professional mix than another clinically appropriate model.

Productive efficiency should not be confused with productivity. Productivity describes the amount produced relative to inputs, while productive efficiency compares performance with the least-cost feasible production process.

Scale efficiency

Scale efficiency concerns whether a provider or service operates at an appropriate size.

A service may experience:

• Increasing returns to scale: Output increases by a greater proportion than inputs.
• Constant returns to scale: Output increases in the same proportion as inputs.
• Decreasing returns to scale: Output increases by a smaller proportion than inputs.

A technically efficient provider may still be scale inefficient if it operates at a size that is too small or too large relative to the estimated production technology.

Scale decisions should also consider access, resilience and geographical coverage. Centralising services may reduce unit costs while increasing travel burdens or reducing timely access.

Dynamic efficiency

Dynamic efficiency concerns how resource use, innovation and outcomes change over time.

It may involve:

• investment in new technology;
• workforce development;
• organisational learning;
• prevention;
• research;
• digital infrastructure;
• adoption of innovation; and
• replacement of obsolete practices.

An allocation that appears efficient in the short term may be inefficient over a longer horizon if it discourages valuable innovation, reduces workforce capacity or fails to prevent future illness.

Conversely, investment in a new technology is not dynamically efficient merely because it is innovative. Its future benefits and opportunity costs must still be assessed.

Efficiency and productivity

Productivity measures the relationship between quantities of outputs and inputs.

Efficiency compares observed performance with what is feasible or desirable given available alternatives and objectives.

Productivity can increase because:

• staff work more intensively;
• technology improves;
• the input mix changes;
• lower-value activities are removed;
• quality falls;
• easier patients are selected; or
• measurement changes.

Not every productivity increase represents an efficiency improvement. The analyst must examine the effect on quality, outcomes, case mix, access and other relevant objectives.

Efficiency and cost saving

A cost-saving action reduces expenditure.

An efficiency improvement produces the same or greater value using fewer resources, or greater value using the same resources.

Cost saving is not necessarily efficient when it:

• reduces health outcomes disproportionately;
• lowers quality;
• creates harmful delays;
• transfers costs to patients or another sector;
• worsens access;
• increases future expenditure; or
• removes a service whose benefits exceed its costs.

Likewise, an efficiency improvement does not always reduce total spending. Resources released through improved efficiency may be redeployed to produce additional health or other valued outcomes.

Efficiency and cost-effectiveness

Cost-effectiveness compares the additional costs and outcomes of alternative interventions.

Efficiency is broader. It may concern:

• how a provider converts inputs into outputs;
• whether a service uses the least-cost input combination;
• whether programmes are funded at the appropriate level;
• whether resources are allocated across the system appropriately; or
• whether innovation improves performance over time.

A cost-effective intervention can support allocative efficiency when it represents a better use of resources than the alternatives it displaces. However, a favourable cost-effectiveness result does not demonstrate that an organisation delivers the intervention technically efficiently.

Similarly, a technically efficient provider may deliver interventions that are not cost-effective.

Efficiency and opportunity cost

Opportunity cost is the value of the next-best alternative forgone when resources are allocated to a particular use.

Efficiency analysis requires attention to opportunity cost because using resources in one activity prevents their use elsewhere.

An allocation is not efficient merely because the selected activity produces benefits. The relevant comparison is whether those resources could produce greater value through another feasible use.

When a health system operates under a fixed budget, additional expenditure on one intervention may displace health-producing activity elsewhere. The health forgone is the health opportunity cost of the allocation.

Efficiency and equity

Efficiency and equity are related but distinct objectives.

Efficiency concerns the relationship between resources and valued outcomes. Equity concerns how health, access, costs and opportunities are distributed.

An allocation that maximises total health may not:

• prioritise people with the greatest severity;
• reduce health inequalities;
• protect disadvantaged groups;
• provide equal access; or
• distribute financial burdens fairly.

Equity considerations may legitimately modify an allocation that would otherwise maximise aggregate outcomes.

These value judgements should be stated explicitly. Equity should not be treated as an unexplained inefficiency, and efficiency claims should not conceal who gains and who loses.

Efficiency and quality

Activity-based measures can reward volume without reflecting quality.

A healthcare efficiency assessment should consider whether differences in measured output are accompanied by differences in:

• mortality;
• complications;
• readmissions;
• patient-reported outcomes;
• safety;
• continuity of care;
• patient experience; and
• appropriateness of treatment.

A provider producing more procedures from the same inputs is not necessarily more efficient if those procedures are unnecessary or associated with poorer outcomes.

Quality adjustment may be incorporated into the output measure, examined separately or included through multiple-output methods. The chosen approach should be transparent.

Efficiency and case mix

Healthcare providers may treat populations with different levels of need, risk and complexity.

A provider treating more complex patients may require greater resources or produce fewer measured outputs without being inefficient.

Comparisons may need to account for:

• age;
• comorbidity;
• disease severity;
• socioeconomic conditions;
• emergency status;
• treatment complexity;
• referral patterns; and
• factors outside the provider’s control.

Inadequate case-mix adjustment can penalise providers serving high-need populations and create incentives to avoid complex patients.

Risk adjustment should improve comparability without concealing genuine differences in care or access.

A corrected hospital example

Suppose two hospitals each report 10,000 outpatient consultations in one year.

• Hospital A uses £2 million in measured operating resources.
• Hospital B uses £1.6 million.

The simple output-to-input ratios are:

$$ \frac{10{,}000}{£2{,}000{,}000}

0.005 \text{ consultations per pound} $$

$$ \frac{10{,}000}{£1{,}600{,}000}

0.00625 \text{ consultations per pound} $$

Hospital B records more consultations per pound under this simple measure.

That calculation does not establish that Hospital B is more efficient overall. A valid comparison would also examine:

• patient complexity;
• health outcomes;
• quality;
• waiting times;
• follow-up requirements;
• avoidable admissions;
• staff mix;
• teaching or research responsibilities; and
• differences in recorded costs.

The result should therefore be described as a basic productivity comparison until the relevant differences and feasible production frontier have been assessed.

Measuring efficiency with frontier methods

Frontier methods compare decision-making units with an estimated best-practice production frontier.

Data Envelopment Analysis

Data Envelopment Analysis is a non-parametric method that constructs a frontier using observed combinations of multiple inputs and outputs.

It can:

• accommodate several inputs and outputs;
• estimate relative efficiency scores;
• identify comparator units; and
• estimate potential input reductions or output increases.

Its results are sensitive to:

• the selected inputs and outputs;
• measurement error;
• sample size;
• unusual observations;
• assumptions about returns to scale; and
• the fact that the frontier reflects the best observed units rather than an independently proven optimum.

Stochastic Frontier Analysis

Stochastic Frontier Analysis is a parametric method that estimates a production or cost frontier while attempting to distinguish inefficiency from statistical noise.

It requires assumptions about:

• the functional form;
• the distribution of inefficiency;
• the distribution of random error;
• explanatory variables; and
• the production process.

Different assumptions can produce different efficiency estimates.

Neither method proves that a high-performing unit delivers clinically appropriate, equitable or socially desirable care unless those dimensions are represented adequately.

Benchmarking

Benchmarking compares performance with another provider, group, standard or period.

A benchmark may be:

• the highest observed performance;
• a peer-group average;
• a statistical frontier;
• a clinical standard;
• a target;
• past performance; or
• an external reference.

Meeting a benchmark does not automatically establish efficiency. The benchmark itself may be inefficient, poorly adjusted or unrelated to the decision-maker’s objective.

Benchmark comparisons should describe why the reference is appropriate and how differences in context were addressed.

Efficiency at different levels

Intervention level

Economic evaluation can examine whether one intervention provides better value than relevant alternatives.

Provider level

Hospitals, clinics and other organisations can be compared in terms of resources, services, quality and outcomes.

Programme level

Decision-makers can examine whether resources within a programme are used effectively and whether the programme’s scale is appropriate.

Health-system level

Resources can be compared across diseases, services, regions and sectors to assess whether the overall allocation advances population objectives.

Efficiency at one level does not guarantee efficiency at another. A highly efficient provider can operate within an inefficient system allocation, while an efficient programme choice can be implemented inefficiently.

Multiple inputs and outputs

Healthcare production usually involves several inputs and outputs.

Combining them into a single measure may require:

• prices;
• preference weights;
• quality adjustments;
• statistical estimation;
• optimisation;
• distance functions; or
• explicit decision weights.

Weights influence the result. An efficiency score can change when the analyst changes which inputs and outputs are included or how they are valued.

Analysts should avoid combining heterogeneous services without explaining the weighting method.

Uncertainty in efficiency analysis

Efficiency estimates may be uncertain because of:

• sampling variation;
• measurement error;
• model specification;
• missing data;
• coding differences;
• input and output selection;
• price variation;
• case-mix adjustment;
• changes over time; and
• assumptions about the production frontier.

Appropriate analysis may include:

• confidence intervals;
• bootstrapping;
• sensitivity analysis;
• alternative model specifications;
• subgroup analysis;
• outlier assessment; and
• validation against clinical and operational evidence.

Small differences in efficiency scores should not be treated as meaningful when uncertainty is substantial.

Behavioural responses and unintended incentives

Efficiency measures can influence behaviour.

Poorly designed indicators may encourage organisations to:

• select easier patients;
• avoid complex cases;
• increase measured activity without improving outcomes;
• reduce quality;
• shift costs to another organisation;
• change coding practices;
• delay necessary care; or
• focus on measured outputs while neglecting unmeasured services.

Performance systems should therefore examine incentives, gaming risks and unintended consequences.

Improving efficiency

Potential efficiency improvements may include:

• reducing ineffective or low-value care;
• improving coordination;
• preventing avoidable complications;
• redesigning care pathways;
• using an appropriate staff mix;
• reducing unnecessary variation;
• improving procurement;
• strengthening primary and preventive care;
• adopting cost-effective technologies;
• improving information systems;
• releasing genuinely reusable capacity; and
• reallocating resources toward higher-value activities.

A claimed saving should identify whether resources are:

• cash-releasing;
• redeployable;
• fixed in the short term;
• tied to another purpose; or
• theoretical rather than practically recoverable.

An efficiency improvement is meaningful only when the released resources or increased output can advance a valued objective.

Common misunderstandings

Efficiency means spending less

Lower expenditure may reduce valuable outcomes. Efficiency concerns the relationship between resources and value, not expenditure alone.

More activity means greater efficiency

Higher activity may reflect unnecessary care, lower quality or different patient complexity.

Productivity and efficiency are identical

Productivity is an observed output-to-input relationship. Efficiency compares performance with a feasible or desirable reference.

A technically efficient provider is allocatively efficient

Technical efficiency concerns production. Allocative efficiency concerns whether resources are directed to the most valuable uses.

Cost-effectiveness proves provider efficiency

Cost-effectiveness compares interventions. It does not establish that an organisation delivers the selected intervention efficiently.

Efficiency and equity are opposites

They are different objectives that may align or conflict depending on the decision.

Every efficiency gain releases money

Some improvements release time or capacity rather than cash. Others may be difficult to redeploy.

Frontier scores are objective facts

Frontier results depend on data, model choices, comparators and assumptions.

What transparent efficiency reporting should show

A transparent efficiency analysis should identify:

• the decision-making units;
• the objective of the analysis;
• the analytical perspective;
• the inputs;
• the outputs and outcomes;
• quality measures;
• the population and case mix;
• the time period;
• the comparator or frontier;
• prices and resource valuations;
• the treatment of multiple inputs and outputs;
• the efficiency orientation;
• assumptions about scale;
• statistical methods;
• uncertainty;
• excluded variables;
• potential behavioural incentives; and
• limitations affecting interpretation.

The report should state whether it is measuring productivity, technical efficiency, productive efficiency, allocative efficiency, scale efficiency or another defined construct.

Key distinction

Productivity describes how much output is produced from inputs.

Technical efficiency asks whether more output could be produced from the same inputs or the same output produced with fewer inputs.

Productive efficiency asks whether the output is produced using the least-cost feasible combination of inputs.

Allocative efficiency asks whether resources are distributed among activities in a way that best advances the stated objectives.

Efficiency should not be reduced to spending less or producing more activity without regard to outcomes, quality, opportunity cost and equity.

Sources

• Farrell MJ. The Measurement of Productive Efficiency. Journal of the Royal Statistical Society: Series A. 1957.
• Coelli TJ, Rao DSP, O’Donnell CJ, Battese GE. An Introduction to Efficiency and Productivity Analysis. Springer.
• Hollingsworth B. The measurement of efficiency and productivity of health care delivery. Health Economics. 2008.
• Palmer S, Torgerson DJ. Definitions of efficiency. BMJ. 1999.
• Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. Oxford University Press.
• Culyer AJ, Newhouse JP, editors. Handbook of Health Economics. Elsevier.