Utility

Concept

Theoretically, Utility is a cardinal measure of the strength of preference for a health state, representing the desirability of that state on a scale anchored by full health and death. Within health economics, utility is grounded in expected utility theory and multi-attribute utility theory, providing the basis for valuing health outcomes under certainty and uncertainty. Utility enables health-related quality of life to be incorporated into economic evaluation through the calculation of quality-adjusted life years (QALYs).

Mathematically, utility is represented as a numerical value on a preference scale, conventionally ranging from 0 for death to 1 for full health, although values below 0 may be assigned to health states considered worse than death. Utility values are estimated using recognised elicitation methods such as Standard Gamble, Time Trade-Off, or Discrete Choice Experiments with duration, and are incorporated into QALY calculations by weighting survival time according to health-related quality of life.

In practice, utility values are obtained directly from preference elicitation exercises or indirectly from validated preference-based instruments such as the EQ-5D, HUI, AQoL, or SF-6D using published value sets. These utilities are applied in cost-utility analyses, decision-analytic models, and health technology assessments to compare interventions on a common preference-based outcome scale.

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Purpose

Used to quantify preferences for health states, enabling the estimation of quality-adjusted life years and supporting cost-utility analysis, decision modelling, and health technology assessment.

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Mathematical Formulae

Primary Formula

QALY = ????� U?T?

where:

• U? = utility associated with health state i
• T? = time spent in health state i

Supporting Formulae

For a single health state:

QALY = U ? T

Expected utility:

EU = ????� p?U?

where:

• p? = probability of outcome i
• U? = utility of outcome i

Related Mathematical Methods

• Expected utility theory
• Multi-attribute utility theory
• Standard Gamble
• Time Trade-Off
• Discrete Choice Experiment with duration
• Quality-adjusted life year estimation
• Preference weighting

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Example

A patient has a utility value of 0.82 after treatment and remains in this health state for 4 years.

QALY = 0.82 ? 4 = 3.28

The intervention therefore produces 3.28 quality-adjusted life years over the evaluation period.

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Excel Implementation

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VBA (Optional)

Automate retrieval of utility values from published tariffs and calculate patient-level or cohort QALYs across multiple health states.

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Sources

• von Neumann J, Morgenstern O. Theory of Games and Economic Behavior. Princeton University Press.
• Torrance GW. Social preferences for health states: An empirical evaluation of three measurement techniques. Socio-Economic Planning Sciences. 1976;10(3):129?136.
• Brazier J, Ratcliffe J, Salomon JA, Tsuchiya A. Measuring and Valuing Health Benefits for Economic Evaluation. Oxford University Press.
• Drummond MF, et al. Methods for the Economic Evaluation of Health Care Programmes. Oxford University Press.
• NICE. Health Technology Evaluation Manual.