Utility Weight

Concept

Theoretically, Utility Weight is a numerical preference value representing the health-related quality of life associated with a specific health state. Utility weights are grounded in expected utility theory and preference-based health measurement, expressing the desirability of a health state on a scale anchored at 1 for full health and 0 for death, although values below zero may be assigned to health states considered worse than death. In health economics, utility weights are fundamental inputs for calculating quality-adjusted life years (QALYs) and comparing the value of alternative healthcare interventions.

Mathematically, a utility weight is a scalar coefficient applied to time spent in a health state to quantify quality-adjusted survival. Utility weights are obtained from preference elicitation methods such as the time trade-off, standard gamble or discrete choice experiments and are incorporated into additive models of health benefit. Where health states vary over time, different utility weights are assigned to each period and aggregated to estimate total quality-adjusted survival.

In practice, utility weights are estimated using validated preference-based instruments including EQ-5D, HUI, AQoL and SF-6D, together with nationally derived value sets. Health economic models assign utility weights to each health state, treatment period or adverse event, allowing QALYs to be accumulated across the model horizon. Parameter uncertainty is commonly represented using beta distributions during probabilistic sensitivity analysis.

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Purpose

Used to quantify health-related quality of life, calculate quality-adjusted life years and compare the health benefits of competing healthcare interventions in economic evaluation.

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Mathematical Formulae

Primary Formula

For a health state,

Q = u ? t

where:

• Q = quality-adjusted life years
• u = utility weight
• t = time spent in the health state

Supporting Formulae

Multiple health states:

Q = �???� u?t?

Mean utility estimate:

u? = (1/n) �???� u?

Related Mathematical Methods

• Quality-adjusted life year calculation
• Expected utility theory
• Time trade-off
• Standard gamble
• Discrete choice experiments
• Preference-based measurement
• Probabilistic sensitivity analysis

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Example

Patients receiving standard care have a utility weight of 0.68, while patients receiving a new intervention have a utility weight of 0.82.

If both groups survive for five years,

Standard care:

Q = 0.68 ? 5 = 3.40 QALYs

New intervention:

Q = 0.82 ? 5 = 4.10 QALYs

The intervention therefore produces an incremental gain of

4.10 ? 3.40 = 0.70 QALYs.

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Excel Implementation

Function	Example Formula	Health Economics Application
SUMPRODUCT	=SUMPRODUCT(B2:B11,C2:C11)	Calculate total QALYs by multiplying utility weights by time spent in each health state
AVERAGE	=AVERAGE(B2:B201)	Estimate the mean utility weight from patient-level data
XLOOKUP	=XLOOKUP(A2,UtilityTable!A:A,UtilityTable!B:B)	Retrieve the utility weight assigned to each health state
IF	=IF(A2=""Dead"",0,B2)	Apply zero utility to the death state
BETA.INV	=BETA.INV(RAND(),25,8)	Sample utility weights during probabilistic sensitivity analysis

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VBA (Optional)

Automate assignment of health-state utility weights and calculation of cumulative QALYs across all simulated model cycles.

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Sources

• Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press; 2015.
• Briggs AH, Claxton K, Sculpher MJ. Decision Modelling for Health Economic Evaluation. Oxford University Press; 2006.
• Torrance GW. Measurement of Health State Utilities for Economic Appraisal. Journal of Health Economics. 1986;5(1):1-30.
• EuroQol Group. EuroQol?A New Facility for the Measurement of Health-Related Quality of Life. Health Policy. 1990;16(3):199-208.
• NICE. Health Technology Evaluation Manual.