Health State Utility Value

What a health state utility value represents

It combines several aspects of health into a scale anchored by conventions for full health and death, allowing time in different health states to be converted into quality-adjusted life-years. This page explains the scale, valuation methods, QALY calculations, data choices, uncertainty and modelling pitfalls.

An HSU value is not a clinical score, a probability or a percentage of health. Its meaning depends on the health-state description, valuation method, respondent population and value set used.

The utility scale is anchored but not always bounded by zero and one

HSU values are conventionally anchored at:

$$u(\text{dead})=0$$

and:

$$u(\text{full health})=1$$

Some valued health states can have negative values, representing states judged worse than dead under the valuation method. Zero and one are therefore anchors rather than universal mathematical bounds. Values above one are usually inconsistent with the conventional health-utility scale unless a particular method and interpretation explicitly support them.

The distance between values is intended to have interval-scale meaning for QALY calculation. A change from 0.4 to 0.6 is treated as the same utility gain as a change from 0.7 to 0.9 for the same duration, although the empirical and normative assumptions behind that interpretation should be recognised.

Utility converts time into quality-adjusted life-years

If utility is constant at (u) for (t) years, QALYs are:

$$Q=u\times t$$

If utility varies continuously over time:

$$Q=\int_0^T u(t)\,dt$$

With utility observed at discrete times and linear interpolation assumed, the trapezoidal estimate is:

$$\widehat{Q} = \sum_{i=0}^{n-1} \frac{t_{i+1}-t_i}{2} \left[u(t_i)+u(t_{i+1})\right]$$

Time must be expressed in years if the intended output is QALYs. Utility over six months is multiplied by 0.5 years, not by six without unit conversion.

A worked QALY calculation

Suppose a person spends two years in a health state with utility 0.75 and then one year in a state with utility 0.50. Ignoring discounting, total QALYs are:

$$Q =(0.75\times2)+(0.50\times1) =1.50+0.50 =2.00\text{ QALYs}$$

If an intervention instead maintains utility 0.75 for all three years, QALYs are:

$$Q_{\text{intervention}} =0.75\times3 =2.25\text{ QALYs}$$

The incremental health benefit is:

$$\Delta Q=2.25-2.00=0.25\text{ QALYs}$$

This calculation assumes that the utilities are applicable to the modelled population and that changes occur at the stated boundaries.

Direct methods value a described health state

Direct elicitation asks respondents to evaluate a health state using a preference-based task. The state may be hypothetical or experienced by the respondent. Different tasks encode different assumptions and can yield systematically different values.

Common direct methods include:

Visual analogue scale scores are not automatically utilities suitable for QALY construction. Direct-method protocols, framing and handling of states worse than dead materially affect results.

Time trade-off converts a time exchange into utility

In a basic time trade-off task, a respondent is indifferent between (t) years in impaired health state (H) and (x) years in full health. Under the method's assumptions, the utility of (H) is:

$$u(H)=\frac{x}{t}$$

If a respondent regards 10 years in state (H) as equivalent to 7 years in full health:

$$u(H)=\frac{7}{10}=0.70$$

The formula assumes constant proportional trade-off and the protocol's treatment of time preferences. Variants are required to value states considered worse than dead, and values can depend on duration, framing and lead-time or lag-time conventions.

Standard gamble uses indifference under risk

In a standard-gamble task, a respondent chooses between living in health state (H) with certainty and a gamble producing full health with probability (p) or immediate death with probability (1-p). At indifference and under expected-utility assumptions:

$$u(H) =p\,u(\text{full health}) +(1-p)u(\text{dead}) =p$$

If indifference occurs at (p=0.80), the estimated utility is 0.80. The method can be influenced by risk attitudes, probability comprehension and the emotional meaning of death, so its assumptions should not be hidden behind the simple formula.

Indirect methods combine a descriptive system with a value set

Preference-based measures ask respondents to describe their health across standard dimensions. The resulting health profile is converted into a utility using a value set estimated from valuation data. The questionnaire response alone is not the HSU value; the scoring algorithm and jurisdiction-specific value set complete the calculation.

Examples of generic preference-based instruments include EQ-5D, Health Utilities Index, SF-6D and AQoL families. They differ in dimensions, response levels, valuation studies and sensitivity across health conditions. Condition-specific preference-based measures also exist but may reduce comparability across diseases.

An analysis should identify:

• The exact instrument and version.
• The respondent-completed descriptive profile.
• The value-set country, jurisdiction and version.
• The valuation method and source population.
• Any crosswalk, mapping or proxy response.
• Rules for missing dimensions and invalid profiles.

Changing the value set can change both absolute utilities and incremental QALYs.

Patient and public values answer different questions

People experiencing a health state may value it differently from members of the general public imagining it. Adaptation, information, expectations and lived experience can influence patient values. Public values may align with a societal decision-making perspective, while patient values can better reflect experienced wellbeing.

The appropriate source depends on the decision framework and jurisdiction. Analysts should not mix perspectives across model states without a clear rationale. Sensitivity analysis can show whether choosing patient rather than public values changes the decision.

Proxy respondents may be necessary for young children or people unable to self-report, but proxy perspective should be specified. A proxy can report the patient's perceived health or value the state from the proxy's own perspective; these are not equivalent.

Value sets are jurisdiction- and time-specific evidence

A value set reflects the preferences, sampling, protocol and modelling choices of a particular valuation study. Values from one country are not automatically transferable to another because population preferences, institutional guidance and valuation conventions can differ.

Selection should consider:

• The decision-maker's preferred instrument and value set.
• The target jurisdiction and population.
• Whether the version matches the collected descriptive data.
• The age group and proxy rules.
• The valuation study's quality and current acceptance.
• Whether a newer value set replaces or supplements an earlier one.

A value-set choice is methodological, not merely a software lookup. The chosen source and sensitivity alternatives should be documented.

Baseline utility and treatment effects must be aligned

Economic models often need utility by health state, treatment arm, event status and time. Utilities can be modelled as state values, treatment-specific values, regression predictions or repeated measurements. The structure should avoid attributing the same health effect twice.

For example, if a model's progression-free and progressed states already capture quality-of-life differences caused by disease severity, adding a separate disease-severity decrement may double count the same loss. A treatment-related utility benefit should be added only if it remains after the state definition and evidence are considered.

Baseline imbalance in trial utility can also distort incremental QALYs. Appropriate regression adjustment can improve precision and align comparisons, but the estimand, missing-data method and repeated-measure correlation should be specified.

Utility decrements describe event-related losses

A utility decrement, or disutility, represents a reduction from a stated baseline utility. If baseline utility is (u_0) and a decrement (d) applies:

$$u=u_0-d$$

If the decrement lasts for duration (\Delta t) years, its QALY loss under a constant-effect assumption is:

$$\Delta Q=d\times\Delta t$$

A decrement of 0.10 lasting three months gives:

$$\Delta Q =0.10\times\frac{3}{12} =0.025\text{ QALYs}$$

The decrement's reference state and duration must be clear. A decrement estimated against general-population utility may not be additive to a disease-state utility estimated in a different population.

Comorbidities require a defensible combination rule

When a person has multiple conditions, adding separate decrements can produce implausibly low utilities and assumes no interaction. Taking the minimum condition-specific utility assumes the worst condition fully determines health. Multiplicative rules impose another unverified structure.

Common approaches include:

$$u_{AB}^{\text{additive}} =u_{\text{base}}-d_A-d_B$$

and, under a simple multiplicative approach with full health as the reference:

$$u_{AB}^{\text{multiplicative}} =u_Au_B$$

Neither rule is universally correct. Direct evidence for joint health states or regression models estimated from people with multimorbidity are preferable when the combination materially affects results.

Age and background health influence utility

General-population utility often declines with age and varies with sex, socioeconomic circumstances and comorbidity. A model that assigns utility one to everyone without the target condition can overstate health, particularly over a lifetime horizon. Age-adjusted population norms may provide a more appropriate ceiling or baseline.

One approach applies a proportional disease effect to age-specific population utility:

$$u_{\text{disease},a} =u_{\text{population},a}\times r_{\text{disease}}$$

Another subtracts an absolute decrement. The two approaches behave differently at older ages and should be justified and tested. Population norms and disease utilities must use compatible instruments and value sets.

Death and terminal periods need explicit timing

Death is assigned utility zero from the time of death. A model should not accrue living-state utility after death or apply a temporary end-of-life decrement to periods already represented by a terminal state. Timing within a cycle can affect QALYs and may require within-cycle correction.

States worse than dead can have negative utility before death. Replacing all negative values with zero changes the valuation evidence and can bias comparisons, particularly for interventions that reduce time in severe health states.

Mapping predicts utility when preference-based data are absent

Mapping estimates HSU values from another measure, clinical variables or patient characteristics. A regression function may take the form:

$$E[u\mid z] =g(z;\beta)$$

where (z) contains source-measure scores and other predictors. Mapping adds model uncertainty and may compress the utility distribution, especially at very good or very poor health.

A mapping study should be applicable to the target population, outcome range, instrument version and value set. External validation, prediction error and uncertainty in mapped means matter. Mapping should not be described as directly observed utility.

Repeated utility measurements create missing-data challenges

Utility is commonly measured at several trial visits. Missing observations may arise from illness, dropout or death and are often related to health. Complete-case analysis or last observation carried forward can bias QALYs when missingness is informative or health changes over time.

Analyses can use multiple imputation, mixed models, joint models or other methods appropriate to the estimand and missingness assumptions. Death is not an ordinary missing utility observation; post-death utility is structurally zero. Sensitivity analysis should examine departures from the assumed missing-data mechanism.

Discounting changes the contribution of future utility

When future health is discounted continuously at rate (r), discounted QALYs are:

$$Q_{\text{disc}} = \int_0^T u(t)e^{-rt}\,dt$$

For discrete annual periods with end-of-period timing, one convention is:

$$Q_{\text{disc}} = \sum_{t=0}^{T} \frac{Q_t}{(1+r)^t}$$

The exact timing convention should match the model and jurisdictional guidance. Discounting should not be embedded invisibly inside the utility value because that prevents consistent changes to the discount rate or accrual timing.

Utility uncertainty should preserve bounds and correlation

HSU estimates have sampling uncertainty, and utilities from the same study, health states or regression model can be correlated. Probabilistic sensitivity analysis should represent that joint uncertainty rather than draw every state value independently.

Possible approaches include:

• Drawing regression coefficients jointly from their variance–covariance matrix.
• Bootstrapping participants while preserving repeated measurements.
• Using bounded distributions when values are genuinely restricted to an interval.
• Using empirical or mixture distributions when mass points and negative values matter.
• Applying ordered or hierarchical parameterisations so clinically ordered states do not reverse implausibly.

A beta distribution is restricted to zero through one and therefore cannot directly represent negative utilities. Rescaling or another distribution is required when states worse than dead are possible.

Health-state utility is distinct from related measures

Several quantities describe health but are not interchangeable with HSU values. Keeping them distinct prevents incorrect QALY calculations.

A disability weight is not simply one minus any available utility value unless the two measures were deliberately constructed as complements under compatible methods.

Common errors can materially change cost-effectiveness

Utility inputs often have a large influence on incremental QALYs, yet their source and construction can be obscured in models. Every value should remain traceable to its health state, instrument, value set and population.

• Treating zero and one as hard bounds discards valid negative values for states worse than dead.
• Using a questionnaire score as a utility without preference-based valuation misstates the outcome.
• Mixing value sets across states creates inconsistent utility scales.
• Applying both state values and overlapping decrements double counts health loss.
• Adding several comorbidity decrements can generate implausible utilities.
• Treating mapped utility as directly observed understates model dependence.
• Assigning utility after death overstates QALYs.
• Ignoring missing-not-at-random utility data can bias trial-based estimates.
• Using months as years changes QALYs by a factor of 12.
• Drawing correlated utilities independently can exaggerate or understate incremental uncertainty.
• Rounding utility values before accumulation can distort small QALY differences over long horizons.

A defensible health-state-utility workflow

A high-quality utility analysis links every value to the decision perspective, health-state definition, respondent source and valuation method. The workflow should make it possible to reproduce both the base-case QALYs and their uncertainty.

1. Define the role: State which model states, events, populations and time periods require utility values.
2. Choose the perspective: Identify whether public, patient or proxy preferences are appropriate under the decision framework.
3. Select the instrument: Match the descriptive system, version and sensitivity to the target condition and jurisdiction.
4. Select the value set: Use the required country, population, protocol and scoring algorithm consistently.
5. Review applicability: Check health-state definitions, age, severity, treatment, timing and respondent characteristics.
6. Construct utilities: Apply state values, decrements, interactions and comorbidity rules without overlap or double counting.
7. Calculate QALYs: Align utility with survival, time units, within-cycle timing and discounting.
8. Address missingness: Separate death from missing observations and test assumptions about unobserved utility.
9. Propagate uncertainty: Preserve coefficient covariance, repeated-measure dependence, bounds and structural alternatives.
10. Report transparently: Provide sources, instruments, value sets, formulas, assumptions, sensitivity analyses and limitations.

A health state utility value is useful only when its valuation context matches the decision model. Numerical precision cannot compensate for an inappropriate instrument, population, value set or health-state definition.