Time Trade-Off

Time Trade-Off in Health State Valuation

In a time trade-off task a respondent compares two lives, a longer one spent in a described health condition and a shorter one spent in full health, and the interviewer shortens or lengthens the healthy life until the two seem equally good. The ratio of the two durations at that point is read as a utility on the scale where full health is 1 and dead is 0, which is exactly the weight a QALY calculation needs. The UK EQ-5D value sets used in NICE appraisals were built from public time trade-off interviews, so design choices in the task, such as the search for indifference and the handling of states worse than dead, travel into the QALY gains of many cost-utility analyses. The wider choice between direct valuation and a questionnaire with a value set belongs to direct elicitation, and the risk-based alternative is the standard gamble.

The exchange of life years for health

Attema and colleagues, reviewing variants of the method, describe the core task as imagining a defined number of years in an impaired health state and then stating the number of years in full health at which the respondent is indifferent between the two. With full health normalised to 1, the value of the impaired state is the ratio of the two periods.

$$u = \frac{x}{t}$$

where $u$ is the health state utility value of the impaired state, $x$ is the number of years in full health at the indifference point, and $t$ is the number of years in the impaired state, with death assumed to follow both lives.

The NICE manual (PMG36, section 4.3.2) explains that a QALY multiplies the time spent in each health state by its utility. At indifference the respondent treats $x$ years at utility 1 as worth $t$ years at utility $u$, so $x = t \times u$, and the task is the QALY model run backwards to recover the weight. Torrance, reviewing utility measurement for economic appraisal in 1986, described the method for both chronic and temporary health states and for states considered better and worse than death.

Most studies use duration in full health as the response variable. Attema and colleagues report that fixing the healthy period and asking instead for the duration in the impaired state that makes the two lives equal generally gives much lower values, so the choice of response variable is an important design decision.

How interviewers find the indifference point

Attema and colleagues state that the general view is that a choice-based iteration process works better than asking directly for an indifference value, and they describe three common search procedures. Bisection halves the remaining interval with each question and so uses a fixed number of steps, top-down titration adds or removes one time unit per question, as in the UK measurement and valuation of health (MVH) study, and a ping-pong search alternates between high and low offers.

The search procedure is not neutral. Attema and colleagues report that values are between 0.10 and 0.15 higher with titration than with ping-pong, and they cite evidence of an upward shift in values with higher starting points, a form of anchoring bias in elicitation. Many protocols open with a dominance check, offering $t$ years in the state against $t$ years in full health, because a respondent who picks the impaired life may not yet have understood the task.

Non-trading is common. Attema and colleagues cite an average of 57% of respondents who would not trade any time, and they argue that excluding them is inappropriate when, for some people, the value of life approaches infinity.

Valuing states worse than dead

The conventional task cannot produce a negative value, because $x$ cannot fall below zero. The MVH protocol, as described by Attema and colleagues, used a sorting question in which the respondent chose between immediate death and $t$ years in the state. A respondent who preferred death was then offered immediate death against a life combining a period in full health with a period in the state, and the healthy period was lengthened or shortened until the two were equal.

$$u = -\frac{x}{t - x}$$

where $u$ is the value of the state judged worse than dead, $x$ is the number of years in full health within the life that the respondent judges equal to immediate death, and $t - x$ is the number of years in that life spent in the state. The equation follows from setting $x + (t - x)u = 0$.

As $x$ approaches $t$ the value falls without limit. Attema and colleagues note that in most EQ-5D-3L valuation studies the smallest tradable unit was 3 months, so the lowest achievable value was minus 39, and that a common transformation constrains such values to minus 1.

$$u' = \frac{u}{1 - u}$$

where $u'$ is the transformed value and $u$ is the raw negative value. For the MVH task this simplifies to $u' = -x/t$, so the rescaled value is the share of the life spent in full health, entered with a minus sign. Only negative values are transformed, so a step below zero no longer means the same as a step of equal size above zero.

Lead-time variants add years in full health before both lives so that one task covers both sides of zero. Attema and colleagues report that pilot studies suggested a framing effect that drags down values for states better than dead, and Janssen and colleagues describe how such framing effects prompted the composite time trade-off used in EQ-5D-5L studies. Devlin and colleagues describe the composite task as a conventional 10-year trade that switches, when all the time is traded, to 10 years of lead time followed by 10 years in the state, with a minimum value of minus 1.

Assumptions behind the ratio

Janssen and colleagues name two assumptions. Under constant proportional trade-off the fraction of the horizon given up is the same whatever the horizon, and the lead-time stage of the composite task also assumes additive independence, so the value of the state in one period does not depend on health in the other. Attema and colleagues report that values are often found to vary with the time frame, although no systematic direction has emerged, and that most studies use a 10 or 20 year frame.

Time preference is one source of departure that Attema and colleagues discuss in detail. The ratio treats a year 9 years from now as worth the same as a year starting today, so a respondent who discounts the future gives up distant years cheaply. Attema and colleagues report that neglecting time preferences causes TTO scores to be underestimated, and list correction strategies such as eliciting time preferences separately or correcting all values with one fixed discount rate. If a respondent discounts life years at a constant continuous rate, setting the discounted length of the two lives equal gives a corrected value.

$$u_r = \frac{1 - e^{-rx}}{1 - e^{-rt}}$$

where $u_r$ is the value corrected for discounting, $r$ is the respondent's continuous annual discount rate, $x$ is the number of years in full health at indifference, and $t$ is the number of years in the impaired state. When $r$ is zero the expression reduces to $x/t$.

Attema and colleagues add that the choice of time frame trades realism against distorting effects such as loss aversion and time preference.

Worked example with a severe state and five respondents

All numbers in this example are illustrative. A model needs utilities for a moderate and a severe state of a chronic condition, and the states are valued with a 10-year time trade-off, using the MVH procedure for states judged worse than dead.

1. Value the moderate state. One respondent is indifferent between 10 years in the moderate state and 7 years in full health, so $u = 7/10 = 0.70$.

2. Correct for time preference. If the same respondent discounts at an illustrative $r = 0.05$, then the numerator is $e^{-0.35}$ subtracted from one, or 0.2953, and the denominator is $e^{-0.5}$ subtracted from one, or 0.3935, so $u_r = 0.2953 / 0.3935 = 0.75$. Ignoring discounting understates the value by 0.05.

3. Value the severe state, better-than-dead answers. Three respondents accept 2, 1 and 0.5 years in full health, giving 0.20, 0.10 and 0.05.

4. Value the severe state, worse-than-dead answers. Two respondents prefer immediate death to 10 years in the severe state. The first is indifferent between death and a life of 2 years in full health and 8 years in the state, so $u = -2/8 = -0.25$. The second needs 9.75 years in full health alongside 0.25 years in the state, so $u = -9.75/0.25 = -39$.

5. Average the raw values. The sum is 0.20 + 0.10 + 0.05 − 0.25 − 39 = −38.90 and the mean is −38.90 / 5 = −7.78. One response drives the result, while the median is 0.05.

6. Transform the negative values. With $u' = u/(1 - u)$, the first becomes $-0.25 / 1.25 = -0.20$, which equals $-2/10$, and the second becomes $-39 / 40 = -0.975$, which equals $-9.75/10$. The sum is 0.35 − 1.175 = −0.825 and the mean is −0.825 / 5 = −0.165.

7. Convert to QALYs. A treatment that holds a patient in the moderate state for 2 years instead of the severe state gains 0.70 + 0.165 = 0.865 per year, or 0.865 × 2 = 1.73 undiscounted QALYs. With the raw mean the gain would be (0.70 + 7.78) × 2 = 16.96 QALYs, far more than the 2 years of life involved.

8. Interpretation. The handling of worse-than-dead answers, a choice made by the analyst, changes the QALY gain almost tenfold, since 16.96 / 1.73 = 9.8, and the discounting correction moves the moderate value by a further 0.05. Each value therefore needs its time frame, search procedure and worse-than-dead method reported with it.

Time trade-off values in UK value sets and NICE appraisal

In the UK the method reaches most appraisals indirectly, through value sets. Dolan reports that TTO valuations of 42 EuroQol states were elicited from a representative sample of the UK population and modelled to build a tariff for all 243 EQ-5D states. Devlin and colleagues note that this EQ-5D-3L value set gives 1 for no problems and minus 0.594 for the worst state, and NICE DSU Technical Support Document 8 describes the EQ-5D value set as obtained from a representative sample of the UK general population using the time trade-off.

The EQ-5D-5L value set for the UK, by Rowen and colleagues, was generated from 1,200 composite time trade-off interviews covering 102 health states with a representative sample of UK adults, and modelled with a random effects Tobit model. The NICE interim methods statement PMG51, published on 27 August 2026, makes the EQ-5D-5L descriptive system and this value set NICE's preferred approach for adults, to be used for appraisal topics whose invitation to participate is issued after its publication.

In PMG36, section 4.3.1 asks for utility based on public preferences using a choice-based method, and section 4.3.5 states that different methods produce different utility values. Devlin and colleagues describe the time trade-off as accepted by NICE as a choice-based approach.

Time trade-off beside other valuation methods

In the standard gamble the price is a risk of death, so attitude to risk and expected utility assumptions enter the value, while in the time trade-off the price is life expectancy, so time preference enters instead. A visual analogue scale rating involves no choice between options, so it falls outside the choice-based methods that PMG36 section 4.3.1 asks for.

In the England EQ-5D-5L study, Devlin and colleagues explain that the time trade-off gives values anchored at 1 and 0, while their discrete choice experiment tasks, which made no reference to duration, give relative values without anchors, and they combined the two in a hybrid model.

Common misreadings of time trade-off values

Time trade-off numbers are often lifted out of their study without the design choices behind them. Four errors recur.

1. Treating the value as a probability or a percentage of health. A value of 0.70 means 7 healthy years were judged equal to 10 years in the state.
2. Pooling values from different variants. Search procedures, lead time and time frames all shift the numbers.
3. Averaging untransformed MVH negative values. A single answer near minus 39 can dominate a mean, as the worked example shows.
4. Ignoring time preference and the time frame. Uncorrected values understate the utility, and constant proportional trade-off is often violated.

Sources

• Attema AE, Edelaar-Peeters Y, Versteegh MM, Stolk EA. Time trade-off: one methodology, different methods. European Journal of Health Economics. 2013;14(Suppl 1):S53-S64. https://doi.org/10.1007/s10198-013-0508-x
• Brazier JE, Longworth L. NICE DSU Technical Support Document 8: An introduction to the measurement and valuation of health for NICE submissions. Decision Support Unit; August 2011. https://doi.org/10.15131/shef.data.33738301
• Devlin NJ, Shah KK, Feng Y, Mulhern B, van Hout B. Valuing health-related quality of life: an EQ-5D-5L value set for England. Health Economics. 2018;27(1):7-22. https://doi.org/10.1002/hec.3564
• Dolan P. Modeling valuations for EuroQol health states. Medical Care. 1997;35(11):1095-1108. https://pubmed.ncbi.nlm.nih.gov/9366889/
• Janssen BMF, Oppe M, Versteegh MM, Stolk EA. Introducing the composite time trade-off: a test of feasibility and face validity. European Journal of Health Economics. 2013;14(Suppl 1):S5-S13. https://doi.org/10.1007/s10198-013-0503-2
• National Institute for Health and Care Excellence. Interim methods statement: implementing the EQ-5D-5L value set (PMG51). Published 27 August 2026. Sections 1.7 and 1.17. https://www.nice.org.uk/process/pmg51
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). Published 31 January 2022, last updated 13 October 2026. Sections 4.3.1, 4.3.2 and 4.3.5. https://www.nice.org.uk/process/pmg36
• Rowen D, Mukuria C, Bray N, et al. A United Kingdom value set for the EQ-5D-5L. Value in Health. 2026;29(5):858-869. https://doi.org/10.1016/j.jval.2026.03.008
• Torrance GW. Measurement of health state utilities for economic appraisal. Journal of Health Economics. 1986;5(1):1-30. https://pubmed.ncbi.nlm.nih.gov/10311607/