Concept Architecture
Concept
Theoretically, Time Trade-Off (TTO) is a preference elicitation method used to measure the utility of health states by asking individuals to trade length of life for improved health-related quality of life. It is founded on utility theory and assumes that individuals can express the value of a health state through choices between living a longer period in an impaired health state or a shorter period in full health. The method produces cardinal utility values that are suitable for quality-adjusted life year (QALY) estimation and health technology assessment.
Mathematically, the Time Trade-Off is represented by the ratio of the duration in full health to the duration in the impaired health state at the point of indifference. Assuming full health has a utility of 1 and death has a utility of 0, the utility of the health state is estimated directly from the proportion of life expectancy respondents are willing to sacrifice. Extensions of the method exist for health states considered worse than death.
In practice, respondents are presented with a series of hypothetical choices in which the duration of life in full health is varied until they become indifferent between the two alternatives. The resulting utility values are used to construct value sets for preference-based measures such as the EQ-5D and are incorporated into cost-utility analyses to estimate QALYs.
Purpose
Used to elicit health state utility values by measuring the amount of life expectancy individuals are willing to trade for full health, supporting QALY estimation and cost-utility analysis.
Mathematical Formulae
Primary Formula
U = x?t
where:
- U = utility of the health state
- x = years in full health at the point of indifference
- t = years in the impaired health state
Supporting Formulae
Quality-adjusted life years:
QALY = U ? T
where:
- U = utility derived from the Time Trade-Off
- T = time spent in the health state
Related Mathematical Methods
- Utility theory
- Preference elicitation
- Health state valuation
- Cardinal utility measurement
- Quality-adjusted life year estimation
- Preference weighting
Example
A respondent is indifferent between living 10 years with chronic heart failure and living 8 years in full health.
U = 8?10 = 0.80
The utility value assigned to the chronic heart failure health state is 0.80.
If the individual remains in this health state for 5 years:
QALY = 0.80 ? 5 = 4.0
The health outcome is equivalent to 4.0 quality-adjusted life years.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
/ | =B2/C2 | Calculates the Time Trade-Off utility value from years in full health and years in the impaired health state. |
| IF | =IF(C2>0,B2/C2,"""") | Prevents calculation when the duration is invalid. |
| PRODUCT | =D2*E2 | Calculates QALYs by multiplying utility by survival time. |
| AVERAGE | =AVERAGE(D2:D101) | Estimates the mean utility across respondents. |
VBA (Optional)
Automate iterative Time Trade-Off interviews by adjusting life durations until the respondent's point of indifference is reached and recording utility values.
Sources
- Torrance GW. Social preferences for health states: An empirical evaluation of three measurement techniques. Socio-Economic Planning Sciences. 1976;10(3):129?136.
- Dolan P. Modeling valuations for EuroQol health states. Medical Care. 1997;35(11):1095?1108.
- 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.
Related Concepts (2)
Library
Publications
2
Measuring and Valuing Health Benefits for Economic Evaluation — Brazier, Ratcliffe, Salomon & Tsuchiya, 2nd Edition ed., 2017 (Oxford University Press)
The comprehensive text on the measurement and valuation of health benefits for economic evaluation — defining health, valuation techniques (time trade-off, standard gamble), whose values to use, preference-based measures (EQ-5D, SF-6D), and the construction of QALYs.
BookView source →NICE DSU Technical Support Document 8: An Introduction to the Measurement and Valuation of Health for NICE Submissions — Brazier, Rowen, TSD 8 ed., 2011 (NICE Decision Support Unit (University of Sheffield))
An introduction to the measurement and valuation of health for NICE submissions — the QALY, health-state utility values, generic preference-based measures, and the requirements of the NICE reference case.
Tools & Resources
2
EQ-5D Value Sets and Analysis Tools — EuroQol Research Foundation, Current online resource ed., 2026 (EuroQol Research Foundation)
Official resources for selecting and applying instrument- and country-specific EQ-5D value sets used in QALY estimation.
Web ResourceView source →EQ-5D Index Calculator (Economics Network) — The Economics Network / healtheconomics.org, Spreadsheet tool ed., 2023 (Economics Network, University of Bristol)
A free downloadable spreadsheet calculator that converts EQ-5D descriptive-system responses into index utility values, widely used as a teaching and quick-reference tool for QALY estimation.
Excel ToolView source →
Frequently Asked Questions (6)
What is the time trade-off?
A health state valuation method asking how many years in full health a respondent would consider equal to a longer period in an impaired state.
Source: Torrance 1976
Who developed the time trade-off method?
The time trade-off was introduced by George Torrance and colleagues in the early 1970s as a simpler alternative to the standard gamble for valuing health states. Rather than asking respondents to reason about probabilities, which many find difficult, it asks them to trade length of life against its quality, a comparison thought to be more intuitive. The method was developed specifically for measuring health state values in economic evaluation. Torrance, Thomas and Sackett (1972) set out the original approach.
Source: Torrance, Thomas & Sackett 1972
How does the time trade-off work?
The respondent is asked to compare a fixed period of life in the impaired state with a shorter period in full health, and the length of the full-health period is adjusted until the two are judged equally desirable. At indifference, the utility of the impaired state equals the full-health time divided by the impaired-state time. For example, indifference between ten years in the state and eight in full health gives a utility of 0.8.
Source: Torrance 1976
Why is the time trade-off used?
The time trade-off is used because it yields utilities on a cardinal scale from a choice that respondents often find easier to grasp than the probabilities of the standard gamble, since trading years of life is more concrete than reasoning about risk. It avoids the risk attitudes that affect the standard gamble. Widely used to derive value sets for instruments such as the EQ-5D, it is a standard method for eliciting health-state utilities.
Source: Torrance 1976
What are the limitations of the time trade-off?
The time trade-off is affected by attitudes to time, since respondents may discount future years, which mixes time preference with the valuation of the state, and it can give different values from the standard gamble for the same state. Valuing states worse than death, and very short durations, raises difficulties. Some respondents are unwilling to trade any time. These features complicate its use, though it remains among the most common valuation methods.
Source: Torrance 1976
How does the time trade-off differ from the standard gamble?
The time trade-off values a state through the sacrifice of length of life, asking how many years of full health equal a longer time in the state, so it reflects attitudes to time, whereas the standard gamble values it through a choice under risk, varying a probability of death, so it reflects attitudes to risk. Both are choice-based methods yielding cardinal utilities, but they draw on different trade-offs and can give different values for the same state.
Source: Torrance 1976
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 2 Sep 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/time-trade-off
- Term code
- HE-EE-HU-078
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