QALYs from periods of constant utility

Signature

QALY = sum_(t=1)^T [u_t * d_t]

• T Number of periods of constant utility in the time horizon (count)

Function

Quality-adjusted survival function

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Implementations

• Excel

  Sum utility-weighted durations

  Excel multiplies each period's utility by its duration in years and adds the products. Durations recorded in months are divided by 12 first.

  =SUMPRODUCT(Utilities,DurationsYears)

Assumptions

• Utility constant within each period

  Each period carries one utility value. Health that changes within a period needs shorter periods or the area-under-the-curve form with interpolation between observations.

• Common anchors and one value set

  Every utility value uses the same instrument and value set, anchored at 1 for full health and 0 for dead, across all periods and all options compared. NICE notes that different methods and instruments produce different utility values that cannot always be compared.

• Durations in years ending at death

  Durations are expressed in years, so months and days are converted, and they cover only time alive. No period after death contributes to the total.

• Preference conditions of the QALY model

  Multiplying utility by time relies on conditions on preferences; NICE gives constant proportional trade-off and additive independence between health states as examples and expects evidence to be produced if they are inappropriate in a particular case.

• Discounting applied after the calculation

  The formula gives undiscounted QALYs. Where guidance requires discounting, each period's QALYs are discounted to the reference time with the present-value formula on the discount-rate page, at 3.5% a year in the NICE reference case, with a stated timing convention.

Worked examples

• Two six-month periods

  A person spends six months at utility 0.60 and six months at utility 0.80. Each period is 0.5 years, so the periods contribute 0.30 and 0.40 QALYs, giving 0.70 QALYs over the year. The result is 0.70 quality-adjusted life years, not 0.70 calendar years.

  T = 2; u_t = [0.60,0.80]; d_t = [0.5,0.5]; QALY = 0.70

• A period in a state worse than dead

  A person spends one year at utility 0.70, three months (0.25 years) in a state valued at minus 0.20 under the value set used, and nine months (0.75 years) at utility 0.50. The contributions are 0.70, minus 0.05 and 0.375 QALYs, giving 1.025 QALYs. The negative value is retained and lowers the total. The figures are illustrative.

  T = 3; u_t = [0.70,-0.20,0.50]; d_t = [1,0.25,0.75]; QALY = 1.025

Common errors

• Durations left in months

  Entering a six-month period as 6 rather than 0.5 multiplies that period's QALYs by 12.

• Replacing a missing utility with zero

  A missing observation is unknown. Setting it to zero equates it with death and understates QALYs; an explicit interpolation, imputation or modelling rule is needed.

• Adding QALYs from different value sets

  QALYs calculated with different instruments or tariffs are not on a common scale, so adding them across periods or comparing them between options mixes incompatible measures.

• Leaving the timing convention unstated when discounting

  Three years at utility 0.80 discounted at 3.5% give 2.320 QALYs when each year is counted at its start but 2.241 when counted at its end, so the convention is reported and applied to every option.

Sources

• NICE manual on calculating QALYs

  National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). Published 31 January 2022, last updated 31 March 2026. Chapter 4 Economic evaluation, sections 4.2.15 (assumptions underlying the QALY), 4.3.2 (time in each health state multiplied by its utility, valued relative to perfect health and death), 4.3.5 (different methods produce utility values that cannot always be compared) and 4.5.1 (3.5% a year for costs and health effects).

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• Methods textbook for QALY calculation

  Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford: Oxford University Press; 2015.

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