Signature
Q_hs = sum_(t=0)^T [L_t * U_t / (1 + r)^t]
| Inputs | Definition | Unit |
|---|---|---|
L_t | Average of the proportions alive at the start and end of year t after the starting age, from the life table survivors, assuming deaths spread evenly through the year | years per person alive at the starting age |
U_t | Mean general-population utility at the age reached in year t, for the same sex | utility, no unit |
r | Annual discount rate, 0.035 in the NICE reference case | proportion per year |
t | Years elapsed since the starting age, running 0, 1, 2 and so on to T, used as the discounting exponent so that the first year is undiscounted | years |
Q_hs | Remaining discounted QALYs of the general population of one sex from the starting age | discounted QALYs per person |
|---|
TNumber of years from the starting age to the last age in the life table (years)
Function
Severity shortfall function
Maps the remaining discounted QALYs expected for an age- and sex-matched general population, and for people with the condition under current NHS care, to absolute and proportional QALY shortfall. NICE uses whichever measure implies greater severity to set a weight on the incremental QALYs of a new technology.
Try this function
Implementations
Excel
Life-table QALYs in one cell
With years lived in LifeYears, utility norms in Utilities and the year index from 0 in YearIndex, all in columns of equal length, Excel returns the discounted QALYs.
=SUMPRODUCT(LifeYears,Utilities/(1+DiscountRate)^YearIndex)
Assumptions
Period life table and population utility norms
Survival comes from national period life tables, for which the DSU guide recommends England 2017 to 2019 at the time of writing, and utility from general-population survey norms under the value set in use.
Deaths spread evenly within each year
L_t is the mean of the proportions alive at the start and end of year t, a half-cycle correction that assumes deaths occur evenly through the year.
Worked examples
Three-year illustration of the life-table sum
With proportions alive of 1, 0.98, 0.95 and 0.91 at the start of successive years, L_t is 0.99, 0.965 and 0.93. With utility norms of 0.85, 0.84 and 0.83 and a 3.5% rate, the first three years contribute about 2.3453 QALYs. The table is illustrative and truncated; a real calculation runs to age 100.
L_t = [0.99,0.965,0.93]; U_t = [0.85,0.84,0.83]; r = 0.035; T = 2; t = [0,1,2]; Q_hs = 2.3453
Common errors
Discounting from calendar age instead of the starting age
The exponent counts years from the starting age, so the first year is undiscounted. Using age x itself as the exponent discounts every year by a further i years and shrinks Q_h far below the cut-offs.
Sources
Life-table method for general-population QALYs
Wailoo A. NICE DSU Technical Support Document 23: A guide to calculating severity shortfall for NICE evaluations. Sheffield: Decision Support Unit, ScHARR, University of Sheffield; January 2024, updated September 2026. Appendix 1 (proportion of deaths, survivors and years lived with half-cycle correction, quality adjustment by age, discounting to the starting age and weighting by sex), section 3.1 (period life tables for England, 2017 to 2019) and section 3.6 (discounting at 3.5%).
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