Functions & Formulae

Each applied formula has its own function page, with a signature, implementations, and tests.

Severity shortfall function

s(Q_h,Q_c) = (AS,PS)

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.

  • Absolute and proportional QALY shortfall

    AS = Q_h - Q_c; PS = (Q_h - Q_c) / Q_h

    Absolute shortfall subtracts the expected remaining QALYs of people with the condition under current care from those of the matched general population. Proportional shortfall divides the same difference by the general-population QALYs. Both look forward from the point at which the technology would be used, so health already lost does not count, and both are discounted at the reference-case rate.

  • Discounted general-population QALYs from a life table

    Q_hs = sum_(t=0)^T [L_t * U_t / (1 + r)^t]

    Sums, over each year of remaining life from the starting age, the expected years lived multiplied by the age-specific utility norm and discounted to the starting age. Here t counts years from the starting age i, so t equals x minus i for age x, and the sum runs to the last age in the life table, usually 100. It is carried out separately for each sex, and the two results are weighted by the proportion female to give Q_h.

  • Severity QALY weight from the shortfall bands

    w = 1 + 0.2 * ((AS >= 12) or (PS >= 0.85)) + 0.5 * ((AS >= 18) or (PS >= 0.95))

    Returns the NICE severity weight from absolute and proportional shortfall. The weight is 1.7 if absolute shortfall is at least 18 or proportional shortfall at least 0.95, 1.2 if absolute shortfall is at least 12 or proportional shortfall at least 0.85, and 1 otherwise. The measure implying greater severity decides, and a value on a cut-off takes the higher band. Each comparison returns 1 when true and 0 when false.