Functions & Formulae

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

EQ-5D-3L value set scoring function

u(l_MO, l_SC, l_UA, l_PD, l_AD; theta) = U

Maps an EQ-5D-3L profile, the level from 1 to 3 reported on each of mobility, self-care, usual activities, pain or discomfort and anxiety or depression, to a single utility under the coefficients of a chosen value set. The main-effects form with a constant for any departure from full health and an N3 term for any dimension at level 3 is the one Dolan used for the UK time trade-off tariff, and many of the time trade-off sets tabulated in the EuroQol reference volume follow it. It is the EQ-5D-3L counterpart of the additive 15D score in HE-FM-15D-001, and the utilities it returns are the weights in QALYs from periods of constant utility (HE-FM-QALY-001) and the baselines for utility decrements (HE-FN-DISU-001). Notation follows the EQ-5D-3L Value Set article.

  • EQ-5D-3L utility as one minus a constant, level decrements and an N3 term

    U = 1 - alpha * D - (beta_MO + beta_SC + beta_UA + beta_PD + beta_AD) - gamma * N_3

    Subtracts from full health a constant for any problem at all, the decrement attached to the level reported on each of the five dimensions and a single N3 decrement when any dimension is at level 3. The decrements are zero at level 1, so state 11111 scores 1, and the constant and N3 term are each charged once whatever the number of dimensions with problems. Any value set of this form can be scored by entering its own coefficients, and HE-FM-EQ3L-002 fixes them at the UK tariff.

  • UK MVH time trade-off EQ-5D-3L tariff from five reported levels

    D = min(l_MO + l_SC + l_UA + l_PD + l_AD - 5, 1); N_3 = min(max(l_MO - 2, 0) + max(l_SC - 2, 0) + max(l_UA - 2, 0) + max(l_PD - 2, 0) + max(l_AD - 2, 0), 1); U = 1 - 0.081 * D - 0.069 * (min(l_MO - 1, 1) - max(l_MO - 2, 0)) - 0.314 * max(l_MO - 2, 0) - 0.104 * (min(l_SC - 1, 1) - max(l_SC - 2, 0)) - 0.214 * max(l_SC - 2, 0) - 0.036 * (min(l_UA - 1, 1) - max(l_UA - 2, 0)) - 0.094 * max(l_UA - 2, 0) - 0.123 * (min(l_PD - 1, 1) - max(l_PD - 2, 0)) - 0.386 * max(l_PD - 2, 0) - 0.071 * (min(l_AD - 1, 1) - max(l_AD - 2, 0)) - 0.236 * max(l_AD - 2, 0) - 0.269 * N_3

    Scores a profile with the coefficients of Dolan's UK time trade-off tariff, the constant 0.081, the level 2 and level 3 decrements of each dimension and the N3 decrement 0.269. The level 2 indicator of a dimension is written min(l minus 1, 1) minus max(l minus 2, 0) and the level 3 indicator max(l minus 2, 0), which the site calculator can evaluate. The scale runs down to minus 0.594 for state 33333, below the value of dead.

  • QALY difference between two EQ-5D-3L states and the share due to N3

    dQ = (U_a - U_b) * T; s_N3 = gamma * (N3_b - N3_a) / (U_a - U_b)

    Multiplies the utility gap between the state a treatment keeps patients in and the state it avoids by the years spent there, and finds what share of the gap the N3 decrement explains. Both utilities come from one value set of the main-effects form, and the QALY step is HE-FM-QALY-001 applied to one period, the decrement-times-duration loss of HE-FM-DISU-001 read as a gain. A large share shows that much of a modelled QALY gain rests on a single coefficient.

EQ-5D-3L Value Set — Functions & Formulae | HealthEconomics.wiki