Functions & Formulae

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

Disability weight scaling of time lived with a non-fatal health state

YLD = sum_(s) [P_s * DW_s]

Maps time lived in a non-fatal health state to healthy time lost by multiplying it by the state's disability weight, on a scale where 0 is equivalent to full health and 1 to death. The products give years lived with disability (YLD), which add to years of life lost to give DALYs. When people have several conditions, weights are combined multiplicatively and the combined loss is shared among the conditions. The notation follows the Disability Weight article.

  • Years lived with disability from prevalent cases and a disability weight

    YLD = P * DW

    Multiplies the number of people living with a sequela over one year by its disability weight, the GBD 2010 prevalence method, without age weighting or discounting. A weight of 0.05 means that 20 years lived in the state count as one year of healthy life lost. YLDs for a disease are the sum over its sequelae.

  • Share of a combined disability weight attributed to one condition

    DW_j_star = DW_12 * DW_j / (DW_1 + DW_2)

    Splits a combined weight among the conditions that produce it in proportion to their stand-alone weights, so that cause-specific YLDs add to the comorbidity-adjusted total. The attributed share is not the gain from curing that condition, which compares the weights with and without it.

  • Comorbidity-adjusted years lived with disability per person for two independent conditions

    y_12 = 1 - (1 - y_1) * (1 - y_2)

    Combines the YLD rates of two conditions, each prevalence times weight, under independent co-occurrence and the multiplicative weight rule. Because the expected combined weight over people with neither, one or both conditions equals one minus the product of one minus each YLD rate, the adjustment needs no count of comorbid people. Multiplying by the population gives total YLDs.

  • DALYs averted by an intervention that lowers disability weights in two groups

    DALY_av = n_1 * (w_1_pre - w_1_post) + n_2 * (w_2_pre - w_2_post)

    Adds, over the groups treated, the number of people times the fall in their disability weight for the year, for an intervention that changes non-fatal health only. For people with another condition the before and after weights are combined weights, so the gain from relieving one condition is smaller than its stand-alone weight. Dividing the intervention cost by the result gives cost per DALY averted, as in HE-FM-ICER-001 with DALYs averted as the effect.

  • Disability weight from the first person trade-off question (life extension)

    DW = 1 - N_ref / N_eq

    Derives a weight from the number of people with a condition whose one-year life extension a respondent judges equal to extending the lives of a reference number of people without it: one minus the ratio. This GBD 1990 question (PTO1) was criticised by Arnesen and Nord for presupposing that extending a disabled person's life is worth less.

  • Disability weight from the second person trade-off question (cures)

    DW = N_life / N_cure

    Derives a weight from the number of cures of a chronic condition that a respondent judges equal to prolonging the lives of a reference number of people: the reference number divided by the number of cures. Unlike PTO1, this question does not presuppose that disabled people's lifetime is devalued.