Functions & Formulae

Years lived with disability counted from incident cases or from prevalent cases of a sequela

YLD_inc = sum_(s) [I_s * DW_s * L_s]; YLD_prev = sum_(s) [P_s * DW_s]

• Incidence-based years lived with disability for one sequela without discounting

  YLD_inc = I * DW * L

  Counts the new cases of a sequela in the reference year and multiplies them by the disability weight and by the average duration of a case until remission or death, so all of each case's future health loss is assigned to the year, and the age, in which it begins. This is the form used by the GBD 1990 study and WHO's updates before 2010, here without their discounting and age weighting.

• Continuously discounted years lived with disability per incident case and for a cohort of new cases

  YLD_case = DW * (1 - exp(-r * L)) / r; YLD_d = I * YLD_case

  Under the pre-2010 convention each new case's future years with the condition were discounted from onset. With continuous discounting at rate r and no age weighting, L years at weight DW are worth DW times (1 minus e to the minus rL) over r present years, so a long-lasting condition loses most in the conversion.

• Prevalence-based years lived with disability k years after incidence of a fixed-duration condition changes

  YLD_prev = (k * I_new + (L - k) * I_old) * DW

  For a condition that lasts exactly L years, the people living with it in the reference year are the last L annual cohorts. If incidence changed from I_old to I_new k years ago, with this year counted as one of the k, then k cohorts are of the new size and L minus k of the old, and the prevalence-based count is their person-years times the weight. It reaches the new incidence-based count only when the last of the old cohorts has recovered, L years after the change.