Signature
YLD_case = DW * (1 - exp(-r * L)) / r; YLD_d = I * YLD_case
| Inputs | Definition | Unit |
|---|---|---|
DW | Unit: none, from 0 to 1 | — |
r | 0.03 in the original DALY | proportion per year, above zero |
L | Unit: years | — |
I | Unit: cases | — |
YLD_case | Unit: years | — |
|---|---|---|
YLD_d | Unit: years | — |
Function
Years lived with disability counted from incident cases or from prevalent cases of a sequela
Multiplies time spent with a non-fatal health state by its disability weight, counting the time either from the cases that begin in the reference year (all their future health loss, the GBD 1990 incidence perspective) or from everyone living with the state in the reference year (that year's health loss only, the perspective of GBD 2010 onwards and WHO's Global Health Estimates). Prevalence-based YLDs for one sequela are HE-FM-DWT-001 and their comorbidity adjustment HE-FM-DWT-004 on the disability weight page; steady-state prevalence from incidence and duration is HE-FM-XSD-002. Notation follows the Years Lived with Disability article.
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Implementations
Excel
Discounted years lived with disability per case and per cohort from named cells
With DisWeight, DiscRate, DurationYrs and IncCases named, the formulas return the discounted YLDs per case and for the cohort, held in YLDCase and YLDDisc.
=DisWeight*(1-EXP(-DiscRate*DurationYrs))/DiscRate; =IncCases*YLDCase
Assumptions
Continuous discounting from the year of onset without age weighting
Health loss is discounted continuously at a constant rate from onset, with the same weight throughout the case; the original DALY also multiplied each year by an age weight, which this form leaves out, as the article does.
Worked examples
Condition with 100 new cases, a weight of 0.20 and 10 years at 3 per cent
Ten years at 3 per cent are worth 8.639 present years, so each case gives 1.7279 discounted YLDs and the 100 new cases 172.8, against 200 undiscounted; the gap of 27.2 comes from the convention alone, as in the article.
DW = 0.2; r = 0.03; L = 10; I = 100; YLD_case = 1.7279; YLD_d = 172.8
YLDs averted each year by 50 prevented cases
A programme that prevents 50 cases a year averts 100 undiscounted YLDs over the 10 years each case would have lasted, or 86.4 with continuous discounting at 3 per cent, as in the article.
DW = 0.2; r = 0.03; L = 10; I = 50; YLD_case = 1.7279; YLD_d = 86.4
Larson's case with a weight of 0.6 for 10 years
One case at weight 0.6 for 10 years at 3 per cent gives 5.1836 discounted YLDs, the value Larson reproduces from Fox-Rushby and Hanson.
DW = 0.6; r = 0.03; L = 10; I = 1; YLD_case = 5.1836; YLD_d = 5.1836
Forty years at full weight
Forty years at 3 per cent are worth about 23.3 present years before any disability weight is applied, as in the article.
DW = 1; r = 0.03; L = 40; I = 1; YLD_case = 23.29; YLD_d = 23.29
Common errors
Discounting YLDs from onset and YLLs from death
WHO records that in the original DALY the discounting of YLDs started at the year of incidence and that of YLLs at the year of death, an inconsistency avoided when GBD 2010 and WHO dropped discounting from burden estimates.
Mixing continuous discounting of health with discrete discounting of costs
Larson shows that counting each of 10 years at the start of the year and discounting at 3 per cent gives 8.786 against the continuous 8.639, a difference of 1.7 per cent; a cost-effectiveness analysis with DALYs should state which convention it uses and apply it to costs and health alike.
Applying a 3 per cent discount to prevalence-based YLDs
A prevalence-based count records only the health loss lived in the reference year and has no future stream to discount; discounting belongs to the incidence-based count or to a model of an intervention's future effects.
Sources
Larson on the continuous-time YLD formula and its discrete-time counterpart
Larson BA. Calculating disability-adjusted-life-years lost (DALYs) in discrete-time. Cost Effectiveness and Resource Allocation. 2013;11:18. doi:10.1186/1478-7547-11-18 (full text read). Equation 2: for 10 years lived disabled at weight 0.6, YLD(3, 0) = 0.6 x (1 / 0.03) x (1 minus e^(minus 0.03 x 10)) = 5.1836. Table 1 and text: discrete-time discounting with each year counted at the beginning of the year gives 8.786 for 10 years, the continuous answer is 8.6394, and the 1.7% difference is minor.
WHO on dropping discounting and age weighting from burden estimates
World Health Organization. WHO methods and data sources for global burden of disease estimates 2000-2019. Global Health Estimates Technical Paper WHO/DDI/DNA/GHE/2020.3. Geneva: WHO; 2020 (full text read). Section 2.3: WHO adopted the same approach as GBD 2010, computing DALYs with a time discount rate of 0% and no age weighting; this avoids the inconsistency in the original DALY method, where the start time for discounting YLDs was the year of incidence whereas that for YLLs was the year of death.
Fox-Rushby and Hanson on DALY calculations in cost-effectiveness analysis
Fox-Rushby JA, Hanson K. Calculating and presenting disability adjusted life years (DALYs) in cost-effectiveness analysis. Health Policy and Planning. 2001;16(3):326-331. doi:10.1093/heapol/16.3.326 (abstract read). Abstract: many current analyses are not comparable or transferable because the assumptions used differ or are unclear; the paper suggests minimum reporting criteria for using DALYs in cost-effectiveness analysis.
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