Signature
DALY_av = n_1 * (w_1_pre - w_1_post) + n_2 * (w_2_pre - w_2_post)
| Inputs | Definition | Unit |
|---|---|---|
n_1 | Number of people treated who have only the target condition | people |
w_1_pre | Disability weight of the first group without the intervention | none |
w_1_post | Disability weight of the first group with the intervention | none |
n_2 | Number of people treated who also have another condition | people |
w_2_pre | Combined weight of the second group without the intervention | none |
w_2_post | Weight of the second group with the intervention, the weight of the remaining condition | none |
DALY_av | Healthy years gained by the treated groups | DALYs |
|---|
Function
Disability weight scaling of time lived with a non-fatal health state
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.
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Implementations
Excel
DALYs averted from named group sizes and weights
With GroupOneN, GroupOnePre, GroupOnePost, GroupTwoN, GroupTwoPre and GroupTwoPost named, the formula returns DALYs averted, held in DALYsAverted; cost per DALY averted is =ProgrammeCost/DALYsAverted.
=GroupOneN*(GroupOnePre-GroupOnePost)+GroupTwoN*(GroupTwoPre-GroupTwoPost)
Assumptions
Intervention changes non-fatal health only when counting DALYs averted
Mortality is unchanged, so years of life lost are untouched and only the YLD term changes; WHO-CHOICE population models allow an intervention to change the disability weight as one of its rates.
Weights from one set with the multiplicative rule for comorbid people
Before and after weights for comorbid people are combined weights (HE-FM-DWT-002) from the same weight set as the stand-alone weights.
Worked examples
DALYs averted by relieving condition B in 100 people with B only and 10 who also have A
Health loss falls from 0.30 to zero in the first group and from 0.37 to 0.10 in the second: 30 plus 2.7 gives 32.7 DALYs averted. At a cost of 16,350 international dollars the programme costs 500 per DALY averted, as in the article.
n_1 = 100; w_1_pre = 0.3; w_1_post = 0; n_2 = 10; w_2_pre = 0.37; w_2_post = 0.1; DALY_av = 32.7
DALYs averted with the comorbidity overlap ignored
Crediting all 110 people with the stand-alone weight of 0.30 gives 33.0 DALYs averted, overstating the gain; the error grows with the share of treated people who have both conditions.
n_1 = 110; w_1_pre = 0.3; w_1_post = 0; n_2 = 0; w_2_pre = 0.37; w_2_post = 0.1; DALY_av = 33
Common errors
Using the attributed disability weight share as the DALY gain
Crediting 0.2775 per comorbid person (the share attributed to condition B) instead of the 0.27 change in weight gives 32.775 DALYs averted; attribution and gain answer different questions.
Ignoring the weight set's uncertainty
Each GBD weight has an uncertainty interval and revised descriptions moved some weights well outside earlier intervals, so cost per DALY averted should be recomputed across plausible weights.
Sources
WHO-CHOICE health states valued with GBD disability weights that interventions can change
Bertram MY, Lauer JA, Stenberg K, Tan Torres Edejer T. Methods for the economic evaluation of health care interventions for priority setting in the health system: an update from WHO CHOICE. International Journal of Health Policy and Management. 2021;10(11):673-677. doi:10.34172/ijhpm.2020.244. Methods: population models move people between health states by incidence, remission and fatality rates, and time in each state is valued with GBD disability weights to measure health loss; the epidemiological rate an intervention affects may be incidence, remission, case-fatality or disability weight; results reported as cost per healthy life year gained.
Combined weights for comorbid people in GBD 2010
Vos T, Flaxman AD, Naghavi M, et al. Years lived with disability (YLDs) for 1160 sequelae of 289 diseases and injuries 1990-2010: a systematic analysis for the Global Burden of Disease Study 2010. The Lancet. 2012;380(9859):2163-2196. doi:10.1016/S0140-6736(12)61729-2. Methods: combined disability weight one minus the product of one minus each weight, apportioned in proportion to stand-alone weights.
Canonical Identity
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