Signature
DW_12 = 1 - (1 - DW_1) * (1 - DW_2)
| Inputs | Definition | Unit |
|---|---|---|
DW_1 | Weight of condition 1 on its own | none |
DW_2 | Weight of condition 2 on its own | none |
DW_12 | Weight for a person with conditions 1 and 2 | none |
|---|
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.
Try this function
Implementations
Excel
Combined disability weight from two named weights
With the stand-alone weights in WeightOne and WeightTwo, the formula returns the combined weight, held in CombinedWeight. For several weights in a range, =1-PRODUCT(1-WeightRange) entered as an array formula gives the same rule.
=1-(1-WeightOne)*(1-WeightTwo)
Assumptions
Multiplicative combination of disability weights for comorbid health loss
Each condition removes the same proportion of the health left by the other. Vos and colleagues report that tests on real data suggested the multiplicative model was the most appropriate.
Weights from the same set and on the same scale
Both stand-alone weights come from one weight set and are at least 0 and at most 1.
Worked examples
Combined disability weight for conditions A and B
A person with condition A (0.10) and condition B (0.30) has a combined weight of 1 minus 0.90 x 0.70, or 0.37, below the 0.40 that addition would give.
DW_1 = 0.1; DW_2 = 0.3; DW_12 = 0.37
Combined disability weight for two mild conditions
Two conditions of weight 0.05 each combine to 0.0975, close to their sum of 0.10 because mild weights barely overlap (computed here for illustration).
DW_1 = 0.05; DW_2 = 0.05; DW_12 = 0.0975
Combined disability weight for a severe and a moderate condition
Weights of 0.71 and 0.30 combine to 0.797, where addition would give 1.01, more than death (computed here for illustration).
DW_1 = 0.71; DW_2 = 0.3; DW_12 = 0.797
Common errors
Adding weights for people with several conditions
Addition overstates health loss and can exceed 1 for severe combinations; WHO notes that at the oldest ages summed YLDs may approach or exceed the person-years lived.
Applying the multiplicative disability weight rule to dependent conditions
The multiplicative rule is applied to co-occurrence simulated under independence; Vos and colleagues note that YLDs might be slightly overestimated where one disease makes another more or less likely.
Sources
Combined disability weight as one minus the product of one minus each weight
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: the combined disability weight for a simulated individual with two or more disorders is one minus the product of one minus each disability weight; tests on real data such as MEPS suggested the multiplicative model was the most appropriate; Discussion: YLDs might be slightly overestimated where substantial dependent comorbidity exists.
WHO multiplicative disability weight model for individuals with multiple conditions
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. Section 2.5: the disability weight for individuals with multiple conditions is estimated assuming a multiplicative model, DW(1+2) = 1 minus (1 minus DW1) x (1 minus DW2); summed YLDs may approach or exceed 100 per cent of person-years at the oldest ages.
Canonical Identity
Stable URI · Machine-readable · Resolvable · CC BY 4.0