Disability Weight

Disability Weight and the Valuation of Non-Fatal Health Loss in DALYs

Time lived with a non-fatal condition enters the disability-adjusted life year only after it has been scaled by a disability weight, so the weights decide how much of a population's disease burden is attributed to illness rather than to early death. The same weights carry through into cost per DALY averted estimates used for priority setting in low- and middle-income settings. The Global Burden of Disease (GBD) study first set the weights through expert panels using the person trade-off and later moved to population surveys built on paired comparisons. How the weights are applied to years lived with disability when people have more than one condition matters as much as the values themselves, and the weights differ from QALY utility weights in both direction and origin. They have also drawn sustained equity critiques.

Reading the zero-to-one scale

A disability weight expresses the severity of a health state relative to two anchors. In the GBD 2010 study a value of 0 implies a state equivalent to full health and 1 a state equivalent to death, and "disability" means any short-term or long-term loss of health rather than its legal sense. A weight of 0.05 therefore means that 20 years lived in the state count the same as one year of life lost to premature death.

Weights attach to health states, not diagnoses. For GBD 2010, 1,160 sequelae of 289 diseases and injuries were mapped to 220 health states, each defined by a short lay description of its symptoms and functional consequences. The construct has also narrowed. GBD 1990 did not clearly separate health from wellbeing, whereas from GBD 2010 the aim has been to measure health loss, and the World Health Organization (WHO) methods document states that the weights should reflect population judgements about how healthy a state is, not the worth of persons or the stigma of a condition.

Expert panels and the person trade-off in GBD 1990

The first DALY calculations needed a way to put time with a disability on the same footing as time lost to death. Murray's 1994 technical paper defined six classes of disability severity, each with a weight between 0 and 1, alongside an exponential age weighting function and a 3% discount rate. The 1996 revision of GBD 1990 set weights for 483 sequelae, using judgements from small groups of health-care professionals and two forms of the person trade-off.

In the version described by Arnesen and Nord, the first question (PTO1) asked how many people with a condition would need a one-year life extension to match extending the lives of 1,000 people without it; an answer of 8,000 gave a weight of 1 minus 1,000/8,000, or 0.875. The second (PTO2) asked how many cures would match prolonging 1,000 lives, so judging 5,000 cures of blindness equivalent implied a weight of 0.2. Where the two answers disagreed, panellists had to revise them until they matched. Dutch researchers later used the same method, while participants in a European multi-country study rejected the GBD version of the person trade-off on ethical grounds.

Paired comparisons and population health equivalence in GBD 2010 and 2013

For GBD 2010 the weights were re-estimated from surveys of the public rather than expert panels. Household surveys in Bangladesh, Indonesia, Peru, Tanzania and the USA (13,902 respondents, 2009 to 2010) were combined with an open-access web survey (16,328 respondents, 2010 to 2011). The main question was a paired comparison, in which respondents read lay descriptions of two hypothetical people with different health states and said which person was healthier. Responses were analysed with probit regression, in which the probability of a choice depends on the difference between the scale values of the two states.

$$\Pr(j \text{ judged healthier than } k) = \Phi(\beta_j - \beta_k)$$

where $\Phi$ is the standard normal cumulative distribution function and $\beta_j$ and $\beta_k$ are the estimated scale values of states $j$ and $k$, a higher value indicating a healthier state.

Paired comparisons place states relative to one another but give no anchor at full health or death. One web survey version therefore asked population health equivalence questions for 30 states. In the form later reused in Europe, respondents compared a programme preventing 1,000 cases of an illness causing rapid death with one preventing between 1,500 and 10,000 cases of a non-fatal illness with lifelong consequences, and chose the greater health benefit. These responses anchored the probit results to the zero-to-one scale, with rescaling in logit space and 95% uncertainty intervals from 1,000 bootstrap samples. Results correlated at 0.9 or more between each survey and the pooled data except in Bangladesh (0.75); 58 of the 220 weights (26%) were below 0.05, and the highest were acute schizophrenia (0.76) and severe multiple sclerosis (0.71).

For GBD 2013, web surveys in Hungary, Italy, the Netherlands and Sweden added 30,660 respondents to the 30,230 from GBD 2010 and covered 183 states, 30 with revised descriptions and 18 new. Weights common to both rounds correlated at 0.992, but revised descriptions moved some sharply, and complete hearing loss rose from 0.033 to 0.215. Responses were insensitive to whether states were framed as temporary or chronic. The European population health equivalence answers were too noisy to support rescaling, so that study added no new evidence on trade-offs between fatal and non-fatal outcomes.

Applying weights to YLD when conditions co-occur

Since GBD 2010, YLDs have been calculated as the prevalence of each sequela multiplied by its disability weight, without age weighting or discounting. The basic formula and severity distributions are covered on the DALY page; the point specific to the weights is how they are combined when one person has several conditions. Simply adding YLDs across causes overstates health loss, and WHO notes that at the oldest ages summed YLDs may approach or exceed the person-years lived.

GBD 2010 simulated 20,000 individuals for each age, sex, country and year, assumed that conditions occur independently, and combined weights multiplicatively.

$$DW_{1+2} = 1 - (1 - DW_1)(1 - DW_2)$$

where $DW_1$ and $DW_2$ are the weights of each condition on its own and $DW_{1+2}$ is the combined weight for a person with both. The combined weight was then shared in proportion to the stand-alone weights.

$$DW_j^{*} = DW_{1+2} \times \frac{DW_j}{DW_1 + DW_2}$$

where $DW_j^{*}$ is the part attributed to condition $j$. Vos and colleagues note that YLDs might be slightly overestimated where substantial dependent comorbidity exists. Using GBD 2004 YLDs, WHO reports that adjustment for independent comorbidity reduced global all-age YLDs by 6% and YLDs at ages 60 and over by 11%.

Worked example with two conditions and a treatment programme

The figures are illustrative and not taken from a GBD table. In a population of 10,000 adults followed for one year, condition A affects 1,000 people (weight 0.10) and condition B affects 500 people (weight 0.30), a prevalence of 0.05; condition B also causes 80 years of life lost.

1. Unadjusted YLD. Prevalence is multiplied by weight and summed.

$$YLD_A + YLD_B = 1{,}000 \times 0.10 + 500 \times 0.30 = 250$$

where $YLD_A$ and $YLD_B$ are years lived with disability for each condition.

2. Overlap and combined weight. Under independence $N_{AB}$, the number with both, is 10,000 × 0.10 × 0.05 (the prevalences of A and B), or 50, leaving 950 with A only and 450 with B only. Their combined weight is calculated as follows.

$$DW_{A+B} = 1 - (0.90 \times 0.70) = 1 - 0.63 = 0.37$$

where $DW_{A+B}$ is the weight for a person with both conditions, below the 0.40 that addition would give.

3. Adjusted total.

$$YLD_{total} = 950 \times 0.10 + 450 \times 0.30 + 50 \times 0.37 = 95 + 135 + 18.5 = 248.5$$

where $YLD_{total}$ is the comorbidity-adjusted YLD, 1.5 below the unadjusted 250.

4. Attribution and DALYs. Condition A's share of the combined weight is 0.37 × 0.10/0.40, or 0.0925, and condition B's is 0.2775. Condition A's burden is therefore 95 + 50 × 0.0925, or 99.625 DALYs, since it causes no deaths. Condition B's burden adds its years of life lost.

$$DALY_B = YLL_B + 135 + 50 \times 0.2775 = 80 + 148.875 = 228.875$$

where $YLL_B$ is the 80 years of life lost. The two totals sum to 328.5 DALYs.

5. Cost per DALY averted. An illustrative programme relieves the non-fatal state of condition B for the year in 100 people with B only and 10 who also have A. It does not change mortality, so the 80 years of life lost are untouched. Health loss falls from 0.30 to zero in the first group but only from 0.37 to 0.10 in the second, which gives the total below.

$$\text{DALYs averted} = 100 \times 0.30 + 10 \times (0.37 - 0.10) = 30 + 2.7 = 32.7$$

Here each term is people treated multiplied by the fall in their weight. At a cost of 16,350 international dollars, the programme costs 500 international dollars per DALY averted.

The gain from treating a person who also has condition A is 0.27, which is 10% smaller than the 0.30 gained by a person with condition B alone. Ignoring the overlap would credit 33.0 DALYs averted, and the error grows with the share of treated people who have both conditions. The 0.27 averted also differs from the 0.2775 attributed to condition B in step 4, because attribution shares a combined weight while the gain compares weights before and after treatment.

How disability weights differ from QALY utility weights

Disability weights and health state utility values both place time in ill health on a scale anchored by full health and death, but they point in opposite directions and come from different questions. The table summarises the differences.

Because the constructs and tasks differ, 1 minus a disability weight is not a utility value. Sassi showed that, for an intervention against a non-fatal disease, the relationship between QALYs gained and DALYs averted depends on age at onset, duration, and the utility and disability weights used.

Disability weights in cost per DALY averted analyses

Disability weights become an economic quantity when DALYs measure effect in cost-effectiveness analysis. WHO's Choosing Interventions that are Cost-Effective (WHO-CHOICE) programme uses generalised cost-effectiveness analysis, measuring DALYs averted against a null scenario without the interventions and costs in international dollars. In its 2021 methods update, population models move people between health states and value time in each state with GBD disability weights, and the disability weight is one of the rates an intervention can change.

The 2021 update reports results as cost per healthy life year gained, to separate a gain measure from the GBD DALY as a loss measure, and keeps the cost per DALY metric because it is preferred in low- and middle-income settings and no single database of QALY weights covers every disease state and country. Earlier WHO-CHOICE work called interventions very cost-effective below average per capita income per DALY averted and cost-effective below three times that figure; the 2021 update uses no cost-effectiveness threshold. Because the weight multiplies every year of non-fatal health loss, the weight set flows directly into the ratio. The GBD 2013 revision raised the weight for complete hearing loss more than sixfold, and DALYs averted by preventing it would rise roughly in proportion (exactly so for people with no other condition).

Equity and validity critiques

The weights have been criticised for how they were obtained and for what they imply about disabled people. Arnesen and Nord argued that PTO1 presupposed that extending a disabled person's life is worth less, and that forced agreement between two different questions produced artefacts rather than real preferences. They also stated the broader objection that the DALY attaches lower value to life-extending programmes for disabled people, which follows from the arithmetic, since a death averted in someone who lives on with a weight above zero yields fewer DALYs averted than the same death averted in someone in full health.

Age weighting and discounting drew related objections. After a 2011 consultation with philosophers, ethicists and economists, GBD 2010 dropped age weighting as hard to justify in a measure of health loss, and the experts also advised against discounting; WHO adopted a 0% discount rate and no age weighting following consultations in 2012. Reidpath and colleagues argued that fixed weights ignore context, so blindness carries the same weight in the United Kingdom as in Niger, understating burden in disadvantaged populations. The GBD 2010 survey correlations were offered as evidence of shared values, although its household surveys omitted population health equivalence questions and so could not test whether fatal and non-fatal trade-offs agree across countries.

Some GBD 2010 weights also lacked face validity. WHO's methods document records that the weight for blindness fell to 0.20 from 0.60 and reports Nord's argument that asking who is healthier leads respondents to regard blind people as not ill. WHO adds that the same point may explain unreasonably low weights for other states, such as deafness (0.03). Revised GBD 2013 descriptions for hearing loss and spinal cord lesions raised those weights substantially, showing how far a weight depends on the wording of its health state.

Common misreadings of disability weights

Most errors come from treating the weights as more general than they are. Wider calculation errors are covered on the DALY page, and the points below concern the weights themselves.

• Mixing weight sets. GBD 2010, GBD 2013 and WHO revisions differ for some states, so a study should name its set.
• Adding weights or converting them to utilities. Co-occurring conditions need the multiplicative rule, and 1 minus a weight is not a QALY weight.
• Reading a weight as a verdict on a person. The weights quantify health loss in a described state, not wellbeing, legal disability ratings or the value of a life.
• Ignoring uncertainty. Each GBD weight has an uncertainty interval, and revised descriptions have moved some weights well outside earlier intervals, so analyses should vary the weights.

Sources

• Arnesen T, Nord E. The value of DALY life: problems with ethics and validity of disability adjusted life years. BMJ. 1999;319(7222):1423-1425. doi:10.1136/bmj.319.7222.1423
• 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
• Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford: Oxford University Press; 2015.
• Haagsma JA, Maertens de Noordhout C, Polinder S, Vos T, Havelaar AH, Cassini A, et al. Assessing disability weights based on the responses of 30,660 people from four European countries. Population Health Metrics. 2015;13:10. doi:10.1186/s12963-015-0042-4
• Hutubessy R, Chisholm D, Tan-Torres Edejer T. Generalized cost-effectiveness analysis for national-level priority-setting in the health sector. Cost Effectiveness and Resource Allocation. 2003;1:8. doi:10.1186/1478-7547-1-8
• Murray CJL. Quantifying the burden of disease: the technical basis for disability-adjusted life years. Bulletin of the World Health Organization. 1994;72(3):429-445.
• Reidpath DD, Allotey PA, Kouame A, Cummins RA. Measuring health in a vacuum: examining the disability weight of the DALY. Health Policy and Planning. 2003;18(4):351-356. doi:10.1093/heapol/czg043
• Salomon JA, Vos T, Hogan DR, Gagnon M, Naghavi M, Mokdad A, et al. Common values in assessing health outcomes from disease and injury: disability weights measurement study for the Global Burden of Disease Study 2010. The Lancet. 2012;380(9859):2129-2143. doi:10.1016/S0140-6736(12)61680-8
• Salomon JA, Haagsma JA, Davis A, de Noordhout CM, Polinder S, Havelaar AH, et al. Disability weights for the Global Burden of Disease 2013 study. The Lancet Global Health. 2015;3(11):e712-e723. doi:10.1016/S2214-109X(15)00069-8
• Sassi F. Calculating QALYs, comparing QALY and DALY calculations. Health Policy and Planning. 2006;21(5):402-408. doi:10.1093/heapol/czl018
• Vos T, Flaxman AD, Naghavi M, Lozano R, Michaud C, Ezzati 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
• 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. Sections 2 and 3.