Signature
DALY = D * L + S * DW * T
| Inputs | Definition | Unit |
|---|---|---|
D | Number of cohort members who die at the start, all at the same age | deaths |
L | Standard remaining life expectancy at the age of death, the years lost per death | years |
S | Number of cohort members who survive and live with the condition | people |
DW | Disability weight of the condition in this scenario, with 0 equivalent to full health and 1 to death | none |
T | Years each survivor lives with the condition before full recovery | years |
DALY | DALYs incurred by the cohort in one scenario, without discounting | years of healthy life lost |
|---|
Function
Disability-adjusted life years for a cause or a scenario from years of life lost and years lived with disability
Maps the deaths and the non-fatal health loss from a cause, or in one scenario of an economic evaluation, to disability-adjusted life years (DALYs) by adding the years of life lost (YLL) to the years lived with disability (YLD), each calculated by its own formula. YLLs are deaths times a standard loss function of the age at death (HE-FN-YLL-001, HE-FM-YLL-001, with the discounted form HE-FM-YLL-003 and the age-group total HE-CF-YLL-001), and YLDs are prevalent cases times a disability weight (HE-FM-DWT-001) or incident cases times the weight and the duration (HE-FN-YLD-001, HE-FM-YLD-001, discounted in HE-FM-YLD-002). This package adds the sum itself, the DALYs of a cohort in one scenario, DALYs averted and cost per DALY averted between two scenarios, the continuously discounted cohort form and the DALY rate per 100,000 population. DALYs averted by a change in disability weights alone, with mortality unchanged, are HE-FM-DWT-005, and the general incremental ratio is HE-FM-ICER-001. Notation follows the Disability-Adjusted Life Year article.
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Implementations
Excel
Undiscounted cohort DALYs from named scenario cells
With Deaths, StdLE, Survivors, DisWeight and DurationYrs named for one scenario, the first formula returns the scenario's DALYs, held in CohortDALY. The second sets Survivors from the cohort size in CohortSize, so that deaths prevented move into the survivors automatically.
=Deaths*StdLE+Survivors*DisWeight*DurationYrs; =CohortSize-Deaths
Assumptions
Deaths at one age and illness of one length and weight in a cohort DALY scenario
All deaths occur at the start and at one age, and every survivor lives exactly T years with the condition at one weight, as in the article's illustrative cohort. No discounting or age weighting is applied, as in burden estimates from GBD 2010 onwards, and HE-FM-DALY-004 gives the discounted form. Deaths at several ages need one YLL term for each age (HE-CF-YLL-001), and cases of different lengths one YLD term for each.
Survivors outlive the period of illness in a cohort DALY scenario
No survivor dies during the T years with the condition, and T is no longer than L. If death follows a period of illness, the years of life lost begin at the death, as in the Fox-Rushby and Hanson case that Larson recalculates.
Worked examples
Article's cohort of 200 adults without the treatment programme
Without treatment 20 of 200 adults aged 40 die, each losing 45 standard years, and the 180 survivors live 10 years at a weight of 0.3, giving 900 YLLs and 540 YLDs, or 1,440 DALYs. All inputs are illustrative, as in the article.
D = 20; L = 45; S = 180; DW = 0.3; T = 10; DALY = 1440
Article's cohort of 200 adults with the treatment programme
With treatment 8 die and the 192 survivors live the same 10 years at a weight of 0.1, giving 360 YLLs and 192 YLDs, or 552 DALYs. The 12 people whose deaths are prevented add 12 YLDs, since they live with the condition too.
D = 8; L = 45; S = 192; DW = 0.1; T = 10; DALY = 552
Common errors
People saved left out of the survivors in the programme scenario
Keeping the survivors at 180 when the programme cuts deaths to 8 gives 540 DALYs with the programme in place of 552, so DALYs averted rise by 12 to 900 (computed here for illustration). The people whose deaths are prevented live with the condition and add YLDs, the mechanism behind Arnesen and Nord's equity critique.
Local survival in one scenario and the standard life table in the other
In the article's step 5 the 12 people saved are credited with 360 life-years under 30 years of local survival and 540 under the standard of 45 years. Counting the comparator's 20 deaths at the standard (900 YLLs) and the programme's 8 deaths at local survival (240 YLLs) credits 660 YLLs averted, more than either consistent choice gives (computed here for illustration). The life expectancy is chosen once for both scenarios and reported, and Airoldi and Morton trace the different rankings given by DALYs and QALYs to this use of life expectancy tables.
Sources
WHO formulas for years of life lost and incidence-based years lived with disability
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, YLL(c,s,a,t) = N(c,s,a,t) x L(s,a), deaths times a standard loss function of the age at death, and the incidence form used by GBD 1990, YLD(c,s,a,t) = I(c,s,a,t) x DW(c,s,a) x L(c,s,a,t), incident cases times the disability weight times the average duration of the case until remission or death.
Arnesen and Nord on the lower value the DALY gives to extending disabled people's lives
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 (full text read). The authors argue that the DALY approach implicitly attaches lower value to life-extending programmes for disabled people than to the same programmes for people without disability.
Airoldi and Morton on life expectancy tables in DALY and QALY rankings
Airoldi M, Morton A. Adjusting life for quality or disability, stylistic difference or substantial dispute. Health Economics. 2009;18(11) 1237-1247 (abstract read). With no age weighting and common discounting and weights, interventions are ranked in a systematically different way, a difference determined by the use of life expectancy tables to set the years of life lost and not by a health or disability perspective.
Canonical Identity
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