Age Weighting

Age Weighting in the GBD and in HTA

Age weighting means counting a year of healthy life as worth more or less according to the age at which it is lived. In health economics the term refers mainly to the age weights built into the original Global Burden of Disease (GBD) disability-adjusted life year, which gave a year in young adulthood more weight than a year in infancy or old age, and which GBD 2010 and the World Health Organization (WHO) later removed. It still matters because age-weighted and unweighted DALYs are not comparable, and priority by age is still debated in QALY-based appraisal. Years of life lost and years lived with disability, the components it acted on, have their own pages.

The age-weight function in the original DALY

Murray's 1994 technical paper on the DALY treated the value of time lived at different ages as one of four social choices in a burden measure. It captured that value with an exponential function, which the paper's abstract says reflects the dependence of the young and the elderly on adults. The function used in the GBD and in later teaching material is shown below.

$$W(x) = C x e^{-\beta x}$$

where $W(x)$ is the weight given to a year of life lived at age $x$, $x$ is age in years, $\beta$ is a constant set at 0.04 and $C$ is a scaling constant, 0.1658. Larson reports that, with $\beta$ at 0.04, $C$ was chosen so that global DALYs were the same with and without age weighting in the 1990 GBD study. Murray's 1994 paper used 0.16243.

The weight peaks where the derivative is zero, at $x = 1/\beta$, which is age 25. It starts at zero at birth, rises through childhood, exceeds 1 between roughly ages 8.5 and 55.5, and then declines slowly. A WHO burden of disease guide by Prüss-Üstün and colleagues plots this curve against reported preferences and states the intent, which was that the GBD chose to value a year of life in young adulthood more than a year in old age or infancy.

Combining age weights with discounting

The standard DALYs of the original GBD and of WHO updates combined age weights with 3% time discounting, and both applied to YLLs and YLDs. The Prüss-Üstün guide gives the combined formula for a single death, with a modulation constant that switches the age weights on or off.

$$YLL = \frac{KCe^{ra}}{(r+\beta)^2}\left[e^{-(r+\beta)(L+a)}\left(-(r+\beta)(L+a)-1\right) - e^{-(r+\beta)a}\left(-(r+\beta)a-1\right)\right] + \frac{1-K}{r}\left(1-e^{-rL}\right)$$

where $a$ is the age at death, $L$ is the standard life expectancy at that age, $r$ is the discount rate (0.03 in the standard DALY), $\beta$ and $C$ are the age-weight constants above, and $K$ is the age-weighting modulation constant, from 0 (no age weights) to 1 (full age weights). The YLD formula is the same expression multiplied by the disability weight, with $a$ the age at onset and $L$ the duration. WHO's 2026 methods document reports that, with discounting and age weights, a death in infancy corresponded to 33 DALYs and deaths at ages 5 to 20 to around 36.

Worked example with weights at three ages and deaths at 5 and 40

The numbers below are illustrative. They use the GBD constants ($C$ of 0.1658 and $\beta$ of 0.04, with $K$ of 0 or 1 and $r$ of 0 or 0.03) but a simple assumed standard in which every death removes the years up to age 80, rather than the GBD standard life table.

1. Weights at three ages. At birth $W(0) = 0$. At 25, $W(25) = 0.1658 \times 25 \times e^{-1} = 1.525$. At 70, $W(70) = 0.1658 \times 70 \times e^{-2.8} = 0.706$, less than half the weight at 25. For the deaths below, the weight at age 5 is 0.679 and at age 40 is 1.339.

2. Undiscounted age-weighted YLLs. With no discounting and full age weights, the YLL is the integral of the weight over the years lost.

$$YLL_{aw} = \frac{C}{\beta^2}\left[(1+\beta a)e^{-\beta a} - (1+\beta(a+L))e^{-\beta(a+L)}\right]$$

where $YLL_{aw}$ is the undiscounted age-weighted YLL for one death and $C/\beta^2$ = 103.625. A death at 5 loses 75 years, so the value is 103.625 × (0.98248 − 0.17120) = 84.07. A death at 40 loses 40 years, giving 103.625 × (0.52493 − 0.17120) = 36.66.

3. All four conventions. The full formula above gives the remaining cells in the table.

4. What the numbers show. The weight at age 5 is low, yet age weighting raises the child death by 12% and lowers the death at 40 by 8%, because the child's lost years pass through every high-weight age while the adult's all fall after the peak. Discounting compresses the gap between the two deaths and age weighting partly restores it. In 1996 Barendregt and colleagues showed that the YLL is already an age-weighting system that favours the young, and adding the GBD weights shifted extra emphasis to deaths at ages 0 to 27, not to the middle-age range where the weight itself exceeds 1.

Why GBD 2010 and WHO dropped age weights

After GBD 1990 the age weights, like the DALY's other value choices, attracted sustained debate. WHO's methods document records that GBD 2010 held a consultation in July 2011 with 21 philosophers, ethicists and economists. Once the DALY was defined as a measure of health loss rather than of broader social welfare, WHO's account continues, it was difficult to justify age weights, and GBD 2010 dropped them. The GBD 2010 DALY paper by Murray and colleagues states that neither YLLs nor YLDs were age-weighted or discounted.

WHO adopted the same approach, a 0% discount rate and no age weighting, after informal consultations in 2012. It reports that dropping the two conventions together substantially increased the absolute number of DALYs and raised the share at younger and older ages.

The case for and against weighting years by age

Murray's 1994 paper based age weights on dependence, noting little formal work on preferences and choosing $\beta$ by informal polling. The Prüss-Üstün guide notes that Murray and Acharya argued age weights are not inequitable in themselves, since everyone potentially lives through every age, and that the choice drew on studies reporting a broad social preference for a year lived by a young adult.

Anand and Hanson concluded in 1997 that the implications of age weighting and discounting were unacceptable, and that DALY proponents failed to separate measuring the burden of disease from allocating resources. The same guide summarises two lines of objection. Some reject age weights on equity grounds, holding every year of life of equal value, and others on empirical grounds, holding that the standard weights do not reflect actual social values.

Equity offers a different rationale for favouring the young. In 1997 Williams explored the fair innings argument. It holds that everyone is entitled to a normal span of health and that the judgement is about a whole lifetime, and it reflects aversion to inequality; he concluded that it requires greater discrimination against the elderly than efficiency alone would. Because it favours whoever has had fewer years, it does not give children low weight as the GBD hump does. Tsuchiya, Dolan and Shaw outline the three main concepts of ageism, which are health maximisation, productivity and fair innings. Williams' quantification of it is covered under social welfare function.

What preference studies show about age

Stated preference studies give partial support to unequal treatment by age, but no agreed shape. Busschbach, Hessing and de Charro asked 30 students and 35 elderly people to compare imaginary renal patients of different ages; except for the very young, respondents judged health in early life twice as important as in the last decade of life. In a UK study, Tsuchiya, Dolan and Shaw found broad support for priority to younger over older people, justified by both productivity and fair innings reasoning.

A 2015 systematic review by Gu and colleagues of 64 studies of public views on priority setting found that, despite heterogeneity, the young are favoured over the old. The Prüss-Üstün guide acknowledges that the studies behind the GBD weights do not all agree that younger and older ages should receive less weight, nor on the size of the differences. Taken together, the evidence supports priority for younger over older people more clearly than the GBD hump with its low weights for young children.

How age enters QALY-based appraisal without an age weight

Cost-utility analysis carries no explicit age weight. Table 4.1 of the NICE manual (PMG36) states that an additional QALY has the same weight regardless of the other characteristics of the people receiving it, except in specific circumstances, and section 6.2.10 says the committee will regard all QALYs as being of equal weight in the reference case. Age still enters through remaining life expectancy and, under section 4.3.7, through adjusting long-run utility values for the decline in quality of life seen in the general population.

The severity modifier is the nearest NICE comes to an age-related weight, though it is not one. Sections 6.2.12 to 6.2.18 and Table 6.1 set QALY weights of 1.2 and 1.7 according to absolute shortfall or proportional shortfall, both measured against the general population with the same age and sex distribution. Wailoo and colleagues, writing with NICE staff, note that shortfall-based severity has an intrinsic link with age because life expectancy enters the calculation. In their appraisal sample, absolute shortfall fell with age (though the relationship was flat between 40 and 60), every decision with an absolute shortfall above 18 QALYs had a starting age below 20, and the former end-of-life modifier applied almost exclusively above age 40. The weights are covered under equity-weighted analysis.

Age weights compared with discounting and equity weights

Age weighting is easily confused with three other adjustments. Each responds to a different feature of a year.

• Discounting values a year by when it occurs; age weighting by the age of the person living it. A year lived at 50 by someone aged 40 today is discounted for a ten-year delay and age-weighted at 50. The discount rate is a separate choice.
• Disability weights value the severity of a health state, not the age at which it is lived.
• Equity weights in QALY analysis attach to who gains and are applied in a decision analysis, not built into a burden measure.

Common misreadings of age weighting

Three errors recur when age-weighted figures are reused. Most treat a historical convention as current or read the weight curve in isolation.

1. Assuming child deaths counted less. The weight at age 5 is low, but a death at 5 removes the high-weight adult years, so it counted for more under age weighting.
2. Mixing conventions. GBD results from 2010 onwards and WHO estimates after its 2012 decision are unweighted and undiscounted, so they cannot be compared directly with standard GBD 1990 or earlier WHO figures.
3. Reusing the constant. The value 0.1658 for $C$ was set so that global DALYs matched in the 1990 study; Larson judged its logic for cost-effectiveness analysis not especially solid.

Sources

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