Discounting and Age Weighting in the DALY Measure
This section briefly reviews the rationale and implementation of discounting and age weights in the standard DALY. To denote different choices for the discount rate and age weights, we use the notation DALYs(r, K), where r is the discount rate in percent (not a fraction as in the GBD 1990 study) and K is the age-weighting modulation factor, a parameter that allows uniform (K = 0) or the GBD nonuniform (K = 1) age weighting to be used. With this notation, DALYs(3,0) denotes the DALY with a 3 percent discount rate and uniform age weights as used in the Disease Control Priorities Project (DCPP) and DALYs(3,1) denotes the 3 percent discount rate and varying age weights as used in the GBD study. Similarly, we may refer to the DALY components of years of life lost due to premature mortality (YLL) and years of healthy life lost due to disability (YLD) as YLL(r, K) or YLD(r, K) using the same convention.
Discounting
Discounting future benefits is standard practice in economic analysis. Murray (1996) and Murray and Acharya (1997) review the theoretical and empirical arguments for and against discounting with a specific emphasis on health, including the possibility of negative discount rates. In addition to individual discounting and discount rates, policies dealing with risk must address the issue of benefits for different populations across time. As a result, these policies must address ethical and analytical dilemmas related to the valuation of current and future health and welfare in the form of social discount rates (Kneese 1999).
Some have argued that discounting should not be applied to future health gains or losses because health is not commensurable with money and cannot be reinvested elsewhere, but most criticisms of discounting in relation to the DALY have focused on the functional form and the level chosen (Fox-Rushby 2002). Epidemiologists and demographers, who tend to focus on measuring or estimating years of life or health without"valuing"either, rarely use discounting. Murray and Acharya (1997) conclude that the strongest argument for discounting is the disease eradication and health research paradox. According to this argument, not discounting future health would lead to the conclusion that all of society's health resources should be invested in research programs or programs for disease eradication, which produce an infinite stream of benefits, rather than any programs that improve the health of the current generation. Such an excessive intergenerational "sacrifice" is a particularly powerful argument for discounting future health (Parfit 1984). Note that this argument does not claim that future welfare or health is less valuable than current welfare or health, but rather uses discounting as a tool to avoid excessive sacrifice by the current generation to the point of investing all resources in future health.
Murray and Acharya argue that the social discount rate should be smaller than the return on capital investment, but note that the choice of a discount rate for health benefits, even if technically desirable, may result in morally unacceptable allocations between generations (see also Dasgupta, Maler, and Barrett 1999). Because of the complexities in the choice of discount rate, the 1990 GBD study published discounted and undiscounted estimates of the global burden of disease (Murray and Lopez 1996a).
The U.S. Panel on Cost-Effectiveness in Health and Medicine has recommended that health economic analyses use a 3 percent real discount rate to adjust both costs and health outcomes (Gold and others 1996), but that analysts should examine the sensitivity of the results to the discount rate. The 1990 GBD study, the updated estimates published in recent World Health Organization (WHO) world health reports, and the DCPP have all used 3 percent discounting for DALYs.
Age Weighting
The 1990 GBD study weighted a year of healthy life lived at young ages and older ages lower than years lived at other ages. This choice was based on a number of studies that indicated a broad social preference to value a year lived by a young adult more highly than a year lived by a young child or an older adult (Murray 1996). Not all such studies agree that the youngest and oldest ages should be given less weight; nor do they agree on the relative magnitude of the differences.
Age weights are perhaps the most controversial value choice built into the DALY. Criticisms of age weights have fallen into five categories:
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Age weighting is unacceptable on equity grounds and every year of life is of equal value (Anand and Hanson 1997).
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Age weights are not empirically based and have not been validated for large populations.
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Age weights do not reflect social values; for example, the DALY values the life of a newborn about equally to that of a 20-year-old, whereas the empirical data suggest a fourfold difference (Bobadilla 1996; see also chapter 6 in this book).
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Age weights result in more YLL for deaths at all ages from birth to 39 compared with discounted YLL not weighted by age (Barendregt, Bonneux, and van der Maas 1996).
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Age weights add an extra level of complexity to burden of disease analysis that obscures the method and makes little overall difference to the rankings of diseases and injuries.
Murray and Acharya (1997) argue that age weights are not in themselves inequitable, because everyone potentially lives through every age, and that they do reflect legitimate societal priorities. As discussed in chapter 3, the DCPP uses uniform age weights and thus values a year of healthy life equally at all ages. Chapter 6 presents an analysis in which a more extreme form of age weighting is applied to the deaths of young children.
Discounting, Age Weights, and the YLL Loss Function
DALYs are calculated as the sum of YLL from a cause and the YLD for incident cases of the health condition (see chapter 3 for more details). Murray (1996) provides general formulas for YLL and YLD that allow the annual discount rate r and the age-weighting parameters (K, C, Beta) to be varied. When K is set equal to 1, then the DALY includes an age-weighting function of the form Cxe-Betax, where x is the age in years and Beta and C are constants. For the 1990 GBD study, Murray and Lopez chose Beta = 0.04. The value of Beta = 0.04 was chosen to give an age pattern similar to that seen in available empirical data. C is a parameter chosen to ensure that the total global DALYs are the same with and without age weighting, estimated at C = 0.1658 for the 1990 GBD study. Figure 5.1 illustrates the form of the age-weighting function for Beta = 0.02, 0.04, and 0.06. For the other two choices of Beta (0.02 or 0.06), the value of C was varied to ensure the same area under the curve from age 0 to 100 years.
[Figure
5.1]
The age-weighting function specifies the relative value of a year of life lived at different ages either for YLD or YLL estimates. To estimate the total years of life lost due to death at age x, the age-weighting function is integrated over all ages above x. Table 5.1 shows the resulting loss function for selected exact ages, also plotted in figure 5.2 for females. The male-female gap in YLL(0,0), 2.5 years at birth, is reduced to 0.1 years for YLL(3,1) (figure 5.3). Figure 5.4 shows the effect on YLL of varying the parameter Beta in the age-weighting function. Values of Beta higher than 0.04 give relatively greater weight to younger ages and less to older ages; values of Beta lower than 0.04 give relatively lower weight to younger ages and more to older ages.
[Figure
5.2]
[Figure
5.3]
[Figure
5.4]
[Table .]
Table 5.2 further examines the effects of varying the parameter Beta in the age-weighting function on the weights applicable at different ages. For the standard DALY, Beta = 0.04 implies a maximum age weight of 1.52 at age 25, and the age weight is greater than 1 over the range 8.4 to 54.2 years. Compare this with Beta = 0.03, which gives a maximum age weight of 1.29 at age 33.3 years with a prime age range (weight greater than 1) of 14.9 to 63.0 years. Note that the choice of Beta = 0.03 gives a prime age range that matches fairly typical ages for formal entry and exit from work in many societies (Mahapatra 2001). We do not consider variations in Beta further here. Sensitivity analyses for GBD 2001 that follow compare standard age weights (Beta = 0.4) with uniform age weights.
[Table .]
