The Global Burden of Disease

The Global Burden of Disease (GBD) is ‘a systematic, scientific effort to quantify the comparative magnitude of health loss due to diseases, injuries and risk factors by age, sex and geographies for specific points in time’ (Murray et al, p20631; Murray et al, p12). Since its first publication in the early 1990s, the GBD has grown to be a worldwide endeavour drawing on the expertise of several principal actors in global health.3 Historically, epidemiologists have concerned themselves chiefly with the mortality in a population and mortality rates and deaths averted were the standards for measuring disease burden.4 5 The GBD, however, aims to integrate morbidity and mortality into disability-adjusted life years (DALYs). This summary measure is a significant contribution to studies of global health, as mortality alone cannot adequately capture what is intuitively understood by ‘the burden of disease’. To measure disease burden, we need to take account of both morbidity and mortality.

The DALY metric—the aggregation of years lived with disability (YLDs) and years of life lost (YLLs)—has become popular in the global health community. Publications using DALYs regularly feature in top journals, like The Lancet and the New England Journal of Medicine,1 3 6 and major organisations, like WHO and the World Bank,7 use DALY estimates. Furthermore, the GBD study—which uses the DALY as its health metric—is used as evidence for informed policy-making.8 Yet, if the DALY is not conceptually sound, we risk ranking disabilities wrongly, measuring inequality in health on false premises, and perhaps even ranking health programmes suboptimally.

It is, therefore, vital that all the assumptions underlying the DALY are as well founded, coherent and plausible as possible. The DALY model relies on several assumptions that have been revised over the years.2 Previous operationalisations of the DALY included age-weighting, time discounting, sex differentiation and the use of Japanese life tables as a yardstick for an ideal lifespan to compute YLLs. Current practices, such as involving the public in setting disability weights (DWs) for the calculation of YLDs or using synthetic life tables across the globe for estimating the YLL at the time of death, reflect changing assumptions and recognition of the potential for improvement in the measure.8–12

Nonetheless, there is at least one critical assumption that, we maintain, has not been given enough attention: the assumption that it makes sense to aggregate YLLs with YLDs into DALYs. ⁱ The aim of this paper is to address that underlying assumption.

The DALY model

The DALY model was developed during the late 1980s and early 1990s, building on earlier time-based measures for quantifying health.4 5 13 14 The GBD 1990 launched the DALY, and its raison d'être was to obtain an integrated measure of morbidity and mortality. Since its conception, the DALY has primarily been concerned with individual burden. However, the need to clarify how death can be an individual burden may have been veiled from the first DALY model as this included age-weighting to reflect the ‘[s]ocial [burden] of the time lived at different ages’ (Murray, pp434–436).15 Following a methodological debate during the ensuing decades, societal burden has been excluded. The most recent DALY model has been revised with the explicit aim to reflect the individual’s own burden of disease, exclusively.ⁱⁱ ,2 Accordingly, the DALY needs to incorporate a well-founded account of the individual burden of death which sets this paper’s topic at centre stage.

Today, DALYs measure the unhealth in a population understood as aggregated individual burden. 1 Unlike most other time-based health-outcome measures—such as the quality-adjusted life year (QALY), which tries to put a value on the time spent in various (health) states16—the DALY purports to measure health impairment directly.

Some will suggest that our critique of the DALY will affect the QALY to an equal degree, partly because of the common misconception that ‘DALYs are inverse QALYs’.9 17–19 In fact, the DALY differs fundamentally from the QALY in at least two important respects. First, the DALY is a so-called negative gap-measure purporting to quantify the burden suffered as a consequence of experienced unhealth directly.2 8 15 In contrast, the QALY measures the value of being alive. Second, while the QALY does not require any particular value associated with ‘being dead’, the DALY is defined in terms of such a burden. In the words of Murray and colleagues: ‘[t]he basic unit of measurement for [the DALY] is lost years of healthy life’ (p14).2 Taken together, the DALY thus assumes and relies on a coherent concept of the individual burden associated with ‘being dead’. The QALY model does not. The QALY is a pure time-based measure of the value of time spent alive relative to one’s health state.

While it is common to describe the QALY model as assigning the zero value to ‘being dead’,16 this is merely a heuristic. In fact, the QALY assigns, in the limit, zero value as time approaches zero which is what endows the QALY model with ratio scale properties, rather than just interval scale properties.20 The primary attribute of death in the QALY model is that for the dead, time is no more; accordingly, there is nothing to be valued. We can however extend the QALY model by assigning zero to ‘being dead’. In fact, this is the only consistent extension of the QALY model, compatible with the necessary assumption that the dead are expelled from the matrix of time.

To sum up, the QALY is concerned with living individuals exclusively, and nothing in the QALY model corresponds to the YLL. When an individual die, intraindividual QALY aggregation ends. In the DALY model, YLLs—which does not happen during your life—are integral. The estimation of QALY values requires comparing various durations of time spent in different health states, and never relies on any direct comparisons with death. The DALY, on the other extreme, postulates that a year of ‘being dead’ is a viable unit for burden. While the QALY losses estimated for a deceased individual may be said to assume something about the non-aggregation of QALYs after death, this is, in fact, not part of the QALY model itself. In the DALY model, the burden of death is interwoven into its fabric. This latter observation contradicts the widely held belief that DALYs are inverse QALYs, and suggests that this heuristic for understanding one of these models in terms of the other has been extrapolated too far. While the QALY resides among the living, the DALY model must cross the river Styx.

See figure 1 for a graphical illustration. For the DALY, as we argue below, the situation is entirely different.

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Figure 1

The quality-adjusted life year (QALY) model. Figure 1 illustrates the QALY for one individual. In panel 1 the leftmost dashed vertical line represents the time of diagnosis and a possibility for starting up with treatment. This is followed by one of two counterfactual scenarios: One scenario is illustrated by the solid green curve (we refer to this as  ) and represents the likely progression without treatment. This scenario results in a number of experienced QALYs that is equal to the area under the curve (AUC) denoted  (see panel 2). The alternative scenario is illustrated by the dashed green line (we refer to this as  ) and represents the likely progression with treatment. In this alternative, the QALYs experienced are represented by the AUC denoted  (see panel 2). The difference in accrued QALYs between these two counterfactual scenarios is the QALY gain, here represented by the area . In order to calculate  we need not rely on the assumption that the value of ‘being dead’ is 0. We see that the QALY gain  can be computed as the difference between the two areas: However, if one would like (as is often convenient) to compute this difference as the integral between two curves—viz as roughly the area beneath the dashed black curve—then the scenario without treatment must be equipped with a value   for the part of the integral where only  is initially defined; as   is a priori only defined between 0 and  . In order to be consistent with the QALY paradigm   must satisfy the equation:  This equation  obviously obtains if and only if

Years of life lost

The fundamental principle that ‘[t]ime is the unit of measure for the burden of disease’ has been retained from the original formulation of the DALY (Murray et al, p132; Murray, p4312). The DALY component the YLL is by definition taken as a burden. It is assumed to be quantified by itself: the number of years in the gap between the time of an individual’s death and some ideal length of life is defined as identical to the burden imposed on that individual by his/her death. There are many issues pertaining to estimating the ideal remaining lifespan of an individual at the time of his/her premature death. However, the previous paragraph covers the fundamental definition of the YLL: burden equals the number of life years lost.

Years lived with disability

To integrate mortality—measured by the YLL—and morbidity, the DALY model includes a second component: the YLD. In order to define the YLD, time is again taken as the basic unit of measurement.2 Previous works on the YLD have relied on QALY-type measurements, including standard gamble, time trade-off and person trade-off.15 21 Furthermore, in line with the explicit aim of not measuring disvalue as such, but rather ‘objective unhealth’, the current YLD relies on a representative sample of laymen’s evaluation of the degree of unhealth represented by various medical conditions, suitably described by an expert panel. The DWs are then assigned based on a mixture of two methods: the person trade-off and latent utility-like discrete choice tasks.2

This procedure results in DWs (DW_A ) for the various conditions A, which yield YLDs when multiplied by duration T:

The DALYs are then computed as the sum of the YLDs and the YLLs (see figure 2).

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Figure 2

The DALY model. Lifetime DALYs for an individual with two periods of illness, followed by premature death. The yellow and red colours represent YLDs and YLLs, respectively. The YLD areas are delineated by the duration on the time axis and the disability weights DW_i for the two conditions. The light red area is defined by erecting a rectangle of height 1 over the dark red line segment representing the number of years of life lost to premature death. The total of the light red and yellow areas constitutes the DALY. The DALY model assumes that it makes sense to attribute a burden of 1 to the YLLs; we challenge this assumption. DALYs, disability-adjusted life years; YLDs, years lived with disability; YLLs, years of life lost.

But note how the equation reduces to 0 if time is zero. This equation hints as to what we view as the problem with the current DALY: the YLD is a measure of an inherently two-dimensional construct with unit DW×T—burden of disability times duration. The YLL, on the other hand, is by definition a one-dimensional construct, measured by its duration only. Unless a sound DW for ‘being dead’ can be produced, one cannot add YLLs and YLDs together in its current form. The reason is that the first has unit time, while the latter has unit disability times time. An analogy would be adding a length to an area.

There are at least two objections to this dimensional concern. First, some may maintain that the DWs are mere scalars which means that the YLD measures a percentage of the YLL. Then, being blind (DW=0.19: this and later DWs are taken from Salomon et al’s 2015 publication21) for 1 year equals 19% of ‘being dead for 1 year’.ⁱⁱⁱ However, if the YLL is merely a one-dimensional stretch of time, it does not yet embody any burden or disvalue which can be scaled. There is nothing—corresponding to disvalue—to calculate 19% from. Surely, to be blind for 1 year is not the same as ‘being dead’ for 19% of 365 days, that is, 69.35 days. The DW must, rather, relate to the disvalue of ‘being dead’. The YLD, on the other hand, is two-dimensional as it cannot exist independently of time and that—je ne sais quoi—without which the YLD would be time only.

Second, the antipodal objection is to maintain that the intended interpretation of the YLL is that its DW ‘DW_Death ’ is equal to 1—by definition. This defence is circular: the YLD is supposed to be defined in terms of the YLL and therefore cannot appeal to some value of being alive. Of course, our issue is not with the choice of 1, but rather we question the assumption that any DW can be assigned to ‘being dead’ if YLLs is the foundational concept.

Where does this leave the current DALY? The burden of death is defined to be the number of years lost compared with an ideal lifespan. The burden of living with morbidity is morbidity’s duration weighted by a comparison with living in full health. But recall that the yardstick for the DALY is the burden of death, not the other way around. The burden of blindness is supposedly not compared with not being blind, but rather how much less it burdens you than ‘being dead’. The DALY is, therefore, not a gap-measure until one applies an account of how death burdens someone compared with being alive (in full health) compared with being blind (compared with being in full health). This seeming circularity is a problem for the DALY.

Incommensurability

The DALY model claims equivalence between YLLs and YLDs. The crucial question is if such equivalence makes sense? Whether or not it is meaningful to aggregate YLLs and YLDs into one summary number is partly a question of the commensurability of these quantities. There is a vast literature on commensurability.22–24 However, the question of whether the YLL and the YLD are, in fact, commensurable has received limited attention.

To begin with, two values are incommensurable when they lack a common measure. There are stronger and weaker types of incommensurability. Strong incommensurability occurs when something cannot be compared at all. One standard definition is that two values are strongly incommensurable when ‘the one is neither more valuable than the other, nor less, and not of equal value’ (Bradley et al, eds, p79).25 Strong incommensurability would apply to YLDs and YLLs if, as far as they are individual burdens, nothing can be said as to which is the lesser, nor if they are equal. It is no trivial matter to establish commensurability for YLLs and YLDs. After all, the YLL and the YLD seemingly lack a common yardstick, as individual YLLs do not appear to have a temporal extension for anyone.

A weaker type of incommensurability is called trumping or lexical orderings. The latter term derives from the fact that such orders resemble the alphabetical ordering of finite letter combinations. Lexical incommensurability does not deny that the incommensurable magnitudes are ordered or that they belong to the same class of entities but rather that the problem is to measure them in a common finite unit since they inhabit different ‘tiers of importance’. Such orderings must, if they are to be represented numerically, be mapped to number systems which contain so-called non-standard numbers.^iv

The commensurability of the YLD and the YLL

We take the DALY to posit that YLDs and YLLs are commensurable. It appears more than reasonable to postulate that morbidity (and therefore YLDs) burdens the individual who embodies that morbidity. But accounting for how exactly death (understood as YLLs) burdens the deceased is demanding. To elaborate: the dying process burdens the living individual and is accounted for by the YLD. Note that when we talk about death, we do not mean this process of dying. By death, we refer to the instant in which someone goes from being alive to not living. We assume that death implies permanent non-existence,26 which makes ‘being dead’ an oxymoron. ‘Being dead’ would, if anything, mean the absence of any health state. It appears that the two constructs we are trying to relate via a common measure might not even belong to the same domain.

A viable avenue of inquiry should begin with the following question: Can death be bad for the individual who dies? If the answer is negative, we must conclude that YLLs cannot be an individual burden. This implies that the YLD and the YLL are incommensurable, as illustrated in figure 2. If the answer is affirmative, on some account X, we can proceed to the next question: Does X provide commensurability between the YLD and the YLL?

There are several arguments against the view that death is bad for those who die, and the three strongest of them concern experience, time and symmetry. According to the experience argument, burdens are something we must experience. But, we cannot experience while ‘being dead’. Thus, death cannot be bad for us. According to the time argument, most burdens begin at a time and are bad for us through time but there is no time when death is bad for us. When we are alive, we have not lost our lives, and when we ‘are dead’, we do not exist. Therefore—the argument goes—death cannot be bad for us.^v According to the symmetry argument, we do not consider the non-existence before our lives as a burden, so why should the non-existence after ^vi our lives—death—be one?27 Any of these three Epicurean arguments makes it questionable whether the YLL quantifies an individual burden at all.^vii

Notice how the YLD is unaffected by these arguments. First, morbidity is usually something that people experience. Second, morbidity happens at a time and is harmful through time. Third, it is not unreasonable that we count people’s past and future morbidity as equally bad in the GBD. Accordingly, there are several significant asymmetries between the YLD and the YLL, which we have summarised in table 1.

Two things being different in important aspects do not, in and of itself, imply their incommensurability. But if these three arguments are correct, then the YLL cannot be an individual burden and so YLDs and YLLs are incommensurable qua individual burdens.

In brief, the above poses two foundational problems for the DALY. First, we must provide a reasonable account of the burden associated with YLLs that overcomes the three Epicurean arguments. Second, this account must give rise to a notion of burden that makes YLLs commensurable with YLDs.

Three responses

We can think of at least three responses to this incommensurability problem—ignore, accept or rescue (see figure 3). 

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Figure 3

Three responses. We explore three possible responses to the incommensurability problem, two of which we consider untenable (1 and 2). On the rescue strategy (3) there are two main avenues: (3.1) argues that YLDs and YLLs, in fact, quantify something other than individual burden, while (3.2) (which we endorse) argues that the YLD and the YLL can be commensurable—as individual burden—conditional on adopting a counterfactual account of harm. YLDs, years lived with disability; YLLs, years of life lost.