The disvalue of death in the global burden of disease

Abstract

In the Global Burden of Disease study, disease burden is measured as disability-adjusted life years (DALYs). The paramount assumption of the DALY is that it makes sense to aggregate years lived with disability (YLDs) and years of life lost (YLLs). However, this is not smooth sailing. Whereas morbidity (YLD) is something that happens to an individual, loss of life itself (YLL) occurs when that individual's life has ended. YLLs quantify something that involves no experience and does not take place among living individuals. This casts doubt on whether the YLL is an individual burden at all. If not, then YLDs and YLLs are incommensurable. There are at least three responses to this problem, only one of which is tenable: a counterfactual account of harm. Taking this strategy necessitates a re-examination of how we count YLLs, particularly at the beginning of life.

Keywords: concept of health; death; epidemiology; perinatal mortality; quality/value of life/personhood.

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 ${\displaystyle {\mathsf{h}}_{\mathsf{1}}}$) 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${\displaystyle A}$ (see panel 2). The alternative scenario is illustrated by the dashed green line (we refer to this as ${\displaystyle {\mathsf{h}}_{\mathsf{2}}}$) and represents the likely progression with treatment. In this alternative, the QALYs experienced are represented by the AUC denoted ${\displaystyle B=A+A^{\prime }}$ (see panel 2). The difference in accrued QALYs between these two counterfactual scenarios is the QALY gain, here represented by the area ${\displaystyle A^{\prime }}$. In order to calculate${\displaystyle A^{\prime }}$ we need not rely on the assumption that the value of ‘being dead’ is 0. We see that the QALY gain${\displaystyle A^{\prime }}$ can be computed as the difference between the two areas:${\displaystyle A^{\prime }=B-A.}$ 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 ${\displaystyle {\mathsf{u}}_{\text{amthrm}\mathsf{d}\mathsf{e}\mathsf{a}\mathsf{t}\mathsf{h}}}$ for the part of the integral where only ${\displaystyle {\mathsf{h}}_{\mathsf{2}}}$ is initially defined; as ${\displaystyle {\mathsf{h}}_{\mathsf{1}}}$ is a priori only defined between 0 and ${\displaystyle {\mathsf{t}}_{\mathsf{1}}}$. In order to be consistent with the QALY paradigm ${\displaystyle {\mathsf{u}}_{\mathsf{d}\mathsf{e}\mathsf{a}\mathsf{t}\mathsf{h}}}$ must satisfy the equation:${\displaystyle \begin{array}{l}{\int }_{\mathsf{0}}^{{\mathsf{t}}_{\mathsf{2}}}{\mathsf{h}}_{\mathsf{2}}\mathsf{(}\mathsf{x}\mathsf{)}\mathrm{d}\mathsf{x}\mathsf{-}{\int }_{\mathsf{0}}^{{\mathsf{t}}_{\mathsf{1}}}{\mathsf{h}}_{\mathsf{1}}\mathsf{(}\mathsf{x}\mathsf{)}\mathrm{d}\mathsf{x}\mathsf{=}{\int }_{\mathsf{0}}^{{\mathsf{t}}_{\mathsf{1}}}{\mathsf{h}}_{\mathsf{2}}\mathsf{(}\mathsf{x}\mathsf{)}\mathsf{-}{\mathsf{h}}_{\mathsf{1}}\mathsf{(}\mathsf{x}\mathsf{)}\mathrm{d}\mathsf{x}\mathsf{+}{\int }_{{\mathsf{t}}_{\mathsf{1}}}^{{\mathsf{t}}_{\mathsf{2}}}{\mathsf{h}}_{\mathsf{2}}\mathsf{(}\mathsf{x}\mathsf{)}\mathsf{-}{\mathsf{u}}_{\mathrm{d}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{h}}\mathrm{d}\mathsf{x}.\end{array}}$ This equation  obviously obtains if and only if ${\displaystyle {\mathsf{u}}_{\mathrm{d}\mathrm{e}\mathrm{a}\mathrm{t}\mathrm{h}}\mathsf{=}\mathsf{0.}}$

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.

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.