I

There is obviously a myriad of differences between lifetime QALY and lifetime well-being.14 Lifetime QALY is a technical, well-defined summary measure of how valuable the health in a life is. Lifetime well-being is a contested concept that is used to describe how good a life is for the person who leads it. In this section, I will focus on a particular set of formal differences between lifetime QALY and lifetime well-being: lifetime QALY relies on assumptions of strict additivity, atomism and intertemporal separability of sublifetime attributes, whereas lifetime well-being does not rely on assumptions of additivity (strict or otherwise), atomism or intertemporal separability.9

The assumptions in focus can be given the following descriptions: 

Strict additivity

A unit of measurement (eg, lifetime QALY) is strictly additive with respect to sublifetime attributes (eg, sublifetime health states expressed in QALYs) in case it is a summation of the sublifetime attributes that gives equal weight to each sublifetime attribute.

Consider an example: the unit of measurement ‘lifetime earning’ is strictly additive. It measures how much money an individual earns over her whole life by adding together the earnings the individual has at the different periods of her life, and it gives equal weight to each period so that earning £20 000 at age 20 and earning £20 000 at age 40 contribute with equal amounts (ie, £20 000) to lifetime earning.

Atomism

A lifetime unit of measurement is atomistic in case it is determined independently of the features of other people in the population.

Consider an example: the unit of measurement of lifetime earning is atomistic. It measures how much money an individual earns over her whole life independently of how much other people earn so that earning £20 000 in a society of poor people and earning £20 000 in a society of rich people contribute with equal amounts (ie, £20 000) to lifetime earning.

Intertemporal separability

The contribution of a sublifetime attribute to the lifetime unit of measurement is independent of other sublifetime attributes.

Consider an example: the unit of measurement lifetime earning respects intertemporal separability. It measures how much money an individual earns over her whole life by adding together the earnings the individual has at the different periods of her life, and the contribution of a sublifetime attribute is independent of other sublifetime attributes so that earning £20 000 contributes with the same amount (ie, £20 000) to lifetime earning regardless of previous and future earnings. 

Like lifetime earning, lifetime QALY is both strictly additive and atomistic, and thereby it also respects intertemporal separability. It is a summary measure of an individual’s sublifetime QALYs and it does not take intrapersonal or interpersonal distributions into account. Sublifetime QALYs contribute with the same amount to lifetime QALY regardless of other sublifetime QALYs of the same individual and regardless of what features other individuals in the population might have.

One could of course suggest that also lifetime well-being have these properties, and that prioritarians should establish who is worse off with a concept of lifetime well-being that respects intertemporal separability. However, as will be clear later, such a concept of lifetime well-being commits prioritarians to deeply counterintuitive positions. As Matthew Adler has pointed out, explicitly rejecting these assumptions is a way to save prioritarianism from otherwise counterintuitive positions.9

In order to understand the sort of commitments that follows from accepting strict additivity, atomism and intertemporal separability, some examples might be useful. The following is a variant of the examples Dennis McKerlie introduced to discuss equality and time.16 A general conclusion from the extensive debate around this kind of examples is that intertemporal separability is a very problematic assumption.9–11

Consider table 1. These might be plausible outcomes. Individual A suffers from severe mental illness that periodically completely incapacitates her; this condition improves with age. Individual B suffers from a mental illness that results in identical quality-adjustments for each life year. Individual C suffers from a mental illness; this condition deteriorates with age.  The commitment to intertemporal separability entails that, with respect to lifetime QALY, there is no difference between these three lives that are all 80 years long with the following distributions of sublifetime QALYs.

Because lifetime QALY assumes strict additivity, atomism and intertemporal separability, there can be no question that these lives are equivalent with respect to lifetime QALY (each individual has 55 QALYs). This follows analytically from how lifetime QALY is defined. One should, thus, according to lifetime QALY prioritarianism, give equal priority to and be indifferent with respect to all possible benefits of equal magnitude in this outcome, regardless of who the beneficiary is and regardless of when she receives it. The view tells us to be indifferent with respect to bringing A up to 11 during age 1–20 or bringing B up to 14.75 during age 41–60 and so on.

Likewise, proponents of lifetime QALY prioritarianism have to accept that D and D′ are equally well off in terms of what matters for priority setting in table 2.

Consider how these might be plausible outcomes. In outcome 1, D leads a life characterised by perfect health till age 40 and thereafter deteriorating health, whereas E is blessed with 80 years of perfect health. In outcome 2, D′ leads a life that is identical to D’s, whereas E′ around age 50 gets a nasty cancer that she manages to recover from, but which returns and causes significant problems until E′ eventually dies prematurely. D′ is better off than E′.

The fact that D is worse off than E in outcome 1 and D′ is better off than E′ in outcome 2 cannot influence how D compares to D′ in case one has assumed atomism. Lifetime QALY prioritarianism tells us to be indifferent towards improving the health of D or of D′.

By contrast, lifetime well-being does not assume additivity, atomism or intertemporal separability, which means that prioritarians who believe that benefits to individuals who are worse off in terms of lifetime well-being matter more can rank A, B and C, as well as D and D′ differently with respect to who is worse off even if sublifetime QALYs are the only attributes that distinguish these individuals from each other. In the next section, I will argue that prioritarians should rank these individuals differently than lifetime QALY prioritarianism as they should reject intertemporal separability and possibly also atomism.

II

Lifetime QALY prioritarianism fails to provide a reasonable specification of priority to the worse off because it is a mistake to assume intertemporal separability of sublifetime attributes and possibly also atomism when what matters for priority setting is measured. These assumptions might be reasonable for some technical concept of health, but they are not plausible when the purpose is to rank how well off people are in terms of health in a priority-implying sense. In this section, I will first address intertemporal separability and argue that this condition fails in contexts of priority setting that is based on who is worse off and thereafter suggest that also the atomism assumption is problematic. Importantly, if any of these assumptions is abandoned, there is reason to reject lifetime QALY prioritarianism.

Intertemporal separability of attributes such as sublifetime QALYs is a problematic assumption of any lifetime unit of measurement. This assumption states that the contribution of a sublifetime attribute is independent of other sublifetime attributes. This entails that whether a life improves or deteriorates in terms of the attribute is irrelevant when the lifetime assessment is made.

Consider A, B and C from the previous section. Although these lives contain the same amount of QALYs, they do not seem to be equally good with respect to health. A endures significant ill health in her youth, but after this period, her health steadily improves and her life story will with respect to health be a successful one. Those who favour life stories with this shape will hold that A is better off than B, who leads a life with constant, invariable health problems. Yet, also a life filled with constant health problems might be better than a deteriorating life. C is very healthy till age 20, but from her 20s and onwards, things only get worse. These individuals should not be ranked as equally badly off with respect to health in the priority-implying sense as the shape a life has matters. Many would share my intuition that C is worse off than B, and that B is worse off than A because it appears better to have a life that improves (eg, diminishing depression) than to have a life that is stable (eg, stable depression), and it is better to have a life that is stable than to have a life that deteriorates (eg, increasing depression).

Rejecting intertemporal separability has considerable support in the research on the importance of life stories. There is overwhelming evidence from the research on individuals’ preferences regarding the sequence of attributes that people prefer improvement over time generally speaking.17 Studies that focus specifically on health confirm that people prefer improvement over time also in this specific domain.9 18 Proponents of the use of QALY generally accept that survey results have some bearing on normative questions (surveys are often used to establish how to quality-adjust life years).14 It would therefore be peculiar if they dismissed the relevance of these surveys.

Yet, besides survey results, there is also philosophical arguments claiming that life stories and intrapersonal distributions of attributes matter for lifetime well-being. Most famous of these is perhaps Velleman’s thought experiment of two lives with equal amount of well-being that is distributed in different ways over the lives. While the first life progressively gets better, the second progressively gets worse. Most people would agree with Velleman that the former is a better life.19 20

Finally, if the above argument is not convincing, consider table 3 which presents a very special case of unequal intrapersonal distributions that lifetime QALY prioritarianism is committed to consider equally good in the priority-implying sense.

G and H have the same amount of lifetime QALYs (35), and according to lifetime QALY prioritarianism, benefits to G and H (eg, an additional QALY to either when they are between 21 and 40) should be given the same priority. This appears absurd. G dies at age 40, while H reaches age 80. H lives a whole 40 years longer than G. This is 40 years to see one’s own children grow up, 40 years to get grandchildren, 40 years to pursue a passion, 40 years to love and be loved. G and H are not equally well off with respect to health and intertemporal separability should be rejected so that this can be taken into account when priority is established.

Otherwise put, a plausible approach to who is worse off must reject strict additivity and take personal narratives into account.19 20 Two individuals can have equal amounts of health but be differently well off with respect to health depending on how the health is distributed. By comparison, two individuals can have the same amount of lifetime earning but be differently well off with respect to lifetime earning, for example in case one person earns almost all her money in the very end of her life while the other person has the earnings evenly distributed across her life. Life stories and intrapersonal distributions of attributes matter to how good a life on the whole is, and it must be taken into account when individuals are compared. As lifetime QALY prioritarianism is committed to rejecting the importance of life stories and intrapersonal distributions of attributes (in particular sublifetime QALYs), it is committed to getting things wrong.

The atomism assumption made by lifetime QALY prioritarianism is problematic in relation to the leap the principle makes between adding up sublifetime QALYs and a normative assessment of who is worse off in the priority-implying sense. In case one were only interested in valuing health and in ranking people in terms of this, assuming atomism seems plausible. Yet, proponents of lifetime QALY prioritarianism are interested in measuring who is worse off in a priority-implying sense, which renders further aspects of the population relevant.

Consider outcomes 1 and 2 above. Imagine that the two outcomes represent two populations in two different countries that do not interact with each other. The populations are of equal size, and both populations are divided into two groups of equal size (D-types and E-types in the first population, and D′-types and E′-types in the second population). Through a benevolent intervention, one can restore perfect health to every individual in group D or to every individual in group D′. Lifetime QALY prioritarianism tells us to be indifferent towards this.

Being indifferent towards these options seems mistaken. The individuals in D seem worse off than the individuals in D′ with respect to health, because it is worse to suffer from health problems if one is surrounded by people who are better off. There are many reasons for this. For example, health disparities make it worse to have illnesses as they entail unequal access to status goods, inequality of opportunity and unequal access to political participation.21 22 Health disparities might benefit the better off and make the worse off group even worse off.

In summary, how well off someone is with respect to health cannot be distinguished from how health is distributed across her life, and it cannot be distinguished from how healthy other people are. By relying on assumptions of strict additivity, atomism and intertemporal separability, lifetime QALY cannot take these aspects into account. Lifetime QALY prioritarianism is, thereby, relying on an indicator of who is worse off, which does not reflect how well off people are with respect to health.

III

In this paper, I have questioned how reasonable it is to use lifetime QALY as a ground for establishing who is worse off when priority is ascribed to benefits to the worse off in priority setting. Lifetime QALY is a summary measure of how much health individuals have. I have argued that it does not reflect how badly off someone is with respect to health in the priority-implying sense and that it constitutes a poor ground for establishing priorities.

I have not attempted to argue against the use of QALY, or lifetime QALY, in priority setting in a more general sense. Summary measures of health like these might have an important role to play in priority setting. I have only claimed that lifetime QALY is a poor indicator of who is worse off in the priority-implying sense. Yet, it is worth pointing out that those who use QALY in conventional ways are committed to assumptions of strict additivity, atomism and lifetime separability of sublifetime QALY and the argument of this paper is generalizable in the sense that it shows that these assumptions are problematic every time one makes a normative comparative judgement of how well off two individuals are. These problems should be taken into account any time QALY is used with normative purposes.

The arguments above do not provide reason to abandon prioritarianism coupled with the view that how well off persons are over their complete lives matters for priority setting, but they show that summary measures of health that assume strict additivity, atomism and intertemporal separability should not be used to establish who is worse off. Alternative specifications of prioritarianism for priority setting must be developed.23 One might, for example, replace lifetime QALY with weighted lifetime QALY and use some more nuanced function to aggregate sublifetime QALYs. One might attempt to develop quality-adjustments of life years that reflect the value of certain life shapes. Or one might abandon QALY as the unit of measurement in favour of a unit of measurement that represents the value of health and promote ‘lifetime value of health’ prioritarianism.14 Like well-being, ‘weighted lifetime QALY’ and ‘lifetime value of health’ are not concepts that are committed to additivity, atomism and intertemporal separability.