Population health is usually measured with an average, such as health-adjusted life expectancy. This ignores inequality in health and lifespan. It is inconsistent with social preferences for extending a shorter health-adjusted life rather than a longer one by the same amount (Dolan et al., 2005, Dolan and Tsuchiya, 2012, Robson et al., 2023). It contravenes the prioritarian ethic of favouring the worse off (Parfit, 2000, Rawls, 1971). If there is aversion to inequalities in health and lifespan, then health-adjusted life expectancy will give an incomplete impression of population health and this may influence resource allocation to and within a health system. For example, failure to take account of the lifespan inequality generated by diseases that are most prevalent in childhood will lower their perceived burdens and, possibly, the priority accorded to them. The population health impact of low-prevalence, high-severity diseases will appear smaller than would be apparent if consideration were given to the health inequality they generate.

To enhance health monitoring and so better inform health policy and planning, we introduce a measure of population health that is sensitive to inequality in both age-specific health and health-adjusted lifespan. The normative foundation of the measure lies in two ethical principles that we assume social preferences over the distributions of health and lifespans adhere to. First, at each age, a health improvement for one individual combined with a same-sized health deterioration for a healthier individual would raise social welfare. Second, a social decision maker would also consent to a change that added one year to a shorter life and subtracted one year from a longer life. We use nested equity equivalents (Berger and Emmerling, 2020) to allow for the aversion to inequality in health and lifespan encapsulated by these two principles. The measure — equivalent health-adjusted lifespan (EHAL) — is a life years metric and nests health-adjusted life expectancy (HALE).

To ensure maximum applicability, we deliberately constrain the measure to require no more data than HALE: a health-extended period life table (Sullivan, 1971) and a health index of disease severity. Consequently, EHAL is both a generalisation of HALE (and life expectancy) and always a feasible alternative to it. As far as we know, our population health measure is the only one that is sensitive to inequality in the distributions of both health and lifespan and does not require estimation or simulation of their joint distribution.

With a period life table, individual lifetime health profiles are not observed. Conditional on sex, there are no differences in ex ante health or lifespan. Our task is to aggregate over distributions of both health at each age and ages at death. We do this by first calculating the equally distributed equivalent (EDE) health at each age. This is the mean health penalised for health inequality using an assumed degree of inequality aversion. Then, we aggregate the age-specific EDE health over ages at death, again imposing a penalty that increases with the assumed aversion to inequality in health-adjusted lifespans. In contrast, HALE is obtained from a linear aggregation of mean age-specific health over the age-at-death distribution without any penalty for inequality in either health or lifespan.

A life years metric lacks comparability with costs of investments in population health and does not monetize the social value of health returns on such investments. To address these limitations, we derive the societal willingness to pay for an improvement in the distribution of population health that is sensitive to inequality in both age-specific health and health-adjusted lifespan. This distributionally sensitive valuation of change in population health is a function of the relative change in EHAL and parameters that reflect a budget constraint and willingness to sacrifice consumption for health and lifespan.

We make a number of contributions to the measurement and valuation of population health. We extend Silber’s (Silber, 1983) equivalent length of life (ELL) measure that adjusts life expectancy for lifespan inequality. This has been applied within and between countries (Le Grand, 1987, Shkolnikov et al., 2003, Muszyńska and Janssen, 2016, Goerlich, 2020) and is used to produce the inequality-adjusted Human Development Index (Hicks, 1997, Alkire and Foster, 2010, Foster et al., 2005, United Nations Development Programme, 2020). Our measure adds adjustments for mean health and health inequality to the ELL adjustment for lifespan inequality.

The contribution of our money metric to previous approaches to the valuation of population health gains (Murphy and Topel, 2006, Hall and Jones, 2007) is through the incorporation of aversion to inequality in both health and lifespan. Murphy and Topel (2006) extend estimation of the value of life and lifespan (Schelling, 1968, Usher, 1973, Rosen, 1988) to partially include the value of health. However, they only capture the indirect effect of health on lifetime utility through the optimal consumption path and do not allow for the value of reduced health inequality. Edwards (2013) and Córdoba and Ripoll (2017) extend the value of a statistical life (VSL) framework to allow for aversion to lifespan inequality but do not incorporate the value of health and aversion to health inequality.2 Our measure captures the value of both health and longevity allowing for aversion to inequality in each dimension. This recognises that the value of progress against disease lies not only in the consequent increase in health-adjusted life expectancy but also in reduced exposure to variation of health and lifespan.

Adler et al. (2021) use a prioritarian social welfare function (Atkinson, 1970) to derive a value of mortality risk reduction that respects the fair innings principle: the social value of an extra year of life is greater when it extends a life that is otherwise shorter (Harris, 2006, Bognar, 2015). We adopt a social welfare function in the same family and so ensure that our measure respects the prioritarian ethic that any given benefit contributes most to social welfare when it goes to the worst off (Parfit, 2000). While the general normative foundation for our approach is consistent with that adopted by Adler et al. (2021), our objective is different and our contribution differs in two main respects. First, we allow welfare to depend on health and derive a measure that is sensitive to the distribution of health (and lifespan), not only to change in mortality risk. Second, we obtain a money metric valuation of changes in the distributions of health and lifespan. We derive the latter measure from willingness to sacrifice consumption for health and lifespan, which brings us somewhat closer to the VSL approach.

Hougaard et al. (2013) identify restrictions on social preferences that are required for a population health evaluation function (PHEF) to capture, in a single number, the two-dimensional health of individuals in a population. For example, reliance on aggregate quality-adjusted life years (QALYs) requires an assumption, among others, of indifference to inequality in quantity of life across individuals with equal quality of life. The authors identify distributionally sensitive PHEFs that, like our EHAL, relax this assumption.3 Our objective is different. It is to add distributional sensitivity to measures that summarise population health captured by a health-extended period life table. Hence, we do not define each individual by a fixed number of remaining life years and an age invariant health level, and then assume individual-level observation of each dimension of health. Rather, we start with a hypothetical cohort of individuals, each facing a risk of death and a distribution of health in each year of life. We allow for aversion to cohort inequality in both lifespan and health at each age.

We illustrate our approach by conducting distributionally sensitive measurement and valuation of population health levels and trends in Sub-Saharan Africa (SSA) from 1990 to 2019. We use data from the Global Burden of Disease (GBD) (Global Burden of Disease Collaborative Network, 2021) to simulate age-specific health distributions and age-at-death distributions for each sex. We derive population health metrics from these distributions under assumptions about the degree of inequality aversion. The analysis reveals that sensitivity to inequality in age-specific health has relatively little impact on the change in population health over the period. This is reassuring for the use of HALE. Sensitivity to inequality in health-adjusted lifespan has a large impact. Even allowing for only moderate aversion to inequality in health and lifespan, HALE increased by around 28% over the period, while EHAL increased by around 70% due to steeper reductions in mortality at younger ages.

We measure the contribution of each of 293 diseases to the overall disease burden in SSA. We do this by eliminating morbidity and mortality caused by each disease from the health-extended life table, simulating counterfactual health distributions and age-at-death distributions without the disease, recomputing HALE and EHAL under this counterfactual, and subtracting the respective measure obtained from the complete life table. This reveals that using EHAL rather than HALE substantially increases the burdens of communicable, maternal, neonatal, and nutritional diseases (CMNNs), which are more prevalent at younger ages, relative to the burdens of non-communicable diseases (NCDs), which are more prevalent at older ages. Allowing for distributional sensitivity greatly reduces the extent to which the NCD burden is converging on the CMNN burden and negates a previous finding that the NCD burden had overtaken the CMNN burden in SSA (Gouda et al., 2019).

Allowing for distributional sensitivity causes steep increases in the estimated welfare cost of CMNNs. For example in 2019, adjustment for effects on health and lifespan inequality increases the monetary equivalent of the burden of lower respiratory infections (LRI), diarrheal diseases, and malaria each by at least eight percentage points of Gross Domestic Product (GDP). Without distributional sensitivity, we estimate that LRI imposed a burden equivalent to around 6.5% of GDP. With distributional sensitivity, the estimate increases to 16.1%. In contrast, distributional sensitivity reduces the welfare costs of some NCDs with particularly high prevalence at older ages. For example, the monetary equivalent of the burden of ischemic heart disease/stroke falls from 4.5% of GDP without adjusting for effects on health and lifespan inequality to 3.9% with adjustment. Distributional sensitivity also affects the overall value of trends in population health. It increases the estimated welfare gain from improvements in population health in SSA between 1990 and 2019 from around 46.5% of baseline GDP to 67%. Such changes could influence investments in health systems and the prioritisation of disease programmes within them.

The paper proceeds as follows. In Section 2, we first derive our distributionally sensitive population health measure and then use it to obtain a money equivalent of health change and disease burden that takes account of how the impact of a disease on health and lifespan inequality affects willingness to pay to eliminate it. Section 3 describes the GBD data and explains how we use them to simulate health and age-at-death distributions that, in turn, are used to calculate the population health measures. Section 4 gives the results of the application to population health and disease burden in SSA. The final section concludes by discussing limitations and potential applications.