Premature Deaths, Statistical Lives, and Years of Life Lost: Identification, Quantification, and Valuation of Mortality Risks

Abstract

Mortality effects of exposure to air pollution and other environmental hazards are often described by the estimated number of "premature" or "attributable" deaths and the economic value of a reduction in exposure as the product of an estimate of "statistical lives saved" and a "value per statistical life." These terms can be misleading because the number of deaths advanced by exposure cannot be determined from mortality data alone, whether from epidemiology or randomized trials (it is not statistically identified). The fraction of deaths "attributed" to exposure is conventionally derived as the hazard fraction (R - 1)/R, where R is the relative risk of mortality between high and low exposure levels. The fraction of deaths advanced by exposure (the "etiologic" fraction) can be substantially larger or smaller: it can be as large as one and as small as 1/e (≈0.37) times the hazard fraction (if the association is causal and zero otherwise). Recent literature reveals misunderstanding about these concepts. Total life years lost in a population due to exposure can be estimated but cannot be disaggregated by age or cause of death. Economic valuation of a change in exposure-related mortality risk to a population is not affected by inability to know the fraction of deaths that are etiologic. When individuals facing larger or smaller changes in mortality risk cannot be identified, the mean change in population hazard is sufficient for valuation; otherwise, the economic value can depend on the distribution of risk reductions.

Keywords: Attributable death; disability-adjusted life year; environmental burden of disease; hazard fraction; premature death; value per statistical life; years of live lost.

Figure 1

Probability distribution of age of death showing alternative possible fractions of deaths advanced by age. Colors correspond to age at which individual would die in Smokeville.

Figure 2

Annual hazard, survival, and marginal distribution of deaths by age. Exposed (h ₁, solid curves) are for US males (2014 period lifetable http://www.ssa.gov/oact/STATS/table4c6.html). Unexposed (h ₀, dashed curves) are for annual hazard = (2/3) annual hazard if exposed. The short horizontal line segment in the middle panel is the years of life lost by individuals dying at age 75 when all deaths are etiologic, that is, S ₀ ⁻¹[S ₁(75)] – 75 in expression (7).

Figure 3

VSL is the slope of the individual's indifference curve at current wealth w and survival probability 1 – h. The value of a reduction in risk from h to h – r can be measured as compensating variation c or equivalent variation m. For r ≈ 0, c ≈ m ≈ r • VSL (for clarity, the value of r in the figure is much larger than is usually relevant).