Analysis of air pollution mortality in terms of life expectancy changes: relation between time series, intervention, and cohort studies

BACKGROUND: Information on life expectancy change is of great concern for policy makers, as evidenced by the discussions of the so-called "harvesting" issue (i.e. the question being, how large a loss each death corresponds to in the mortality results of time series studies). METHODS: Whereas most epidemiological studies of air pollution mortality have been formulated in terms of mortality risk, this paper shows that a formulation in terms of life expectancy change is mathematically equivalent, but offers several advantages: it automatically takes into account the constraint that everybody dies exactly once, regardless of pollution; it provides a unified framework for time series, intervention studies and cohort studies; and in time series and intervention studies, it yields the life expectancy change directly as a time integral of the observed mortality rate. RESULTS: Results are presented for life expectancy change in time series studies. Determination of the corresponding total number of attributable deaths (as opposed to the number of observed deaths) is shown to be problematic. The time variation of mortality after a change in exposure is shown to depend on the processes by which the body can repair air pollution damage, in particular on their time constants. Hypothetical results are presented for repair models that are plausible in view of the available intervention studies of air pollution and of smoking cessation. If these repair models can also be assumed for acute effects, the results of cohort studies are compatible with those of time series. CONCLUSION: The proposed life expectancy framework provides information on the life expectancy change in time series studies, and it clarifies the relation between the results of time series, intervention, and cohort studies.