Background: Information on life expectancy (LE) change is of great concern for policy makers, as evidenced by discussions of the "harvesting" (or "mortality displacement") issue, i.e. how large an LE loss corresponds to the mortality results of time series (TS) studies. Whereas loss of LE attributable to chronic air pollution exposure can be determined from cohort studies, using life table methods, conventional TS studies have identified only deaths due to acute exposure, during the immediate past (typically the preceding one to five days), and they provide no information about the LE loss per death.
Methods: We show how to obtain information on population-average LE loss by extending the observation window (largest "lag") of TS to include a sufficient number of "impact coefficients" for past exposures ("lags"). We test several methods for determining these coefficients. Once all of the coefficients have been determined, the LE change is calculated as time integral of the relative risk change after a permanent step change in exposure.
Results: The method is illustrated with results for daily data of non-accidental mortality from Hong Kong for 1985 - 2005, regressed against PM10 and SO2 with observation windows up to 5 years. The majority of the coefficients is statistically significant. The magnitude of the SO2 coefficients is comparable to those for PM10. But a window of 5 years is not sufficient and the results for LE change are only a lower bound; it is consistent with what is implied by other studies of long term impacts.
Conclusions: A TS analysis can determine the LE loss, but if the observation window is shorter than the relevant exposures one obtains only a lower bound.