On the relationship between time-series studies, dynamic population studies, and estimating loss of life due to short-term exposure to environmental risks

There is a growing concern that short-term exposure to combustion-related air pollution is associated with increased risk of death. This finding is based largely on time-series studies that estimate associations between daily variations in ambient air pollution concentrations and in the number of nonaccidental deaths within a community. Because these results are not based on cohort or dynamic population designs, where individuals are followed in time, it has been suggested that estimates of effect from these time-series studies cannot be used to determine the amount of life lost because of short-term exposures. We show that results from time-series studies are equivalent to estimates obtained from a dynamic population when each individual's survival experience can be summarized as the daily number of deaths. This occurs when the following conditions are satisfied: a) the environmental covariates vary in time and not between individuals; b) on any given day, the probability of death is small; c) on any given day and after adjusting for known risk factors for mortality such age, sex, smoking habits, and environmental exposures, each subject of the at-risk population has the same probability of death; d) environmental covariates have a common effect on mortality of all members of at-risk population; and e) the averages of individual risk factors, such as smoking habits, over the at-risk population vary smoothly with time. Under these conditions, the association between temporal variation in the environmental covariates and the survival experience of members of the dynamic population can be estimated by regressing the daily number of deaths on the daily value of the environmental covariates, as is done in time-series mortality studies. Issues in extrapolating risk estimates based on time-series studies in one population to estimate the amount of life lost in another population are also discussed.