1 Department of Biostatistics, Bloomberg School of Public Health, Johns Hopkins University, Baltimore, MD.
2 Department of Epidemiology, Bloomberg School of Public Health, Johns Hopkins University, Baltimore, MD.
Received for publication January 2, 2003; accepted for publication February 5, 2003.
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INTRODUCTION |
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If individuals who were severely ill and were expected to die shortly were the only people affected by current levels of air pollution, reducing ambient concentrations would not necessarily increase life expectancy significantly. This phenomenon of only brief advancement of the timing of death has been referred to as "short-term mortality displacement," as well as by the unfortunate term "short-term harvesting." While no lives should be shortened by air pollution, society suffers a much smaller loss if air pollution affects only frail persons without great loss of life expectancy. Our paper (2) was motivated by the need to find methods of assessing short-term harvesting for studies of air pollution and other environmental agents.
In this rejoinder to the commentary of Dr. Richard Smith (3), we briefly 1) review the conceptual framework under which short-term harvesting would occur, 2) illustrate how our timescale model would detect short-term harvesting, and 3) summarize the statistical evidence supporting short-term harvesting.
A compartmental model (46) sets a biomedical stage for approaching the assessment of short-term harvesting. Suppose that the population can be divided into two groups according to susceptibility to an air pollution episode: low-risk and high-risk. On any given day, people in the low-risk pool can become frail and move into the high-risk pool (T1) and people in the high-risk pool can become healthier and move into the low-risk pool (T2) or can exit the high-risk pool by dying (T3). Assuming a steady-state condition, T3 = T1 T2; that is, there is equilibrium between the number of people who die (T3) and the number of people who enter the susceptible pool (T1), net the number of people who recover (T2). We assume that under short-term harvesting, an air pollution episode would affect only transition out of the high-risk pool (T3), without increasing net recruitment into the high-risk pool (T1 T2). Therefore, for some days after an air pollution episode, the susceptible pool would be depleted, and the daily death count would be diminished. (See Schwartz (6) for further details.)
This phenomenon can be further described by a distributed lag model (79) that includes several lags of the pollution variables:
where l represents the percentage increase in mortality associated with a 10-unit increase in the air pollution level l days after an air pollution episode. Under short-term harvesting, we would expect to see an increase in deaths above the baseline level for L1 days after the air pollution episode, followed by another L2 days of decrease owing to the depletion of the pool. If the air pollution episode affected "only" the high-risk pool, as in the case considered here, the area above the baseline (the number of deaths attributable to the episode) would be roughly equal to the area below the baseline (the number of deaths necessary to replenish the high-risk pool). Figure 1 illustrates a hypothetical sinusoidal time course of lagged air pollution effects with L1 = L2 = L and with rebounds of L = 1, 3, and 7 days, respectively.
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Figure 2 shows the timescale estimates of particulate matter effects made with our approach for the three cases. We found that under a distributed lag model with l having wavelengths of 2, 6, and 14 days, we detect air pollution effects at timescales of <3.5 days, 510 days, and 1020 days, respectively. This indicates that the greatest air pollution effect occurs at the timescales determined by the true distributed lag model.
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In summary, in response to Dr. Smiths first conclusion, we interpret our figures 1 and 2 as showing a correspondence between the true time-lagged response to an air pollution event and our timescale estimates and as distinguishing short-term harvesting from other forms of time-lagged exposure-response relations with an air pollution event (such as averages of past exposures).
Is there evidence to support the existence of short-term harvesting? To address this question, we need to test the hypothesis that there exists an association between air pollution and mortality at the shortest timescales. Looking at table 1 of our manuscript (2), we have found that the pooled estimates at timescales shorter than 3.5 days are equal to 0.07 percent (95 percent confidence interval: 0.40, 0.27) for total mortality, 0.06 percent (95 percent confidence interval: 0.39, 0.51) for cardiovascular and respiratory mortality, and 0.26 (95 percent confidence interval: 0.75, 0.24) for other-causes mortality, providing evidence contrary to the hypothesis that the pollution-mortality association is largely or entirely due to short-term harvesting.
A related question is: Are air pollution effects at medium and long timescales (harvesting-resistant) smaller than the effects of air pollution at shorter timescales (harvesting-prone)? Figure 3 shows the 12 relative rates of mortality (for four cities and the three specific mortality groups) at timescales less than 5 days ( ) versus estimates calculated at timescales greater than 5 days (
). The square is placed at the weighted averages of the 12 coefficients
, with the weights being equal to the inverse of their statistical variances. The two segments represent the 95 percent confidence intervals of the weighted averages. Note that almost all of the coefficients are above the diagonal. The posterior probability that
is larger than
is 0.01, and it remains small when we average the relative rates using a random-effect model with a substantial amount of heterogeneity. In addition, this posterior probability is still very small when we choose as cutoff points timescales smaller than 3.5 days or timescales smaller than 10 days (equal to 0.006 and 0.12, respectively). In summary, this data analysis suggests that "harvesting-resistant" estimates are larger than "harvesting-prone" estimates; this is inconsistent with a phenomenon of short-term harvesting only. Note that these results are not suggesting that air pollution affects only healthy people. Rather, our results are consistent with all persons being affected by air pollution, not only the very frail.
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Thus, our timescale approach is able to detect short-term harvesting within the conceptual framework described by a compartment model with high-risk and low-risk pools of individuals. Although this is a reasonable starting point and makes the problem identifiable, the model must be a simplistic approximation of reality. Additionally, the sensitivity of the results to the degree of adjustment for confounding factors, although investigated in many sensitivity analyses, remains an issue. Because the information in time-series analyses comes from the variability across time in exposure and outcome, air pollution effects corresponding to slowly varying exposures (that is, air pollution components at timescales longer than 30 days and average past exposure of at least 30 days) are very unstable. Finally, the limited number of cities for which daily data are available further increases uncertainty. In summary, we certainly agree with Dr. Smiths general message: Results of any model of the relation between air pollution and mortality require careful interpretation, with consideration of the assumptions made and the sensitivity of the findings to those assumptions.
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ACKNOWLEDGMENTS |
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NOTES |
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REFERENCES |
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