Response to Dr. Smith: Timescale-dependent Mortality Effects of Air Pollution

Abstract

Time-series studies have indicated that there is an association between day-to-day variation in ambient air pollution concentrations and day-to-day variation in numbers of deaths, after data are controlled for more slowly varying confounding factors such as weather, seasonality, and longterm trends. However, the estimated coefficients in the timeseries studies are uninformative as to the amount of life lost due to pollution exposure, particularly within susceptible populations (1). 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 (4–6) 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: lowrisk 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 (7–9) that includes several lags of the pollution variables: