State-space modeling of the relationship between air quality and mortality.

A portion of a population is assumed to be at risk, with the mortality hazard varying with atmospheric conditions including total suspended particulates (TSP). This at-risk population is not observed and the hazard function is unknown; we wish to estimate these from mortality count and atmospheric variables. Consideration of population dynamics leads to a state-space representation, allowing the Kalman Filter (KF) to be used for estimation. A harvesting effect is thus implied; high mortality is followed by lower mortality until the population is replenished by new arrivals. The model is applied to daily data for Philadelphia, PA, 1973-1990. The estimated hazard function rises with the level of TSP and at extremes of temperature and also reflects a positive interaction between TSP and temperature. The estimated at-risk population averages about 480 and varies seasonally. We find that lags of TSP are statistically significant, but the presence of negative coefficients suggests their role may be partially statistical rather than biological. In the population dynamics framework, the natural metric for health damage from air pollution is its impact on life expectancy. The range of hazard rates over the sample period is 0.07 to 0.085, corresponding to life expectancies of 14.3 and 11.8 days, respectively.