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Modifications of BME Analysis 193

EXAMPLE 9.15: Participate matter has been associated with public health risks
by a number of authors (e.g., Anderson et al, 1992; USEPA, 1996; 1997).
These risks are associated mainly with paniculate matter of aerodynamic par-
ticle size of lOfim or smaller. The PMio is a possible confounding factor, since
it may have a causal association with death rate, while being correlated with
temperature data. The PMio data were obtained from the Aerometric Infor-
mation Retrieval System (AIRS) of the USEPA (U.S. Environmental Protection
Agency). The data used in this study were collected at 47 monitoring stations
located throughout the State of North Carolina (Fig. 9.12). Also shown in
3
Figure 9.12 are the contour lines of PMio concentration (in /^g/m ), e.g., for
August 31, 1995. In order to assess the confounding effect of PMio, we define
the PEP parameter /3 DXp = (EDXP - E DP)/E D, where E DXp is the mor-
tality prediction error using temperature exposure, PMio, and death-rate data,
while EDP is the prediction error using only death-rate and PM 10 data. As be-
fore, the D(s, t), X(s, t), and P(s, t) represent death-rate, cold temperature
exposure, and PMio distributions, respectively.

Figure 9.12. Locations of the 47 North Carolina monitoring stations for PMio
data (circles). Also shown are the contour lines of PMio concentration
3
(in /xg/m ) for August 31, 1995.

Including PMio in the analysis resulted in a total of six covariance and
cross-covariance models (as compared to only three covariance models used
in Example 9.14). All six covariance and cross-covariance models were spa-
tially isotropic and temporally stationary (Christakos and Serre, 2000a). The
physical variables (temperature exposure and PMio distributions) exhibited
considerably larger spatial correlation ranges than the death-rate distribution.
The spatiotemporal distributions of exposure to cold temperature X and of
PMio concentrations P were found to be negatively correlated (i.e., as the
temperature T drops, the exposure to cold temperature X increases and the
concentration P decreases). Moreover, exposure to colder temperatures and