figure 18.8 The rotating rectangular regions centered at (for example) the centroid of zip code 15213 that are used to determine if a person is exposed to anthrax.

figure 18.8 The rotating rectangular regions centered at (for example) the centroid of zip code 15213 that are used to determine if a person is exposed to anthrax.

the zip code of the home location of the person, the location of the release, and the angle of the release. The spatial model assigns a probability of 1.0 for Exposed to Anthrax to anyone who has the same home zip code as the zip code of the hypothesized anthrax release, regardless of the angle of release. For people outside of the release zip code, we consider them to be potentially exposed to anthrax if their home zip code is within a rectangular region that originates at the cen-troid of the hypothesized release zip code and is oriented according to the angle of the release variable. As an example, suppose the release occurs in 15213. The two small circles in Figure 18.8 represent zip code centroids. The circle in the center of the figure is for zip code 15213. The circle in the bottom right is for zip code 15132. There are eight rectangular regions centered at the centroid of zip code 15213. If a person has a home zip in 15132, and the angle of release is SE, then we would consider that person to be potentially exposed to anthrax. The actual probability of being exposed to anthrax is computed by decaying the value 1.0 by a half for every three miles of distance between the release zip code's centroid and the person's home zip code centroid. The distance of three miles was obtained by manually tuning the model over data sets produced by the simulator; these data sets were distinct from the data sets that we used to evaluate PANDA. The width of the rectangle is set to be approximately three miles, which was chosen by calculating the average area per zip code in Allegheny County, determining the diameter of a circle with this average area, and then assigning that diameter as the width. The length of the rectangle is assumed to extend to infinity, as shown by the arrows in Figure 18.8.

figure 18.9 The person model modified to incorporate spatial information.

Figure 18.10 illustrates another variation on the spatial model, which we will call the spatial model with temporal fluctuation nodes. This version of the spatial model contains three additional nodes for Season, Day of Week, and Time of Day, which are intended to capture the fluctuations in the number of ED cases due to these three factors. The Season node takes on the values of Spring, Summer, Fall, or Winter. The Day of Week node can be assigned one of the possible seven names of the day of the week. We allow the Time of Day node to have three possible discrete values of 12:00 midnight to 8:00 am, 8:00 am to 4:00 pm, and 4:00 pm to 12:00 midnight.

We evaluated both spatial models over the 96 simulated test data sets for the 1.0 concentration that were previously used. The false-positive rate was measured over the period of January 4, 2002 until the start of the simulated release for the particular data set. The results are shown in Figure 18.11. Adding spatial information improves the detection time significantly. Adding the temporal fluctuation nodes in addition to the spatial information produces only a slight improvement over the spatial model. The largest difference in detection time between the nonspatial and either of the spatial models is approximately 9.7 hours. The maximum widths of the 95% confidence intervals for the nonspatial, spatial, and spatial with temporal fluctuation nodes models are ± 1.64,1.68, and 1.65 hours, respectively.

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