Consider healthcare utilization records in which respiratory symptoms are a part of the recorded chief complaint. This is an example of an important data stream to monitor because there are several severe outbreak diseases, such as anthrax, which might be revealed by a blip in respiratory cases. It is also an interesting data stream to model because, even without any abnormal outbreak, respiratory cases vary considerably throughout the year and between years, according to the timing, severity and length of the annual influenza outbreak. In order to simulate such data we begin with a smoothly varying (and entirely fictitious) level of influenza in the population over a three-year period, shown in Figure 14.3.
Sadly, real healthcare utilization data rarely looks so smooth. This is partly because counts of physician and emergency department cases are drawn from a small population of people sufficiently ill to seek health care. On any given day, the expected count of people sick enough to decide to seek medical attention varies according to the smooth count. But the actual count will have random variation. One reasonable way to simulate the actual counts is to draw them from a Poisson distribution with mean proportional to expected count (why this is reasonable is a technical detail that we will not pursue any further here). When we simulate counts of people wishing to utilize health-care services, we get Figure 14.4.
For many sources of data, Figure 14.4 is, unfortunately, not the end of the story. For a variety of reasons, the actual number of healthcare visits is affected by the day of the week. For example, on the weekend, and particularly on Sundays, patients are more likely to wait until early the following week to seek care. Holidays, such as Thanksgiving and July 4th, have a similar effect. When these effects are simulated, we see the data in Figure 14.5.
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