Of course, most gamblers do not have the training (or the inclination) to apply the principle of maximum expected utility in such a formal manner. Part of the reason is that, in most games, the prize is the same (money) and its interaction with probability of winning is relatively simple. However, there are many real-world games of chance in which the prizes are far more complex. The prizes may be denominated in lives saved or lost, economic loss, and disruption to a city. Each prize can involve a mixture of lives saved or lost, money, and disruption. In these situations, decision makers often turn to professionals who have the training to assist with such decisions.
In this section, we present an analysis of the decision to issue a boil-water advisory or to wait for the results of definitive testing. We use this example to explain the process of decision analysis. Note that, our example decision analysis is similar but not identical to the decision problem faced by the IMT in Glasgow. The IMT was faced with evidence of contamination of the water. In our example, the decision maker is faced with early evidence of an outbreak of cryp-tosporidiosis in people—evidence that is suggestive but not conclusive of an outbreak. In particular, the decision maker is confronted with an increase in sales of diarrhea remedies (Figure 29.1). We analyze a decision problem related to the Glasgow incident, but to simplify the analysis, we consider a variant in which the evidence of a potential health threat comes from sales of diarrhea remedies instead of water quality. Our research group conducted a decision analysis of this particular situation, hence, it is available to present as an example (Wagner et al., 2005).
We considered the Chicago metropolitan area to make our study concrete. We chose Chicago because we had previously studied detectability of Cryptosporidium outbreaks from sales of diarrhea remedies in Chicago. Chicago is served by two water treatment plants, and we assumed that each treatment plant serves half of the city. We model the situation in which there is a biosurveillance system that analyzes the sales data for the area served by one of the plants. Every day, the biosurveillance system determines whether the level of sales exceeds a threshold and, if so, alerts the biosurveillance staff. The staff then faces a decision to act now (issue a boil-water advisory) or wait for the results of definitive testing of individuals with diarrhea or definitive testing of the water.
Our example is representative of many decisions health departments face as a result of increased monitoring of time-series data to achieve earlier detection of outbreaks. This example, incidentally, is the only decision analysis of a biosurveillance decision that exists, to our knowledge.
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