In our empirical tests, we use a model similar to the example model shown in Figure 18.2, with two primary differences: (1) we do not use the Terror Alert Level node, and (2) we use a more complex person model. Figure 18.4 shows the person model we use.
The meanings of the nodes are listed below. For each underlined variable, its conditional probability table was estimated from a training set consisting of one year's worth of ED patient data from the year 2000. The variables in boldface were estimated from U.S. Census data about the region.
4 We abuse notation somewhat by using Pi here to denote a class, whereas previously it has been used to denote an object.
The remaining variables had their respective probabilities (whether prior or conditional) assessed subjectively; these assessments were informed by the literature and by general knowledge about infectious diseases.
Time of Release: This is the hypothesized day that anthrax was released, if ever. It has the states never, today, yesterday, and day before yesterday.
Location of Release: This is the hypothesized location at which the anthrax was released, if released anywhere. It has the states: nowhere, and one state for each of about 100 zip codes being covered by the model. In the current model, we assume only a single point of release.
Home Zip: This node represents the location of the person's home zip code; it can take on one of about 100 zip codes in Allegheny County, Pennsylvania, which is the region being modeled. There is currently a "catch-all'' zip code called other that represents patients who do not live in Allegheny County, but who are seen in EDs there. In the initial prototype being described here, we make the very simplifying assumption that only individuals with a home zip code in the zip code of release will become infected with anthrax. In Section 4.5 we relax this assumption.
Age Decile: This node represents the individual's age, which can take one of 9 values: 0,1 ... 8 corresponding to (0-10 years), (10-20 years),..., (>80 years), respectively.
Gender: This represents the gender of the individual, taking values female and male.
Anthrax Infection: This node represents whether or not the individual has been infected with a respiratory anthrax infection within the past 72 hours. This node takes the following states: AAA (indicating that anthrax was absent for the past three days), AAI (indicating that within the past 24 hours the patient was infected with anthrax and still is infected), AII (indicating that the patient was infected with anthrax between 24 and 48 hours ago and is still infected now), and finally, III (indicating that the patient was infected between 48 and 72 hours ago and continues to be infected now). There are in principle four other states that this node could have (IAA, IIA, IAI, and AIA); however, we make the assumption that once a person gets anthrax, he or she maintains the disease for at least three days, so these other states have probability zero. In future work, we plan to extend the Anthrax Infection variable (as well as other temporal variables described here) to model over more than three days.
Other ED Disease: This variable is conceptually similar to Anthrax Infection, but it denotes instead some other disease or disorder, which by definition is sufficient to cause the individual to go into the ED, but is not an anthrax infection. This node has the same type of states as Anthrax Infection.
Respiratory from Anthrax: Indicates that the individual is showing respiratory symptoms (e.g., cough) due to anthrax. It has states similar to those of Anthrax Infection.
Respiratory from Other: Respiratory symptoms from ED disease other than anthrax.
Respiratory Symptoms: Node indicating whether or not the patient exhibits respiratory symptoms. It is a "logical OR'' function of Respiratory from Anthrax and Respiratory from Other.
Respiratory When Admitted: This node represents whether the person has respiratory symptoms when he or she is seen in the ED. It has states True, False, and Unknown. If the person was admitted to the ED today, then we typically know whether the value is True or False; otherwise the value is Unknown. For those patients admitted to the ED, the value of this variable is based on a patient's chief complaint as given to the triage nurse in the ED.
ED Admit from Anthrax: Indicates that the person was admitted to the ED due an anthrax infection.
ED Admit from Other: Indicates that the person was admitted to the ED due to a disease other than an anthrax infection.
ED Admission: Indicates the day (if any) that the person was admitted to the ED within the past 72 hours. It is a "logical OR'' function of ED Admit from Anthrax and ED Admit from Other. We currently do not model the possibility that a person could be admitted more than once. To do so, the de-identified data that we receive on each patient could be extended to include a unique integer for the patient that does not reveal the patient's personal identity.
We emphasize that the current model, which is presented here for illustration, is an initial prototype, which we are refining and extending.
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