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Bayes’ Theorem in the Current Ebola Outbreak

http://www.globalresearch.ca/ebola-in-the-united-states-the-probability-of-fraud/5408066

The article above is written by Associate Professor Dr. Jason Kissner of California State University about the Ebola outbreak. Claims are made that U.S. government is lying about important aspects regarding the outbreak. Two main arguments result from the article: the idea that the current strain of Ebola involved in the outbreak is more dangerous than the U.S. government admits due to the potential to be more readily aerosolized. The second argument is that the current outbreak in the U.S. is from a sponsored bioterror attack. Thus, it advice is given to be wary and suspect fraud regarding the current events of the outbreak.

This may seem unrelated to Networks, however in discussion of the second argument, the author brings up nurse Pham’s scenario and involves Bayes’ Theorem to offer some “compelling” “probabilistic reasons” to suspect that at least some features of the outbreak are fraudulent. Recapping the scenario, the CDC claims that Pham was infected due to a breach of protocol, however the specific breach is not given. Pham was given a blood transfusion by an Ebola survivor and her condition was upgraded to “good”. None of Duncan’s (the initial case in Dallas bringing Ebola to the United States) contacts were infected. Formally, the only evidence given to the public that Pham was infected with Ebola was a positive Ebola test result.

After the recap, the probability is examined. Is the positive test result important or is it meaningless? The author acknowledges that the probability of a false-positive is very low without the information about the probability that Pham was in a position to contract the disease, however the author argues that the test result can be extremely misleading to the point where it may, in fact, be more likely to be wrong that right. The author further explains by giving an example scenario:

“Suppose that in a population of 10,000 people only 10 [0.1%] have Ebola.  If only 1% of cases produce a false positive under this supposition, 100 cases will test positive that do not in fact have the disease.  So, even if the Ebola test used on Pham correctly identifies 100% of the true positive cases, the 10 positive cases correctly identified would be overwhelmed by the 100 false positives, such that a positive test result would yield only a 10/100, or 10% chance of Ebola infection.”

Thus, it is extremely important to note the relevant prior population and associated probability.

To write this out in the form of Bayes’ theorem

1

With A being the event that a person has Ebola and B being the event that the test returns positive. This can be rewritten as:

2

Plugging in the numbers from the scenario one gets:

3

Since the only information given was that a positive test result was returned, the positive test result may not hold as much meaning as one would think since the false-positive rate is not known. Thus without any information on how Pham was infected, a lot is reliant on probability and the question of false positive comes up. If she had no exposure to Duncan, her result would hold no meaning. A friend of Pham’s reported that she only had contact with him at one point in time. Thus, the probability that Pham was infected seems shaky especially given the fact that many of Duncan’s other contacts in his U.S. apartment (nor any of the other 70 health care workers exposed to him) did not develop Ebola infections.

While the article itself takes a very accusatory tone, it offers some interesting insights to an important upcoming issue using the skills learned in class.

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