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Authoritative statistical innumeracy

June 4, 2012

or why the Boston Globe really ought to do a cursory amount of fact-checking.

This article recounts the issue of deciding whether to get (expensive) rabies shots after a bat got into a house, and quotes a nurse as claiming that the risk of a rabies exposure in that situation was one in 400 million.

This reply asserts that this is an example of how risk intolerance raises medical costs, and also makes that claim that the drive to the hospital for the shots was riskier than the bat exposure.

It would be a gosh-darn shame if two articles took a bogus statistic for granted to make conclusions (really, to support pre-existing opinions) about our health care system and medical costs, wouldn’t it? If only we had a network of computers and data banks where we could look these things up and check them.So: “From 1990 through 2000, bat RABV variants have emerged as the predominant cause of human rabies in the United States. In the past 11 years, total human rabies deaths have averaged 2.9/year, and 24 (75%) of 32 deaths were due to bat RABV variants.”

And: “Only 2 (8%) of the 24 patients with human rabies caused by bat RABV variants had a definitive history of a bat bite. Nine patients (38%) had a history of direct physical contact with bats, 5 (21%) had a history of a bat inside the living area, and 8 (33%) had no history of proximity to bats (4).”

The one in 400 million figure is completely nuts. For the entire population, every year about 2 people contract rabies (somehow) from a bat. Not “are exposed to rabies”, but actually proceed to the disease and die. In a population of 300 million, that means the risk of death (not exposure) from bat-borne rabies is 1 in 150 million. But wait, there’s more! Most people do not have bats inside their homes. The question here is not “what’s the chance the I’ll die from a rabies-infected bat?”, but “what’s the chance that having a bat in my house exposes me to rabies (that will kill me if I am not vaccinated)?” The population is much smaller, and the event (exposure, not death) is much larger. But what are the ratios? There may be some animal control departments that collect this data, but I couldn’t find them. If we assume 1 home in a hundred, per year, then the population is 100 times smaller, and the risk 100 times larger. The ratio of exposures to deaths is also unclear; if it’s 10-to-1, then the risk is also 10 times larger.

But, aha, there is some data from which we can estimate. “Between 20,000 and 40,000 people in the U.S. receive the rabies vaccine each year, usually after being bitten by an animal” and “Bat bites, which typically occur when a person finds a bat in his home and tries to shoo it out, are responsible for 80% of cases in which the vaccine is given”. If we call it bat-in-home 30,000 vaccinations per year, then one person in 1 in 10,000 receives the rabies vaccine each year because of a bat in their home. Another way of gauging the risk is to consider how many people had a bat in their house, but did not receive the vaccine. For that population, exposure=death, and we know that at least between .4 (history of bat in house, 21% of 2) person per year is exposed. If 1% of the people who report having a bat in their home proceed to being vaccinated, then we know that (1) 1% of the homes in the US have a bat in the living area each year, and know it, and (2) the unvaccinated shared-home-with-bat population of 3,000,000 (100 times 30,000) had .4 exposure (death) per year, or a risk of 1 in 7.5 million. If, on the other hand, 10% of the people who report a bat in their home receive the vaccine, then the risk is 1 in 750,000, and only 1 home in 1000 has a (known) bat in its living area.

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