09 January 2011

Mental illness, crime, and statistics

There was a tragedy yesterday. Because of the perpetrator's YouTube page and reports from people who knew him, the call is going out that he is "mentally disturbed," thus we have our explanation for the shooting. (Assuming you claim that national partisanship also had something to do with it.)

Not so fast warns Vaughan Bell at Slate, taking the misuse of statistics to new heights. He cites a meta-analysis of people with schizophrenia and/or bipolar disorder and concludes, "it's likely that some of the people in your local bar are at greater risk of committing murder than your average person with mental illness." Leaving aside the bizarre semantic construction of people being "at risk" to commit an act, what he says is half-true, but only because he's answering an unimportant question.

When I am trying to determine whether the patient in my exam room may have a coccidioidomycosis infection I do not look at the national prevalence of Valley Fever and conclude that it's very unlikely he does. I have to take into account not only where the exam is being conducted, but where the person is from, what his job and hobbies are and so on. If I used broad, national statistics I would never put Cocci at the top of my differential no matter how well his symptoms match up; however, if I am seeing a farm laborer in the San Joaquin valley, where the incidence of Cocci infections is substantially higher, it's definitely moving up my differential.

Okay, so what is the right question to ask? Well, let us start by looking at those people who have committed a crime (even a violent one). From the American Journal of Psychiatry:
Relative to the comparison subjects, the patients with schizophrenia accumulated a greater total number of criminal convictions (8,791 versus 1,119) and were significantly more likely to have been convicted of a criminal offense (21.6% versus 7.8%) and of an offense involving violence (8.2% versus 1.8%).
Indeed, I'm only giving you a citation for schizophrenia, but the data is there for other disorders if you want to dig it up, I have better things to do. The question is not, "How many people with X commit act A?" The question we need to be asking is, "How many people who commit act A have condition X?"

Mr. Bell begins his closing paragraph by saying, "The fact that mental illness is so often used to explain violent acts despite the evidence to the contrary almost certainly flows from how such cases are handled in the media." Penning this sentence he ought to have realized the flaw in his article: mental illness frequently explaining violent acts is not at all what he debunked. He debunked that the mentally ill frequently commit crime. However, this is categorically different than debunking that violent crime is more frequently committed by the mentally ill.

This is why his closing is so rife with irony, "With this constant misrepresentation, it's not surprising that the public sees mental illness as an easy explanation for heartbreaking events." Misrepresentation indeed.

Update: 1/9/11 7:35 PM MST: Let me try an analogy to explain this since I didn't do a sufficient job initially. Let us imagine a hypothetical world in which Boeing airplanes crash only 1 out of every 150,000,000 (150 million) flights. There are 150,000 commercial flights in the US every day so this would mean that, on average, a Boeing airplane will crash only every 1 thousand days (2.74 years). This seems safe, no?

What if I next told you that among planes that did crash, Boeing accounted for a disproportionate number of them? Imagine Boeing accounts for 25% of all planes in service, but that their planes represent 50% of all crashes. Would Boeing planes now seem exceedingly safe? Absolutely not, as their crash rate is substantially higher than that of other plane manufacturers.

This is the same conflation that Mr Bell has made and it's a very insidious one because it's not intuitive to pick up on. Just because mentally ill individuals are unlikely to commit a violent crime (as are all people) does not mean that they do not represent a disproportionate number of those who do commit a violent crime.

The two statistics may sound interchangeable, but they are not.

1 comment:

  1. Good on you, mate. Well said (your update helps put it succinctly).