## Tuesday, June 11, 2013

### Transitivity, bicycle helmets and teleoanalysis

I've mentioned before on this blog that I get annoyed when people link A to B and B to C and then proceed to assume that the relationship between A and C is just the average/sum/etc of the first two.  In pure mathematics, the technical term for this is transitivity and it tends to be pretty valid.

I learned recently that there is actually a term for this when applied to epidemiology research: teleoanalysis.  Developed in the realm of public health, it's defined as
the synthesis of different categories of evidence to obtain a quantitative general summary of (a) the relation between a cause of a disease and the risk of the disease and (b) the extent to which the disease can be prevented.
It has also been criticized, in large part because it was invented to help support pre-existing assumptions.  Both papers I linked to reference the "does cutting back on saturated fat actually prevent heart disease" controversy as an example.

I was thinking of this recently when reader Dubbahdee sent me this article about bicycle helmet laws.  The issue follows the same formula as above:

A. Bicycle helmets protect cyclists
B. Mandatory helmet laws increase the number of cyclists who wear helmets

Therefore:

C. Bicycle helmet laws save lives

What's interesting is it appears this is not the case.  The paper's authors suggest that increased helmet laws decrease bike ridership, and apparently having lots of bicyclists in an area makes it safer for cyclists in general.  Also, helmet laws seem to potentially inoculate lawmakers against making any bigger changes...the sort that actually help cyclist safety (infrastructure building, etc).

I thought this was interesting because it's absolutely proven that you as an individual should wear a helmet, but the conclusions drawn from that weren't valid.  Someone out there guaranteed that these helmet laws would save x number of lives, and they were wrong.

1. There's lots of examples of the invalidity of teleoanalysis:

Living in New York City is correlated with working on Wall Street and also voting for far-left loonies. Obviously Wall Street is a hotbed of Marxism.

Owning your own home is correlated living in Mississippi or West Virginia and also with being relatively wealthy. Obviously Mississippi and West Virginia must be very rich.

Buying organic food is correlated with having graduated from college which in turn is correlated with supporting nuclear energy. Obviously, organic food stores are an ideal place to collect signatures for a pro-nuclear petition.

Walking to work is correlated with shorter commute times which in turn are correlated with faster transportation. Cars only slow you down.

2. I just remembered an example how transitivity can fail in pure mathematics: "things greater than the same are greater than one another." in Sylvie and Bruno by Lewis Carroll.

3. These slippery equations used to come up in programs for behavioral improvement of high school students. Does drug education actually reduce use, or make use of some drugs seem more normative? Does condom-encouragement increase the number of sexual partners?

My recollection, when I last checked over a decade ago, was that neither side had good numbers, just an assurance that their reading of the tea leaves was correct.

4. See! This is why I love your blog. Before, I just thought the article was about the difference between correlation and causation, a la Joseph.

Now I have learned that it is actually about transitivity and teleoanalysis. That is just about more fun than a human should have on a Friday afternoon.

Can't wait to use these in a sentence. Ideally, both in the same sentence. Woohoo!