Friday, December 3, 2010

Magnitudes? We don't need no stinking magnitudes!

Have you noticed how few people think in any meaningful sense about how large different health risks are? People will know that 'smoking causes cancer' and 'living near power lines causes cancer' and 'eating burnt steak causes cancer'. But they will barely have even a hazy idea about how much the risks of each one is, and probably avoid all three. In reality, they're not even close - you're better off giving up smoking, but not sweating the steak and power lines.

The truth is that magnitudes are hard, so people just don't bother, even though they're really important. Directions are easy, but not actually very useful.

To illustrate, let me give you a range of different statements of different levels of usefulness.

0. 'Smoking is bad'

1. 'Smoking causes lung cancer'

2. 'Smoking increases the risk of lung cancer'

3. 'Smoking is associated with an increased risk of lung cancer'

4. 'Smoking is associated with a ten to twenty times as high chance of developing lung cancer'

5. 'Smoking is associated with a ten to twenty times as high chance of developing lung cancer, the death rate from lung cancer in the male population is around 80 per 100,000, the percentage of males in the US who smoke is 23.1 %, so your chances of dying of lung cancer if male lie between 15 per 100,000 and 26 per 100,000 if you don't smoke, versus between 260 per 100,000 and 297 per 100,000 if you do smoke'

6. 'Smoking is associated with ... [as before] for overweight versus normal weight people, for young vs. old people, for white/black/hispanic/men/women ... '

My hunch is that most people think about things in terms of 1. So let's analyze all the ways that people screw this up.

The difference between 0 and 1 is whether you have any understanding of the actual problem, or just arguing from authority. We can safely skip that one.

The difference between 1 and 2 is about statistics. The first one implies that Smoking = Lung Cancer. It's not clear, but I think people have in mind that smoking is a sufficient condition for eventually getting lung cancer. It's not, and that's a big deal. A bullet to the brain causes death in a very different way than smoking causes lung cancer.

The difference between 2 and 3 is quite well remarked on, as it's the correlation/causation problem. 2 may be right, but 3 is the correct description of what the statistics alone tell us. Still, the causal link with smoking is pretty well established, so I don't quibble with it here.

3 to 4 is the first question of magnitudes. I submit that for the majority of illnesses and risk factors, people have no idea how important various risk factors are. And it's really damn important. Because things that increase risk by a trivial amount probably aren't worth worrying about. (I say 'probably' -we'll return to this in a second). This is the level of information you get from the CDC, the guys who you'd expect to be right on top of things, and not to belittle them, it's important to know. I haven't looked for the burnt steak numbers, but I'm betting they're a lot lower.

4 to 5 tells you how prevalent the disease really is. And this matters a lot in terms of whether you should make real lifestyle changes. Because people care mainly about the actual chance of dying, not about relative changes in the changes of dying. Big percentage changes in things that are very unlikely to begin with don't have much impact. But even small percentage changes in very frequent risks can be worth it. So being 10 to 20 times more likely to acquire lung cancer (~80 per 100,000) is more important than being 10 to 20 times more likely to acquire stomach cancer (~5 per 100,000). When things are quite frequent (heart disease, car crashes) smaller changes get even more significant. Bear in mind the CDC doesn't tell me this - I had to calculate those numbers myself. If anything, I think that these numbers don't look very large, and that's part of the reason the CDC doesn't push them - even if I smoke, the chances of it actually killing me are apparently only 0.3%! Put that way, it doesn't seem like a big deal. Now, this doesn't give me all the information I need (how long did I smoke, what age am I etc.). But it's damn hard to say that this isn't actually relevant.

Finally 5 to 6 tells you how much the effects vary across demographics. It's highly unlikely that every group in society has a 10-20 times higher chance of lung cancer from smoking. And if there's differential impacts, you'd like to know whether it's worth it for you to give up smoking, not for the average person.

The reality is that you need a hell of a lot more information than 'smoking causes cancer' to conclude that it's worth it to give up smoking based on the cancer risk. As Gary Becker put it - it also depends how much you like smoking! And at a bare minimum, it's ridiculous to place the same importance on all risk factors without considering the actual risk they pose.

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