Tuesday, April 13, 2010

Reading the statistics - relative risk

Over at Devil's Kitchen the drink driving debate has once again arisen. Before you read what's there let me hit you with a statistic: In 2008 there were 430 fatalities caused by drink drivers; but there were 2,538 overall. That means by definition 2,108 were caused by sober drivers. So why are we trying to ban drink driving when it's the sober drivers causing 5 times as many deaths?

Because they're not.

What that statistic tells us is that of those involved in a road accident that resulted in a death 5 times as many drivers were sober as drunk; and that's all it tells us.

For those going "Huh?" Let me present a simple example. Take 1,000 drivers and make them drive around a set course; 950 are sober, 50 are legally 'drunk'. So they drive around and at the end of a set period we have had 150 crashes (pretend deaths). 125 involved only sober drivers, 25 involved drunk ones. So again 5 times as many sober as drunk, correct?

Except now we have totals too. 125 sober drivers out of 950 and 25 drunk drivers out of 50; that's 13% and 50%. By that example we can say that drink driving has a definite influence on accidents.

Now read DK's piece and check out the graph he provides taken from an official report. Ignore the inconsistency between text and graph title and concentrate on the graph. This is measuring relative risk.

Relative risk is a simple concept you take a base risk and set it to 1 then assess other risks based on that. So back to my simple example if this time I had 100 sober drivers and they had 10 accidents that 10 would become a 1. If I had 100 drunk drivers and they had 20 accidents then that becomes a 2.

So in this simple example it's an easy way of saying that drinking is twice as risky as being sober when it comes to driving. Everyone happy with that?

Well no, go back to the original and very real statistics that show 5 times as many sober caused deaths as drunk ones and recall this only makes sense when you know how many of each type are actually driving. Tie that to relative risk and you see you can only assess this when you have those figures.

Which we don't have. Oh we can estimate it though. Set up a road block and breathalyser and test everyone who comes through, repeat that up and down the country and use some more statistical tools and you can get an estimate of the proportions of each type. So how many people on the roads at one time... um we don't know, but we can estimate it.

So we're splitting an estimated total, by various estimated percentages to derive a relative risk factor that is being used to set policy.

Well it wouldn't be the first time and I doubt it will be the last.

So one more point but not quite about statistics. Drinking doesn't kill people! It's the impairment in reflexes that creates the accidents. As you drive you're constantly correcting for minor deviations in the road, when drunk you don't react as quickly and then overcompensate causing the erratic driving. Likewise you won't stop at the same speed as you would when non-impaired.

Logically therefore we should be looking at the impairment as the cause and only incidentally at what created it. So drinking causes impairment, ban it. Using a mobile phone while driving causes impairment by distraction, ban it. Except other distractions count to; squabbling children in the back seat, ban them; talkative passengers, ban them; CD/Radio players in the car, ban them.

Imagine a young athlete, a sprinter, with excellent reflexes. Now imagine an nonagenarian. I don't think anyone would disagree that the former would have faster reflexes than the latter; however if we don't test for reflexes, but simply ban the causes of impairment the sprinter could be technically 'drunk' and illegal to drive yet still be able to react faster than the nonagenarian who is sober and legally driving.

I've always said you should look at causes and not symptoms, but sometimes they can be hidden.