# The Ratios of Risk With a Zip!

With summer here, I think it’s time that we continued our discussion on risk. No, I’m not talking about the dangers of your favourite adventure sport… but then I just got back from a trip to Costa Rica as part of the Canadian delegation for the Gateway to Trade  project and I, of course, went ziplining! Awesome.

It’s been a few months so I recommend catching up on Risky Business – Is it all Relative? and Happy New Year and Enjoy some AR&R

Before we get started I want to introduce a student of mine, Indranil Balki, who has agreed to come aboard and help me write this blog. Life is busy for me and I feel bad that I can’t post as much as I would like. So look to find Indranil signing off with me at the bottom of these posts.

When we last left off, we were interested in the idea of comparing risks – how many times more likely is it for a smartphone user to develop smartphone thumb than for a non-smartphone user?

We touched on one way to compare the two groups in the last post, by finding the risk difference A/(A+B) – C/(C+D). But to answer our question, we need a ratio. It turns out that this is called (helpfully) a risk ratio, or relative risk (RR). The RR is given by A/(A+B) divided by C/(C+D). A RR basically compares the risk in the exposed (smartphone owners) and unexposed conditions.

For example, let’s say that 20% of smartphone users developed smartphone thumb and 10% of non-smartphone users developed smartphone thump. Then the RR is 2, meaning that you are twice as likely to get the disease if you own a smartphone than if you don’t.

Well wasn’t that an elegant way to compare the risks between two groups? As you might have guessed, a RR of 1 shows no difference in risk between the groups, and an RR > 2 or <0.5 is usually considered statistically significant.

So let’s say you meet a friend at school and he finally reveals that he has smartphone thumb (don’t worry, it’s not contagious – I think!). Since you’ve been following this blog, you immediately wonder, what’s the probability that he has a smartphone? To answer this reverse question, it turns out that you technically need what is called an odds ratio (OR). The OR is comparable to the RR if the prevalence of the disease is low. But it is a slightly different way to compare risks.

Given that you have smartphone thumb, the odds that you had the exposure are given by the probability that you had a smartphone (A/A+C), divided by the probably that you didn’t have it (C/A+C). This simplifies to A/C. Similarly, the odds of exposure in those without smartphone thumb is B/D. The odds ratio then, is calculated by dividing these 2 odds. OR = A/C ÷ B/D. An OR of, say 3, tells us that there’s a 3 times higher chance your friend has a smartphone than he doesn’t.

Well, that might have been a tough post! Take some time to think about it, have a gander at some ziplining in Costa Rica here and don’t spend too much time on your smartphone…

See you in the blogosphere,

Indranil Balki and Pascal Tyrrell