# Relative Risk – Relative Risks (Measures of Association)

by Raywat Deonandan, PhD
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00:00 much I have gained in terms of health by not doing that behavior. Now let's talk about relative risk. Relative risk is the granddaddy of them all, it's what we always care about the most, it's what would public health officials really rely upon a lot to make decisions about what kinds of behaviors to tackle. So back to our contingency table again, the relative risk is going to be the proportion of our absolute risk in the exposed group over our absolute risk in the unexposed group. Again these terms sound very similar, that's why I want you to be very careful and always refer back to the contingency table because that will help keep it straight in your mind. So again, the cumulative incidence rate in the exposed group, again the incidence of getting lung cancer or the outcome if you do the deed, if you do the exposure, if you smoke, that's a over a + b. The cumulative incidence rate in the unexposed group, again the probability of getting the outcome of lung cancer if you don't smoke, is c over c + d, we've covered that already, those are absolute risks in both categories. If I divide those two I get a relative risk. The incidence rate in the first group divided by the incidence rate in the second group. Now you may recall when we talked about cohort designs versus case-control designs, that we can only compute incidence rate in a cohort design. We can also compute incidence rates in a randomized controlled trial. But in the world of observational study, only in cohort studies can we compute incidence rates. So when I'm talking about relative risks and absolute risks, I'm only talking about cohort studies. Case-control studies we cannot compute relative risks, because we cannot compute incidence rates. To do so, to give a sense of risk in a case-control scenario, we're going to compute something different called an odds ratio and we will tackle that in another lecture.

01:51 Now let’s talk about an example, let's say we have a cohort study, and again a cohort study allows us to compute incidence, because a cohort study is, you may recall, begins by ascertaining exposure status and waiting to see if the outcome manifests. Do you remember that? If you don't, I hope you review it. I'll say it again, a cohort study begins by ascertaining exposure status and waiting until the outcome manifests. So this particular cohort study follows 100 smokers and 100 non-smokers over a ten year period to see which group end up with more lung cancer, straight forward, classic observational cohort study. Let's look at their data. So let's set up a contingency table again, exactly the way that we were doing it every step of the way with our exposure status horizontally and our outcome status vertically. So 75 individuals smoked and got lung cancer, 25 individuals smoked but did not get lung cancer that constitutes 100 of my smokers. Amongst my non-smokers now, 10 people did not smoke and they still got lung cancer, that's an important consideration, something that the lay person often forgets, it's possible to ge the disease, to get the outcome even if you did everything right, because that's the nature of the world. But in this case, in our hypothetical sample, 10 people didn't smoke and they still got lung cancer. That means that 90 of my 100 non-smokers didn't smoke and did not get lung cancer, okay. So I add up all my totals and my marginals and I get these numbers.

03:28 Now my relative risk is going to be the incidence rate in my exposed group divided by the incidence rate in my unexposed group, in other words, the absolute risk in my exposed group divided by the absolute risk in my unexposed group and I get this numbers, 7.5. Is that big? That's a big number, 7.5 we consider to be a very large relative risk, it means that your risk of getting lung cancer if you smoked is 7.5 times more so than if you didn't smoke.

04:00 If it had been one, if the number had been one, that would mean that the risk is equivalent and there is nothing to be said for that, maybe we conclude then that smoking has no relationship with lung cancer, but 7.5 is extraordinarily high. My absolute risk reduction you may recall, is the difference in those two incidence rates. That's exactly when I get 0.65. What does that tell me? It tells me that if I didn't smoke, I can reduce my rate of getting lung cancer by 65%, which is extraordinary. So those two ideas, relative risk and absolute risk reduction give me two separate nuances of information that together, form a comprehensive whole about the power of smoking and causing lung cancer or being associated with lung cancer. Now there is something called relative risk reduction, this is the proportion of baseline risk that is reduced through non-exposure, what does that mean? It means if I don't smoke how much less lung cancer can I expect in the population? It's given by this formula. A relative risk reduction is the absolute risk reduction divided by the incidence rate in the unexposed group. Let's look at an example again. Here is my contingency table and here we have the same example again. We have 100 smokers, 100 non-smokers being followed for 10 years and we see again an absolute incidence rate or absolute risk in the exposed group and absolute risk in the unexposed group. Here are my numbers, same as the previous example, now let's compute my relative risk reduction, that's going to be the absolute risk reduction divided by the incidence rate in the unexposed group, we've done that math already, it's 6.5. What does that mean? It means, by avoiding smoking, reduce the relative risk of lung cancer by 650%, extraordinary.

### About the Lecture

The lecture Relative Risk – Relative Risks (Measures of Association) by Raywat Deonandan, PhD is from the course Measures of Association.

### Included Quiz Questions

1. 0.96
2. 1.04
3. 0.80
4. 0.77
1. E is protective of O (i.e., being exposed to E lessens one's probability of getting O).
2. Those exposed to E have 0.72 times the risk of getting O than do those who have not been exposed to E.
3. E is associated with O (i.e., exposure to E heightens the probability of getting O).
1. 5, 0.20
2. 0.20, 5
3. 5, 5
4. 0.20, 0.20
5. 5.20, 0.5

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