# Contingency Table – Relative Risks (Measures of Association)

by Raywat Deonandan, PhD
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00:01 between whether or not you smoke and whether or not you get lung cancer. So in order to do this, we set up what's called a contingency table. We call it a contingency table because the outcome is contingent upon whether or not you get the exposure. Now pay close attention because the way you set up this table will determine whether or not the formulas that I show you will actually work. It is important to do it this way, where the exposure status is on the horizontal levels of the table and the outcome status is the vertical components of the table. Some textbooks will transpose that information as a way of testing you.

00:32 So if you're referring to a textbook, make sure that they set up their tables the same way that we're doing it here, otherwise the formulas won't work. As well, the positive must be the first thing, for example, whether or not you get the exposure, yes is first, no is second. Yes outcome is first, no outcome is second. It's important that this contingency table looks like your contingency table, otherwise the formulas will not work. So we're going to populate this contingency table with information. For people who smoke and get lung cancer or had a risk factor and get the outcome, we call that A. If you have the exposure and not get the outcome, let's say you're a smoker who doesn't get lung cancer, you're in category B. If you don't smoke and you still get lung cancer, you're category C. And if you don't smoke and you don't get lung cancer, we assume this is the majority of people, that's outcome or category D. Now we have a total number of people in our set, that would be N, we call the sums on the Ns of our contingency table, marginals. So some important concepts to consider, the first is absolute risk. When we talk about risk, we're talking about incidence.

01:45 You may recall that incidence is a proportion of new cases that we encounter, if I start smoking and over some time, I get lung cancer, that my experience represents a single incident case, because it's new. If I had cancer before I started smoking, it's not incident because it is already there. So the absolute risk is, if you're exposed to a factor, what's the risk that you'll get that outcome. If I'm a smoker, what's the risk that I will get lung cancer, that's the absolute risk. The relative risk on the other hand, is when I compare the absolute risk of getting the outcome if I'm a smoker, to the absolute risk of getting the outcome if I'm not a smoker. To put them in general terms, the risk of the outcome when you're exposed versus the risk of the outcome when you're not exposed, that's relative risk. We are also going to explore, in another lecture, attributable risk, that's when we try to compute how much of my outcome was actually due to the behavior that I care about, how much of the lung cancer was actually due to the smoking and not to other factors. So absolute risk again is a proportion of people with a yes outcome. There are two kinds of absolute risk, there is the absolute risk amongst those who did the behavior, in other words, those who were exposed to the exposure and again go back to our contingency table, we give that as a over a + b, the number of people who got the outcome who smoked, divided by all the people who smoked. As opposed to the absolute risk in the unexposed group, that's the number people who got the outcome, in this case lung cancer, divided by everybody who didn't smoke. Two concepts there, absolute risk in the exposed group, absolute risk in the unexposed group. Now I am summarizing it one more time, the cumulative incidence rate amongst the exposed is a over a + b. Again, that's the risk of getting the outcome if you smoked or had the behavior, absolute risk in the exposed group. The cumulative incidence rate in the unexposed group is the other side of the argument, c over c + d.

03:57 In other words, the risk of getting the outcome, lung cancer, if you didn't smoke.

04:06 So back to our table again, you see where those numbers come from. Now let us talk about the absolute risk reduction, that's how much my chances of having the outcome changed by not doing the exposure, my chances of getting lung cancer, how much did that reduce or increase when I didn't smoke. So again, the cumulative incidence rate amongst the exposed group, a over a + b, again, that's my absolute risk in my exposed group. The absolute risk in the unexposed group once again, c over c + d. The difference between the two, that's my absolute risk reduction, how much risk I had, from being exposed to smoking, minus how much risk I had when I didn't smoke, that difference tells me a lot. It tells me how much I have gained in terms of health by not doing that behavior. Now let's talk about

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

### Included Quiz Questions

1. Because the outcome is contingent upon whether or not you get the exposure
2. Because the outcome is non-contingent upon whether or not you get the exposure
3. Because it measures probability
4. Because it consider risky variables
5. Because it discovers contingent outcomes
1. To test to see frequencies of occurrence of the categories of one variable are independent of the frequencies of the categories of a second variable
2. To test to see frequencies of occurrence of the several variable categories at one time
3. To test to see frequencies of occurrence of the categories of independent variables
4. To test to see frequencies of occurrence of the categories of dependent variables
5. To test to see frequencies of occurrence of the categories of constant against variables
1. Chi-square test
2. Test of proportion
3. Z-test
4. Pearson correlation
5. Multiple regression

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