# Attributable Risk – Attributable Risk and Odds Ratio (Measures of Association)

by Raywat Deonandan, PhD

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00:00 So, before we talk about relative risk, relative risk is one of the most important measurements of associating a risky behavior or exposure to an outcome, like a disease.

00:14 But now we’re gonna talk about attributable risks.

00:16 There are two kinds of a attributable risks that we’re gonna learn about.

00:19 Now remembers, some non-smokers also get lung cancer and some people who smoke don’t get lung cancer.

00:26 The question is always how much of the behavior can we attribute to the outcome and how much of the outcome can we attribute to the behavior? That’s what we’ll talk about, attributable risk, sometimes called, excess risk, in other words, how much risk in excess of the baseline does a certain behavior offer? Now, we always go back to our contingency table.

00:49 Setting up the contingency table is really important when doing the calculations that I’m going to show you.

00:55 We always have the exposure on the left side and the outcome on the top.

00:58 The exposure is stratified horizontally, the outcome is stratified vertically and the positives are always first.

01:05 Yes, exposure first; yes, outcome first. Keep that in mind, otherwise, the formulas that we use won’t work out.

01:12 The reduction in the incidence that would have been observed in the population if it had been unexposed is what we care about compared with the actual exposure pattern.

01:24 That’s a complicated way of explaining this.

01:26 What we’re talking about here is something called the population attributable risk, that’s one of the two kinds of attributable risk that we're gonna talk about.

01:34 The PAR is one kind.

01:35 The PAR is asking what are the fraction of cases that would not have occurred in a population if in fact the behavior had been eliminated.

01:44 In other words, if people didn’t smoke, how many fewer cases of lung cancer would there be? That’s the population attributable risk.

01:52 On the other hand, we have something called the attributable risk in the exposed group.

01:57 Now, the population of the attibutable risk we often called the PAR, the attributable risk in the exposed group is called the AR.

02:04 Now, the AR is the difference in the rates of an exposure between the exposed and the unexposed population.

02:11 I know, it sounds complicated. When we do the math, I think it’ll be a little clear.

02:15 In other words the AR is a fraction of how much of an outcome we can say is attributable to a certain exposure.

02:24 Let’s start by examining the attributable risk in the exposed group or the AR.

02:29 As always, we begin with our contingency table. You remember how to set that up, right? Exposure is the horizontal components and the outcome is the vertical components.

02:38 So the formula for attributable risk in the exposed groups is the incidence rate in the exposed group minus the incidence rate in the unexposed group divided by the incidence rate in the exposed group.

02:51 Remember those are, I hope, from a previous lecture, those were the absolute risk values in the various groups.

02:57 Let’s give him by A over A plus B minus C over C plus D, divided by our incidence in the exposed group which again is A over A plus B.

03:07 Now, you have to believe me when I say that the arithmetic works out magically to the relative risk minus one divide by the relative risk; so if you are struggling to remember these formulas that’s probably the easiest way to remember it -- relative risk minus one divided by the relative risk is the attributable risk in the exposed group.

03:26 We’ll work through an example in a bit so just file that away for the moment.

03:30 Now the population attributable risk or PAR on the other hand, is computed a bit differently.

03:36 We still use the same contingency table but with an added nuance, and that is we care about the overall incidence of a diseases in our group.

03:45 The overall incidence is given by everybody who test positive for the outcome - all the cases of lung cancer, for example, divided by everybody in my sample, or A plus C over N.

03:56 So the PAR formula is the incidence totally minus the incidence in the unexposed group divided by the total incidence again, or, again, A plus C over N minus C over C plus D divided by A plus C over N, and that gives me a really complicated formula, I know, but let’s work through an example and hopefully this will be a little clear.

04:20 So the example I like to always use is the relationship between smoking and lung cancer.

04:26 So, again, a cohort study follows a hundred smokers and a hundred non smokers over a ten year period to see who ends up with lung cancer.

04:34 Do you remember what a cohort study is? I hope you do.

04:37 A cohort study moves forward in time.

04:40 They begin ascertaining exposure status and waiting to see if the outcome manifests, so in this case, the cohort study begins by ascertaining smoking status and waiting to see if lung cancer manifests.

04:53 Cohort studies allow us to compute incidence rates, case controlled studies do not, always remember that.

05:00 That’s very important for deciding what kind of risk measurement to compute.

05:04 So here is, again our contingency table.

05:07 We always start with this and if I populate my contingency table with the data from my study, it looks like this.

05:14 Again, there's a hundred smokers, a hundred nonsmokers and they splay out such that 75 of the smokers ended up with lung cancer, 25 of the smokers did not have lung cancer, 10 of the nonsmokers had lung cancer and 90 of the nonsmokers did not have lung cancer, okay! Now, let’s compute our attributable risk numbers.

05:34 The AR is given by our formula of absolute risk in the exposed group minus absolute risk in the unexposed group divided by absolute risk in the exposed group, and that gives me a final number of 86.7%.

05:47 What does that mean? That means that 86.7% of the lung cancer cases were probably due to smoking, cause remember, the reason it’s not a 100% is some of those individuals got cancer without having smoked, that’s the nuance that attributable risk purports to offer.

06:06 Let’s compute the PAR now. If we plugged in our numbers into our formula, we got a PAR of 0.65 oh, sorry 0.765, or 76.5%.

06:18 In other words 76.5% of lung cancer cases would be prevented in our population sample if nobody smoked.

06:25 They both purport to offer the same kind of information but slightly different take on it.

06:31 So remember to use both of them if you’re trying to compute attribution.

The lecture Attributable Risk – Attributable Risk and Odds Ratio (Measures of Association) by Raywat Deonandan, PhD is from the course Measures of Association.

### Included Quiz Questions

1. Cohort study
2. Clinical trial
3. Cross-sectional survey
4. Case-control study
5. Experimental study
1. 78%
2. 50%
3. 99%
4. 25%
5. 66.7%
1. 80%
2. 37%
3. 72%
4. 87%
5. 1%

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Very good definitions for PAR and AR
By Keila O. on 04. March 2021 for Attributable Risk – Attributable Risk and Odds Ratio (Measures of Association)

Thanks! I just wish I could've understood RRR, RR and ARR better in the previous lecture