Okay now we're going to move on and talk about
the odds ratio, which is like a relative risk
but slightly different. You'll probably come
across odds ratios a lot when you read medical
literature, you probably have already. Remember
when we set up our contingency table as we
always do, a contingency table up to this
point has assumed that we can compute incidence
rates. What if we can't compute incidence
rate? Remember relative risks depend on incidence
rates. The relative risk is the absolute risk,
which is an incidence rate in the exposed
group divided by the absolute risk in the
unexposed group. Now remember, case-control
studies cannot measure incidence. They cannot,
so what do you do, I can't compute a relative
risk for a case-control study, we need something
to estimate the relative risk.
Can you guess what that is? You probably can. It's the odds ratio, we mentioned it already.
So the odds ratio can be used to estimate a relative risk, but only when the disease is rare. How do we define rare?
There is some debate on that issue, but most people kind of agree that if the prevalence of a disease is about 10%,
then the odds ratio can be used to estimate a relative risk. That's the major application of a knowledge ratio,
estimating a relative risk. However, a lot of the more complicated analyses, like a logistic regression analysis for example,
gives us odds ratios for a variety of contexts, so you may encounter odds ratios in a variety of your reading,
don't be afraid of it, it's just a kind of relative risk. It's a kind of way of measuring how much risk does this exposure purport to give
versus lack of that exposure. So again, we go back to our contingency table, this is where all the wisdom and all the
techniques arise from, making this table correctly. It's important now to remember what odds are, odds versus probabilities.
The odds of something happening is a probability of that thing happening divided by the probability of that thing not happening.
So in our contingency table, the odds of the outcome happening or the probability of that outcome happening
divided by the probability of it not happening, in other words, a over c. So that's the odds of the exposure in the diseased group.
Now the odds of the exposure in the undiseased group is given by b over d, following the same kind of logic.
The ratio of those two odds is my odds ratio. If I divide those two, I get the odds of exposure amongst the diseased
divided by the odds of the exposure amongst the undiseased, or a divided by c all divided by b divided by d.
There is a lot of dividing going on. I can simplify that formula a bit this way; it's is just a times d over b times c,
the cross products, dividing the cross products. Now let's work through an example. Let's say we had a case-control study,
using six patients with Creutzfeld-Jakob disease.
You may know what Creutzfeld-Jakob disease is. It's a kind of human mad cow disease, really rare,
and we have 10 subjects without Creutzfeld-Jakob disease and we want to see how much of that disease was likely due
to them having eaten beef, because we think that beef is a risk factor for Creutzfeld-Jakob disease.
So I start with my contingency table, let's say that these are my data, keep in mind this is hypothetical artificial data.
In real life the data would be quite different from this. If you look carefully you'll see that I have a total of about 16 patients here
and only six of those 16 have Creutzfeld-Jakob disease, that's a pretty high prevalence.
Really the Creutzfeld-Jakob disease is far rarer than this, so this is artificial data. Now let's computer our odds ratio.
Odds ratio is going to be the cross products divided over each other, 3 times 6 divided by 3 times 4 or 1.5,
what does that mean? It means that the odds of CJD are 50% higher in the group that ate beef
and that lends credence to the idea that beef is a risk factor for Creutzfeld-Jakob disease.
So some final thoughts on relative risk and odds ratio. When we're dealing with ratios, things divided by themselves,
the magic number to think about is 1, if I divide something by itself, I should get 1. If on the other hand, I get a number bigger than 1,
then I know something positive is happening. In other words the exposure is associated with the outcome.
If I get a number less than 1, something negative is happening, in other words the exposure is protective against the outcome.
So how much bigger than 1 or smaller than 1 that depends on your opinion. In general we would like to say that 1.5 or 2
are fairly significant relative risks or odds ratios. If you find numbers of that magnitude or greater,
probably something profound is happening with respect to the relationship between the exposure and the outcome.
So what have we learned? We've learned about the major measurements, relative risks and odds ratios.
We've learned about what they mean and when to use them. We've learned that relative risks are used in cohort studies
and odds ratios in case-control studies because relative risks are about incidence rates and cohort studies
can't compute incidence rates which case-control cannot. We've learned about attributable risk, two kinds in particular,
the population attributable risk and the attributable risk in the exposed group.
We've learned in another lecture about relative risk reduction and absolute risk reduction as well.
Now you're able to calculate two types of attributable risk, the attributable risk in the exposed group
and the population attributable risk and you are also able to calculate the odds ratio,
which is what we do when we can't compute a relative risk due to the fact that case-control studies
can't compute incidence rates. Thank you.