 Hi everyone! It's Monica Wahee here, your friendly neighborhood epidemiologist. One of the measurements we use in epidemiology that is not commonly used outside of epidemiology is called the odds ratio, or OR for short. This little lesson is going to show you how to calculate and interpret the disease OR and the exposure OR from a 2x2 table using the software OR. So here's a blank 2x2 table. First, we are going to go over the disease odds ratio, which is what you would calculate from a cross-sectional study design. When I worked at the U.S. Army in one of our data centers, I noticed that soldiers with college degrees were less likely to be injured. So let's use that as our example. Our binary exposure then is having a college degree, yes, no. I-binary disease or outcome will be having an injury, yes, no. Let's say this is a cross-sectional study. Let's start by filling in the A, B, and A plus B cells for the exposed, or for those with the college degree. Now, we'll fill in the C, D, and C plus D cells for the unexposed. And finally, for the column totals A plus C and B plus D as well as the grand total A plus B plus C plus D. Okay, take a good look at those numbers. Next, we'll go to R and do our calculations using the numbers from this example 2x2 table. So here we are in R. Remember how I said take a good look at those numbers? Here they are at the top. See how we start. We are assigning values to A, B, C, and D corresponding to the values from the 2x2 table. Let's run this and assign those values. Because I said we are making an odds ratio from a cross-sectional study, technically we are going to first calculate the odds of disease in the exposed. In our example, that means the odds of injury among those with college degrees. As you can see, the odds of the outcome in the exposed is calculated as A over B. So let's do that now. Let's look at what value we got. It's a pretty small number, about 0.16. Okay, now we will do the odds in the unexposed. As you can see, this is the calculation C over D. Let's run it. Okay, and let's see what that number looks like. Okay, a little bigger than the last one, 0.37. Now we can calculate the disease odds ratio by dividing the odds in the exposed by the odds in the unexposed. See, that's what I have here. Let's highlight it and run it. Now to look at the OR, let's highlight and run our new variable, disease OR. So this is smaller than 1. It's about 0.44. Now, because this is the disease odds ratio, it would be interpreted like this. Those with college degrees have only 44% the risk of injury compared to those without college degrees. Or you could take 100 minus 44, which is 56, and say those with college degrees have 56% lower odds of having an injury compared to those without college degrees. But that's for a cross-sectional study. What about a case control study? Okay, now let's go back to our 2x2 table and calculate the exposure odds ratio, the one used in case control designs. Remember, in case control designs, you select your cases first. Imagine we were focusing on a particular type of injury, such as motorcycle accidents. Let's hope there are so few that they are considered rare and we can do a case control study. In this example, let's say we found 41 cases. The first thing we do is figure out their exposure status. There. Next, we'd sample a bunch of controls. If we were using the database I used to use at the Army, we could sample these from our records of soldiers who were in the Army and maybe even had a motorcycle but did not get in an accident. And we'd discern their exposure status so we could fill out cells B and D of our 2x2 table. And from this, we calculate our row totals. So you see, same numbers, different study design. So the 2x2 table gets populated in a different order. Now let's go back to R and use these numbers from what's now a case control study to calculate the exposure odds ratio. Okay, here we are back in R. Notice this time we are going to calculate odds of exposure, not disease. So see here, we first calculate the odds of exposure in the disease by dividing A by C. And here, we calculate the odds of exposure in the non-diseased by dividing out B over D. Let's run those. Now we'll take the odds of exposure in the diseased and divide it by the odds of exposure in the non-diseased. And that will be our exposure odds ratio. Let's highlight and run that and then take a look at it. What a surprise! Our exposure OR is identical to our disease OR. Actually, it's not a surprise. There is only one OR per table. The difference is not in the numbers, but the interpretation. In this case, given this is a case control study, we'd interpret this OR to mean cases had 44% of the odds controls had of having a college degree. Or those with an injury had a 56% lower odds of having a degree than those without an injury. But in terms of the actual values, as I just demonstrated to you, there is only one odds ratio in each 2 by 2 table. And we can calculate it using this shortcut formula. AD over BC. Let's run this to convince ourselves. Now let's look at our shortcut OR. It should be the same as our disease OR. Ta-da! It's the same! So to conclude, the OR is easy to calculate with the shortcut formula, but in order to interpret it, you need to know the backstory of the study design it came from. If it's cross-sectional, you will interpret it as the odds of disease, and if it's case control, you are talking about odds of exposure. I hope you enjoyed my little video about odds. I don't know about you, but now I'm going to go play poker.