[MUSIC] We have already discussed the most common measures of frequency. For causal inference and for associations between variables we use a different set of measures, called measures of association. They can be divided in two broad categories, relative and absolute measures. In this lecture, I will focus on the relative measures. The term relative essentially means ratio here. Relative measures that you will come across include the risk ratio, the incidence rate ratio, and the odds ratio. We've seen that the ratio is one quantity divided by another. In the case of risk ratio, or cumulative incidence ratio, the numerator is the risk in the exposed group, and the denominator is the risk in the unexposed group. So how do you calculate the risk ratio? First of all, you need to have two groups to compare. Let's consider the epidemiology classroom example again. We have two groups of students, one exposed to the boring lecturer and one not exposed to him. Among the ten students in Classroom A, where the boring lecturer is, four fall asleep within one hour. Therefore, the risk of sleeping among the exposed students is four over ten, or 0.4 over a one hour period. In classroom B, where the unexposed students are, two out of ten students fall asleep, which constitutes a risk of 0.2 over a one hour period. As I've said, to calculate the risk ratio, you divide the risk of the exposed by the risk of the unexposed. Here, 0.4 over 0.2 equals a risk ratio of 2 over a one hour period. Notice that you always need to mention the time period you are referring to. The question is, how do you interpret the risk ratio? The key value of a risk ratio, of any ratio really, is one. A risk ratio of one means that the risk of disease among the exposed is equal to the risk among the unexposed. Which makes perfect sense, we get a value of one when the numerator and the denominator are equal. If the risk ratio is higher than one, it means that the risk of disease among the exposed is greater than the risk among the unexposed. Finally, a risk ratio lower than one means that the risk of disease among the exposed is smaller than the risk among the unexposed. If we wish to express this in terms of association, a risk ratio of one means that the exposure is not associated with a disease. A risk ratio higher than one means that the exposure is associated with an increased risk of the disease. And a risk ratio lower than one means that the exposure is associated with a decreased risk of the disease. In our example, where the risk ratio is two, we can say that students exposed to the boring lecturer had two times the risk of sleeping compared to those unexposed over the one hour study period. Or that students exposed to the boring lecturer had 100% higher risk of sleeping compared to those unexposed over the one hour study period. I'm saying 100% because number two is 100% higher than one, which is the value indicating our association. If we had a risk ratio of 1.5 I would have said 50% higher risk. The other two ratios that you should be able to estimate, incidence rate ratio and odds ratio, are calculated and interpreted in a very similar way. The incidence rate ratio is calculated by dividing the incidence rate among the exposed by the incidence rate among the unexposed. To get the odds ratio you need to divide the odds of having the disease among the exposed by the odds of having the disease among the unexposed. Interpretation is also similar. For instance, an incidence rate ratio or an odds ratio of one indicate no association. All ratios have no dimensions, so you only need to report the numerical value and the respective time point or study period. Ratios are widely used in epidemiological studies. Even if you never calculate one, there is no doubt that you will need to interpret relative measures of association frequently. So it is really important to understand what they represent. [MUSIC]