# Medical Statistics – Part 7: OR and RR in Observational Studies

Relative risk and odds ratio in observational

studies Do you know the difference when it comes to

using the relative risk and odds ratio in observational studies? Well, that’s the focus of this Chalk Talk

episode. Differentiating between the relative risk

and odds ratio is especially important in the two primary types of observational studies,

namely cohort studies and case-control studies. Let’s take a detailed look at these study

types. Cohort studies compare groups of exposed and

non-exposed individuals. Both groups are followed over time to determine

whether a particular outcome, for example, a specific disease, develops. In contrast, case-control studies recruit

patients with a disease or outcome of interest. These cases are compared with a set of unaffected

healthy individuals termed controls. In contrast to cohort studies, case-control

studies compare the frequency of exposure in both groups. Therefore, the decisive difference between

both studies is that cohort studies compare groups of exposed and non-exposed individuals,

whereas case-control studies compare groups with and without the disease. There’s a general rule when it comes to

using the relative risk and odds ratio in both epidemiological study types: The relative

risk is used in cohort studies, whereas in case-control studies, only the odds ratio

is applied. So, let’s tackle this like a researcher

and start with a research question: Does smoking increase the risk of lung cancer? To answer this question, we could perform

a cohort study and compare a group of smokers with a group of nonsmokers. But we need to ensure that none of the study

participants have lung cancer. We would then follow the participants for

some time to determine whether they develop lung cancer. Alternatively, we could also conduct a case-control

study and select patients with lung cancer, termed cases. As a comparison, individuals without lung

cancer need to be recruited. These are termed controls. The next step is determining the number of

study participants that were smokers. Let’s take a more detailed look at both

study designs: In both studies, we compare two different groups. These are smokers and nonsmokers in the cohort

study, and disease-cased individuals and healthy controls in the case-control study. Accordingly, different aspects are measured

in both studies. On the one side, we’re comparing the occurrence

of lung cancer in the cohort study. On the other side, we’re comparing the smoking

status in the case-control study. This difference is important when it comes

to analyzing our study data. Let’s start with the cohort study. Smokers and nonsmokers were followed for some

time to determine whether they develop lung cancer. Let’s enter the values from our fictional

study in the 2-by-2 table. Of the 100 smokers, 20 developed lung cancer. Of the 100 nonsmokers, 2 developed lung cancer. First, we calculate the relative risk of smokers

and nonsmokers. So, 20 to 100 divided by 2 to 100. The answer is a relative risk of 10. We can now provide an answer to our research

question by stating that the relative risk of smokers developing lung cancer is 10 times

higher than in nonsmokers. Answering our research question using the

case-control study is a bit more difficult. So, why is this the case? First, we don’t separately consider smokers

and nonsmokers in the study. The groups compared are participants with

or without lung cancer. Second, we don’t measure the frequency of

lung cancer but the number of smokers in each group. To illustrate this difference, let’s use

the same values from the cohort study for our case-control study: Of the 22 cases with

lung cancer, 20 participants were smokers and 2 were nonsmokers. Of the 178 controls without lung cancer, 80

were smokers and 98 were nonsmokers. Can you see how we’ve inverted the 2-by-2

table? Now, the study participants with lung cancer

and the participants without lung cancer are on the left side of the table, whereas the

smokers and nonsmokers are now at the top. So, why have we done this? It should help you to understand the following:

The measured value is now at the top of the 2-by-2 table as for the cohort study. Having these numbers, we are now able to answer

the question of what the relative risk is of a study participant with lung cancer being

a smoker compared to a study participant without lung cancer. But this doesn’t correspond with our research

question. We’d like to know whether smoking increases

the risk of developing lung cancer. However, in this situation, a special feature

of the odds ratio comes in handy, which becomes clear in two steps. Let’s change our question to: What is the

odds ratio of a study participant with lung cancer being a smoker compared to a study

participant without lung cancer? Remember that the odds ratio quantifies the

strength of the association between two events, in this case, smoking and lung cancer. We divide the odds of participants with lung

cancer by the odds of participants without lung cancer. So, 20 to 2 divided by 80 to 98 gives us an

odds ratio of 12.25. Now let’s change the question again to what

we’re actually interested in: What is the odds ratio that a smoker is affected by lung

cancer compared to a nonsmoker? We divide the odds of smokers by the odds

of nonsmokers: 20 to 80 divided by 2 to 98 gives us an odds ratio of 12.25. You can see that the results are identical. For the odds ratio, it doesn’t matter which

direction you use in the 2-by-2 table for your calculation. Or, to put it in other words, an identical

odds ratio is obtained regardless of whether you compare the exposed and non-exposed groups

or cases and controls. This is a major advantage of the odds ratio

because it enables us to evaluate the answer to the question that hasn’t yet been closely

examined. In our case-control study, we calculated an

odds ratio of 12.25, and in our cohort study, a relative risk of 10. So, you can see that there isn’t a large

gap between both values. We can even take a further step in our case-control

study: If the disease is rare, we can use the odds ratio as an estimate of the relative

risk. Do you remember the pie chart from one of

the previous Chalk Talk episodes on statistics? To calculate the risk, a slice of cake is

divided by the entire cake. To calculate the odds, a slice of cake is

divided by the rest of the cake that remains on the cake platter. The only difference between both is the denominator

of the fraction. If the disease is very rare, that is, the

slice of cake is relatively small, then the denominator for calculating the odds and risk

are similar. Therefore, it’s also possible to use the

odds ratio as an indication of the size of the relative risk for rare diseases. To be on the safe side, let’s apply the

same calculation method on the left side and calculate the relative risk of a study participant

with lung cancer being a smoker. The risk of a study participant with lung

cancer is divided by the risk of a study participant without lung cancer. So, 20 to 22 divided by 80 to 178. The answer is 2.02, a completely different

result. This has an important consequence, which we

previously mentioned at the beginning of this episode. In case-control studies, the relative risk

is usually unsuitable for allowing an assessment of the extent of the relationship between

exposure and disease. Therefore, the odds ratio is only calculated

in case-control studies, which also serves as an estimate of the relative risk for rare

diseases. Theoretically, cohort studies can measure

both the relative risk and the odds ratio. However, the relative risk is usually preferred,

as it precisely answers the question put forward by the study, which is: Does smoking increase

the risk of developing lung cancer? Have you watched all seven episodes of our

series on statistics? We hope you have! To test your knowledge from previous episodes,

we’ve put together a quiz, which you can access through the link. Good luck!