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!