Relative risk
Do you know how to calculate the relative risk? Don’t worry if you don’t know; we’ll
show you in this second episode of our series on statistics. But first, let’s take a look
at the risk.
In epidemiology, risk is defined as the probability of acquiring disease. Let’s use an example
and look at the risk of smokers developing lung cancer. In a fictional study, 100 smokers
were recruited. Of these 100 participants, 20 were diagnosed with lung cancer. The risk
can be calculated as a proportion: 20 out of 100 participants developed lung cancer.
This corresponds to 20% or 0.2. In other words, based on our fictional study, the risk of
smokers developing lung cancer is 20%.
Now onto the next step. In addition to the 100 smokers in the study, 100 nonsmokers were
also recruited. Of these 100 nonsmokers, 2 participants developed lung cancer. Two out
of 100 is 2% or 0.02. Therefore, the risk of nonsmokers developing lung cancer is 2%.
Up to now, we’ve independently considered the risk of both groups. However, in practice,
these groups are usually compared to one another. In such cases, the question that may arise
is: What’s the difference in the risk of developing lung cancer between smokers and
nonsmokers? This can be calculated by comparing the risk of both groups with one another.
The correct term is relative risk or risk ratio.
In our example, the relative risk is calculated by dividing 20% by 2%, which is 10. So, the
risk of developing lung cancer is 10 times more likely in smokers than in nonsmokers.
In general, the relative risk is calculated by dividing the risk of two different groups.
The risk of the group with the particular characteristic is usually presented as the
numerator of a fraction. This group is called the exposed group. The relative risk is calculated
as the risk of disease in an exposed group divided by the risk of disease in a nonexposed
group.
Now onto the range of values of the relative risk. The relative risk can be expressed as
any number between zero and infinity. If the risk of both groups is identical, then the
risk is divided by the same number. The relative risk is 1. If the risk of the exposed group
is higher than the risk of the nonexposed group, the relative risk is greater than 1.
If the risk of the exposed group is less than the risk of the nonexposed group, the relative
risk is between 0 and 1. This means that there is a decreased risk for the exposed group.
Let’s take a look at a network meta-analysis from a Cochrane Collaboration study in 2017.
A study was performed on 2,345 mountain climbers investigating whether the administration of
the carbonic anhydrase inhibitor acetazolamide affects the risk of developing acute altitude
sickness. The risk of both groups was compared. The risk of mountain climbers developing altitude
sickness under acetazolamide therapy was 11.3%, whereas the risk of mountain climbers without
therapy was 24.1%. The relative risk in the study was, therefore, 11.3% divided by 24.1%,
or 0.47. So, acetazolamide therapy reduces the risk of developing altitude sickness by
almost half.
Are you wondering how acetazolamide reduces the risk? Let’s quickly explore one possible
explanation: Hypoxia at high altitudes leads to hyperventilation
and eventually respiratory alkalosis. In contrast, acetazolamide inhibits carbonic anhydrase
and leads to an increase in bicarbonate excretion via the kidneys, and subsequently metabolic
acidosis. Metabolic acidosis compensates for respiratory alkalosis and supports the body’s
adaptive response to the high altitude.
In summary, the relative risk involves comparing the risks of an outcome between two groups.
It’s calculated by dividing the percentage values of both groups.
Now on to the quiz. Why not test your knowledge in the quiz that we’ve prepared for you?
A cohort study from 2007 investigated the association between the use of beta-lactam
antibiotics and the development of beta-lactam resistant Haemophilus influenzae in children
with respiratory tract infections. Sixty-three children were administered a beta-lactam antibiotic
against the infection, whereas 39 didn’t receive antibiotic therapy. Two weeks after
antibiotic therapy, the children were analyzed to determine whether the Haemophilus influenzae
strain was resistant to beta-lactam antibiotics. In the group of children that received antibiotics,
beta-lactam resistant Haemophilus influenzae was detected in 42 children. In contrast,
beta-lactam resistant Haemophilus influenzae was detected in only 14 children without antibiotic
therapy.
So, now it’s your turn. Calculate the risk of a beta-lactam resistant Haemophilus influenzae
strain in children under beta-lactam antibiotic therapy.
Calculate the risk of a beta-lactam resistant Haemophilus influenzae strain in children
without antibiotic therapy.
And the final task: Calculate the relative risk.
Good luck!
Risk with antibiotics = 42/63 = 0.67 x 100 = 67%
Risk without antibiotics = 14/39 = 0.36 x 100 = 36%
Relative risk = 0.67/0.36 = 1.86