Attributable risk and Number Needed to Harm
Welcome back to our Chalk Talk series on statistics. In this episode, we’ll delve into the attributable
risk. To do so, let’s first quickly recap the last episode using the example of the
fictional study on smoking as a risk factor for lung cancer. The study analyzed 100 smokers
and 100 nonsmokers. The risk of smokers developing lung cancer was 20 out of 100, or 20%. The
risk for nonsmokers was 2 out of 100, or 2%. To compare both groups, we can calculate the
relative risk. This is done by dividing the risk of the exposed group by the risk of the
nonexposed group, which gives us a relative risk of 10.
Let’s move on to the attributable risk. The attributable risk is an additional means
of comparing both groups. It’s the incidence of disease in the exposed group that can be
attributed to the exposure. The risk of the nonexposed group is subtracted from the risk
of the exposed group. So, 20% minus 2% equals 18%.
How do we interpret the attributable risk in our example? Smokers develop lung cancer
in 20% of cases, whereas nonsmokers develop lung cancer in only 2% of cases. The difference
between both groups is 18%. The attributable risk implies that 18% of the study population
developed cancer as a result of smoking.
From the attributable risk, we can also calculate the attributable risk percent. This value
is calculated as the attributable risk divided by the incidence of disease in the exposed
group. In this case, it’s 18% divided by 20%, which is 90%. This attributable risk
percent of 90% implies that cancer development in the 90% of individuals that smoked was
indeed due to smoking.
OK. Now we’ve come to another measure that can be determined from the attributable risk,
the number needed to harm. In epidemiological studies, the number needed to harm is often
abbreviated as NNH. It’s the inverse of the attributable risk, that is, 1 divided
by the attributable risk. In our example, the attributable risk is 18%. The number needed
to harm is calculated by dividing 1 by 18%. 1 divided by 0.18 is approximately 6.
Through its name, the number needed to harm reveals how to interpret the calculated number.
So, based on our study, if six individuals start smoking, then one will eventually develop
lung cancer.
There is also a closely related value for the number needed to harm that emphasizes
another measure; the number needed to treat. But, before we delve into it, we need to go
back to the attributable risk. We previously mentioned that the attributable risk is the
difference in risks between the exposed group and the nonexposed group. The attributable
risk is mostly used as a measure of effect size for risk factors. Correspondingly, there’s
also the absolute risk reduction. It’s calculated as the difference between the nonexposed group
and the exposed group and is usually used as a measure of the protective effects. We
also previously stated that the number needed to harm is the inverse of the attributable
risk. Now, the number needed to treat can be calculated in the same way as the number
needed to harm, but rather from the absolute risk reduction. The number needed to treat
is the average number of patients who need to be treated to prevent one bad outcome.
Now, a note on the range of values of the number needed to treat. The number needed
to treat can have a value ranging between 1 and infinity. The ideal therapy has a number
needed to treat value of 1; it would achieve the desired effect for every individual. In
contrast, a very high number needed to treat value indicates that many patients require
treatment to achieve success in a single case. So, as a general rule: The higher the number
needed to treat value, the less effective the treatment.
Great! We’re glad to see you’ve made it so far. Now, let’s recap the most important
points in this episode. Remember that not only can you compare two groups by dividing
their absolute risk values, but you can also calculate the difference between both risks
- the attributable risk. The attributable risk percent is calculated as the proportion
of cases in exposed individuals that can be attributed to the exposure. Dividing the number
1 by the attributable risk gives you the number needed to harm. The absolute risk reduction
and the number needed to treat work in a similar way, with the exception that they’re usually
applied to protective events.
Now it’s time to put this knowledge into practice. Let’s look at another case study.
In a randomized controlled trial, 432 patients that had undergone upper abdominal surgery
were examined. The aim of the study was to determine whether the occurrence of postoperative
pneumonia can be prevented by performing physiotherapy before surgery. Of the 218 patients that underwent
preoperative physiotherapy, 18 developed pneumonia, whereas of the 214 patients without preoperative
physiotherapy, 42 developed pneumonia.
Calculate the percent reduction of the risk of pneumonia using physiotherapy. Don’t
forget that you first need to calculate the risk in the group with physiotherapy followed
by the risk in the group without physiotherapy. We’d also like to know the number needed
to treat. Good luck!
Risk with physiotherapy = 18/218 = 8%
Risk w/out physiotherapy = 42/214 = 20%
Risk difference = 20% - 8% = 12%