13th February 2024

Relative risks, odds ratios and number needed to treat

Being asked to calculate any of the above from a given scenario is not uncommon in Part 1. We can measure the strength of an observed association between a risk factor and an outcome in relative terms (using risk ratios, incidence rate ratios or odds ratios) or in absolute terms (using risk differences and incidence rate differences).

Remember that the null value for risk/incidence/odds ratios is 1. This is 0 for absolute measurements (i.e., risk and incidence rate differences). The result is statistically insignificant if the confidence interval crosses the null value. 

It is easy to get caught out by a question asking to calculate an odds ratio from a case-control study. This is calculated by dividing the odds of one group by the odds of another group. For example, in this 2×2 table, to calculate the odds ratio of developing mesothelioma in those exposed to asbestos compared to those without asbestos exposure:

Odds of mesothelioma in individuals exposed to asbestos: 10/50 = 0.20

Odds of mesothelioma in individuals unexposed to asbestos: 2/50 = 0.04

Odds ratio = 0.20/0.04 = 5 (i.e., the odds of developing mesothelioma is five times higher in those exposed to asbestos compared to those without)

Number needed to treat (NNT) and number needed to harm (NNH) 

Rather than a relative risk or risk reduction or an odds ratio, an NNT can be a helpful way to summarise the results of a clinical therapeutic trial. An NNT is the number of people who undergo a specific treatment or take a medication in order to prevent an additional adverse outcome. For example, suppose a newly developed antiplatelet has an NNT of 15. In that case, one has to treat 15 people with the antiplatelet to prevent an additional adverse outcome such as a myocardial infarction.

where the ARR =control event rate CER-experimental event rate (EER).

Conversely, the NNH represents the number of people needed to be exposed to a risk factor to result in additional harm.