# Relative risk

 Part of aconvergent series on 2+2=4 v - t - e

 $1+1=\ ?$ This article/section deals with mathematical concepts appropriate for notedscholar.

Relative risk is the percentage change risk associated with one activity over another - such as "going for a drive" compared to "doing nothing". It is the most common value quoted in the media due to the virtue of it being inevitably the largest and most dramatic value available. Although scientists usually report it as a ratio of probabilities, results are commonly discussed as percentages. On its own, the relative risk of an activity or medical intervention is essentially meaningless, it must be used in conjunction with absolute figures - a 100% increase may sound dramatic, but it can be put in context by saying this is a change from 1 in 100,000 to 2 in 100,000. Furthermore, the reference category matters. A 100% change with one reference group sounds much more impressive than the 50% reduction if the two groups were reversed. To make the value even higher, the popular press usually quote the risk relative to doing nothing, as doing nothing is risk free (sort of) while doing anything at all will change it.

## Example

The use and misuse of "relative risk", is best shown with an example - and there are plenty to chose from. For example, one of the many, many headlines that appear on almost every issue of the Daily Mail.[1][2][3]

• Newspaper headline reads: "PAIN PILLS INCREASE HEART ATTACKS BY 24%"

In context, this headline refers to the use of ibuprofen and other painkilling pills, and the increased risks of heart attacks observed (specifically in men over the age of 50, but they usually neglect this fact too). 24% seems like a very dramatic result. Indeed, the headline alone indicates that you should stop using these painkillers if you want to even survive! However, the risk increase quoted is meaningless without the context of the absolute risks.

In terms of absolute risk and the natural frequencies (the most meaningful real-world numbers, rather than more abstract percentages), the risk of a heart attack may start as only about 10 in 1000 for all individuals.[4] This is 1%, so while it's likely that you'll not have a heart attack, it's not completely impossible. The risk of a heart attack is very fluxional and there are much higher and lower risk groups based around age, lifestyle and general health. A relative increase of 24% (about 1/4) would raise this to 1.24%, in terms of real numbers this is about 12-13 heart attacks per 1000 people, an increase of just 2 per 1000 (a risk difference). And the study shows that this is only for intensive users of the drug. So out of 1000 people who are taking intensive doses of pills, we would expect two extra deaths on top of the ten that happen anyway.

Although this increase is significant, it is far more meaningful and far less scaremongering than the relative risk of 24% that was originally given. The causes behind heart attacks are complex and mostly related to general health (levels of exercise, smoking and drinking habits, quality of diet). There will always be a risk associated with medical treatments but these must be weighed using real numbers, not meaningless percentages designed to look large and impressive.