# *Geek Box: Understanding Relative Risk

#### *Geek Box: Understanding Relative Risk

Relative risk is often dismissed as the sensationalist percentages of risk seen in headlines. And to a degree, this is warranted: relative risk and absolute risk are different. For example, if the baseline absolute risk of a disease is 1 out of every 10 people, and an exposure increases the rate to 2 out of 10 people, in relative terms this would be a 100% increase. But if the baseline absolute risk was 5 out of 10 and an exposure increased this to 10 out of 10 people, this would also be a 100% increase, despite 5 more people being diagnosed with a disease being a much greater absolute rate than 1 more.

But let’s reframe this. Suppose the absolute risk for a disease is 40 out of every 1000 people diagnosed – a 4% absolute lifetime risk – and an exposure increases this risk to 57 out of every 1000 people diagnosed – a 5.7% absolute risk. The change in absolute risk is 1.7%, yet 17 more people per 1000 have been diagnosed with a disease because of a particular exposure. This is the part of absolute risk vs. relative risk that is often neglected in the conversation; if the percentage increase in relative risk may seem to inflate the relationship, when we scale up to risk for the entire population, absolute risk increases may diminish the relationship.

So why use relative risk? Because risk is not homogenous across populations. Even where the cause-effect relationship, for example fruit consumption and stroke risk, is nominally the same, the risk between the exposure [fruit] and outcome [stroke] is relative to the characteristics of the population studied: background diet, wider lifestyle factors, environmental exposures, etc. Relativity is therefore a defining feature of risk for the same variable. And in nutritional epidemiology, generally high vs. low intake of the variable of interest is compared.

Let’s illustrate the relativity of risk with an example. Say the baseline absolute risk of stroke is 6% [60 out of 1000. i.e., divide 60 by 1000 which = 0.06, and multiply 0.60 by 100 = 6%]. And we are interested in the effects of consuming >3 servings fruit/d on stroke risk. So we go to southern Italy and we conduct a study in a population that also has a low sodium intake, higher intake of omega-3 polyunsaturated fats and vegetables, and moderate alcohol intake. And after 10-years follow-up, those consuming >3 servings fruit/d have an event rate of 51/1000. This would be a 15% reduction in relative risk, calculating using the following formula: (0.60 – 0.51) / 0.60 = 0.15 or 15%. The absolute risk reduction would be 0.9% [calculated as 0.60 – 0.51 = 0.009 x 100 = 0.9 or 0.9%].

However, we then look at the same exposure – >3 servings fruit/d – in a U.S. cohort with overall higher sodium intake, lower vegetable and omega-3 intake, higher animal fat intake, and higher alcohol intake. And after 10-years follow-up, those consuming >3 servings fruit/d have an event rate of 57/1000: (0.60 – 0.57) / 0.60 = 0.05 or 5%. The absolute risk reduction would be 0.3% [calculated as 0.60 – 0.57 = 0.003 x 100 = 0.3 or 0.3%].

The Italian study could be blown into headlines as “fruit slashes stroke risk by 15%!” but the absolute risk reduction would be 0.9%, while the U.S. study could be blown into “eating fruit does not reduce stroke risk!” but the absolute risk reduction would be 0.3%. Relative risk is important because the background factors to the comparisons between one group and another in a cohort study are relevant to the size of the effect. And please note, baseline absolute stroke risk would not necessarily be the same across populations, but we have stuck with 6% above to keep the example consistent.

The key point is here is that neither finding is “wrong”. It’s just relative. This is why relative risk is important, and useful, so long as you can interpret it appropriately. Remember: the effect of the same exposure is not constant across populations. Relative risk is a way to express that the effect of an exposure on an outcome is not only relative to absolute risk, but to the wider population characteristics of the comparison groups.