Maths in a minute: Individual versus population level risks

Imagine you’re a bird flying over a busy city. You hear the busy bustle of cars honking, musicians busking on street corners, and the clanking of construction as buildings rise and fall. When you look down, people blur together, like tiny moving ants moving in every direction. You don’t see the person and the expression on their faces; you can only observe the enormity of the group, with each person lost in the sea of the crowd around them.

In a similar way, population risks describe the group, overlooking individual situations. For example, a 2019 study examined the links between breast cancer and women on hormone therapy (HRT). It found that about 1 million cases of breast cancer out of a total of 20 million have been linked to hormone therapy. In other words, about 5% of breast cancer cases are linked to hormone therapy. This is useful to doctors and policymakers shaping decisions to help the entire population, but does it help individual women making a decision about her treatment?

To understand personal risk, we want to compare what happens with and without the risk factor. The study estimated that HRT increases the risk of breast cancer later in life by one-third.

Consider 100 women of average weight and aged 50 years old. 50 of these women are on hormone therapy, and 50 are not. We would expect three of the women not on hormone therapy to get breast cancer later in life. With the women on hormone therapy, we would expect it to be four - three because that is the baseline risk, plus one for the additional one-third risk.

As an individual, a woman can now decide whether the benefits she gets from HRT outweigh the risk of developing breast cancer increasing from 6% to 8% for her if she does use it.

Using large numbers to describe how something affects a population isn’t useful for explaining and understanding the risk to one person. Instead, risk should be explained in terms of the original risk to one person compared to the additional risk to one person. Both ways of explaining risks are beneficial in different situations, but the explanation should be aligned to the situation to gain the most understanding and transparency with your audience.

About this article

Jasmine Fischbach is studying Economics and International Business Student at Knoxville, Tennessee in the United States. In spring 2026 she completed an internship with Sense about Science, an independent charity that promotes the public interest in sound science and evidence.