Why isn’t it possible to sum up the death toll from different risk factors?

People may be exposed to different risk factors over their lifetime – like smoking, air pollution and obesity – which can increase their risk of disease and death.

However, the number of deaths caused by each risk factor can’t simply be added up. In this article, I explain why not – and why this is important.

How to understand this concept

There are several reasons why the number of deaths caused by each risk factor can’t simply be added up.

One reason is that multiple risk factors can contribute to a person’s death. Another reason is that these risk factors can interact with each other.

A simple analogy to understand this idea is with the idiom “the straw that broke the camel’s back.”

A camel carrying many items can eventually break its back, even though individual items are light enough to be carried. We could prevent the camel’s back from breaking by removing the hay bale, or removing other luggage, or freeing it from its rider.

In the same way, people can be exposed to different risk factors simultaneously, and they can overlap and interact with each other.

A real-life example is that DNA mutations can be caused by many carcinogens and some pathogens. Our cells have ‘checkpoints’ that prevent DNA mutations from leading to cancer. But, if a sufficient number of mutations occur, they will surpass the checkpoint, and a tumor can develop. This can eventually lead to death.

If people have multiple risk factors, then it’s more likely that the threshold will be surpassed. Having one risk factor can also make someone more vulnerable to another risk factor later on.

This means their death can be prevented in multiple ways. Liver cancer, for example, can be caused by chronic alcohol consumption and some hepatitis viruses, so reducing alcohol consumption or preventing hepatitis virus infections would both reduce the risk of death.

A worked example

In the figure, I have illustrated this with a worked example.

It shows that when multiple risk factors are present, the number (or fraction) of deaths from risk factors can’t be simply summed up.

Above you can see five hypothetical people who died and their previous exposure to risk factors. In pink, you can see their risk from hepatitis C virus, in blue is their risk from smoking, and in yellow is their risk from alcohol consumption.

Each risk factor increased their chance of death, according to the amount of exposure they’ve had. Some of the containers are full – this shows that some people have had sufficient risk exposure to cause death within a given timeframe.

Let’s look at what happens if some of the risk factors were removed.

If one risk factor – for example, hepatitis C – was removed, it reduced the number of deaths by 60%. This is known as the population-attributable fraction of hepatitis C, which means that 60% of deaths were caused by hepatitis C, in the hypothetical example.

If a different risk factor – smoking – was removed, it also reduced the number of deaths by 60%. So 60% of deaths were also caused by smoking.

How many deaths were caused by both of them, taken together? If both risk factors were removed, the number of deaths was reduced by 80%, not 120%.

This illustrates how the deaths from risk factors are not additive – they cannot be added up, and they do not sum up to 100%.

Similarly, if two risk factors have a population-attributable fraction of 50% and 30%, it does not mean that 20% of deaths are caused by unexplained risk factors.¹

Instead, researchers can use other methods to understand the combined contribution of multiple risk factors. These estimates are based on the order of risk factors: for example, they may look at the share of deaths caused by obesity after smoking has been accounted for.²

By interpreting the fractions correctly, we can have a better understanding of the impact of different risk factors combined.

Below, you can see the full illustration.

Conclusion

Although it may sound simple to attribute a person’s death to a single risk factor, this is usually not straightforward. Over a lifetime, people are exposed to various risk factors, which can overlap and interact with each other. This also means the same deaths can be prevented in multiple ways.

By understanding the effects of different risk factors, we can identify better ways to save lives.

Saloni Dattani (2023) - “Why isn’t it possible to sum up the death toll from different risk factors?” Published online at OurWorldinData.org. Retrieved from: 'https://ourworldindata.org/why-isnt-it-possible-to-sum-up-the-deaths-from-different-risk-factors' [Online Resource]

@article{owid-why-isnt-it-possible-to-sum-up-the-deaths-from-different-risk-factors,
    author = {Saloni Dattani},
    title = {Why isn’t it possible to sum up the death toll from different risk factors?},
    journal = {Our World in Data},
    year = {2023},
    note = {https://ourworldindata.org/why-isnt-it-possible-to-sum-up-the-deaths-from-different-risk-factors}
}

Reuse this work freely

All visualizations, data, and code produced by Our World in Data are completely open access under the Creative Commons BY license. You have the permission to use, distribute, and reproduce these in any medium, provided the source and authors are credited.

The data produced by third parties and made available by Our World in Data is subject to the license terms from the original third-party authors. We will always indicate the original source of the data in our documentation, so you should always check the license of any such third-party data before use and redistribution.

All of our charts can be embedded in any site.