How good are you at calculating risk? - Gerd Gigerenzer

A new drug reduces the risk of heart attacks by 40%.

Shark attacks are up by a factor of two.

Drinking a liter of soda per day doubles your chance of developing cancer.

These are all examples of relative risk,

a common way risk is presented in news articles.

Risk evaluation is a complicated tangle of statistical thinking

and personal preference.

One common stumbling block is the difference between

relative risks like these and what are called absolute risks.

Risk is the likelihood that an event will occur.

It can be expressed as either a percentage—

for example, that heart attacks occur in 11% of men

between the ages of 60 and 79—

or as a rate— that one in two million divers along Australia’s western coast

will suffer a fatal shark bite each year.

These numbers express the absolute risk of heart attacks

and shark attacks in these groups.

Changes in risk can be expressed in relative or absolute terms.

For example, a review in 2009 found that mammography screenings

reduced the number of breast cancer deaths from five women in one thousand to four.

The absolute risk reduction was about .1%.

But the relative risk reduction from 5 cases of cancer mortality to four

is 20%.

Based on reports of this higher number,

people overestimated the impact of screening.

To see why the difference between the two ways of expressing risk matters,

let’s consider the hypothetical example of a drug

that reduces heart attack risk by 40%.

Imagine that out of a group of 1,000 people

who didn’t take the new drug, 10 would have heart attacks.

The absolute risk is 10 out of 1,000, or 1%.

If a similar group of 1,000 people did take the drug,

the number of heart attacks would be six.

In other words, the drug could prevent four out of ten heart attacks—

a relative risk reduction of 40%.

Meanwhile, the absolute risk only dropped from 1% to 0.6%—

but the 40% relative risk decrease sounds a lot more significant.

Surely preventing even a handful of heart attacks,

or any other negative outcome, is worthwhile— isn’t it?

Not necessarily.

The problem is that choices that reduce some risks

can put you in the path of others.

Suppose the heart-attack drug caused cancer in one half of 1% of patients.

In our group of 1,000 people,

four heart attacks would be prevented by taking the drug,

but there would be five new cases of cancer.

The relative reduction in heart attack risk sounds substantial

and the absolute risk of cancer sounds small,

but they work out to about the same number of cases.

In real life,

everyone’s individual evaluation of risk will vary

depending on their personal circumstances.

If you know you have a family history of heart disease

you might be more strongly motivated to take a medication

that would lower your heart-attack risk,

even knowing it provided only a small reduction in absolute risk.

Sometimes, we have to decide between exposing ourselves to risks

that aren’t directly comparable.

If, for example, the heart attack drug carried a higher risk

of a debilitating, but not life-threatening,

side effect like migraines rather than cancer,

our evaluation of whether that risk is worth taking might change.

And sometimes there isn’t necessarily a correct choice:

some might say even a minuscule risk of shark attack is worth avoiding,

because all you’d miss out on is an ocean swim,

while others wouldn’t even consider skipping a swim

to avoid an objectively tiny risk of shark attack.

For all these reasons, risk evaluation is tricky at baseline,

and reporting on risk can be misleading,

especially when it shares some numbers in absolute terms

and others in relative terms.

Understanding how these measures work

will help you cut through some of the confusion

and better evaluate risk.