RiskThomas Lumley

Department of StatisticsUniversity of Auckland

The horizontal lines are straight

Your brain tries to be too clever: uses tricks that usually give more accurate results, but that fail here.

Assessing probabilities has the same problem: - our brains rely on tricks that don’t always work - need to learn not to believe our gut feelings - can’t rely on the media to help us.

Illusions

Kill or cure?Help to make sense of the Daily Mail’s ongoing effort to classify every inanimate object into those that cause cancer and those that prevent it.

A 12% increase is one extra case of breast cancer per 100 women

A 17% decrease is five fewer cases of heart disease per 100 women

12% is five times smaller than 17% -- because the baseline risk matters

Experiments show it is easier to understand counts than probabilities

What would happen to 1000 people like you?

Paling Palettes: riskcomm.com

A 75% increase in risk: from four people in 10,000 to seven people in 10,000 Paling Palettes:

riskcomm.com

Or 10,000 people like you?

A 75% increase in risk: from four people in 10,000 to seven people in 10,000 Paling Palettes:

riskcomm.com

Or 10,000 people like you?

Relative or absolute?• We care about absolute risk differences– 10 in 100 vs 11 in 100 risk of breast cancer– is 1 in 100 extra risk worth drinking less?

• Relative risks (risk ratios) are more commonly quoted– 12% increase in risk– less directly useful– but often more transportable from one

setting to another

Up or down?Risk in group A is 11%, in group B is 10%• 10/11=0.909 = 9% decrease?• 11/10 = 1.10 = 10% increase?Exactly equivalent, so either is correct.

Often being in one group is an action, that group usually goes on top, other group is “baseline”10% increase from drinking vs9% decrease from not drinking

Relative or absolute?• Cholesterol-lowering drugs reduce

heart attack risk about 40%• Relative risk is pretty much constant

across population groups• Absolute risk reduction is higher for

high-risk people– 15 in 100 reduced by 40% is 9 in 100– 3 in 100 reduced by 40% is 2 in 100 – 3 in 1000 reduced by 40% is 2 in 1000

Relative risk is the sameActual benefit is not.

Only worth treating people who have high enough risk.

1000 people take the pills.How many benefit?

More risk summariesAbsolute risk reduction:

risk with exposure – risk without exposure 150/1000 – 90/1000 = 60/1000 = 6%Number needed to treat:

Treating 1000 people: 60 people benefit Need to treat 1000/60 = 16 people for one person to benefitIs this worthwhile? How would you decide?

Your turnAbsolute risk reduction:

risk with exposure – risk without exposure 3/1000 – 2/1000 = 1/1000Number needed to treat:

Treating 1000 people: 1 people benefit Need to treat 1000 people for one person to benefit

Risk summariesRelative risk = risk in exposed / risk in unexposedabsolute risk reduction (or increase) = risk in exposed – risk in unexposednumber needed to treat (or harm) = 1/absolute risk difference

Risk perception

Denial: not just a river in Egypt.

Risk perceptionPanic vs denial

• Availability of examples• Familiar story frame• Choice to be exposed or not• Feeling of control (real or not)• “Natural” vs “unnatural”, “unclean”• Risks to children

Rare exposures

NZ Herald

• Baseline risk: 1 in 70• Risk with genetic variant: 1 in 11• Relative risk ≈ 6• Risk increase = 1/11 – 1/70 = 75 per

1000 What else do we need to know?

Translates to about 3/year in NZ

In this example, the genetic variant is carried by about 0.0011% of women

Out of every 10,000 women• 11 will carry the genetic variant• one will get ovarian cancer sometime in her

life• 9989 will not carry the genetic variant• 9989/70 = 143 will end up getting ovarian

cancer

If you could prevent cancer in the high-risk women• Screen 10,000 women for the variant• Find and treat 11 of them • Prevent one case of ovarian cancer

Example: Physicians Health Study

• 22000 physicians randomly assigned to aspirin or placebo, then wait eight yearsTreatment Heart attack No heart

attackTotal

aspirin 104 10933 11037placebo 189 10845 11034total 293 21778 22071

Risk in aspirin group = 104/11037= 0.0094

Risk in placebo group = 189/11034= 0.0171Relative risk = 0.0094/0.0171 =

0.55

In wordsPhysicians allocated to the aspirin group had a 0.55 times lower risk of heart attack than those allocated to placeboorPhysicians allocated to aspirin had 45% lower risk of heart attack than those allocated to placeboother way up: 0.0171/0.0094 = 1.82Physicians allocated to the placebo group had 1.82 times higher risk of heart attack than those allocated to aspirin

Example: Physicians Health Study

• 22000 physicians randomly assigned to aspirin or placebo, then wait eight yearsTreatment Heart attack No heart

attackTotal

aspirin 104 10933 11037placebo 189 10845 11034total 293 21778 22071

Risk in aspirin group = 104/11037= 0.0094

- Risk in placebo group = 189/11034= 0.0171Risk difference = 0.0094 -0.0171 = -0.0077 ≈ 8

per 1000

In wordsFor physicians allocated to the aspirin group, the risk was reduced by 8 heart attacks per thousand.orPhysicians allocated to aspirin had 0.8 percentage point lower risk of heart attack than those allocated to placebo

Summary• Large relative risks make good

stories– but usually either a rare event or a rare

exposure• Convert to number of people per

1000 to get better intuition

• Differences in risk are easier to understand

• Relative risks are more likely to apply across different groups of people.

That’s all, folks.