Risk
Thomas Lumley
Department of Statistics
University of Auckland
Linda is 31 years old, single, outspoken, and very bright. She
majored in philosophy. As a student, she was deeply concerned
with issues of discrimination and social justice, and also
participated in anti-nuclear demonstrations.
Which is more probable?
a. Linda is a bank teller.
b. Linda is a bank teller and a member of Greenpeace.
Are there more English words starting with ‘e’ or with ‘e’ as the
third letter?
During September 2001, what was the leading preventable cause
of death in the United States?
Illusions
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.
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
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
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 vs
9% 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
1000 people take the pills.
How many benefit?
Relative risk is the same
Actual benefit is not.
Only worth treating
people who have high
enough risk.
More risk summaries
Absolute 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 benefit
Is this worthwhile? How would you decide?
Your turn
Absolute risk reduction:
risk with exposure – risk without exposure
3/1000 – 2/1000 = 1/1000
Number needed to treat:
Treating 1000 people: 1 people benefit
Need to treat 1000 people
for one person to benefit
Risk summaries
Relative risk
= risk in exposed / risk in unexposed
absolute risk reduction (or increase)
= risk in exposed – risk in unexposed
number needed to treat (or harm)
= 1/absolute risk difference
Risk perception
Denial: not just a river in Egypt.
Risk perception
Panic 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 years
Treatment
Heart attack
No heart attack
Total
aspirin
104
10933
11037
placebo
189
10845
11034
total
293
21778
22071
Risk in aspirin group = 104/11037 = 0.0094
Risk in placebo group = 189/11034 = 0.0171
Relative risk
= 0.0094/0.0171 = 0.55
In words
Physicians allocated to the aspirin group had a
0.55 times lower risk of heart attack than those
allocated to placebo
or
Physicians allocated to aspirin had 45% lower
risk of heart attack than those allocated to
placebo
other way up: 0.0171/0.0094 = 1.82
Physicians 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 years
Treatment
Heart attack
No heart attack
Total
aspirin
104
10933
11037
placebo
189
10845
11034
total
293
21778
22071
Risk in aspirin group
- Risk in placebo group
= 104/11037 = 0.0094
= 189/11034 = 0.0171
Risk difference = 0.0094 -0.0171 = -0.0077 ≈ 8 per 1000
In words
For physicians allocated to the aspirin group, the
risk was reduced by 8 heart attacks per
thousand.
or
Physicians 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.