1. Thomas Lumley Department of Statistics University of Auckland
Risk
Thomas Lumley
Department of Statistics
University of Auckland

2. 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.

3. 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.

6. 12% is five times smaller than 17%
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

7. Experiments show it is easier to understand counts than probabilities
What would happen to 1000 people like you?
Paling Palettes: riskcomm.com

8. from four people in 10,000 to seven people in 10,000
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

9. from four people in 10,000 to seven people in 10,000
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

10. 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

11. 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

12. 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

13. 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.

14. 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?

15. 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

16. 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

17. Denial: not just a river in Egypt.
Risk perception
Denial: not just a river in Egypt.

19. 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

20. Rare exposures
NZ Herald

21. 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

22. In this example, the genetic variant is carried by about 0
In this example, the genetic variant is carried by about % 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

23. 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 =
Risk in placebo group = 189/11034 =
Relative risk = / = 0.55

24. 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: / = 1.82
Physicians allocated to the placebo group had 1.82 times higher risk of heart attack than those allocated to aspirin

25. 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 =
- Risk in placebo group = 189/11034 =
Risk difference = = ≈ 8 per 1000

26. 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

27. 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.

28. That’s all, folks.