# Risk Thomas Lumley Department of Statistics University of Auckland.

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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?

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

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?

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

Relative risk is the same Actual benefit is not. Only worth treating people who have high enough risk. 1000 people take the pills. How many benefit?

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 TreatmentHeart attackNo heart attackTotal aspirin1041093311037 placebo1891084511034 total2932177822071 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 TreatmentHeart attackNo heart attackTotal aspirin1041093311037 placebo1891084511034 total2932177822071 Risk in aspirin group =104/11037= 0.0094 - Risk in placebo group =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.

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