1. Communicating for a Knowledge Society
Communicating Risk and Uncertainty
Anna McHardy
Department of Mathematics

2. 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.

3. What is Risk?
Researchers describe risk as the estimated chance of getting a disease during a certain time period, such as within the next 10 years, or during your lifetime.

4. Study: Example 1

5. Why do doctors prescribe aspirin to heart attack victims?
In 1988 the results of the Physicians’ Health Study Research Group study were reported in the New England Journal of Medicine.

6. The reference class matters
From which group was the data collected?
A reliable risk statement will always tell you exactly. For instance:
US male physicians for the heart attack and aspirin experiment.
Always identify the reference class for yourself.

7. Why do doctors prescribe aspirin to heart attack victims?
In this study male physicians (aged from 40 to 84) were randomly assigned to two groups.
One group took an aspirin every second day and the other group took a placebo (a pill with no active ingredient which looked just like an aspirin).
The participants did not know whether they were taking aspirin or the placebo.

8. Why do doctors prescribe aspirin to heart attack victims?
Treatment
Heart attack
No heart attack
Total
Aspirin
104
10933
11037
Placebo
189
10845
11034
293
21778
22071

9. Why do doctors prescribe aspirin to heart attack victims?
Treatment
Heart attack
risk
Risk as a rate per 1000
Relative risk
Using placebo as the baseline
Aspirin
104/11037=
9.42 per 1000
9.42/17.13=
0.55
Placebo
189/11034=
17.13 per 1000

10. The risk of having a heart attack for those taking aspirin every second day is 0.55 the risk for those taking a placebo - a 45% decrease in risk.
Roughly speaking the difference is approximately 1 person in 100 having a heart attack if they take aspirin as opposed to approximately 2 people in 100 having a heart attack if they don’t take anything.

11. Study: Example 2

12. In 2006 the results of a study carried out among Jewish children born in Israel during 6 consecutive years in the 1980s were published in the Archives of General Psychiatry.
The objective of the study was to examine the relationship between father’s age at birth of child (offspring) and their risk of autism.

13. The offspring were assessed for autism at age 17 years.
Father’s age group
Autism
No autism
Total 34
60 654
60 688 62
67 211
67 273
≥ 40 14
4 296
4 310
Totals
110
132

14. Risk Father’s age group Autism risk Risk as a rate per 1000
Relative risk
Using as baseline
34/60 688=
0.56
62/67273=
0.922
0.922/0.56=
1.64
≥ 40
14/4310=
3.25
3.25/0.56=
5.8

15. Interpretation
The risk of having a child with autism for those in the age group is 1.6 times the risk for those in the age group (percentage change is 64%).
The risk of having a child with autism for those in the 40+ age group is 6 times the risk for those in the age group (percentage change is 479%).
Remember the numbers per 1000:
age group it is 0.55
age group it is 1.62
40+ age group it is 3.25

16. How to understand risk in 13 clicks

30. Reckoning with Risk
Gigerenzer, Gerd (2002). Reckoning with Risk London: Penguin Books
Chapter One: Uncertainty
Let’s demystify a couple of concepts around risk!

31. Test results may be false
Disease
Yes No
Positive
True positive
[Sensitivity of the test]
False positive
Negative
False negative
True negative
[Specificity of the test]

32. It all depends on risk taking behaviour for HIV testing
No known risk taking behaviour, German men:
About 0.01% have HIV;
If have HIV, 99.9% chance test will be positive;
If does not have HIV, 99.9% chance test will be negative.
Think of men . . .

33. It is a good idea to make a table like this
Positive
Negative
Totals
HIV 1
No HIV 10
9 989
9 999 11
10 000

34. 10 000 men with no known risk-taking behaviour
1 will have HIV and will test positive;
9999 will not have HIV;
99.9% of 9999 = 9989 men whose test will be negative;
So 10 will not have HIV and yet will test positive;
Altogether 11 will test positive, but only 1 will have HIV.

35. For risk takers
Think of men who engage in risk taking behaviour;
150 can be expected to have HIV and most likely all will test positive;
9850 are not infected and 10 will test positive;
160 test positive and 150 have the virus.
What is the chance one of these men who has a positive test, does not have HIV?
1/151 =

36. What is the chance one of these men who has a positive test, does not have HIV?
Negative
Totals
HIV
150
No HIV 10
9 840
9 850
160
10 000

37. Side Effects of Prozac
If a man takes Prozac, there is a 30% to 50% chance he will have a sexual problem.
What does this mean?
Very hard to know.
Solution: person giving the information needs to specify the reference class and the risk.
For instance, For 10 men who take prozac, 3 -5 will have a problem.

38. Mammograms
A 40 year-old friend has a positive result after a mammogram.
How likely is she to have breast cancer?

39. Mammogram Probabilities
The probability a woman aged 40 has breast cancer is about 1%.
If she has cancer, the probability she tests positive on a mammogram is 90%.
If she does not have cancer, the probability she tests positive is 9 percent.
What are the chances a woman who tests positive has breast cancer?

40. It helps to set up a table (keep in mind that this relates to a woman aged 40)
Disease
Positive test per 1000
Negative test per 1000
Total
Cancer 90 10
100
No cancer
891
9009
9900
Totals
981
9019
10000

41. Think Frequencies Imagine 10000 woman aged 40:
100 have breast cancer and 90 will probably test positive, but 10 will test negative;
9900 don’t have breast cancer, but about 891 of them will also test positive and 9009 will test negative;
981 have tested positive and 90 have cancer;
The chance of having breast cancer given a positive test is 9.2%.

42. One for you to try:
For symptom-free people over 50 who are screened using the hemoccult test for colorectal cancer:
The probability one of these people has colorectal cancer is 0.3%;
If a person has colorectal cancer, the probability is 50% he/she has a positive test;
If a person does not have colorectal cancer, the probability is 3% he/she has a positive test;
What is the probability a person (symptom free, over 50) who has a negative test actually has colorectal cancer?

43. Using a table Disease Positive per 10 000 Negative Totals CR cancer 1530
No CR cancer
299
9 671
9970
314
9 686
10 000

44. Think about 10 000 people 30 will have CR cancer;
Of these, 15 will test negative;
9970 will not have CR cancer;
Of these, 9671 will test negative;
9686 will test negative of whom 15 have CR cancer;
probability of having the disease if test is negative is 15/9686 or approx 0.15%.
A small chance?

45. DNA tests
The probability of a DNA match occurring by chance is 1 in
Rephrase it: Out of every people, 1 will show a match.
Think about the size of the population: if people live in your city, then 10 would have DNA that matches the sample.

46. Franklin’s Law Nothing is certain except death and taxes!
Despite all the efforts to reassure us it is not so, we live in a twilight of uncertainty!
What can we do?

47. Gerd’s advice
Use frequencies (numbers, not probabilities or percentages) to think about probabilities;
Find out the reference class;
Remember the experts may not understand either;
Think for yourself.

48. Test your knowledge of risk:
For men in the U.S., the lifetime risk of prostate cancer is nearly 17 percent. What does this mean?
Choose 1 or 2 or 3:
In general about 17 of every 100 males in the United States will be diagnosed with prostate cancer during their lifetime. This is the absolute risk of prostate cancer for U.S. males.
Every man in the U.S. has a 17 percent chance of dying from prostate cancer.
If a man is over 40, his chance of getting prostate cancer in the next year is almost 17 percent.

49. Test your knowledge of risk:
For men in the U.S., the lifetime risk of prostate cancer is nearly 17 percent. What does this mean?
Choose 1 or 2 or 3:
In general about 17 of every 100 males in the United States will be diagnosed with prostate cancer during their lifetime. This is the absolute risk of prostate cancer for U.S. males.
Every man in the U.S. has a 17 percent chance of dying from prostate cancer.
If a man is over 40, his chance of getting prostate cancer in the next year is almost 17 percent.

50. Test Your knowledge of risk
African American men have a relative risk of 1.2 for diagnosis of prostate cancer when compared to White men. What does this mean?
Choose 1 or 2 or 3
1. The risk of a diagnosis of prostate cancer is linked to where African American men live. 
2. Overall, African American men are more likely to be diagnosed with prostate cancer than White men.
3. Fewer African American men than White men will be diagnosed with prostate cancer.

51. Test Your knowledge of risk
African American men have a relative risk of 1.2 for diagnosis of prostate cancer when compared to White men. What does this mean?
Choose 1 or 2 or 3
1. The risk of a diagnosis of prostate cancer is linked to where African American men live. 
2. Overall, African American men are more likely to be diagnosed with prostate cancer than White men.
3. Fewer African American men than White men will be diagnosed with prostate cancer.

52. Night work linked to higher cancer risks
NZ Herald 18 March 2009
One report on which the IARC based its findings showed a 36 per cent greater risk of breast cancer for women who had worked night shifts for more than 30 years, compared with women who had never worked nights. 
Cancer researcher Professor Neil Pearce, of Massey University, said the link was well proven in animal studies and there was "some evidence in humans". A 36 per cent increased risk was "not huge" but breast cancer was the most common cancer in women, "so it's not a trivial risk".

53. What is the breast cancer risk in NZ?
NZ Breast Cancer Facts 
Each year approximately 2,400 New Zealand women and approximately 20 men are diagnosed with breast cancer. For every person who is diagnosed, other people are affected including husbands, wives, partners, children, family, and friends. Over a year, this adds up to thousands of people affected.
In New Zealand, women have an average risk of 11% (or 1 in 9) of being diagnosed with breast cancer at some time in their lives. This means the chance that they will never have breast cancer is 89%. As indicated in the following table, the younger a woman is, the lower her personal risk.
In addition, recent research from Australia, the United Kingdom and Europe is showing a trend towards a 1 in 8 lifetime risk of a woman being diagnosed with breast cancer; the United States is showing a 1 in 7 risk.

54. NZ Breast Cancer Table Age Risk Risk Percent 30s 1 in 204 0.5% 40s
1.5%
50s
1 in 35
2.8%
60s
1 in 33
3.0%
70s
1 in 38
2.6%

55. A 36% increase in risk
If a woman has worked nights or shifts for more than 30 years, she will be in her 50s.
Risk of breast cancer in 50s = 2.8%
36% of 2.8% = 1.008%
Add 36% to 2.8%, increased risk is
2.8% % ≈ 3.8%

56. NZ Herald 26 March 2009

57. Save your bacon Read the article and identify
The specific population which was studied.
The inferences made.
The changed risks mentioned. Are they increases or decreases?
The extra information you would need to evaluate the change in risk.