Communicating for a Knowledge Society

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Communicating for a Knowledge Society

• Communicating Risk and Uncertainty

Anna McHardy Department of Mathematics
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Kill or cure? Help to make sense of the Daily
Mails ongoing effort to classify every inanimate
object into those that cause cancer and those
that prevent it.
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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.

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Study Example 1
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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.

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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.

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Why do doctors prescribe aspirin to heart attack
victims?

• In this study 22 071 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.

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Why do doctors prescribe aspirin to heart attack
victims?
Treatment Heart attack No heart attack Total
Aspirin 104 10933 11037
Placebo 189 10845 11034
Total 293 21778 22071
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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 0.00942 9.42 per 1000 9.42/17.13 0.55
Placebo 189/11034 0.01713 17.13 per 1000
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• 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 dont take
  anything.

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Study Example 2
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• In 2006 the results of a study carried out among
  132 271 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 fathers age at birth of
  child (offspring) and their risk of autism.

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The offspring were assessed for autism at age 17
years.
Fathers age group Autism No autism Total
15 - 29 34 60 654 60 688
30 - 39 62 67 211 67 273
40 14 4 296 4 310
Totals 110 132 132 271
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Risk
Fathers age group Autism risk Risk as a rate per 1000 Relative risk Using 15-29 as baseline
15 - 29 34/60 688 0.00056 0.56
30 - 39 62/67273 0.000922 0.922 0.922/0.56 1.64
40 14/4310 0.00325 3.25 3.25/0.56 5.8
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Interpretation

• The risk of having a child with autism for those
  in the 30 - 39 age group is 1.6 times the risk
  for those in the 15 - 29 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 15 - 29 age group (percentage change
  is 479).
• Remember the numbers per 1000
• 15 - 29 age group it is 0.55
• 30 - 39 age group it is 1.62
• 40 age group it is 3.25

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How to understand risk in 13 clicks

• http//news.bbc.co.uk/2/hi/uk_news/magazine/793738
  2.stm

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Reckoning with Risk

• Gigerenzer, Gerd (2002). Reckoning with Risk
  London Penguin Books
• Chapter One Uncertainty
• Lets demystify a couple of concepts around
  risk!

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Test results may be false
Test Result Disease Disease
Test Result Yes No
Positive True positive Sensitivity of the test False positive
Negative False negative True negative Specificity of the test
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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 10 000 men . . .

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It is a good idea to make a table like this
Positive Negative Totals
HIV 1 0 1
No HIV 10 9 989 9 999
Totals 11 9 989 10 000
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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.

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For risk takers

• Think of 10 000 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?

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What is the chance one of these men who has a
positive test, does not have HIV?
Positive Negative Totals
HIV 150 0 150
No HIV 10 9 840 9 850
Totals 160 9 840 10 000
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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.

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Mammograms

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

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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?

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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
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Think Frequencies

• Imagine 10000 woman aged 40
• 100 have breast cancer and 90 will probably test
  positive, but 10 will test negative
• 9900 dont 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.

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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?

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Using a table
Disease Positive per 10 000 Negative per 10 000 Totals
CR cancer 15 15 30
No CR cancer 299 9 671 9970
Totals 314 9 686 10 000
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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?

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DNA tests

• The probability of a DNA match occurring by
  chance is 1 in 100 000.
• Rephrase it Out of every 100 000 people, 1 will
  show a match.
• Think about the size of the population if 1 000
  000 people live in your city, then 10 would have
  DNA that matches the sample.

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Franklins 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?

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Gerds 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.

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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.

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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.

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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.

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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.

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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".

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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.

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NZ Breast Cancer Table 
Age Risk Risk Percent
30s 1 in 204 0.5
40s 1 in 67 1.5
50s 1 in 35 2.8
60s 1 in 33 3.0
70s 1 in 38 2.6
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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 1.008 3.8

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NZ Herald 26 March 2009
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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.