Decision and Causality

1
Decision and Causality

• Necessity. Objectives.
• Recommendations?
• Options/Alternatives.
• Consequences Likelihood and Importance
• Compare the alternatives.
• Feasibility and contingency plans.
• Cost of deciding.

2
Decision and Causality

• Evaluate causal models
• Based on Giere, Understanding Scientific
  Reasoning, 4th ed, 1997

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Decision and Causality

• Evaluate causal models
• Does saccharin cause cancer?

4
Decision and Causality

• Evaluate causal models
• Does saccharin cause cancer?
• Experiment on rats fed on 5 saccharin for 2
  generations.

5
Decision and Causality

• Evaluate causal models
• Does saccharin cause cancer?

6
Decision and Causality

• Significance probability of this deviation from
  expected value by chance alone.

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Decision and Causality

• Does saccharin cause cancer?
• Yes, but in rats and in high doses. However,
  could have small effect in humans.

8
Modelling the experiment
1st Generation
Hypothetical sample
Saccharin
Hyp. All C (X)
F(E)7/78
Random
Real Pop (U)
Random
P7,5
152
Random
Hyp.. No C (K)
No saccharin
Hypothetical sample
F(E)1/74
9
Modelling the experiment
2nd Generation
Hypothetical sample
Saccharin
Hyp. All C (X)
F(E)14/94
Random
Real Pop (U)
Random
P0,3
183
Random
Hyp.. No C (K)
No saccharin
Hypothetical sample
F(E)0/89
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Modelling the experiment
Randomized experimental design, RED Take random
sample from real population. Split and randomly
assign cause to a group. This group functions as
a sample of the hypothetical population X
(eXperimental) The other group functions as a
sample of the hypothetical population K
(Kontrol)
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Modelling the experiment
Can we do this with people?...
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Modelling the experiment
Can we do this with people?... In 1747, James
Lind carried out a controlled experiment to
discover a cure for scurvy. (from
http//en.wikipedia.org/wiki/Design_of_experiments
)
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Modelling the experiment
Lind selected 12 men from the ship, all suffering
from scurvy, and divided them into six pairs,
giving each group different additions to their
basic diet for a period of two weeks. The
treatments were all remedies that had been
proposed at one time or another.
14
Modelling the experiment

• cider
• elixir vitriol
• seawater
• garlic, mustard and horseradish
• vinegar
• two oranges and one lemon every day.

15
Modelling the experiment
Can we do this with people?... It depends on the
issues. Ethical concerns may prevent this
approach (cannot force people to smoke, for
example)
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Modelling the experiment
For human testing it is also important to use
blinded or double blinded experiments Blinded
The subjects do not know to which group they
belong Double-blind Neither the subjects nor
the evaluators know to which group each subject
belongs.
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Modelling the experiment
Double-blind studies are least susceptible to
bias (the experimenter wants some result, placebo
effect, etc)
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Modelling the experiment
One alternative Prospective study. Select
individuals based on the presence or absence of
the possible cause (e.g. smokers and
non-smokers) Wait, and check for the correlation
of the effect with the possible cause. (a time
delay correlation)
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Model of Prospective Study
Framingham study In 1950, selected 3074 men and
3433 women at random, ages 30-59. Examined every
2 years for 20 years. Coronary Heart Disease
(CHD) at ages 40-49 Men 29 Women 14
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Model of Prospective Study
Framingham study Controlling for other
factors Coronary Heart Disease (CHD) at ages
40-49 Men Smoking 22 Non-S11 Women
Smoking 7 Non-S6
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Model of Prospective Study
Framingham study Controlling for other
factors Coronary Heart Disease (CHD) at ages
40-49 Coffee drinkers also had significantly
more CHD than non-drinkers. Could it be
correlation with tobacco?
22
Model of Prospective Study
Framingham study Controlling for other
factors Coronary Heart Disease (CHD) at ages
40-49 Coffee drinkers also had significantly
more CHD than non-drinkers. Could it be
correlation with tobacco?
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Model of Prospective Study
Framingham study Controlling for other
factors Coronary Heart Disease (CHD) at ages
40-49 Coffee drinkers also had significantly
more CHD than non-drinkers. Nonsmokers had no
difference in CHD as a function of coffee
drinking.
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Model of Prospective Study
Men aged 30-39
Frequency of E
Farmingham
X fx(CHD)22
Smokers
Nonsmokers
Random
K fk(CHD)11
All C
No C
Nonrandom
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Model of Prospective Study
A prospective study (or experiment) examines the
correlation between two factors, but the possible
cause is chosen before the effect is
evident. There may be effects from other
factors, but these can be accounted for, and a
prospective study can be quite conclusive
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Model of Prospective Study
Example 1960s, National Cancer Institute
(USA) 37,000 smokers and 37,000 nonsmokers After
3 years smokers had Double death rate Double
death rate from heart disease Nine times death
rate from lung cancer Correlated with time,
amount, inhalation Decreased death rate for
former smokers
27
Modelling the experiment
A different approach Breast cancer and
contraception In the 1980s, UK researchers
questioned women who had breast cancer and were
younger than 36 years old. 755 responded. For
each of these women researchers selected one
woman at random with no breast cancer.
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Modelling the experiment
A different approach Each woman was interviewed
about children, marriage, cohabitation, oral
contraceptives, etc.
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Modelling the experiment
Results Women using oral contraceptives for more
than 4 years
30
Modelling the experiment
A retrospective study Selects sample based on
the effect and tries to reason backwards towards
cause. Most susceptible to bias. In this
case Response Surveillance Recall Interview
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Modelling the experiment
Response bias Only some women agreed to
participate, and this may not be a random
sample Surveillance Women using contraceptives
go to the doctor more often
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Modelling the experiment
Recall Subjects may not remember past events
accurately, or may have a biased
memory. Interview Interviewers knew
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Modelling the experiment
Results Women using oral contraceptives for more
than 4 years
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Model, Retrospective Study
Frequency of C
Women UK
X fx(OC-22)68
Cancer
No cancer
Match?
K fk(OC-22)69
All E
No E
Nonrandom
35
Evaluate the model

• Model and Population
• Sample Data
• Experimental design
• Random Sampling and bias
• Significance
• Summary and conclusion

36
Decision and Causality

• Decision is related to causal models
• Because we need to understand the effects our
  decisions will cause, and
• Because we need to decide which experiments to do
  to test causal models

37
Designing an experiment

• Necessity. Objectives.
• Recommendations?
• Options/Alternatives.
• Consequences Likelihood and Importance
• Compare the alternatives.
• Feasibility and contingency plans.
• Cost of deciding.

38
Designing an experiment

• Examples
• Second hand smoking causes cancer?
• Necessity important to determine effect
• Recommendations? Similar to smoking?
• Options RED, Prospective, retrospective
• Consequences RED may be unethical, prospective
  takes too long
• Compare Retrospective
• Feasibility Feasible
• Cost of deciding

39
Designing an experiment

• Examples
• Does birth date affect personality (according to
  astrology)?
• Necessity not much
• Recommendations? No
• Options RED, Prospective, retrospective
• Consequences No bad consequences, RED is most
  reliable
• Compare Best is double blind RED
• Feasibility Double blind may not be feasible.
• Cost of deciding

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Designing an experiment

• Examples
• Shawn Carlson, 1989
• http//psychicinvestigator.com/demo/AstroSkc.htm
• 30 astrologers were asked to match 116 natal
  charts each to one of 3 personality profiles
  (using the California Personality Inventory, with
  the agreement of the astrologers)

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Designing an experiment

• Examples

42
Designing an experiment

• Examples
• Does birth date affect personality (according to
  astrology)?
• In this case we do not test the actual causal
  model of birth date and personality. But the
  absence of a correlation between the astrologers
  predictions and CPI shows there is no causal
  relation between the factors identified. A causal
  relation implies a correlation.

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Consequences

• Consequences are an important part of any
  decision.
• Decisions under uncertainty consequences must be
  weighted with the probability.

44
Consequences

• Example
• 0.3 probability of child having Downs if mother
  over 35
• 0.5 probability of miscarriage from
  amniocentesis.
• Is it worth the risk? It depends on the utility
  values

45
Consequences

• Example
• Biofuel may reduce carbon emissions by a small
  fraction (industrialized agriculture demands lots
  of fuel).
• However, crops used for fuel will raise food
  prices globally.

46
Consequences

• Example
• Biofuel may reduce carbon emissions by a small
  fraction (industrialized agriculture demands lots
  of fuel).
• However, crops used for fuel will raise food
  prices globally.
• Lowering consumption could be an answer. But what
  is the cost of decreased economic growth?