Decision and Causality 1. Necessity. Objectives. 2. Recommendations? 3. Options/Alternatives. 4....
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Transcript of Decision and Causality 1. Necessity. Objectives. 2. Recommendations? 3. Options/Alternatives. 4....
Decision and CausalityDecision and Causality
1.1. Necessity. Objectives.Necessity. Objectives.2.2. Recommendations?Recommendations?3.3. Options/Alternatives.Options/Alternatives.4.4. Consequences: Likelihood and Consequences: Likelihood and
Importance Importance 5.5. Compare the alternatives. Compare the alternatives. 6.6. Feasibility and contingency plans. Feasibility and contingency plans. 7.7. Cost of deciding.Cost of deciding.
Decision and CausalityDecision and Causality
Evaluate causal modelsEvaluate causal models
Based on Giere, Understanding Based on Giere, Understanding Scientific Reasoning, 4th ed, 1997Scientific Reasoning, 4th ed, 1997
Decision and CausalityDecision and Causality
Evaluate causal modelsEvaluate causal models
Does saccharin cause cancer?Does saccharin cause cancer?
Decision and CausalityDecision and Causality
Evaluate causal modelsEvaluate causal models
Does saccharin cause cancer?Does saccharin cause cancer?
Experiment on rats fed on 5% Experiment on rats fed on 5% saccharin for 2 generations.saccharin for 2 generations.
Decision and CausalityDecision and Causality
Evaluate causal modelsEvaluate causal models
Does saccharin cause cancer?Does saccharin cause cancer?
Decision and CausalityDecision and Causality
Significance: probability of this Significance: probability of this deviation from expected value by deviation from expected value by chance alone.chance alone.
Decision and CausalityDecision and Causality
Does saccharin cause cancer?Does saccharin cause cancer?
Yes, but in rats and in high doses. Yes, but in rats and in high doses. However, could have small effect in However, could have small effect in humans.humans.
Modelling the Modelling the experimentexperiment
Real
Pop (U)
Hyp.
All C (X)
Hyp..
No C (K)
152Random
Saccharin
F(E)=7/78
No saccharin
F(E)=1/74
Random
Random
Hypothetical sample
1st Generation
P=7,5%
Hypothetical sample
Modelling the Modelling the experimentexperiment
Real
Pop (U)
Hyp.
All C (X)
Hyp..
No C (K)
183Random
Saccharin
F(E)=14/94
No saccharin
F(E)=0/89
Random
Random
Hypothetical sample
2nd Generation
P=0,3%
Hypothetical sample
Modelling the Modelling the experimentexperiment
Randomized experimental designRandomized experimental design, RED, RED
Take random sample from real Take random sample from real population.population.
Split and randomly assign cause to a Split and randomly assign cause to a group.group.
This group functions as a sample of This group functions as a sample of the hypothetical population X the hypothetical population X (eXperimental)(eXperimental)
The other group functions as a sample The other group functions as a sample of the hypothetical population K of the hypothetical population K («Kontrol»)(«Kontrol»)
Modelling the Modelling the experimentexperiment
Can we do this with people?...Can we do this with people?...
Modelling the Modelling the experimentexperiment
Can we do this with people?...Can we do this with people?...
In 1747, James Lind carried out a In 1747, James Lind carried out a controlled experiment to discover a controlled experiment to discover a
cure for scurvy.cure for scurvy.
(from http://en.wikipedia.org/wiki/Design_of_experiments)(from http://en.wikipedia.org/wiki/Design_of_experiments)
Modelling the Modelling the experimentexperiment
Lind selected 12 men from the ship, Lind selected 12 men from the ship, all suffering from scurvy, and divided all suffering from scurvy, and divided them into six pairs, giving each group them into six pairs, giving each group different additions to their basic diet different additions to their basic diet for a period of two weeks. The for a period of two weeks. The treatments were all remedies that had treatments were all remedies that had been proposed at one time or another. been proposed at one time or another.
Modelling the Modelling the experimentexperiment
1.1. cider cider
2.2. elixir vitriolelixir vitriol
3.3. seawaterseawater
4.4. garlic, mustard and horseradishgarlic, mustard and horseradish
5.5. vinegar vinegar
6.6. two oranges and one lemon every two oranges and one lemon every day.day.
Modelling the Modelling the experimentexperiment
Can we do this with people?...Can we do this with people?...
It depends on the issues. Ethical It depends on the issues. Ethical concerns may prevent this approach concerns may prevent this approach (cannot force people to smoke, for (cannot force people to smoke, for example)example)
Modelling the Modelling the experimentexperiment
For human testing it is also important For human testing it is also important to use blinded or double blinded to use blinded or double blinded experiments:experiments:
Blinded: The subjects do not know to Blinded: The subjects do not know to which group they belongwhich group they belong
Double-blind: Neither the subjects nor Double-blind: Neither the subjects nor the evaluators know to which group the evaluators know to which group each subject belongs. each subject belongs.
Modelling the Modelling the experimentexperiment
Double-blind studies are least Double-blind studies are least susceptible to bias (the experimenter susceptible to bias (the experimenter wants some result, placebo effect, etc)wants some result, placebo effect, etc)
Modelling the Modelling the experimentexperiment
One alternative: One alternative:
Prospective study.Prospective study.
Select individuals based on the Select individuals based on the presence or absence of the possible presence or absence of the possible cause (e.g. smokers and non-smokers)cause (e.g. smokers and non-smokers)
Wait, and check for the correlation of Wait, and check for the correlation of the effect with the possible cause.the effect with the possible cause.
(a “time delay” correlation…)(a “time delay” correlation…)
Model of Prospective Model of Prospective StudyStudy
Framingham study:Framingham study:
In 1950, selected 3074 men and 3433 In 1950, selected 3074 men and 3433 women at random, ages 30-59.women at random, ages 30-59.
Examined every 2 years for 20 years.Examined every 2 years for 20 years.Coronary Heart Disease (CHD) at ages 40-49:Coronary Heart Disease (CHD) at ages 40-49:
Men: 29%Men: 29%
Women: 14%Women: 14%
Model of Prospective Model of Prospective StudyStudy
Framingham study:Framingham study:
Controlling for other factorsControlling for other factors
Coronary Heart Disease (CHD) at ages 40-49:Coronary Heart Disease (CHD) at ages 40-49:
Men: Men: Smoking: 22%Smoking: 22% Non-Non-S:11%S:11%
Women: Women: Smoking: 7%Smoking: 7% Non-S:6%Non-S:6%
Model of Prospective Model of Prospective StudyStudy
Framingham study:Framingham study:
Controlling for other factorsControlling for other factors
Coronary Heart Disease (CHD) at ages 40-49:Coronary Heart Disease (CHD) at ages 40-49:
Coffee drinkers also had significantly Coffee drinkers also had significantly more CHD than non-drinkers.more CHD than non-drinkers.
Could it be correlation with tobacco?Could it be correlation with tobacco?
Model of Prospective Model of Prospective StudyStudy
Framingham study:Framingham study:
Controlling for other factorsControlling for other factors
Coronary Heart Disease (CHD) at ages 40-49:Coronary Heart Disease (CHD) at ages 40-49:
Coffee drinkers also had significantly Coffee drinkers also had significantly more CHD than non-drinkers.more CHD than non-drinkers.
Could it be correlation with tobacco?Could it be correlation with tobacco?
Model of Prospective Model of Prospective StudyStudy
Framingham study:Framingham study:
Controlling for other factorsControlling for other factors
Coronary Heart Disease (CHD) at ages 40-49:Coronary Heart Disease (CHD) at ages 40-49:
Coffee drinkers also had significantly Coffee drinkers also had significantly more CHD than non-drinkers.more CHD than non-drinkers.
Nonsmokers had no difference in CHD Nonsmokers had no difference in CHD as a function of coffee drinking.as a function of coffee drinking.
Model of Prospective Model of Prospective StudyStudy
Farmingham
Men aged 30-39
Smokers Nonsmokers
Random
X fx(CHD)=22%
K fk(CHD)=11%
NonrandomAll C No C
Frequency of E
Model of Prospective Model of Prospective StudyStudy
A A prospectiveprospective study (or experiment) study (or experiment) examines the correlation between two examines the correlation between two factors, but the possible cause is factors, but the possible cause is chosen before the effect is evident.chosen before the effect is evident.
There may be effects from other There may be effects from other factors, but these can be accounted factors, but these can be accounted for, and a prospective study can be for, and a prospective study can be quite conclusivequite conclusive
Model of Prospective Model of Prospective StudyStudy
Example: Example: 1960s, National Cancer Institute (USA)1960s, National Cancer Institute (USA)
37,000 smokers and 37,000 nonsmokers37,000 smokers and 37,000 nonsmokers
After 3 years smokers hadAfter 3 years smokers had
Double death rateDouble death rate
Double death rate from heart diseaseDouble death rate from heart disease
Nine times death rate from lung cancerNine times death rate from lung cancer
Correlated with time, amount, inhalationCorrelated with time, amount, inhalation
Decreased death rate for former smokersDecreased death rate for former smokers
Modelling the Modelling the experimentexperiment
A different approach: A different approach:
Breast cancer and contraceptionBreast cancer and contraception
In the 1980s, UK researchers In the 1980s, UK researchers questioned women who had breast questioned women who had breast cancer and were younger than 36 cancer and were younger than 36 years old. 755 responded.years old. 755 responded.
For each of these women researchers For each of these women researchers selected one woman at random with selected one woman at random with no breast cancer.no breast cancer.
Modelling the Modelling the experimentexperiment
A different approach:A different approach:
Each woman was interviewed about Each woman was interviewed about children, marriage, cohabitation, oral children, marriage, cohabitation, oral contraceptives, etc.contraceptives, etc.
Modelling the Modelling the experimentexperiment
Results: Women using oral Results: Women using oral contraceptives for more than 4 yearscontraceptives for more than 4 years
Modelling the Modelling the experimentexperiment
A A retrospectiveretrospective study: study:
Selects sample based on the effect Selects sample based on the effect and tries to reason backwards towards and tries to reason backwards towards cause.cause.
Most susceptible to bias. In this case:Most susceptible to bias. In this case:
ResponseResponse
SurveillanceSurveillance
RecallRecall
InterviewInterview
Modelling the Modelling the experimentexperiment
Response bias:Response bias:
Only some women agreed to Only some women agreed to participate, and this may not be a participate, and this may not be a random samplerandom sample
Surveillance:Surveillance:
Women using contraceptives go to the Women using contraceptives go to the doctor more oftendoctor more often
Modelling the Modelling the experimentexperiment
Recall:Recall:
Subjects may not remember past Subjects may not remember past events accurately, or may have a events accurately, or may have a biased memory.biased memory.
Interview:Interview:
Interviewers knewInterviewers knew
Modelling the Modelling the experimentexperiment
Results: Women using oral Results: Women using oral contraceptives for more than 4 yearscontraceptives for more than 4 years
Model, Retrospective Model, Retrospective StudyStudy
Women UK
Cancer No cancer
Match?
X fx(OC-22)=68%
K fk(OC-22)=69%
NonrandomAll E No E
Frequency of C
Evaluate the modelEvaluate the model
1.1. Model and PopulationModel and Population
2.2. Sample DataSample Data
3.3. Experimental designExperimental design
4.4. Random Sampling and biasRandom Sampling and bias
5.5. SignificanceSignificance
6.6. Summary and conclusionSummary and conclusion
Decision and CausalityDecision and Causality
Decision is related to causal models:Decision is related to causal models:
Because we need to understand the Because we need to understand the effects our decisions will cause, andeffects our decisions will cause, and
Because we need to decide which Because we need to decide which experiments to do to test causal experiments to do to test causal modelsmodels
Designing an experimentDesigning an experiment
1.1. Necessity. Objectives.Necessity. Objectives.2.2. Recommendations?Recommendations?3.3. Options/Alternatives.Options/Alternatives.4.4. Consequences: Likelihood and Consequences: Likelihood and
ImportanceImportance 5.5. Compare the alternatives. Compare the alternatives. 6.6. Feasibility and contingency plans. Feasibility and contingency plans. 7.7. Cost of deciding.Cost of deciding.
Designing an experimentDesigning an experiment
Examples:Examples:Second hand smoking causes cancer?Second hand smoking causes cancer?1.1. Necessity: important to determine effectNecessity: important to determine effect2.2. Recommendations? Similar to smoking?Recommendations? Similar to smoking?3.3. Options: RED, Prospective, retrospectiveOptions: RED, Prospective, retrospective4.4. Consequences: RED may be unethical, Consequences: RED may be unethical,
prospective takes too long…prospective takes too long…5.5. Compare: RetrospectiveCompare: Retrospective6.6. Feasibility: FeasibleFeasibility: Feasible7.7. Cost of deciding: …Cost of deciding: …
Designing an experimentDesigning an experiment
Examples:Examples:Does birth date affect personality (according to Does birth date affect personality (according to
astrology)?astrology)?
1.1. Necessity: not much…Necessity: not much…2.2. Recommendations? No…Recommendations? No…3.3. Options: RED, Prospective, retrospectiveOptions: RED, Prospective, retrospective4.4. Consequences: No bad consequences, RED Consequences: No bad consequences, RED
is most reliableis most reliable5.5. Compare: Best is double blind REDCompare: Best is double blind RED6.6. Feasibility: Double blind may not be Feasibility: Double blind may not be
feasible.feasible.7.7. Cost of deciding: …Cost of deciding: …
Designing an experimentDesigning an experiment
Examples:Examples:
Shawn Carlson, 1989Shawn Carlson, 1989http://psychicinvestigator.com/demo/AstroSkc.htmhttp://psychicinvestigator.com/demo/AstroSkc.htm
30 astrologers were asked to match 30 astrologers were asked to match 116 natal charts each to one of 3 116 natal charts each to one of 3 personality profiles (using the personality profiles (using the California Personality Inventory, California Personality Inventory, with the agreement of the with the agreement of the astrologers)astrologers)
Designing an experimentDesigning an experiment
Examples:Examples:Does birth date affect personality Does birth date affect personality
(according to astrology)?(according to astrology)?
In this case we do not test the actual causal In this case we do not test the actual causal model of birth date and personality. But model of birth date and personality. But the absence of a correlation between the the absence of a correlation between the astrologers’ predictions and CPI shows astrologers’ predictions and CPI shows there is no causal relation between the there is no causal relation between the factors identified. factors identified. A causal relation A causal relation implies a correlation.implies a correlation.
ConsequencesConsequences
Consequences are an important part Consequences are an important part of any decision.of any decision.
Decisions under uncertainty: Decisions under uncertainty: consequences must be weighted consequences must be weighted with the probability.with the probability.
ConsequencesConsequences
Example:Example:
0.3% probability of child having 0.3% probability of child having Down’s if mother over 35Down’s if mother over 35
0.5% probability of miscarriage from 0.5% probability of miscarriage from amniocentesis.amniocentesis.
Is it worth the risk? It depends on the Is it worth the risk? It depends on the utility values…utility values…
ConsequencesConsequences
Example:Example:
Biofuel may reduce carbon emissions Biofuel may reduce carbon emissions by a small fraction (industrialized by a small fraction (industrialized agriculture demands lots of fuel).agriculture demands lots of fuel).
However, crops used for fuel will raise However, crops used for fuel will raise food prices globally.food prices globally.
ConsequencesConsequences
Example:Example:
Biofuel may reduce carbon emissions Biofuel may reduce carbon emissions by a small fraction (industrialized by a small fraction (industrialized agriculture demands lots of fuel).agriculture demands lots of fuel).
However, crops used for fuel will raise However, crops used for fuel will raise food prices globally.food prices globally.
Lowering consumption could be an Lowering consumption could be an answer. But what is the cost of answer. But what is the cost of decreased economic growth?decreased economic growth?