Transcript Causation_and_the_Rules_of_Inference

Causation and the Rules
of Inference
Classes 4 and 5
Arlington Heights and Causal
Reasoning in Law
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Claim: Both the Housing Authority (MHDC) and a specific
individual claimed injury based on the Village’s zoning actions
to disallow construction of Lincoln Green, a multi-family
housing development.
 Plaintiff asserted an “actionable causal relationship”
between the Village’s action and his alleged injury
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Court of Appeals reversed the District Court ruling and held
that the “ultimate effect” of the rezoning was racially
discriminatory, and would disproportionately affect Blacks
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Challenge: Was the Village’s zoning ordinance racially
motivated? Was there intent to discriminate?
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SCOTUS: Disparate impact is not sufficient evidence to claim
discrimination. Affirmative proof of discriminatory intent is
needed to show Equal Protection violation
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Washington v Davis – intent is shown by factors such as:
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Facts –
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27 African American residents in town of 64,000 in preceding census
Developer had track record of building low-income housing, the Order wanted to
create such housing
Most residents in new housing were likely to be African Americans
Opponents cited likely drop in property values that would follow the construction
Historical context – town had remained nearly all white as areas around it
became economically diverse, thereby limiting access of non-whites to the new
better paying jobs
Court uses a complex causation argument to work around discriminatory
intent
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Disproportionate impact
Historical background of the challenged decision
Specific antecedent events
Departures from normal procedures
Contemporary statements of the decision makers
“Rarely can it be said that a[n] “administrative body … made a decision
motivated by a single concern…or even a ‘dominant’ or ‘primary’ one (citing
Washington v Davis)
Re-zoning denial wasn’t a departure from ‘normal procedural sequence’ (565566)-- ??
How would you prove the claim that there was a discriminatory intent that
produced a disparate impact? How would you prove it with certainty?
Causal Reasoning
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Elements of causation in traditional positivist
frameworks (Hume, Mill, et al.)
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Correlation
Temporal Precedence
Constant Conjunction (Hume)
• Cause present-cause absent demand
• Threshold effects – e.g., dose-response curves (Cranor at
18)
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Absence of spurious effects
Challenges
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Indirect causation
Distal versus proximal causes temporally
Leveraged causation
Multiple causation versus spurious causation
Temporal delay
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Modern causal reasoning implies a dynamic relationship, with
observable mechanisms, not just a set of antecedent
relationships and correlations. Why does the light go out when
we throw the switch? Why does the abused child grow up to
become an abuser? How do fetuses exposed to Bendectin
develop birth defects? Why did people stop committing
suicide in the UK in the 1950s when the gas pipes were
sealed off?
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Valid causal stories have utilitarian value
 Causal theories are essentially good causal stories
 Causal mechanisms are reliable when they can support
predictions and control, as well as explanations
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We distinguish causal description from causal
explanation
 We don’t need to know the precise causal mechanisms to
make a “causal claim
 Instead, we can observe the relationship between a
variable and an observable outcome to conform to the
conceptual demands of “causation”
Criteria for Causal Inference
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Strength (is the risk so large that we can easily rule out other
factors)
Consistency (have the results have been replicated by different
researchers and under different conditions)
Specificity (is the exposure associated with a very specific
disease as opposed to a wide range of diseases)
Temporality (did the exposure precede the disease)
Biological gradient (are increasing exposures associated with
increasing risks of disease)
Plausibility (is there a credible scientific mechanism that can
explain the association)
Coherence (is the association consistent with the natural history
of the disease)
Experimental evidence (does a physical intervention show
results consistent with the association)
Analogy (is there a similar result to which we can draw a
relationship)
Source: Sir Austin Bradford Hill, The Environment and Disease: Association or Causation, 58 Proc. R.
Soc. Med. 295 (1965)
Alternate Paths: Experimental v.
Epidemiological Causation
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Experiments test specific hypotheses through
manipulation and control of experimental
conditions
 Epidemiological studies presumes a probabilistic
view of causation based on naturally occurring
observations
• Challenges of observational studies? (Cranor at 31)
“A’s blow was followed by B’s death” versus “A’s
blow caused B’s death”
 We usually are striving toward a “but for” claim,
and these are two different pathways to ruling in or
out competing causal factors
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Errors in Causal Inference
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Two Types of Error
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Type I Error (α) – a false positive, or the probability of
falsely rejecting the null hypothesis of no relationship
Type II Error (β) – a false negative, or the probability
of falsely accepting the null hypothesis of no
relationship
The two types of error are related in study design,
and one makes a tradeoff in the error bias in a study
Statistical Power = 1 – β -- probability of correctly
rejecting the null hypothesis
In regulation, we care more about false
negatives
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Medication
What about in criminal trial outcomes? Both Type I
and Type II errors are problems.
http://www.intuitor.com/statistics/T1T2Errors.html
Interpreting Causal Claims
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Landrigan, the Court observes that
many studies conflate the magnitude of
the effect with statistical significance:
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Can still observe a weak effect that is
statistically significant (didn’t happen by
chance)
Can observe varying causal effects at
different levels of exposure, causal effect is
not indexed
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Alternatives to Statistical Significance
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Odds Ratio – the odds of having been exposed given the
presence of a disease (ratio) compared to the odds of not having
been exposed given the presence of the disease (ratio)
Risk Ratio – the risk of a disease in the population given
exposure (ratio) compared to the risk of a disease given no
exposure (ratio, or the base rate)
Attributable Risk –
(Rate of disease among the unexposed – Rate of disease among the exposed)
(Rate of disease among the exposed)
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Effect Size versus Significance
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Such indicia help mediate between statistical significance and
effect size, which are two different ways to think about causal
inference
Can there be causation without significance? Yes
• Allen v U.S. (588 F. Supp. 247 (1984)
• In re TMI, 922 F. Supp. 997 (1996)
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Thresholds
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Asbestos Litigation – relative risk must exceed 1.5,
while others claim 2.0 relative risk and 1.5 attributable
risk
• RR=1.24 was “significant” but “…far removed from proving
‘specific’ causation” (Allison v McGhan, 184 F 3d 1300 (1999))
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Probability standard seems to be at 50% causation, or
a risk ratio of 2.0 (“ a two-fold increase” – Marder v GD
Searle, 630 F. Supp. 1087 (1986)).
Landrigan – 2.0 is a “piece of evidence”, not a
“password” to a finding of causation
• But exclusion of evidence at a RR=1.0 risks a Type II error
Foundational Requirements for
Causal Inference
Theory – should lead to observables
 Replicability – transparency of theory, data and method
 Control for Rival Hypotheses and “Third Factors”
 Pay Attention to Measurement
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Validity and Reliability
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Relevance of Samples, Size of Samples, Randomness
of Samples, Avoid Selection Bias in Samples
 Statistical Inferences and Estimation – use triangulation
through multiple methods
 Research should produce a social good
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Peer review contributes to evolution of theory
Research data should be in the public domain via data archiving
Case Study
 Pierre
v Homes Trading Company
 Lead paint exposure in childhood
produced behavioral and social
complications over the life course,
resulting in criminal activity and depressed
earnings as an adult
 Evidence – epidemiological study of birth
cohort exposed to lead paint in childhood
and their future criminality and life
outcomes
Illustrating Complex Causation