Causation and the Rules of Inference

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Causation and the Rules of Inference

• Classes 4 and 5

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Arlington Heights and Causal Reasoning in Law

• Claim Both the Housing Authority (MHDC) and a
  specific individual claimed injury based on the
  Villages zoning actions to disallow construction
  of Lincoln Green, a multi-family housing
  development.
• Plaintiff asserted an actionable causal
  relationship between the Villages action and
  his alleged injury
• 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
• Challenge Was the Villages zoning ordinance
  racially motivated? Was there intent to
  discriminate?
• 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
• Disproportionate impact
• Historical background of the challenged decision
• Specific antecedent events
• Departures from normal procedures
• Contemporary statements of the decision makers
• Facts
• 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
• Rarely can it be said that an administrative
  body made a decision motivated by a single
  concernor even a dominant or primary one
  (citing Washington v Davis)
• Re-zoning denial wasnt a departure from normal
  procedural sequence (565-566)-- ??
• How would you prove the claim that there was a
  discriminatory intent that produced a disparate
  impact? How would you prove it with certainty?

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Causal Reasoning

• Elements of causation in traditional positivist
  frameworks (Hume, Mill, et al.)
• Correlation
• Temporal Precedence
• Constant Conjunction (Hume)
• Cause present-cause absent demand
• Threshold effects e.g., dose-response curves
  (Cranor at 18)
• Absence of spurious effects
• Challenges
• 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?
• 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
• We distinguish causal description from causal
  explanation
• We dont 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

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Criteria for Causal Inference

• 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)
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Alternate Paths Experimental v. Epidemiological
Causation

• 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)
• As blow was followed by Bs death versus As
  blow caused Bs 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

• Two Types of Error
• Type I Error (a) a false positive, or the
  probability of falsely rejecting the null
  hypothesis of no relationship
• Type II Error (ß) 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 ß -- probability of
  correctly rejecting the null hypothesis
• In regulation, we care more about false negatives
• Medication
• What about in criminal trial outcomes? Both Type
  I and Type II errors are problems.

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http//www.intuitor.com/statistics/T1T2Errors.html
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Interpreting Causal Claims

• In Landrigan, the Court observes that many
  studies conflate the magnitude of the effect with
  statistical significance
• Can still observe a weak effect that is
  statistically significant (didnt 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
• 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)
• Effect Size versus Significance
• 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
• Asbestos Litigation relative risk must exceed
  1.5, while others claim 2.0 relative risk and
  1.5 attributable risk
• RR1.24 was significant but far removed from
  proving specific causation (Allison v McGhan,
  184 F 3d 1300 (1999))
• 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 RR1.0 risks a
  Type II error

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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
• Validity and Reliability
• 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
• Peer review contributes to evolution of theory
• Research data should be in the public domain via
  data archiving

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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

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Illustrating Complex Causation