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Causation and the Rules of Inference

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Title: Causation and the Rules of Inference


1
Causation and the Rules of Inference
  • Classes 4 and 5

2
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

3
  • 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?

4
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

5
  • 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

6
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)
7
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

8
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.

9
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10
http//www.intuitor.com/statistics/T1T2Errors.html
11
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

12
  • 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)

13
  • 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

14
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

15
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

16
Illustrating Complex Causation
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