Causation_and_the_Rules_of_Inference.ppt - Columbia Law School

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Causation_and_the_Rules_of_Inference.ppt - Columbia Law School Powered By Docstoc
					Causation and the Rules
     of Inference
      Classes 4 and 5
     Arlington Heights and Causal
           Reasoning in Law
   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

   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 Village’s 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
   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
        “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’ (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?
               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
       Absence of spurious effects
   Challenges
       Indirect causation
       Distal versus proximal causes temporally
       Leveraged causation
       Multiple causation versus spurious causation
       Temporal delay
   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
      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
      Strength (is the risk so large that we can easily rule out other
      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

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
 Experiments test specific hypotheses through
  manipulation and control of experimental
 Epidemiological studies presumes a probabilistic
  view of causation based on naturally occurring
      • 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
     Errors in Causal Inference
   Two Types of Error
       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
       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
       Medication
       What about in criminal trial outcomes? Both Type I
        and Type II errors are problems.
  Interpreting Causal Claims
 InLandrigan, 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 (didn’t happen by
      Can observe varying causal effects at
       different levels of exposure, causal effect is
       not indexed
   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
       Can there be causation without significance? Yes
         • Allen v U.S. (588 F. Supp. 247 (1984)
         • In re TMI, 922 F. Supp. 997 (1996)
   Thresholds
       Asbestos Litigation – relative risk must exceed 1.5,
        while others claim 2.0 relative risk and 1.5 attributable
         • RR=1.24 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 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
       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
              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
Illustrating Complex Causation

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