Title: Causation and the Rules of Inference
1Causation and the Rules of Inference
2Arlington 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?
4Causal 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
6Criteria 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)
7Alternate 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
8Errors 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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10http//www.intuitor.com/statistics/T1T2Errors.html
11Interpreting 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
14Foundational 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
15Case 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
16Illustrating Complex Causation