Causation and the Rules Causation and the Rules of Inferenceof Inference

Classes 4 and 5Classes 4 and 5

Arlington Heights and Causal Arlington Heights and Causal Reasoning in LawReasoning in Law

Claim: Both the Housing Authority (MHDC) and a specific Claim: Both the Housing Authority (MHDC) and a specific individual claimed injury based on the Village’s zoning actions to individual claimed injury based on the Village’s zoning actions to disallow construction of Lincoln Green, a multi-family housing disallow construction of Lincoln Green, a multi-family housing development. development.

Plaintiff asserted an “actionable causal relationship” between Plaintiff asserted an “actionable causal relationship” between the Village’s action and his alleged injurythe Village’s action and his alleged injury

Court of Appeals reversed the District Court ruling and held that Court of Appeals reversed the District Court ruling and held that the “ultimate effect” of the rezoning was racially discriminatory, the “ultimate effect” of the rezoning was racially discriminatory, and would disproportionately affect Blacksand would disproportionately affect Blacks

Challenge: Was the Village’s zoning ordinance racially Challenge: Was the Village’s zoning ordinance racially motivated? Was there intent to discriminate?motivated? Was there intent to discriminate?

SCOTUS: Disparate impact is not sufficient evidence to claim SCOTUS: Disparate impact is not sufficient evidence to claim discrimination. Affirmative proof of discriminatory intent is discrimination. Affirmative proof of discriminatory intent is needed to show Equal Protection violationneeded to show Equal Protection violation

Washington v DavisWashington v Davis – intent is shown by factors such as: – intent is shown by factors such as: Disproportionate impactDisproportionate impact Historical background of the challenged decisionHistorical background of the challenged decision Specific antecedent eventsSpecific antecedent events Departures from normal proceduresDepartures from normal procedures Contemporary statements of the decision makersContemporary statements of the decision makers

Facts – Facts – 27 African American residents in town of 64,000 in preceding census27 African American residents in town of 64,000 in preceding census Developer had track record of building low-income housing, the Order wanted to Developer had track record of building low-income housing, the Order wanted to

create such housingcreate such housing Most residents in new housing were likely to be African AmericansMost residents in new housing were likely to be African Americans Opponents cited likely drop in property values that would follow the constructionOpponents cited likely drop in property values that would follow the construction Historical context – town had remained nearly all white as areas around it Historical context – town had remained nearly all white as areas around it

became economically diverse, thereby limiting access of non-whites to the new became economically diverse, thereby limiting access of non-whites to the new better paying jobs better paying jobs

Court uses a complex causation argument to work around discriminatory Court uses a complex causation argument to work around discriminatory intentintent

““Rarely can it be said that a[n] “administrative body … made a decision motivated 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 by a single concern…or even a ‘dominant’ or ‘primary’ one (citing Washington v Davis)Davis)

Re-zoning denial wasn’t a departure from ‘normal procedural sequence’ (565-Re-zoning denial wasn’t a departure from ‘normal procedural sequence’ (565-566)-- ??566)-- ??

How would you prove the claim that there was a discriminatory intent that How would you prove the claim that there was a discriminatory intent that produced a disparate impact? How would you prove it produced a disparate impact? How would you prove it with certaintywith certainty??

Causal ReasoningCausal Reasoning Elements of causation in traditional positivist Elements of causation in traditional positivist

frameworks (Hume, Mill, et al.) frameworks (Hume, Mill, et al.) CorrelationCorrelation Temporal PrecedenceTemporal Precedence Constant Conjunction (Hume)Constant Conjunction (Hume)

• Cause present-cause absent demandCause present-cause absent demand• Threshold effects – e.g., dose-response curves (Cranor at Threshold effects – e.g., dose-response curves (Cranor at

18)18) Absence of spurious effectsAbsence of spurious effects

ChallengesChallenges Indirect causationIndirect causation Distal versus proximal causes temporallyDistal versus proximal causes temporally Leveraged causationLeveraged causation Multiple causation versus spurious causationMultiple causation versus spurious causation Temporal delayTemporal delay

Modern causal reasoning implies a dynamic relationship, with Modern causal reasoning implies a dynamic relationship, with observable mechanisms, not just a set of antecedent observable mechanisms, not just a set of antecedent relationships and correlations. Why does the light go out when relationships and correlations. Why does the light go out when we throw the switch? Why does the abused child grow up to we throw the switch? Why does the abused child grow up to become an abuser? How do fetuses exposed to Bendectin become an abuser? How do fetuses exposed to Bendectin develop birth defects? Why did people stop committing develop birth defects? Why did people stop committing suicide in the UK in the 1950s when the gas pipes were suicide in the UK in the 1950s when the gas pipes were sealed off?sealed off?

Valid causal stories have utilitarian valueValid causal stories have utilitarian value Causal theories are essentially good causal storiesCausal theories are essentially good causal stories Causal mechanisms are reliable when they can support Causal mechanisms are reliable when they can support

predictions and control, as well as explanationspredictions and control, as well as explanations

We distinguish We distinguish causal descriptioncausal description from from causal causal explanationexplanation We don’t need to know the precise causal mechanisms to We don’t need to know the precise causal mechanisms to

make a “causal claimmake a “causal claim Instead, we can observe the relationship between a Instead, we can observe the relationship between a

variable and an observable outcome to conform to the variable and an observable outcome to conform to the conceptual demands of “causation”conceptual demands of “causation”

Criteria for Causal InferenceCriteria for Causal Inference StrengthStrength (is the risk so large that we can easily rule out other (is the risk so large that we can easily rule out other

factors)factors) ConsistencyConsistency (have the results have been replicated by different (have the results have been replicated by different

researchers and under different conditions)researchers and under different conditions) SpecificitySpecificity (is the exposure associated with a very specific (is the exposure associated with a very specific

disease as opposed to a wide range of diseases)disease as opposed to a wide range of diseases) TemporalityTemporality (did the exposure precede the disease) (did the exposure precede the disease) Biological gradientBiological gradient (are increasing exposures associated with (are increasing exposures associated with

increasing risks of disease)increasing risks of disease) PlausibilityPlausibility (is there a credible scientific mechanism that can (is there a credible scientific mechanism that can

explain the association)explain the association) CoherenceCoherence (is the association consistent with the natural history (is the association consistent with the natural history

of the disease)of the disease) Experimental evidenceExperimental evidence (does a physical intervention show (does a physical intervention show

results consistent with the association)results consistent with the association) AnalogyAnalogy (is there a similar result to which we can draw a (is there a similar result to which we can draw a

relationship)relationship)

Source: Sir Austin Bradford Hill, The Environment and Disease: Association or Causation, 58 Proc. R. Soc. Med. 295 (1965)

Experiments test specific hypotheses through Experiments test specific hypotheses through manipulation and control of experimental manipulation and control of experimental conditionsconditions

Epidemiological studies presumes a probabilistic Epidemiological studies presumes a probabilistic view of causation based on naturally occurring view of causation based on naturally occurring observationsobservations

• Challenges of observational studies? (Cranor at 31)Challenges of observational studies? (Cranor at 31) ““A’s blow was followed by B’s death” versus “A’s A’s blow was followed by B’s death” versus “A’s

blow caused B’s death”blow caused B’s death” We usually are striving toward a “but for” claim, We usually are striving toward a “but for” claim,

and these are two different pathways to ruling in or and these are two different pathways to ruling in or out competing causal factorsout competing causal factors

Alternate Paths: Experimental v. Alternate Paths: Experimental v. Epidemiological CausationEpidemiological Causation

Errors in Causal InferenceErrors in Causal Inference Two Types of ErrorTwo Types of Error

Type I ErrorType I Error ( (αα) ) – a false positive, or the probability of – a false positive, or the probability of falsely rejecting the null hypothesis of no relationshipfalsely rejecting the null hypothesis of no relationship

Type II ErrorType II Error ( (ββ) ) – a false negative, or the probability – a false negative, or the probability of falsely accepting the null hypothesis of no of falsely accepting the null hypothesis of no relationshiprelationship

The two types of error are related in study design, and The two types of error are related in study design, and one makes a tradeoff in the error bias in a studyone makes a tradeoff in the error bias in a study

Statistical Power = 1 – Statistical Power = 1 – ββ -- probability of correctly -- probability of correctly rejecting the null hypothesisrejecting the null hypothesis

In regulation, we care more about false In regulation, we care more about false negativesnegatives MedicationMedication What about in criminal trial outcomes? Both Type I What about in criminal trial outcomes? Both Type I

and Type II errors are problems.and Type II errors are problems.

http://www.intuitor.com/statistics/T1T2Errors.html

Interpreting Causal ClaimsInterpreting Causal Claims In In LandriganLandrigan, the Court observes that , the Court observes that

many studies conflate the magnitude of many studies conflate the magnitude of the effect with statistical significance: the effect with statistical significance: Can still observe a weak effect that is Can still observe a weak effect that is

statistically significant (didn’t happen by statistically significant (didn’t happen by chance)chance)

Can observe varying causal effects at Can observe varying causal effects at different levels of exposure, causal effect is different levels of exposure, causal effect is not indexednot indexed

Alternatives to Statistical SignificanceAlternatives to Statistical Significance Odds RatioOdds Ratio – the odds of having been exposed given the – the odds of having been exposed given the

presence of a disease (ratio) compared to the odds of not having presence of a disease (ratio) compared to the odds of not having been exposed given the presence of the disease (ratio)been exposed given the presence of the disease (ratio)

Risk RatioRisk Ratio – the risk of a disease in the population given – the risk of a disease in the population given exposure (ratio) compared to the risk of a disease given no exposure (ratio) compared to the risk of a disease given no exposure (ratio, or the base rate)exposure (ratio, or the base rate)

Attributable RiskAttributable Risk – – (Rate of disease among the unexposed – Rate of disease among the exposed)(Rate of disease among the unexposed – Rate of disease among the exposed)

(Rate of disease among the exposed)(Rate of disease among the exposed)

Effect Size versus SignificanceEffect Size versus Significance Such indicia help mediate between statistical significance and Such indicia help mediate between statistical significance and

effect size, which are two different ways to think about causal effect size, which are two different ways to think about causal inferenceinference

Can there be causation without significance? YesCan there be causation without significance? Yes• Allen v U.SAllen v U.S. (588 F. Supp. 247 (1984). (588 F. Supp. 247 (1984)• In re TMI, 922 F. Supp. 997 (1996) In re TMI, 922 F. Supp. 997 (1996)

ThresholdsThresholds Asbestos Litigation – relative risk must exceed 1.5, Asbestos Litigation – relative risk must exceed 1.5,

while others claim 2.0 relative risk and 1.5 attributable while others claim 2.0 relative risk and 1.5 attributable riskrisk

• RR=1.24 was “significant” but “…far removed from proving RR=1.24 was “significant” but “…far removed from proving ‘specific’ causation” (‘specific’ causation” (Allison v McGhanAllison v McGhan, 184 F 3d 1300 (1999)), 184 F 3d 1300 (1999))

Probability standard seems to be at 50% causation, or Probability standard seems to be at 50% causation, or a risk ratio of 2.0 (“ a two-fold increase” – a risk ratio of 2.0 (“ a two-fold increase” – Marder v GD Marder v GD Searle, 630 F. Supp. 1087 (1986)Searle, 630 F. Supp. 1087 (1986)).).

LandriganLandrigan – 2.0 is a “piece of evidence”, not a – 2.0 is a “piece of evidence”, not a “password” to a finding of causation “password” to a finding of causation

• But exclusion of evidence at a RR=1.0 risks a Type II errorBut exclusion of evidence at a RR=1.0 risks a Type II error

Foundational Requirements for Foundational Requirements for Causal InferenceCausal Inference

Theory – should lead to observablesTheory – should lead to observables Replicability – transparency of theory, data and methodReplicability – transparency of theory, data and method Control for Rival Hypotheses and “Third Factors”Control for Rival Hypotheses and “Third Factors” Pay Attention to Measurement Pay Attention to Measurement

Validity and ReliabilityValidity and Reliability Relevance of Samples, Size of Samples, Randomness Relevance of Samples, Size of Samples, Randomness

of Samples, Avoid Selection Bias in Samplesof Samples, Avoid Selection Bias in Samples Statistical Inferences and Estimation – use triangulation Statistical Inferences and Estimation – use triangulation

through multiple methodsthrough multiple methods Research should produce a social good Research should produce a social good

Peer review contributes to evolution of theoryPeer review contributes to evolution of theory Research data should be in the public domain via data archivingResearch data should be in the public domain via data archiving

Case StudyCase Study Pierre v Homes Trading CompanyPierre v Homes Trading Company Lead paint exposure in childhood Lead paint exposure in childhood

produced behavioral and social produced behavioral and social complications over the life course, complications over the life course, resulting in criminal activity and depressed resulting in criminal activity and depressed earnings as an adultearnings as an adult

Evidence – epidemiological study of birth Evidence – epidemiological study of birth cohort exposed to lead paint in childhood cohort exposed to lead paint in childhood and their future criminality and life and their future criminality and life outcomes outcomes

Illustrating Complex CausationIllustrating Complex Causation