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 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 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

3.  Washington v Davis – intent is shown by factors such as: Disproportionate impact Disproportionate impact Historical background of the challenged decision Historical background of the challenged decision Specific antecedent events Specific antecedent events Departures from normal procedures Departures from normal procedures Contemporary statements of the decision makers Contemporary statements of the decision makers  Facts – 27 African American residents in town of 64,000 in preceding census 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 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 Most residents in new housing were likely to be African Americans Opponents cited likely drop in property values that would follow the construction 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 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 a[n] “administrative body … made a decision motivated by a single concern…or even a ‘dominant’ or ‘primary’ one (citing Washington v Davis) “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)-- ?? 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?

4. Causal Reasoning  Elements of causation in traditional positivist frameworks (Hume, Mill, et al.) Correlation Correlation Temporal Precedence Temporal 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 18)Threshold effects – e.g., dose-response curves (Cranor at 18) Absence of spurious effects Absence of spurious effects  Challenges Indirect causation Indirect causation Distal versus proximal causes temporally Distal versus proximal causes temporally Leveraged causation Leveraged causation Multiple causation versus spurious causation Multiple causation versus spurious causation Temporal delay 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 theories are essentially good causal stories Causal mechanisms are reliable when they can support predictions and control, as well as explanations Causal mechanisms are reliable when they can support predictions and control, as well as explanations  We distinguish causal description from causal explanation We don’t need to know the precise causal mechanisms to make a “causal claim 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” 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.  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)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 Alternate Paths: Experimental v. Epidemiological Causation

8. 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 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 relationship Type II Error (β) – 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 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 Statistical Power = 1 – β -- probability of correctly rejecting the null hypothesis  In regulation, we care more about false negatives Medication Medication What about in criminal trial outcomes? Both Type I and Type II errors are problems. What about in criminal trial outcomes? Both Type I and Type II errors are problems.

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 (didn’t happen by chance) Can still observe a weak effect that is statistically significant (didn’t happen by chance) Can observe varying causal effects at different levels of exposure, causal effect is not indexed 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) 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) 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 – 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 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 Can there be causation without significance? Yes Allen v U.S. (588 F. Supp. 247 (1984)Allen v U.S. (588 F. Supp. 247 (1984) In re TMI, 922 F. Supp. 997 (1996)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 Asbestos Litigation – relative risk must exceed 1.5, while others claim 2.0 relative risk and 1.5 attributable risk RR=1.24 was “significant” but “…far removed from proving ‘specific’ causation” (Allison v McGhan, 184 F 3d 1300 (1999))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)). 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 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 errorBut exclusion of evidence at a RR=1.0 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 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 Peer review contributes to evolution of theory Research data should be in the public domain via data archiving 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