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

2. 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) Absence of spurious effects Absence of spurious effects  Valid causal stories have utilitarian value 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”

3.  “Essentialist” Concerns Cause present-cause absent demand Cause present-cause absent demand Threshold effects Threshold effects Indirect causation Indirect causation Distal versus proximal causes temporallyDistal versus proximal causes temporally Leveraged causationLeveraged causation Temporal delay Temporal delay Multiple causation versus spurious causation Multiple causation versus spurious causation  Experimental versus Epidemiological Causation Experiments test specific hypotheses through manipulation and control of experimental conditions Experiments test specific hypotheses through manipulation and control of experimental conditions Epidemiological studies presumes a probabilistic view of causation based on naturally occurring observations Epidemiological studies presumes a probabilistic view of causation based on naturally occurring observations “A’s blow was followed by B’s death” versus “A’s blow caused B’s death” “A’s blow was followed by B’s death” versus “A’s blow caused B’s death”

4. 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)

5. 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

6. Justice System - Trial Defendant InnocentDefendant Guilty Reject Presumption of Innocence (Guilty Verdict) Type I ErrorCorrect Fail to Reject Presumption of Innocence (Not Guilty Verdict) CorrectType II Error Statistics - Hypothesis Test Null Hypoth TrueNull Hypoth False Reject Null Hypothesis Type I ErrorCorrect Fail to Reject Null Hypothesis CorrectType II Error

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

8. 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

9.  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)

10.  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

11.  Epstein and King “We thus recommend that researchers not change the object of their inferences because causal inference is difficult. Instead, they should make their questions as precise as possible, follow the best advice science has to offer about reducing uncertainty and bias, and communicate the appropriate level of uncertainty readers should have in interpreting their results….” ( 38 ) “We thus recommend that researchers not change the object of their inferences because causal inference is difficult. Instead, they should make their questions as precise as possible, follow the best advice science has to offer about reducing uncertainty and bias, and communicate the appropriate level of uncertainty readers should have in interpreting their results….” ( 38 )

12. Epstein and King – Foundational Requirements  Replicability – transparency of theory, data and method  Social Good Peer Review Peer Review Research data should be in the public domain via data archiving Research data should be in the public domain via data archiving  Theory – should lead to observables  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

13. 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