Download Causation and the Rules of Inference

Causation and the Rules
of Inference
Classes 4 and 5
Causal Reasoning
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Elements of causation in traditional positivist
frameworks (Hume, Mill, et al.)
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Valid causal stories have utilitarian value
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Correlation
Temporal Precedence
Constant Conjunction (Hume)
Absence of spurious effects
Causal mechanisms are reliable when they can support
predictions and control, as well as explanations
We distinguish causal description from causal
explanation
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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”
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“Essentialist” Concerns
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Cause present-cause absent demand
Threshold effects
Indirect causation
• Distal versus proximal causes temporally
• Leveraged causation
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Temporal delay
Multiple causation versus spurious causation
Experimental versus Epidemiological
Causation
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Experiments test specific hypotheses through
manipulation and control of experimental conditions
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”
Criteria for Causal Inference
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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)
Errors in Causal Inference
 Two
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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 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 – β -- probability of
correctly rejecting the null hypothesis
Justice System - Trial
Defendant Innocent
Reject
Presumption
of Innocence
(Guilty
Verdict)
Type I Error
Fail to Reject
Presumption
of Innocence
(Not Guilty
Verdict)
Correct
Statistics - Hypothesis Test
Defendant Guilty
Null Hypoth True
Null Hypoth False
Type I Error
Correct
Correct
Type II Error
Correct
Reject Null
Hypothesis
Type II Error
Fail to Reject Null
Hypothesis
http://www.intuitor.com/statistics/T1T2Errors.html
Interpreting Causal Claims
 In
Landrigan, the Court observes that
many studies conflate the magnitude of
the effect with statistical significance:
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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
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Alternatives to Statistical Significance
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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)
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Effect Size versus Significance
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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)
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Thresholds
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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))
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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
 Epstein
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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)
Epstein and King –
Foundational Requirements
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Replicability – transparency of theory, data and method
Social Good
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Theory – should lead to observables
Control for Rival Hypotheses and “Third Factors”
Pay Attention to Measurement
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Peer Review
Research data should be in the public domain via data archiving
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
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