Counterfactual Methods: Estimating Causal Effects

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Counterfactual Methods Estimating Causal Effects

• Confounding
• Effect-measure modification
• Quantifying bias

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• If civilization is to survive, we must cultivate
  the science of human relationships -- the
  ability of all peoples, of all kinds, to live
  together, in the same world at peace.
  Franklin D. Roosevelt
• What we have to do... is to find a way to
  celebrate our diversity and debate our
  differences without fracturing our communities.
  Hillary Rodham Clinton
• Confounding
• Bias
• Effect-measure modification
• Interaction

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Causal contrast - confounding

• Present if substitute imperfectly represents the
  counterfactual
• Association measure is confounded for a causal
  contrast due to imperfect substitution

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Causal contrast - confounding

• Scenario 1 (target experiences D1) confounding
  occurs if
• Magnitude of confounding

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Causal contrast - confounding

• Scenario 2 (target experiences D0) confounding
  occurs if
• Magnitude of confounding

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Causal contrast - confounding

• Scenario 3 (target experiences ? D1 or D0)
  confounding occurs if either
• Magnitude of confounding

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Causal contrast - confounding

• Magnitude of confounding
• If in any of the scenarios where the direct
  comparison is not equal (1,2) or the product (3)
  does not equal one, the ratio association measure
  (RRassociation) will be confounded for the causal
  contrast (RRcontrast)

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Causal contrast - confounding

• Control of confounding
• Often considering several variables at one while
  keeping them distinct
• Some measured, some not
• Relevant to which variables are controlled,
  status as a confounder magnitude and direction
  of confounding can change considerably
• If balanced out, control of one may actually
  lead to a greater order of magnitude of
  confounding

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Causal contrast - confounding

• Control of confounding
• Depends on creating strata within which the
  no-confounding equalities are satisfied
• Confounders
• Factors that explain or produce confounding
• Explains discrepancy between the counterfactual
  (desired but unobservable) and the substitute

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Causal contrast - confounding

• Example
• Question Does fluoridation treatment reduce the
  incidence of dental caries?
• Target
• Population children in a community
• Time period 3 years post-fluoridation treatment
  of water supply
• Counterfactual argument
• Substitute

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Causal contrast - confounding

• Example
• Comparison of rate in year prior to fluoridation
  (t0-1yr) to rate at three years after
  fluoridation (t3) yields measure of effect or
  measure of association?
• Hint do component rates refer to same or
  different population?
• Confounding
• Does substitute rate equal rate had exposure not
  occurred (counterfactual rate)?

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Effect-measure modifier

• Any factor that modifies the size of a ratio
  effect measure
• Causal risk ratio varies from one population to
  another or from one time period to another in the
  same population
• Consistency of risk ratio therefore not a valid
  causal criterion

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Causal Types

• Exposed Unexposed
• Type 1 No effect - doomed 1 1
• Type 2 Causative susceptible 1 0
• Type 3 Preventive susceptible 0 1
• Type 4 No effect - immune 0 0
• 0 no disease (unaffected) 1 disease
  (affected)
• Greenland Robins, IJE 15413-19, 1986
• from Miettinen, Scand J Work Environ Health,
  121152-8, 1982

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Effect-measure modification

• Why can the size of the causal effect for a given
  pair of exposure distributions be different for
  different targets?
• Definitions
• Pdoomed proportion of individuals with disease
  regardless of exposure
• Pcausative proportion of individuals who get
  disease if and only if exposed
• Ppreventive proportion of individuals who get
  disease if and only if not exposed

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Effect-measure modification

• Proportion who get disease if exposed
• Pdoomed Pcausative
• Proportion who get disease if not exposed
• Pdoomed Ppreventive
• Causal risk ratio

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Effect-measure modification

• Any factor affecting Pdoomed, Pcausative, or
  Ppreventive can be an effect-measure modifier
  (modifies the size of a ratio effect measure)
• Causal risk difference not dependent on Pdoomed
• Therefore, only factors affecting proportions
  susceptible to exposure can modify causal risk
  difference

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Quantification of effect-measure bias

• Measures of association are surrogates for causal
  measures
• How different are they?
• Understanding this is a critical step in study
  interpretation
• Formal evaluation (quantification) of bias
• Sensitivity analysis
• Validation substudies

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Quantification of effect-measure bias

• Counterfactual approach
• RRexpected estimate
• RRcausal?biascounfound?biasf/uloss?biassampling?bi
  asnonresponse?biasexclusion ?biasinfo
• Result used in sensitivity analysis under
  different plausible scenarios