Interpreting Probability in Causal Models for Cancer

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Interpreting Probability in Causal Models for
Cancer

• Federica Russo Jon Williamson
• Philosophy University of Kent

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Overview

• Cancer epidemiology
• Interpretations of probability
• Desiderata
• Frequency-cum-Objective Bayesianism
• Risks, odds and probabilities

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Cancer epidemiology

• A double objective
• Establishing generic claims
• Non-smokers have a statistically significant
  greater risk (25) of lung cancer if their
  spouses are smokers
• Applying the generic in the single-case
• Audry, who has metastatic breast cancer, will
  survive more than 5 years, to extent 0.4
• Both are probabilistic statements

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Interpretations on the market

• Classical and logical
• P ratio of favourable cases / of all
  equipossible cases
• Physical frequency and propensity
• P limiting relative frequency of an attribute
  in a reference class
• P tendency of a type of physical situation to
  yield an outcome
• Subjective
• P quantitative expression of an agents
  opinion,
• degree of belief or epistemic attitude
• Objective Bayesian
• P degree of belief shaped on empirical and
  logical constraints

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Desiderata

• Objectivity
• Account for the objectivity of probability
• Calculi
• Explain how we reason about probability
• Epistemology
• Explain how we can know about probability
• Variety
• Cope with the full variety of probabilistic
  claims
• Parsimony
• Be ontologically parsimonious

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Lets bargain
Class/ Log Prop Freq Subj Emp- Based Obj Bayes
Objectivity ? ? ? ?
Calculi ? ?
Epistemology ? ? ? ? ?
Variety ? ? ?
Parsimony ? ?
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Deal! Frequency-cum-ObjectiveBaysianism

• Pluralism is a viable option
• Generic causal claims require
• a frequency interpretation
• Single-case causal claims require
• an objective Bayesian interpretation
• Objective Bayesianism has
• pragmatic virtues

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Risks, Odds and ProbabilitiesEasy to compute

• Risks and odds compare proportions

Factor Disease Disease
Factor Yes No
Exposed n11 p11 n12 p12
Unexposed n21 p21 n22 p22
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Risks, Odds and ProbabilitiesTricky to interpret

• a RR equal to 2.0 means that an unexposed
  person is twice as likely to have and adverse
  outcome as one who is not exposed
• (Sistrom Garvan 2004)
• odds and probabilities are different ways of
  expressing the chance that an outcome may occur
• (Sistrom Garvan 2004)
• the probability that a child with eczema will
  also have fever is estimated by the proportion
  141/561 (25.1)
• (Bland Altman 2000)

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To sum up

• In the context of cancer epidemiology
• Two categories of causal claims
• Generic single-case
• These are probabilistic
• The market offers
• Classical/Logical, Physical,
• Subjective, Objective Bayesian
• We went for
• Frequency-cum-Objective Bayesianism

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Conclusions and what next?

• Epidemiology
• looks for socio-economic biological causes
• ? Thus its paradigmatic of the
• social and health sciences
• models causal relations with probabilities
• ? Thus it raises genuine interest for the
  philosophy of causality and probability
• is concerned with generic and single-case claims
• ? Thus gives us further questions
• the levels of causation

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• Many thanks to the British Academy and the FSR
  (UcLouvain) for funding the projectCausality
  and the Interpretation of Probability in the
  Social and Health Scienceswww.kent.ac.uk/secl/ph
  ilosophy/jw/2006/CausalityProbability.htm