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Interpreting Probability in Causal Models for Cancer

This paper discusses the interpretation of probability in causal models for cancer epidemiology, addressing different interpretations and their desiderata. It explores the concepts of risks, odds, and probabilities in interpreting probabilistic claims in cancer research. The paper proposes a frequency-cum-objective Bayesian approach as a pragmatic option. The paper concludes by highlighting the relevance of epidemiology in understanding causality and probability in the social and health sciences.

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Interpreting Probability in Causal Models for Cancer

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  1. Interpreting Probability in Causal Models for Cancer Federica Russo & Jon Williamson Philosophy – University of Kent

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

  3. 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

  4. 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 agent’s opinion, degree of belief or epistemic attitude • Objective Bayesian • P = degree of belief shaped on empirical and logical constraints

  5. 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

  6. Let’s bargain

  7. 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

  8. Risks, Odds and Probabilities:Easy to compute Risks and odds compare proportions

  9. Risks, Odds and Probabilities:Tricky 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)

  10. 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

  11. Conclusions and … what next? Epidemiology: • looks for socio-economic & biological causes  Thus it’s 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

  12. Any comments, queries, objections, complaints about the paper?Please call the Helpdesk Many thanks to the British Academy and the FSR (UcLouvain) for funding the project:Causality and the Interpretation of Probability in the Social and Health Scienceswww.kent.ac.uk/secl/philosophy/jw/2006/CausalityProbability.htm

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