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

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

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

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 probabilistic  Both are probabilistic statements

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

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

Let’s bargain Class/ Log PropFreqSubjEmp- Based Obj Bayes Objectivity  Calculi  Epistemology  Variety  Parsimony 

Frequency-cum-ObjectiveBaysianism 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

Risks, Odds and Probabilities: Easy to compute Risks and odds compare proportions FactorDisease YesNo Exposedn 11 p 11 n 12 p 12 Unexposedn 21 p 21 n 22 p 22

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)

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

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

Any comments, queries, objections, complaints about the paper? Please call the Helpdesk Causality and the Interpretation of Probability in the Social and Health Sciences 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 Sciences www.kent.ac.uk/secl/philosophy/jw/2006/CausalityProbability.htm

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