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

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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

• 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

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

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