Interpreting Probability Interpreting Probability in Causal Models for in Causal Models for

CancerCancer

Federica Russo and Jon WilliamsonFederica Russo and Jon WilliamsonPhilosophy, University of Kent

Overview

CausalityCancer epidemiologyVarieties of causal claims

ProbabilityDesiderataFrequency-cum-Objective BayesianismRisks, odds, and probabilities

Cancer epidemiology

Aetiology of cancerBiological and socio-economic causes

Assessment of epidemiological evidenceMechanistic and probabilistic evidenceMeta-analyses

Varieties of causal claims

Establishing generic claimsNon-smokers have a statistically significantgreater risk (25%) of lung cancer if their spouses are smokers

Applying the generic in the single-caseAudry, who has metastatic breast cancer, will survive more than 5 years, to extent 0.4

Both are probabilisticprobabilistic statements

Desiderata

ObjectivityAccount for the objectivity of probability

CalculiExplain how we reason about probability

EpistemologyExplain how we can know about probability

VarietyCope with the full variety of probabilistic claims

Parsimony Be ontologically parsimonious

Frequency -cumcum- Objective Bayesianism

Main worry: variety desideratum

Pluralism is a viable option:Generic causal claims require

a frequencyfrequency interpretation

Single-case causal claims require

an objective Bayesianobjective Bayesian interpretation

Objective Bayesianism:Epistemological and pragmatic virtues

Risks, odds and probabilities:Easy to compute

exp

exp

/

/

/

/

;

un

n n n pRR

n n n p

Odds n nOR

Odds n n

Odds PP Odds

Odds P

11 11 12 11

21 21 22 21

11 12

21 22

1 1

Factor Disease

Yes No

Exposed n11

p11

n12

p12

Unexposed n21

p21

n22

p22

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

Causal models for cancer

Two categories of causal claims:Generic – single-case

These claims are probabilistic

Interpreting probability

Pluralism is a viable option:Frequency-cum-Objective Bayesianism