Interpreting Probability  in Causal Models for Cancer Federica Russo & Jon Williamson Philosophy – University of Kent
Overview <ul><li>Cancer epidemiology </li></ul><ul><li>Interpretations of probability </li></ul><ul><li>Desiderata </li></...
Cancer epidemiology <ul><li>A double objective </li></ul><ul><ul><li>Establishing generic claims </li></ul></ul><ul><ul><l...
Interpretations on the market <ul><li>Classical and logical </li></ul><ul><ul><li>P  = ratio # of favourable cases / # of ...
Desiderata <ul><li>Objectivity </li></ul><ul><ul><li>Account for the objectivity of probability </li></ul></ul><ul><li>Cal...
Let’s bargain Class/ Log Prop Freq Subj Emp- Based Obj Bayes Objectivity     Calculi   Epistemology      Variet...
Deal!  Frequency- cum -ObjectiveBaysianism <ul><li>Pluralism is a viable option: </li></ul><ul><ul><li>Generic causal clai...
Risks, Odds and Probabilities: Easy to compute <ul><li>Risks and odds compare  proportions </li></ul>Factor Disease Yes No...
Risks, Odds and Probabilities: Tricky to interpret <ul><li>…  a RR equal to 2.0 means that an unexposed person is twice as...
To sum up <ul><li>In the context of cancer epidemiology: </li></ul><ul><ul><li>Two categories of causal claims: </li></ul>...
Conclusions and … what next? <ul><li>Epidemiology: </li></ul><ul><ul><li>looks for socio-economic & biological causes </li...
Any comments, queries, objections, complaints about the paper? Please call the Helpdesk Many thanks to the British Academy...
Upcoming SlideShare
Loading in …5
×

Capits Presentation

507 views
462 views

Published on

Published in: Health & Medicine, Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
507
On SlideShare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
3
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide
  • [attention getter] [need] Might seem uncontroversial that health sciences search for causes of disease and for effective treatments. Significant developments in quantitative causal analysis – causality is made operational BUT conceptual issues left open. Phil of proba developed many accounts of the interpretation BUT never approaches interpretation of proba *contextually* [task] As part of our project, J&amp;F looked into a specific context – cancer epidemiology and raised the question of how prob should be intepreted. [main message] Cancer epidemiology is concerned with 2 categories of causal claims – generic and single-case. Both are probabilistic. Argue in favour of a pluralistic interpretation: frequency-cum-objective Bayesian
  • [Browse on topics]
  • Epidemiology is concerned with distribution of diseases in populations and with detecting what causes determine such distributions. Cancer epidemiology tries to map the aetiology of cancer What cancers are due to a certain factor, eg tobacco consumption Which biological factors are carcinogenic What occupational chemicals are carcinogenic What genetic factors predispose or prevent cancer What parts of the population are more exposed to certain factors Particular studies don’t count automatically as epidemiological evidence. Results are further evaluated in meta-analysis – epidemiological evidence evaluated according to specific criteria. 1° objective: establishing generic causal claims (example) 2° objective: the generic claim has to be useful for it to be applied in the single-case (example) Modelling the causal relations at the generic level and inference in the single-case are both probabilistic This is why we raise the question of how probability is to be interpreted NB: not just an “abstract” debate for armchair philosophers – surely the choice of an interpretation has consequences on (or is a consequence of) metaphysics, but there are also crucial pragmatic aspects that enter the choice.
  • [Browse on interpretations]
  • Objectivity Notion of prob that is objective in a logical sense: there is a fact of the matter of what prob is. If 2 agents disagree, then at least one of them must be wrong Calculi A phil theory of prob should yield a notion that satisfies the axioms of prob, otherwise it is a theory of something else Epistemology Come to know about prob in various ways: measure pop freq, appeal to symmetry arguments or sc theories, derive prob from others using prob calculus … Phil theory of prob should how we can use such techniques Variety Claim about single-case or about generic Prob attached to variety of entities (events, sets, variables, sentences, hypotheses) Phil theory of prob should be able to cope with all of them Parsimony Phil theory of prob shouldn’t make unwarranted ontological commitments. If in our ontology we can reduce prob to smth else instead of taking as primitive, should do
  • Objectivity: X Class/Log  different agents can construe different partitions as equipossible X Subj  2 agents disagree, neither of them can be considered wrong X Emp-based  (lesser extent) if freq are known then assignments are not arbitrary V Freq  objectively determined by a reference class V Prop  objectively determined by history of universe up to present time V Obj Bayes  p objectively determined by an agent’s knowledge Calculi X some theories don’t take real numbers but intervals or pairs X von mises freq theory does not satisfy countable additivity Epistemology X class/log/subj  can’t account for widespread use of freq X freq  can’t explain how degree of belief offer access to prob X prop  metaphysical: struggle to identify a precise link with freq V emp-based/obj-bayes  allow background knowledge of any form to constraint degrees of belief Variety X freq/prop  can’t ascribe prob to a hypothesis or to single-cases Parsimony X prop  prob are primitive V degrees of belief, sequences of outcomes (we attach a freq to) are already in our ontology
  • Variety desideratum is quite a stumbling block: some interpretations don’t make sense in the single-case and others do not provide a means for interpreting generic level prob The only viable option seems to be pluralism Emp-bases and obj bayes seem most attractive options: allow using freq in the generic case, then use these freq to constraint single-case degrees of belief This still leaves open the choice btw emp-based subjectivism and obj-bayesianism. Obj-Bayes has a pragmatic virtue: it is on average more cautious when it comes to risky decisions [GIVE EXAMPLE]
  • Medical and epidemiological sciences oft summarize results by means of risks and odds. Results are displayed in 2x2 contingency tables N=number of subjects, P=proportion, a-d labels the 4 cells There is also a mathematical relation btw odds and probabilities Computations are fairly easy
  • Interpretation is tricky 3 remarks: The child in the last quotation doesn’t make sense unless we make clear that it is a statistical individual, ie individual randomly sampled from the population Calculation involve proportions  RR and OR have a preferred generic interpretation, as they do not make sense in the single-case. Consequently, the corresponding prob need freq intepretation RR OR and prob are not *directly* applicable to the single-case – single-case prob ought to be constrained by knowledge of freq data according to obj bayesian approach
  • [Browse on iter of the talk] -
  • Traditionally social sciences look for social causes, health sciences look for biological causes of disease. New paradigm emerging in identifying both social and biological factors of disease. In this sense it is paradigmatic of the social and health sciences Surely quantitative causal analysis has taken a significant step with probabilistic modelling. Genuine phil interest for phil of causality and probability, about methodological, epistemological as well as metaphysical aspects related to causality and probability. What rationale, what notion of causality (epistemic or physical?), how to draw inference from the generic to the single-case and the other way around Being concerned both with the generic and single-case, the problem of the level of causation inexorably raises again. Are there levels? How are they to be conceived of? How are to be related? Are philosophers and scientists talking about the same thing in dealing with the dichotomy population-individual?
  • Capits Presentation

    1. 1. Interpreting Probability in Causal Models for Cancer Federica Russo & Jon Williamson Philosophy – University of Kent
    2. 2. Overview <ul><li>Cancer epidemiology </li></ul><ul><li>Interpretations of probability </li></ul><ul><li>Desiderata </li></ul><ul><li>Frequency- cum -Objective Bayesianism </li></ul><ul><li>Risks, odds and probabilities </li></ul>
    3. 3. Cancer epidemiology <ul><li>A double objective </li></ul><ul><ul><li>Establishing generic claims </li></ul></ul><ul><ul><li>Non-smokers have a statistically significant greater risk (25%) of lung cancer if their spouses are smokers </li></ul></ul><ul><ul><li>Applying the generic in the single-case </li></ul></ul><ul><ul><li>Audry, who has metastatic breast cancer, will survive more than 5 years, to extent 0.4 </li></ul></ul><ul><li>Both are probabilistic statements </li></ul>
    4. 4. Interpretations on the market <ul><li>Classical and logical </li></ul><ul><ul><li>P = ratio # of favourable cases / # of all equipossible cases </li></ul></ul><ul><li>Physical: frequency and propensity </li></ul><ul><ul><li>P = limiting relative frequency of an attribute in a reference class </li></ul></ul><ul><ul><li>P = tendency of a type of physical situation to yield an outcome </li></ul></ul><ul><li>Subjective </li></ul><ul><ul><li>P = quantitative expression of an agent’s opinion, </li></ul></ul><ul><ul><li>degree of belief or epistemic attitude </li></ul></ul><ul><li>Objective Bayesian </li></ul><ul><ul><li>P = degree of belief shaped on empirical and logical constraints </li></ul></ul>
    5. 5. Desiderata <ul><li>Objectivity </li></ul><ul><ul><li>Account for the objectivity of probability </li></ul></ul><ul><li>Calculi </li></ul><ul><ul><li>Explain how we reason about probability </li></ul></ul><ul><li>Epistemology </li></ul><ul><ul><li>Explain how we can know about probability </li></ul></ul><ul><li>Variety </li></ul><ul><ul><li>Cope with the full variety of probabilistic claims </li></ul></ul><ul><li>Parsimony </li></ul><ul><ul><li>Be ontologically parsimonious </li></ul></ul>
    6. 6. Let’s bargain Class/ Log Prop Freq Subj Emp- Based Obj Bayes Objectivity     Calculi   Epistemology      Variety    Parsimony  
    7. 7. Deal! Frequency- cum -ObjectiveBaysianism <ul><li>Pluralism is a viable option: </li></ul><ul><ul><li>Generic causal claims require </li></ul></ul><ul><ul><li>a frequency interpretation </li></ul></ul><ul><ul><li>Single-case causal claims require </li></ul></ul><ul><ul><li>an objective Bayesian interpretation </li></ul></ul><ul><li>Objective Bayesianism have </li></ul><ul><li>pragmatic virtues </li></ul>
    8. 8. Risks, Odds and Probabilities: Easy to compute <ul><li>Risks and odds compare proportions </li></ul>Factor Disease Yes No Exposed n 11 p 11 n 12 p 12 Unexposed n 21 p 21 n 22 p 22
    9. 9. Risks, Odds and Probabilities: Tricky to interpret <ul><li>… 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 … </li></ul><ul><ul><li>(Sistrom & Garvan 2004) </li></ul></ul><ul><li>… odds and probabilities are different ways of expressing the chance that an outcome may occur… </li></ul><ul><ul><li>(Sistrom & Garvan 2004) </li></ul></ul><ul><li>… the probability that a child with eczema will also have fever is estimated by the proportion 141/561 (25.1%) … </li></ul><ul><ul><li>(Bland & Altman 2000) </li></ul></ul>
    10. 10. To sum up <ul><li>In the context of cancer epidemiology: </li></ul><ul><ul><li>Two categories of causal claims: </li></ul></ul><ul><ul><li>Generic – single-case </li></ul></ul><ul><ul><li>These are probabilistic </li></ul></ul><ul><li>The market offers: </li></ul><ul><ul><li>Classical/Logical, Physical, </li></ul></ul><ul><ul><li>Subjective, Objective Bayesian </li></ul></ul><ul><li>We went for: </li></ul><ul><ul><li>Frequency- cum -Objective Bayesianism </li></ul></ul>
    11. 11. Conclusions and … what next? <ul><li>Epidemiology: </li></ul><ul><ul><li>looks for socio-economic & biological causes </li></ul></ul><ul><ul><ul><li> Thus it’s paradigmatic of the </li></ul></ul></ul><ul><ul><ul><li>social and health sciences </li></ul></ul></ul><ul><ul><li>models causal relations with probabilities </li></ul></ul><ul><ul><ul><li> Thus it raises genuine interest for the philosophy of causality and probability </li></ul></ul></ul><ul><ul><li>is concerned with generic and single-case claims </li></ul></ul><ul><ul><ul><li> Thus gives us further questions: </li></ul></ul></ul><ul><ul><ul><li>the levels of causation </li></ul></ul></ul>
    12. 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 Sciences www.kent.ac.uk/secl/philosophy/jw/2006/CausalityProbability.htm

    ×