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BAYESAN STATISTICS FOR CLINICAL INVESTIGATORS

CTOS 2012 - Prague. BAYESAN STATISTICS FOR CLINICAL INVESTIGATORS. Paolo Bruzzi National Institute for Cancer Research Genoa - Italy. “Bayesian”?. Predictive value of diagnostic tests Studies of expression profiles (micorarrays) Trials with a Bayesian component Interim analyses

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BAYESAN STATISTICS FOR CLINICAL INVESTIGATORS

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  1. CTOS 2012 - Prague BAYESAN STATISTICS FOR CLINICAL INVESTIGATORS Paolo Bruzzi National Institute for Cancer Research Genoa - Italy

  2. “Bayesian”? • Predictive value of diagnostic tests • Studies of expression profiles (micorarrays) • Trials with a Bayesian component • Interim analyses • Bayesian design BayesianStatistics!

  3. Differences between Conventional and Bayesian Statistics • Meaning of probability • Use of prior evidence

  4. Conventional P Probability of an observation BayesianProbability Probabilityof a hypothesis

  5. Conventional P Probability of observing what was actually observed if H0 true BayesianProbability Probabilityof H0/H1/H2/H3… givenobserved data (and priordistribution)

  6. Conventional P Probability of the observed difference (if the experimental therapy does not work) BayesianProbability Probabilitythat the experimentaltherapyworks/doesn’t work (givenobserveddifference and priorknowledge)

  7. Examples - Diagnosis Mr. XY shows a lung nodule at TC • Frequentist Probability that Mr. XY shows a lung nodule (if he doesn’t have lung cancer) • Bayesian Probability that Mr. XY has lung cancer (given his nodule and his prior risk)

  8. Examples - Diagnosis Mr. XY shows a lungnodule at TC • Frequentist Probabilitythat Mr. XY shows a lungnodule(ifhedoesn’t havelungcancer) • Bayesian Probabilitythat Mr. XY haslungcancer(givenhisnodule and hispriorrisk)

  9. Examples – Clinical trial Controltherapy (CT): 5/40 responses Experimentaltherapy (ET): 10/40 responses • Frequentist Probabilitytoobserve10/40 vs 5/40 if CT and ET are identical • Bayesian Probabilitythat CT and ET areidentical(given 5/40, 10/40 and priorknowledge)

  10. Examples – Clinical trial Controltherapy (CT): 5/40 responses Experimentaltherapy (ET): 10/40 responses • Frequentist Probabilitytoobserve10/40 vs 5/40 if CT and ET are identicalP= 0.15 Notsignificant Ho (CT & ET identical) NOT REJECTED

  11. Examples – Clinical trial Controltherapy (CT): 5/40 responses Olddrugs, newschedule 10/40 responses • Frequentist Probabilitytoobserve10/40 vs 5/40 if CT and ET are identicalP= 0.15 Notsignificant Ho (CT & ET identical) NOT REJECTED

  12. Examples – Clinical trial Controltherapy (CT): 5/40 responses VeryPromisingther. (ET): 10/40 responses • Frequentist Probabilitytoobserve10/40 vs 5/40 if CT and ET are identicalP= 0.15 Notsignificant Ho (CT & ET identical) NOT REJECTED

  13. Examples – Clinical trial Controltherapy (CT): 5/40 responses Experimentaltherapy (ET): 10/40 responses • Bayesian Probabilitythat CT and ET areidentical ? (given 5/40, 10/40 and priorknowledge) Itdepends on priorknowledge!

  14. Examples – Clinical trial Controltherapy (CT): 5/40 responses Herbal + standard (ET): 10/40 responses • Bayesian Probabilitythat CT and ET areidentical (=herbaltherapynoteffective)? Still high!

  15. Examples – Clinical trial Controltherapy (CT): 5/40 responses VeryPromisingther. (ET): 10/40 responses • Bayesian Probabilitythat CT and ET areidentical (thatis, newtherapynoteffective)? Quite low!

  16. NOTE The different meaning of Bayesian probability in theory, has • Implications for (clinical) decision analysis • No peculiar implications for rare tumors

  17. Differences between Conventional and Bayesian Approaches • Meaning of probability • Use of prior evidence

  18. Conventional P Probability of the observed difference (if the experimental therapy does not work) BayesianProbability Probabilitythat the experimentaltherapyworks/doesn’t work (givenobserveddifference and priorknowledge)

  19. Conventional Statistical Reasoning 1. Starting hypothesis (H0): new treatment = standard one

  20. Conventional Statistical Reasoning 1. Startinghypothesis (H0): new treatment = standard one Todemonstrate: new treatment >> standard, rejectnullhypothesis

  21. Conventional Statistical Reasoning 1. Startinghypothesis (H0): new treatment = standard one Todemonstrate: new treatment >> standard, rejectnullhypothesis Tothispurpose, onlyevidencecollectedwithinone or more trialsaimed at falsifyingit can beused

  22. Conventional Statistical Reasoning 1. Startinghypothesis (H0): new treatment = standard one Todemonstrate: new treatment >> standard, rejectnullhypothesis Tothispurpose, onlyevidencecollectedwithinone or more trialsaimed at falsifyingit can beused -> LARGE SAMPLE SIZE

  23. Conventional Statistical Reasoning Tothispurpose, onlyevidencecollectedwithinone or more trialsaimed at falsifyingit can beused -> LARGE SAMPLE SIZE No useof Externalevidence Evidence in favor of…

  24. Example Question: Efficacy of radiochemotherapy in a tumor type very rare in a site (e.g. squamous histology in stomach c.) External evidence: RX+CTX is effective in squamous cancers in more common sites Evidence in favor of..: The observed response rate is very high (e.g. 6/10)

  25. Does this information affect …. • the sample size of the phase III trial aimed to assess RT+CTX in squamous gastric c. ? • the analysis of its results (p value)?

  26. Squamous gastric cancer Planning a trial of RT+CTX Analysing its results (p value)

  27. Squamous gastric cancer Planning a trial of RT+CTX Herbal therapy Analysing its results (p value)

  28. Squamous gastric cancer Same Sample Size P values Conclusions Planning a trial of RT+CTX Herbal therapy Analysing its results (p value)

  29. Conventional (frequentist) statistical reasoning Exclusive reliance on experimental evidence Large Trials

  30. Large Trials Implication in rare tumors: Generic Selection criteria (All STS’s + Stage + treatment line) • Appropriate for chemotherapy trials • Possibly inappropriate for trials of Targeted Therapies

  31. Conventional (frequentist) statistical reasoning Conventional (frequentist) statisticalreasoning Experimental evidence Bayesianstatisticalreasoning Experimentalevidence + PreviousKnowledge

  32. Bayesian Approach Prior Experimental Evidence Evidence + Posterior Probability Distribution

  33. Conventional Probability Probability of a positive test given disease/no disease (Sensitivity, specificity) BayesianProbability Probabilityofdiseasegiven test result and diseaseprevalence(Predictivevalue)

  34. Previous Knowledge? • Biological rationale • Evidence of activity • Efficacy in other diseases with similarities • Efficacy in other stages of the same disease

  35. Prior evidence in Bayesian statistics • Needed in order to compute posterior probability

  36. Prior evidence in Bayesian statistics • Needed in order to compute posterior probability • It must be transformed into a probability distribution (shape, mean, median, standard deviation, percentiles, etc)

  37. Prior evidence in Bayesian statistics • Needed in order to compute posterior probability • It must be transformed into a probability distribution • Based on • Objective information • Subjective explicit beliefs • Both

  38. Prior evidence in Bayesian statistics • Note: The difference between Bayesian and conventional statistics decreases with increasing strength of the empirical evidence

  39. Prior evidence in Bayesian statistics Difference between Bayesian and conventional statistics Young man, never smoked, no family history Prior probability of lung c.=1/100.000 • Nodule at routine x-ray • Suspicious lesion at TC • Histological confirmation after biopsy Posterior Probability?

  40. Prior evidence in Bayesian statistics Difference between Bayesian and conventional statistics Epidermoid lung cancer: Palliative care prolongs survival: A priori: 1-30% Small monocentric trial: HR= 0.75 (0.55-0.95) Large multicentric trial: HR= 0.8 (0.7 -0.9) Meta-analysis of 8 trials:HR= 0.82 (0.76-0.88)

  41. Prior evidence in Bayesian statistics Frequent tumors Prior direct evidence Estimates Empirical evid. Indirect evidence?

  42. Prior evidence in Bayesian statistics Rare tumors Prior direct evidence Estimates Empirical evid. ? Indirect evidence!

  43. Need to use all the available information • Direct evidence • Experimental • Prior • Indirect evidence

  44. Example Mortality Tumor X Nil vs A 15% vs 12.5% N=12000 P = 0.0007 H0 Rejected: A is effective in X

  45. Example Mortality Tumor X Nil vs A 15% vs 12.5% N=12000 P = 0.0007 Tumor Y Nil vs A 15% vs 7.5% N= 240 P=0.066 H0 not rejected: A not shown effective in y

  46. Prior Information: Mortality Tumor X Nil vs A 15% vs 12.5% N=12000 P = 0.0007 Tumor Y Nil vs A 15% vs 7.5% N= 240 P=0.066

  47. Prior Information: X and Y are BRAF+ Mortality Tumor X Nil vs A 15% vs 12.5% N=12000 P = 0.0007 Tumor Y Nil vs A 15% vs 7.5% N= 240 P=0.066

  48. Prior Information: X and Y are BRAF+A = Anti BRAF Mortality Tumor X Nil vs A 15% vs 12.5% N=12000 P = 0.0007 Tumor Y Nil vs A 15% vs 7.5% N= 240 P=0.066

  49. Prior Information: X and Y are BRAF+A = Anti BRAF Mortality Tumor X Nil vs A 15% vs 12.5% N=12000 P = 0.0007 Tumor Y Nil vs A 15% vs 7.5% N= 240 P=0.066 INTERPRETATION?

  50. A different example

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