OverviewOverviewRole of Bayes in drug/device settingsRole of Bayes in drug/device settingsRole of Bayes in drug/device settingsRole of Bayes in drug/device settingsBayesian design of experimentsBayesian design of experimentsBayesian design of experimentsBayesian design of experimentsBayesian design of experimentsBayesian design of experimentsBayesian design of experimentsBayesian design of experimentsBayesian design of experimentsBayesian design of experimentsBayesian design of experimentsBayesian design of experimentsBayesian clinical trial designBayesian clinical trial designBayesian clinical trial designBayesian clinical trial designBayesian clinical trial designBayesian clinical trial designBayesian clinical trial designBayesian clinical trial designBayesian clinical trial designBayesian clinical trial designBayesian clinical trial designBayesian clinical trial designBayesian clinical trial designBayesian clinical trial designBayesian clinical trial designBayesian clinical trial designResults: Bayesian Design of Study BResults: Bayesian Design of Study BResults: Bayesian Design of Study BResults: Bayesian Design of Study BResults: Bayesian Design of Study BResults: Bayesian Design of Study BAddendum: Is our prior ``ethical''?Addendum: Is our prior ``ethical''?Handling multiple endpointsHandling multiple endpointsHandling multiple endpointsHandling multiple endpointsHandling multiple endpointsHandling multiple endpointsHandling multiple endpointsMultiple stopping criteriaMultiple stopping criteriaMultiple stopping criteriaMultiple stopping criteriaMultiple stopping criteriaMultiple stopping criteriaOverall stopping rule:Overall stopping rule:Overall stopping rule:Advanced models: Adding MCMCAdvanced models: Adding MCMCAdvanced models: Adding MCMCExample: Weibull survival modelExample: Weibull survival modelExample: Weibull survival modelRange of equivalenceRange of equivalenceRange of equivalenceRange of equivalenceThe six possible outcomes and decisionsCommunity of priorsCommunity of priorsCommunity of priorsCommunity of priorsCommunity of priorsCommunity of priorsCommunity of priors (cont'd)Community of priors (cont'd)Community of priors (cont'd)Community of priors (cont'd)Community of priors (cont'd)Community of priors (cont'd)Monitoring plots: full posteriorsMonitoring plots: tail areasMCMC-based Bayesian designMCMC-based Bayesian designMCMC-based Bayesian designMCMC-based Bayesian designMCMC-based Bayesian designMCMC-based Bayesian designBayesian power calculationBayesian power calculationType I error rate calculationType I error rate calculationType I error rate calculationType I error rate calculationCalling WinBUGS from R using BRugsCalling WinBUGS from R using BRugsCalling WinBUGS from R using BRugsCalling WinBUGS from R using BRugsResults from Power.RResults from Power.ROverviewBiostatisticians in the drug and medical deviceindustries are increasingly faced with data that are:highly multivariate, with many important predictorsand response variablestemporally correlated (longitudinal, survival studies)costly and difficult to obtain, but often with historicaldata on previous but similar drugs or devicesBayesian Clinical Trial Design and Analysis – p. 1/31OverviewBiostatisticians in the drug and medical deviceindustries are increasingly faced with data that are:highly multivariate, with many important predictorsand response variablestemporally correlated (longitudinal, survival studies)costly and difficult to obtain, but often with historicaldata on previous but similar drugs or devicesRecently, the FDA Center for Devices has encouragedhierarchical Bayesian statistical approaches –Methods are not terribly novel: Bayes (1763)!But their practical application has only becomefeasible in the last decade or so due to advances incomputing via Markov chain Monte Carlo (MCMC)methods and related WinBUGS softwareBayesian Clinical Trial Design and Analysis – p. 1/31Role of Bayes in drug/device settingsSafety/efficacy studies: Historical data and/orinformation from published literature can be used toreduce sample size, reducing time and expense.Unlimited looks at accumulating data are also permitted(due to different framework for testing).Bayesian Clinical Trial Design and Analysis – p. 2/31Role of Bayes in drug/device settingsSafety/efficacy studies: Historical data and/orinformation from published literature can be used toreduce sample size, reducing time and expense.Unlimited looks at accumulating data are also permitted(due to different framework for testing).Equivalence studies: Bayes allows one to make directstatements about the probability that one drug isequivalent to another, rather than merely “failing toreject” the hypothesis of no difference.Bayesian Clinical Trial Design and Analysis – p. 2/31Role of Bayes in drug/device settingsSafety/efficacy studies: Historical data and/orinformation from published literature can be used toreduce sample size, reducing time and expense.Unlimited looks at accumulating data are also permitted(due to different framework for testing).Equivalence studies: Bayes allows one to make directstatements about the probability that one drug isequivalent to another, rather than merely “failing toreject” the hypothesis of no difference.Meta-analysis: Bayes facilitates combining disparatebut similar studies of a common drug or device.Bayesian Clinical Trial Design and Analysis – p. 2/31Role of Bayes in drug/device settingsSafety/efficacy studies: Historical data and/orinformation from published literature can be used toreduce sample size, reducing time and expense.Unlimited looks at accumulating data are also permitted(due to different framework for testing).Equivalence studies: Bayes allows one to make directstatements about the probability that one drug isequivalent to another, rather than merely “failing toreject” the hypothesis of no difference.Meta-analysis: Bayes facilitates combining disparatebut similar studies of a common drug or device.Hierarchical models: Realistic models can be fit tocomplicated, multilevel data (e.g., multiple observationsper patient, or multiple patients per clinical site),accounting for all sources of uncertainty.Bayesian Clinical Trial Design and Analysis – p. 2/31Bayesian design of experimentsConsider again our usual normal/normal model (withσ2= 1 for now), and we wish to testH0: θ = 0 versus Ha: θ > 0 .Bayesian Clinical Trial Design and Analysis – p. 3/31Bayesian design of