Bayesian Statistics & Innovative Trial Design April 3, 2006 Jane Perlmutter [email protected] Topics Introduction Bayesian vs. Frequentists Statistics Some Innovative Designs Adaptive Designs Random Discontinuation Designs Out of the Box Designs Conclusions

Common Goals: Efficient & Effective Drug Development Effective: Evidence based Statistically sound Ethical Efficient: As rapid as possible, without compromising science or safety As inexpensively as possible, with out compromising science or safety Assumptions Creative, innovative thinking about trial design can improve efficiency without compromising effectiveness Innovative trial designs can have much leverage, because they can be

applied to trials involving any disease or treatment Topics Introduction Bayesian vs. Frequentists Statistics Some Innovative Designs Adaptive Designs Random Discontinuation Designs Out of the Box Designs Conclusions Frequentist vs Bayesian Methods Issue

Frequentist Bayesian Methods Methods Prior information Informally used in design other than in the study being analyzed Interpretation of the A fixed state of nature parameter of interest Basic question How likely is the data, given a particular value of the parameter? Presentation of results Interim analyses P values and estimates adjusted for the number of analyses Conditional power analyses Dealing with subsets in trials Adjusted P values (e.g.,

Bonferroni) Used formally by specifying a prior probability distribution An unknown quantity which can have a probability distribution Plot of posterior distributions of the parameter, calculation of specific posterior probabilities of interest, and use of the posterior distribution in formal decision analysis Inference not affected by he number or timing of interim analyses Predictive probability of getting a firm conclusion Subset effects shrunk towards zero by skeptical prior Spiegelhalter, D. J. et.al. An Introduction to Bayesian Methods in Health Technology Assessment, BMJ, 319, 508-511 (1999). Bayesian Approach Inference Subjective

Component e.g. prior results, theoretical basis Data Component i.e. current experiment Opportunities Afforded by Bayesian Approaches Use Hierarchical Models to focus on optimal Drugs Dosages Sub-groups Use Adaptive Designs to Increase proportion of patients receiving best treatment Completing trial more rapidly with fewer patients

Challenges Raised by Bayesian Approaches Challenge Computationally intractable Subjectivity associated with prior probabilities Solution Use Monte Carlo simulation methods Use multiple scenarios and conduct sensitivity analyses or use uniform priors Strengths & Weaknesses

Weaknesses of Frequentist Approach Tend to answer wrong question Often violate likelihood principle Output in very useful for decision making Too easy to apply mindlessly Subjective component is hidden Analysis is often too simplistic and can be misleading Overuse of hypothesis testing framework Strengths of Bayesian Approach Answer right question and agree with natural common sense Likelihood principle consistently followed Output ideal for decision making Force careful thought of model and prior probabilities Typically more thorough and transparent Allow formal incorporation of relevant information other than data immediately at hand Lend themselves to messy, multiple data sets (e.g., meta-analysis)

Winkler, R.L. Why Bayesian Analysis Hasnt Caught on in Healthcare Decision Making, International Journal of Technology Assessment in Health Care, 17:1, 56-66 (2001). Barriers to Accepting Bayesian Approaches There is significant inertia and comfort with the status quo Most people are taught frequentist methods Limited resources are devoted to developing bio-statistical innovation Journal editors and the FDA have been ambiguous about their acceptance of Bayesian approaches Topics

Introduction Bayesian vs. Frequentists Statistics Some Innovative Designs Adaptive Designs Random Discontinuation Designs Out of the Box Designs Conclusions Adaptive Designs Problems Trials take too long and are too costly Half of patients in trials do not receive optimal treatment

Potential Solution Adaptive Trial Design Randomly & Equally Assign Patient Observe & Predict Responses Randomly & Unequally Assign Patients True Treatme nt Effect? n yes

o If apparent treatment effect is true, groups will diverge & trial can be rapidly completed If apparent treatment effect is random, groups will converge Randomized Discontinuation Design Problem Trials take too long and are too costly Only a small subset of patients is likely to respond to new drugs Potential Solution Randomized Discontinuation Design

Yes All Patients Receive Experimental Treatment 50 % 50 % Respond? Continue on Experimental Treatment } Treatment Effect? Switch to Standard Treatment

Initially all patients receive experimental treatment Superiority is based on known responders only Out-of-the-Box Clinical Trial Problems Patient accrual is slow <50% of eligible patients who are offered trials actually enroll Many patients are uncomfortable with random assignment Out-of-the-Box Trial Design

Potential Solution No No Agree to be Selects own Treatment? in Trial Ye s Experimental Treatment Standard Treatment Randomized Treatment Patient Selected Treatment If no disordinal interaction, fewer randomized patients are

required to achieve same power If there is a patientselection main effect or interaction is found, they may prove interesting Topics Introduction Bayesian vs. Frequentists Statistics Some Innovative Designs Adaptive Designs Random Discontinuation Designs Out of the Box Designs Conclusions

How Advocates Can Accelerate Innovation in Clinical Trial Design Become knowledgeable about sound alternative designs and inform other advocates Ask researchers if they have considered more efficient designs Advocate for more funding of statistical research and training Critically assess potential FDA policy changes, and advocate for constructive change

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