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Bayesian Adaptive Dose Finding Studies: Smaller, Stronger, Faster Scott M. Berry Scott M. Berry

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Dose Finding Trial Generic example. All details hidden, but flavor is the same Delayed Dichotomous Response Combine multiple efficacy + safety in the dose finding decision Use utility approach for combining various goals Multiple statistical goals Adaptive stopping rules Generic example. All details hidden, but flavor is the same Delayed Dichotomous Response Combine multiple efficacy + safety in the dose finding decision Use utility approach for combining various goals Multiple statistical goals Adaptive stopping rules

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Statistical Model The statistical model captures the uncertainty in the process. Capture data, quantities of interest, and forecast future data Be flexible, (non-monotone?) but capture prior information on model behavior. Invisible in the process The statistical model captures the uncertainty in the process. Capture data, quantities of interest, and forecast future data Be flexible, (non-monotone?) but capture prior information on model behavior. Invisible in the process

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Empirical Data Observe Y ij for subject i, outcome j Y ij = 1 if event, 0 otherwise j = 1 is type #1 efficacy response ($$) j = 2 is type #2 efficacy response (FDA) j = 3 is minor safety event Observe Y ij for subject i, outcome j Y ij = 1 if event, 0 otherwise j = 1 is type #1 efficacy response ($$) j = 2 is type #2 efficacy response (FDA) j = 3 is minor safety event

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Efficacy Endpoints Let d be the dose P j (d) probability of event j=1,2; Let d be the dose P j (d) probability of event j=1,2; j (d) ~ N(, 2 ) IG(2,2) N(–2,1) N(1,1) G(1,1)

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Safety Endpoint Let d be the dose P j (d) probability of safety j=3; Let d be the dose P j (d) probability of safety j=3; N(-2,1) N(1,1) G(1,1)

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Utility Function Multiple Factors: Monetary Profile (value on market) FDA Success Safety Factors Utility is critical: Defines ED ? Multiple Factors: Monetary Profile (value on market) FDA Success Safety Factors Utility is critical: Defines ED ?

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Utility Function Monetary FDA Approval P 2 (0) is prob Efficacy #2 success for d=0

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Monetary Utility (Fake)

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U 3 : FDA Success Statistical Significance This is a posterior predictive calculation. The probability of trial success, averaged over the current posterior distribution

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Statistical + Utility Output E[U(d)] E[ j (d)], V[ j (d)] E[P j (d)], V[P j (d)] Pr[d j max U] Pr[P 2 (d) > P 0 ] Pr[ d >> 0 | 250/per arm) each d E[U(d)] E[ j (d)], V[ j (d)] E[P j (d)], V[P j (d)] Pr[d j max U] Pr[P 2 (d) > P 0 ] Pr[ d >> 0 | 250/per arm) each d

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Allocator Goals of Phase II study? Find best dose? Learn about best dose? Learn about whole curve? Learn the minimum effective dose? Allocator and decisions need to reflect this (if not through the utility function) Calculation can be an important issue! Goals of Phase II study? Find best dose? Learn about best dose? Learn about whole curve? Learn the minimum effective dose? Allocator and decisions need to reflect this (if not through the utility function) Calculation can be an important issue!

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Allocator Find best dose? Learn about best dose? Find best dose? Learn about best dose? Find the V* for each dose ==> allocation probs d* is the max utility dose, d** second best Best Dose 2nd Best Dose

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Allocator V*(d0) = V*(d=0) =

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Allocator Drop any r d <0.05 Renormalize Drop any r d <0.05 Renormalize

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Decisions Find best dose? Learn about best dose? Shut down allocator w j if stop!!!! Stop trial when both happen If Pr(P 2 (d*) >> P 0 ) < 0.10 stop for futility Find best dose? Learn about best dose? Shut down allocator w j if stop!!!! Stop trial when both happen If Pr(P 2 (d*) >> P 0 ) < 0.10 stop for futility If found, stop: Pr(d = d*) > C 1 Pr(P 2 (d*) >> P 0 )>C 2

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More Decisions? Ultimate: EU(dosing) > EU(stopping)? Wait until significance? Goal of this study? Roll in to phase III: set up to do this, though goal becomes w 2 and w 3 Utility and why? are critical and should be done--easy to ignore and say it is too hard. Ultimate: EU(dosing) > EU(stopping)? Wait until significance? Goal of this study? Roll in to phase III: set up to do this, though goal becomes w 2 and w 3 Utility and why? are critical and should be done--easy to ignore and say it is too hard.

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Simulations Subject level simulation Simulate 2/day first 70 days, then 4/day Delayed observation exponential mean 10 days Allocate + Decision every week First 140 subjects 20/arm Subject level simulation Simulate 2/day first 70 days, then 4/day Delayed observation exponential mean 10 days Allocate + Decision every week First 140 subjects 20/arm

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Scenario #1 DoseP1P1 P2P2 P3P3 P4P4 UTIL Stopping Rules: C 1 = 0.80, C 2 = 0.90 MAX

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N in #1 #2 #3 N out

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Dose Probabilities P(>>Pbo) P(max) P(2nd) Alloc

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N in #1 #2 #3 N out

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Dose Probabilities P(>>Pbo) P(max) P(2nd) Alloc

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N in #1 #2 #3 N out

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Dose Probabilities P(>>Pbo) P(max) P(2nd) Alloc

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N in #1 #2 #3 N out

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Dose Probabilities P(>>Pbo) P(max) P(2nd) Alloc

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N in #1 #2 #3 N out

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Dose Probabilities P(>>Pbo) P(max) P(2nd) Alloc

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N in #1 #2 #3 N out

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Dose Probabilities P(>>Pbo) P(max) P(2nd) Alloc

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Trial Ends P(10-Dose max Util dose) = P(10-Dose >> Pbo 250/arm) = subjects: 32, 20, 24, 31, 38, 62, 73 per arm P(10-Dose max Util dose) = P(10-Dose >> Pbo 250/arm) = subjects: 32, 20, 24, 31, 38, 62, 73 per arm

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Operating Characteristics Pbo SS Pmax SS66 Pmax

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Operating Characteristics AdaptiveConstant Constant/ No Model P(Sufficient) P(Cap) P(Futility)0.000 P(10mg Best) Mean SS SD SS Mean TDose Max TDose

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Scenario #2 DoseP1P1 P2P2 P3P3 P4P4 UTIL Stopping Rules: C 1 = 0.80, C 2 = 0.90

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Operating Characteristics Pbo SS Pmax SS100 Pmax

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Operating Characteristics AdaptiveConstant Constant/ No Model P(Sufficient) P(Cap) P(Futility) P(5mg Best) Mean SS SD SS Mean TDose Max TDose

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Simulation #3 DoseP1P1 P2P2 P3P3 P4P4 UTIL Stopping Rules: C 1 = 0.80, C 2 = 0.90

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Operating Characteristics Pbo SS Pmax SS87 Pmax

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Operating Characteristics AdaptiveConstant Constant/ No Model P(Sufficient) P(Cap) P(Futility) P(1mg Best) Mean SS SD SS Mean TDose Max TDose

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Scenario #4 DoseP1P1 P2P2 P3P3 P4P4 UTIL Stopping Rules: C 1 = 0.80, C 2 = 0.90

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Operating Characteristics Pbo SS Pmax SS84 Pmax

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Operating Characteristics AdaptiveConstant Constant/ No Model P(Sufficient) P(Cap) P(Futility) Mean SS SD SS Mean TDose Max TDose

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Scenario #5 DoseP1P1 P2P2 P3P3 P4P4 UTIL Stopping Rules: C 1 = 0.80, C 2 = 0.90

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Operating Characteristics Pbo SS Pmax SS56 Pmax

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Operating Characteristics AdaptiveConstant Constant/ No Model P(Sufficient) P(Cap) P(Futility) Mean SS SD SS Mean TDose Max TDose

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Bells & Whistles Interest in Quantiles Minimum Effective Dose Significance, control type I error Seamless phase II --> III Partial Interim Information Biomarkers of endpoint Continuous, Poisson, Survival, Mixed Continuum of doses (IV)--little additional n!!! Interest in Quantiles Minimum Effective Dose Significance, control type I error Seamless phase II --> III Partial Interim Information Biomarkers of endpoint Continuous, Poisson, Survival, Mixed Continuum of doses (IV)--little additional n!!!

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Conclusions Approach, not answers or details! Shorter, smaller, stronger! Better for: Sponsor, Regulatory, PATIENTS (in and out), Science Why study?--adaptive can help multiple needs. Adaptive Stopping Bid Step! Approach, not answers or details! Shorter, smaller, stronger! Better for: Sponsor, Regulatory, PATIENTS (in and out), Science Why study?--adaptive can help multiple needs. Adaptive Stopping Bid Step!

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