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Bayesian Adaptive Dose Finding Studies: Smaller, Stronger, Faster

Bayesian Adaptive Dose Finding Studies: Smaller, Stronger, Faster. Scott M. Berry scott@berryconsultants.com. 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

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Bayesian Adaptive Dose Finding Studies: Smaller, Stronger, Faster

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  1. Bayesian Adaptive Dose Finding Studies: Smaller, Stronger, Faster Scott M. Berry scott@berryconsultants.com

  2. 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

  3. 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

  4. Empirical Data Observe Yij for subject i, outcome j Yij = 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

  5. Efficacy Endpoints • Let d be the dose • Pj(d) probability of event j=1,2; j(d) ~ N(, 2) G(1,1) N(1,1) N(–2,1) IG(2,2)

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

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

  8. Utility Function Monetary FDA Approval P2(0) is prob Efficacy #2 success for d=0

  9. Monetary Utility (“Fake”)

  10. U3: FDA Success Statistical Significance This is a posterior predictive calculation. The probability of trial success, averaged over the current posterior distribution

  11. Statistical + Utility Output • E[U(d)] • E[j(d)], V[j(d)] • E[Pj(d)], V[Pj(d)] • Pr[dj max U] • Pr[P2(d) > P0] • Pr[ d>> 0 | 250/per arm) each d

  12. 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!

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

  14. Allocator V*(d≠0) = V*(d=0) =

  15. Allocator • “Drop” any rd<0.05 • Renormalize

  16. Decisions Pr(d = d*) > C1 If found, stop: • Find best dose? • Learn about best dose? • Shut down allocator wj if stop!!!! • Stop trial when both happen • If Pr(P2(d*) >> P0) < 0.10 stop for futility Pr(P2(d*) >> P0)>C2 If found, stop:

  17. 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 w2 and w3 • Utility and why? are critical and should be done--easy to ignore and say it is too hard.

  18. 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

  19. Scenario #1 MAX Stopping Rules: C1 = 0.80, C2 = 0.90

  20. 18 2 2 0 2 15 0 5 3 5 18 1 1 0 2 20 0 2 1 0 19 0 5 3 1 17 4 4 2 3 Nin #1 #2 #3 Nout 18 3 5 2 2

  21. Dose Probabilities

  22. 18 2 2 0 2 19 1 5 4 1 Nin #1 #2 #3 Nout 20 1 1 0 3 20 0 2 1 0 19 0 5 3 3 25 8 7 2 7 24 5 7 2 7

  23. Dose Probabilities

  24. 19 2 3 0 1 20 1 5 4 0 Nin #1 #2 #3 Nout 21 1 2 0 2 20 0 2 1 0 21 0 5 3 4 29 9 7 2 11 31 6 11 3 17

  25. Dose Probabilities

  26. 20 2 4 0 0 21 1 5 4 4 Nin #1 #2 #3 Nout 23 1 2 0 4 20 0 2 1 0 25 1 5 4 0 36 10 7 3 10 45 10 12 3 16

  27. Dose Probabilities

  28. 20 2 4 0 0 25 1 5 4 6 Nin #1 #2 #3 Nout 26 1 2 0 1 20 0 2 1 0 26 2 6 4 5 44 13 7 3 12 52 10 13 4 15

  29. Dose Probabilities

  30. 21 2 4 0 3 26 1 6 4 5 Nin #1 #2 #3 Nout 26 1 2 0 6 20 0 2 1 0 33 3 7 4 5 52 13 8 4 10 61 15 18 4 12

  31. Dose Probabilities

  32. Trial Ends • P(10-Dose max Util dose) = 0.907 • P(10-Dose >> Pbo 250/arm) = 0.949 • 280 subjects: 32, 20, 24, 31, 38, 62, 73 per arm

  33. Operating Characteristics

  34. Operating Characteristics

  35. Scenario #2 Stopping Rules: C1 = 0.80, C2 = 0.90

  36. Operating Characteristics

  37. Operating Characteristics

  38. Simulation #3 Stopping Rules: C1 = 0.80, C2 = 0.90

  39. Operating Characteristics

  40. Operating Characteristics

  41. Scenario #4 Stopping Rules: C1 = 0.80, C2 = 0.90

  42. Operating Characteristics

  43. Operating Characteristics

  44. Scenario #5 Stopping Rules: C1 = 0.80, C2 = 0.90

  45. Operating Characteristics

  46. Operating Characteristics

  47. 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!!!

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