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

5. 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)

6. 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)

7. 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 ?

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

9. Monetary Utility (Fake)

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

14. 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

15. 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!

16. 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

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

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

19. 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

20. 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.

21. 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

22. Scenario #1 DoseP1P1 P2P2 P3P3 P4P4 UTIL 00.050.060.0500 0.250.050.100.0600 0.50.080.130.0700.063 10.120.170.0800.323 2.50.150.200.0900.457 50.180.230.1000.532 100.250.300.1100.656 Stopping Rules: C 1 = 0.80, C 2 = 0.90 MAX

23. 18 1 0 2 20 0 2 1 0 18 2 0 2 15 0 5 3 5 19 0 5 3 1 17 4 2 3 18 3 5 2 N in #1 #2 #3 N out

24. Dose Probabilities 0.25.512.5510 P(>>Pbo).18.33.27.29.67 P(max).01.04.06.04.33.52 P(2nd).03.06.10.13.35.32 Alloc.06.01.02.04.06.35.46

25. 20 1 0 3 20 0 2 1 0 18 2 0 2 19 1 5 4 1 19 0 5 3 25 8 7 2 7 24 5 7 2 7 N in #1 #2 #3 N out

26. Dose Probabilities 0.25.512.5510 P(>>Pbo).12.38.36.38.92.91 P(max).00.02.04.41.53 P(2nd).00.03.06.07.47.37 Alloc.00.02.04.09.34.51

27. 21 1 2 0 2 20 0 2 1 0 19 2 3 0 1 20 1 5 4 0 21 0 5 3 4 29 9 7 2 11 31 6 11 3 17 N in #1 #2 #3 N out

28. Dose Probabilities 0.25.512.5510 P(>>Pbo).13.39.38.26.97.85 P(max).00.02.03.01.39.55 P(2nd).00.03.10.05.46.35 Alloc.11.00.03.10.05.46.35

29. 23 1 2 0 4 20 0 2 1 0 20 2 4 0 21 1 5 4 25 1 5 4 0 36 10 7 3 10 45 10 12 3 16 N in #1 #2 #3 N out

30. Dose Probabilities 0.25.512.5510 P(>>Pbo).16.41.38.48.93 P(max).00.02.03.04.26.65 P(2nd).00.05.07.10.49.29 Alloc.00.08.11.18.35.28

31. 26 1 2 0 1 20 0 2 1 0 20 2 4 0 25 1 5 4 6 26 2 6 4 5 44 13 7 3 12 52 10 13 4 15 N in #1 #2 #3 N out

32. Dose Probabilities 0.25.512.5510 P(>>Pbo).16.40.31.41.98.89 P(max).00.02.03.06.27.63 P(2nd).00.06.12.48.28 Alloc.16.00.10.04.13.26.30

33. 26 1 2 0 6 20 0 2 1 0 21 2 4 0 3 26 1 6 4 5 33 3 7 4 5 52 13 8 4 10 61 15 18 4 12 N in #1 #2 #3 N out

34. Dose Probabilities 0.25.512.5510 P(>>Pbo).13.36.32.65.96 P(max).00.01.09.08.81 P(2nd).00.05.23.52.15 Alloc

35. 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 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

36. Operating Characteristics Pbo0.250.512.5510 SS392125376389110 Pmax---0.00 0.040.96 SS66 Pmax---0.00 0.010.060.93

37. Operating Characteristics AdaptiveConstant Constant/ No Model P(Sufficient)0.9360.8100.700 P(Cap)0.0640.1900.300 P(Futility)0.000 P(10mg Best)0.960.930.88 Mean SS384459517 SD SS186224235 Mean TDose175412631420 Max TDose481823702341

38. Scenario #2 DoseP1P1 P2P2 P3P3 P4P4 UTIL 00.060.05 00 0.250.100.050.0600 0.50.130.080.0700.063 10.170.120.0800.323 2.50.200.150.1000.452 50.230.180.1500.502 100.250.200.4000.302 Stopping Rules: C 1 = 0.80, C 2 = 0.90

39. Operating Characteristics Pbo0.250.512.5510 SS71274181137172164 Pmax---0.00 0.030.220.600.16 SS100 Pmax---0.00 0.030.200.440.33

40. Operating Characteristics AdaptiveConstant Constant/ No Model P(Sufficient) 0.3140.2660.286 P(Cap) 0.6860.7340.708 P(Futility) 0.000 0.006 P(5mg Best) 0.600.440.58 Mean SS 694702704 SD SS 193190182 Mean TDose 295419331937 Max TDose 44892455.252436

41. Simulation #3 DoseP1P1 P2P2 P3P3 P4P4 UTIL 00.060.05 00 0.10.100.050.0600 0.50.130.080.0700.063 10.300.250.1100.656 2.50.170.120.0800.323 50.200.150.0900.457 100.230.180.1000.532 Stopping Rules: C 1 = 0.80, C 2 = 0.90

42. Operating Characteristics Pbo0.250.512.5510 SS5323281195276102 Pmax---0.00 0.920.000.010.07 SS87 Pmax---0.00 0.830.000.020.15

43. Operating Characteristics AdaptiveConstant Constant/ No Model P(Sufficient)0.9060.5960.708 P(Cap)0.0920.4040.290 P(Futility)0.0020.0000.002 P(1mg Best)0.920.830.87 Mean SS453606542 SD SS187205225 Mean TDose166316621491 Max TDose37712384.252414.25

44. Scenario #4 DoseP1P1 P2P2 P3P3 P4P4 UTIL 00.060.05 00 0.10.070.06 00 0.50.080.07 00 10.090.08 00 2.50.090.080.0900 5 0.080.1000 100.090.080.1100 Stopping Rules: C 1 = 0.80, C 2 = 0.90

45. Operating Characteristics Pbo0.250.512.5510 SS92917566768390 Pmax---0.450.040.070.100.130.21 SS84 Pmax---0.440.040.080.120.150.17

46. Operating Characteristics AdaptiveConstant Constant/ No Model P(Sufficient)0.0040.0060.030 P(Cap)0.4840.5440.752 P(Futility)0.5120.4500.218 Mean SS574589699 SD SS250258196 Mean TDose163716151922 Max TDose3223.52523.752467.75

47. Scenario #5 DoseP1P1 P2P2 P3P3 P4P4 UTIL 00.060.05 00 0.10.060.05 00 0.50.060.05 00 10.060.05 00 2.50.060.05 00 50.060.05 00 Stopping Rules: C 1 = 0.80, C 2 = 0.90

48. Operating Characteristics Pbo0.250.512.5510 SS66775134384143 Pmax---0.900.010.02 0.03 SS56 Pmax---0.860.010.020.03 0.05

49. Operating Characteristics AdaptiveConstant Constant/ No Model P(Sufficient)0.000 0.002 P(Cap)0.1220.1900.362 P(Futility)0.8780.8100.636 Mean SS350395542 SD SS215241 Mean TDose81110861491 Max TDose24042428.752455.5

50. 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!!!

51. 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!