Phase II Selection Design with Adaptive Randomization in a Limited-Resource Environment

1. Phase II Selection Design with Adaptive Randomization in a Limited-Resource Environment Hyung Woo Kim, Ph.D. Takeda Global R & D Center, Inc. Donald A. Berry, Ph.D. M.D. Anderson Cancer Center

2. Overview • Phase 2a designs in oncology • Phase 2 selection design (P2S) with adaptive randomization • Simulation Results • Summary • Discussions

3. Phase 2a Designs in Oncology • Identify promising drugs for further evaluation • Screen out inefficacious drugs

4. Phase 2a Designs in Oncology vs. • Multi-stage (Schultz et al., 1973) • Boundaries: & • Stop & fail to reject Ho • Stop & reject Ho • Continue

5. Phase 2a Designs in Oncology • Simon’s Optimal 2-Stage • Find (n1 , a1) & (n2 , a2) that • Minimizes E(N|H0) or N subject to constraints on type I and type II errors • Fleming’s 2-stage design

6. Example: • Hypothesis to be tested • H0: p = 0.2 vs. H1: p = 0.4 • Ten treatments of interest with • p = 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.4, 0.4, 0.4, 0.6 • Only 200 subjects available • Run one study at a time? – sample size? • Initiate all ten studies at the same time?

7. Example (cont’d): Compare two approaches: • Two-stage study with N = 40,  = .1,  = .10 • Single-stage study with N = 20,  = .1,  = .25 Pr(finding the best treatment) = ? (Based on R=1000 runs) #Trt n rej FP TP #resp ------------------------------------------- 2-stg 7.8 200 3.2 7% 70% 58.8 1-stg 10 200 3.8 9% 81% 60.1

8. Example (cont’d): Compare two approaches: • Two-stage study with N = 40,  = .1,  = .10 • Single-stage study with N = 20,  = .1,  = .25 Pr(finding the best treatment) = ? (Based on R=1000 runs) #Trt n rej FP TP #resp nug? ------------------------------------------- 2-stg 7.8 200 3.2 7% 70% 58.8 75% 1-stg 10 200 3.8 9% 81% 60.1 99%

9. Time to find the best treatment? Best Treatment Found (%) 75% 2-stage Number of Patients

10. Time to find the best treatment? 99% Best Treatment Found (%) 75% 1-stage 2-stage Number of Patients

11. P2S with Adaptive Randomization We need a method that • finds the best/better treatment FASTER • While maintaining comparable (or better) operating characteristics, such as type I and type II errors

12. P2S with Adaptive Randomization • Many Treatments • Limited number of patients • We want to • Treat patients effectively, Learn quickly • Identify better drugs faster • Assign/Treat more patients in the better result group

13. P2S with Adaptive Randomization • When assigning next patient, compute ri = Pr(…|datai) for each drug i • Assign treatments in proportion to ri’s • Drop inefficacious drugs • Efficacious drugs  phase IIb/III

14. Example: • Hypothesis to be tested • H0: p = 0.2 vs. H1: p = 0.4 • Ten treatments of interest with • p = 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.4, 0.4, 0.4, 0.6 • Only 200 subjects available

15. P2S with Adaptive Randomization • Beta-binomial with prior p~Beta(1,1) =u(0,1) • Initial assignment = equally = 1/10 • Randomization probability r = Pr(p > .3 | data) • Update “r” when new outcome is observed • stop in favor of H1 if Pr(p > .2 | data) > 0.995 • stop in favor of H0 if Pr(p < .4 | data) > 0.99 • At trial end, reject H0 if Pr(p > .2 | data) > 0.995

16. S Beta(2, 1) Beta-Binomial Prior Beta(1, 1) Data Post

17. Beta-Binomial Prior Beta(1, 1) S S Data Post Beta(3, 1)

18. Beta-Binomial Prior Beta(1, 1) S S S Data Post Beta(4, 1)

19. F Beta-Binomial Prior Beta(1, 1) S S S Data Post Beta(4, 1)

20. F Beta-Binomial Prior Beta(1, 1) S S S Data Post Beta(4, 2)

21. Beta-Binomial Prior Beta(1, 1) S S F S F Data Post Beta(4, 3)

22. Beta-Binomial Prior Beta(1, 1) S S F F S F Data Post Beta(4, 4)

23. r = Pr(p > .3 | data) 0.70 with Beta (1,1) 0.91 0.49 0.97 0.78 0.78 0.34 0.99 0.24

24. r.ratio (normalized) 1.00 1.30 0.70 1.39 1.12 1.12 0.49 1.42 0.34

25. When to stop? Pr(p > .2 | data) > 0.995 Pr(p < .4 | data) > 0.99

26. Example (cont’d): Compare two approaches: • Single-stage study with N = 20,  = .1,  = .25 • P2S with adaptive randomization (Based on R=1000 runs) #Rx n rej FP TP #resp nug? ------------------------------------------- 1-stg 10 200 3.8 9% 81% 60.1 99% ------------------------------------------- P2S 10 196 3.5 5% 81% 54.7 99%

27. Reason for smaller # of response?

28. Time to find the best treatment?

29. Time to find the best treatment? 99% Best Treatment Found (%) P2S 1-stage Number of Patients

30. Can r be more/less flexible? c c r = Pr(p > .3 | data)

31. Can r be more/less flexible? 99% Best Treatment Found (%) c = 3 c = 2 c = 1/2 Number of Patients

32. What if min(n) = 10 is required? Pr(p > .2 | data) > 0.995 Pr(p < .4 | data) > 0.99

33. What if min(n) = 10 is required?

34. What if min(n) = 10 is required? 99% Best Treatment Found (%) P2S 1-stage Number of Patients

35. In practice, • Outcomes may not be observed right away • Lag time between the first dose of treatment and the observation of outcome • e.g., Outcomes from 1st subject is observed when the 30th subject is enrolled • May cause inefficiency in operating characteristics • Simulate!

36. Comparisons Note: Reject H0 if Pr(p > .2 | data) > 0.995 Note: Reject H0 if Pr(p > .2 | data) > 0.99

37. Delayed response by n = 30? Best Treatment Found (%) P2S(2) P2S(1) 1-stage Number of Patients

38. Summary • When we have many treatments with limited resources (e.g., budget, patients) • Look at accumulating data • Update probabilities • Modify future course of trial using adaptive randiomization • Gain efficiency

39. In practice, • Should give details in protocol • Simulate to find operating characteristics • Could be used in the early phase of development process (non-registrational) • Require more time to prepare • Require additional tools: EDC, IVRS • Require response to be measured quickly

40. Thank you! • Discussion

41. Backup

42. Q: unlimited patients resources? • Hypothesis to be tested • H0: p = 0.3 vs. H1: p = 0.5 • Three treatment arms of interest: • Standard Trt + Dose A • Standard Trt + Dose B • Standard Trt + Dose C Drug A Drug B Drug C can be Case 1 Case 2 Case 3 0.3 0.4 0.2 0.3 0.5 0.2 0.3 0.6 0.5

43. H0: P  0.3 vs. H1: P  0.5 • Two Stage Design (N = 120) • At n = 20; a1 6; r1 12 • At n = 40; a2 16; r2  17 • P2S with adaptive randomization (N = 120) • Prior p~Beta(1,1) • r= Pr(p>.4|Data) • Stop in favor of H0 if Pr(p < .5 | data) > 0.99 • Stop in favor of H1 if Pr(p > .3 | data) > 0.995 • At trial end, reject H0 if Pr(p > .3 | data) > 0.995

44. Operating Characteristics Case 1

45. Operating Characteristics Case 2

46. Operating Characteristics Case 3

47. Time to find the best treatment? p=(0.2, 0.2, 0.5) 100 Best Treatment Found (%) 90.5% 83.5% 80 Adaptive(c=2) 60 Two-stage Adaptive(c=1) 40 20 0 0 20 40 60 80 100 120 Number of Patients

48. Time to find the best treatment? p=(0.4, 0.5, 0.6) 100 99.9% 98.1% Best Treatment Found (%) Adaptive (c=2) 80 60 Adaptive (c=1) Two-stage 40 20 0 0 20 40 60 80 100 120 Number of Patients

49. Apply to Phase 2b Design? • Control arm: assign a fixed randomization ratio (e.g, x % of patients are always assigned to the control) • Treatment arms are compared against • Control arm • Other treatments arms • Drop inferior arms • Keep control arms to the end