BAYESIAN ADAPTIVE DESIGN & INTERIM ANALYSIS

1. BAYESIAN ADAPTIVE DESIGN & INTERIM ANALYSIS Donald A. Berry dberry@mdanderson.org

2. Some references • Berry DA (2003). Statistical Innovations in Cancer Research. In Cancer Medicine e6. Ch 33. BC Decker. (Ed: Holland J, Frei T et al.) • Berry DA (2004). Bayesian statistics and the efficiency and ethics of clinical trials. Statistical Science.

3. Benefits • Adapting; examples • Stop early (or late!) • Change doses • Add arms • Drop arms • Final analysis • Greater precision (even full follow-up) • Earlier conclusions

4. Goals • Learn faster: More efficient trials • More efficient drug/device development • Better treatment of patients in clinical trials

5. OUTLINE: EXAMPLES • Extraim analysis • Modeling early endpoints • Seamless Phase II/III trial • Adaptive randomization • Phase II trial in AML • Phase II drug screening process • Phase III trial

6. EXTRAIM ANALYSES* • Endpoint: CR (detect 0.42 vs 0.32) • 80% power: N = 800 • Two extraim analyses, one at 800 • Another after up to 300 added pts • Maximum n = 1400 (only rarely) • Accrual: 70/month • Delay in assessing response *Modeling due to Scott Berry <scott@berryconsultants.com>

7. After 800 pts accrued, have response info on 450 pts • Find pred prob of stat sig when full info on 800 pts available • Also when full info on 1400 • Continue if . . . • Stop if . . . • If continue, n via pred prob • Repeat at 2nd extraim analysis

8. vs 0.80

9. MODELING EARLY ENDPOINTS: LONGITUDINAL MARKERS • Example CA125 in ovarian cancer • Use available data from trial (& outside of trial) to model relationship over time with survival, depending on Rx • Predictive distributions • Use covariates • Seamless phases II & III

10. CA125 data & predictive distributions of survival for two of many patients* ——> *Modeling due to Scott Berry <scott@berryconsultants.com>

11. Patient #1 Treatment Days

12. Patient #1

13. Patient #2 Days

14. Patient #2

15. Methods • Analytical • Multiple imputation

16. SEAMLESS PHASES II/III* • Early endpoint (tumor response, biomarker) may predict survival? • May depend on treatment • Should model the possibilities • Primary endpoint: survival • But observe relationships *Inoue, et al (2002 Biometrics)

17. Conventional drug development Survivaladvantage Market Good resp No survivaladvantage Not No resp Stop Phase 3 Phase 2 > 2 yrs 6 mos 9-12 mos Seamless phase 2/3 < 2 yrs (usually)

18. Seamless phases • Phase 2: 1 or 2 centers; 10 pts/mo, randomize E vs C • If pred probs “look good,” expand to Phase 3: Many centers; 50 pts/mo (Initial centers continue accrual) • Max n = 900 [Single trial: survival data combined in final analysis]

19. Early stopping • Use pred probs of stat sig • Frequent analyses (total of 18) using pred probs to: • Switch to Phase 3 • Stop accrual for • Futility • Efficacy • Submit NDA

20. Comparisons Conventional Phase 3 designs: Conv4 & Conv18, max N = 900 (samepower as adaptive design)

21. Expected N under H0

22. Expected N under H1

23. Benefits • Duration of drug development is greatly shortened under adaptive design: • Fewer patients in trial • No hiatus for setting up phase 3 • All patients used for • Phase 3 endpoint • Relation between response & survival

24. Possibility of large N • N seldom near 900 • When it is, it’s necessary! • This possibility gives Bayesian design its edge [Other reason for edge is modeling response/survival]

25. ADAPTIVE RANDOMIZATIONGiles, et al JCO (2003) • Troxacitabine (T) in acute myeloid leukemia (AML) combined with cytarabine (A) or idarubicin (I) • Adaptive randomization to: IA vs TA vs TI • Max n = 75 • End point: Time to CR (< 50 days)

26. Adaptive Randomization • Assign 1/3 to IA (standard) throughout (until only 2 arms) • Adaptive to TA and TI based on current results • Results 

28. Drop TI Compare n = 75

29. Summary of results CR < 50 days: • IA: 10/18 = 56% • TA: 3/11 = 27% • TI: 0/5 = 0% Criticisms . . .

30. SCREENING PHASE II DRUGS • Many drugs • Tumor response • Goals: • Treat effectively • Learn quickly

31. Standard designs • One drug (or dose) at a time; no drug/dose comparisons • Typical comparison by null hypothesis: RR = 20% • Progress hopelessly slow!

32. Standard 2-stage design First stage 20 patients: • Stop if ≤ 4 or ≥ 9 responses • Else second set of 20

33. An adaptive allocation • When assigning next patient, find r = P(rate ≥ 20%|data) for each drug • Assign drugs in proportion to r • Add drugs as become available • Drop drugs that have small r • Drugs with large r  phase 3

34. Suppose 10 drugs, 200 patients Identify nugget … With probability: In average n: 9 drugs have mix of RRs 20% & 40%, 1 has 60% (“nugget”) >99% 110 <70% Adaptive Standard 50 Standard Adaptive Adaptive also better at finding “40%”, & sooner

35. Suppose 100 drugs, 2000 patients Identify nugget … With probability: In average n: 99 drugs have mix of RRs 20% & 40%, 1 has 60% (“nugget”) >99% 1100 <70% Adaptive Standard 500 Standard Adaptive Adaptive also better at finding “40%”, & sooner

36. Consequences • Treat pts in trial effectively • Learn quickly • Attractive to patients, in and out of the trial • Better drugs identified sooner; move through faster

37. PHASE III TRIAL • Dichotomous endpoint • Q = P(pE > pS|data) • Min n = 150; Max n = 600 • After n = 50, assign to arm E with probability Q • Except that 0.2 ≤ P(assign E) ≤ 0.8 • (Not “optimal,” but …)

38. Recommendation to DSMB to • Stop for superiority if Q ≥ 0.99 • Stop accrual for futility if P(pE – pS < 0.10|data) > PF • PF depends on current n . . .

39. PF

40. Common prior density for pE & pS • Independent • Reasonably non-informative • Mean = 0.30 • SD = 0.20

42. Updating After 20 patients on each arm • 8/20 responses on arm 1 • 12/20 responses on arm 2

44. Assumptions • Accrual: 10/month • 50-day delay to assess response

45. Need to stratify. But how? Suppose probability assign to experimental arm is 30%, with these data . . .

47. One simulation; pS = 0.30, pE = 0.45 Superiority boundary Final Std 12/38 19/60 20/65 Exp 38/83 82/167 87/178

48. One simulation; pE = pS = 0.30 Futility boundary 9 mos.EndFinal Std 8/39 15/57 18/68 Exp 11/42 32/81 22/87

49. Operating characteristics

50. FDA: Why do this? What’s the advantage? • Enthusiasm of PIs • Comparison with standard design . . .