Bayesian Adaptive Designs for Targeted Therapy Development for Cancer and Beyond

1. University of Pennsylvania Annual Conference onStatistical Issues in Clinical Trials: Statistical Issues in Targeted Therapies Bayesian Adaptive Designs for Targeted Therapy Development for Cancer and Beyond J. Jack Lee, Ph.D. Department of Biostatistics University of Texas M. D. Anderson Cancer Center April 29, 2009

2. Premise • Many new targeted agents • Many, many more potential combination therapies • Don’t know the best dose, schedule • Targeted agents do not work for all patients or may not work at all • May or may not know the predictive markers • May or may not know how best to gauge the treatment effect • response rate, disease stabilization, improved survival • Limited patient population enrolled in clinical trials • Time is of the essence

3. Clinical Trials Design Goals (Good Operating Characteristics) • Be able to answer the question correctly • Low prob of choosing undesirable tx • Control Type I (false positive) error rate • High prob of choosing desirable tx • Control Type II (false negative) error rate / maintain high stat. power • Be able to answer the question quickly: less N • Identify a subset of subjects who may respond better to a targeted treatment • Who will respond? Who will not? • Give better tx to pts - Enhance ethics • Treat more (less) subj in the arms doing well (not working) • Align pts with best available treatments based on pt characteristics • Allow changes on treatment arm(s) • Terminate the non-performing arm(s) early • Add promising new treatment(s)

4. Design Goals Summary We want a design that is : • Accurate • Efficient • Ethical • Flexible • Smart – Since we don’t know all the facts at the beginning of the trial, we need to continue tolearnduring the trial

5. What is the solution? Adaptive Designs! Adaptive designs are ideal for learning!

6. What Are Adaptive Designs? • Trials that use interim data to guide the study conduct • Determine the dose level adaptively • Determine how to treat the next patient adaptively • dose level • Adaptive randomization • Interim analysis for early stopping • Due to harmful effect (toxicity) • Due to beneficial effect (efficacy) • Due to futility (no improvement over standard treatment of lack of efficacy) • Change treatment during the trial • Adding new treatments • Dropping bad treatments • Sample size re-estimation

7. Goals for AR • Individual Ethics • Assign patients into the better treatment arms with higher probabilities • Maximize total number of successes in the trial • Group Ethics • Maximize study power for testing the effectiveness between treatments • Maximize total number of successes both in and beyond the trial • Competing goals

8. Two Treatments,No Markers

9. Simple Adaptive Randomization (AR) The next patient will be assigned to TX1 with • Consider two treatments, binary outcome • First n pts equally randomized (ER) into TX1 and TX2 • After ER phase, • Note that is a tuning parameter •  = 0, ER •  = , “play the winner” • Continue the study until reaching early stopping criteria or maximum N

12. AR rate to TX 1=

13. AR rate to TX 1=

14. Example: Randomized Two-Arm Trial • Frequentist’s approach • Ho: P1 = P2 vs. H1: P1 < P2 P1 = 0.3, P2 = 0.5, =.025 (one-sided), 1 = .8 N1 = N2 = 103, N = 206 • Bayesian approach with adaptive randomization • Consider P1 and P2 are random; Give a prior distribution; Compute the posterior distribution after observing outcomes • Randomize more patients proportionally into the arm with higher response rate • At the end of trial, • Prob(P1 > P2) > 0.975, conclude Tx 1 is better • Prob(P2 > P1) > 0.975, conclude Tx 2 is better • At interim, • Prob(P1 > P2) > 0.999, Stop the trial early, conclude Tx 1 is better • Prob(P2 > P1) > 0.999, Stop the trial early, conclude Tx 2 is better

15. AR Comparisons Use the AR program from http://biostatistics.mdanderson.org/SoftwareDownload/

16. AR Comparisons

17. AR Comparisons

18. Personalized Medicine Journal of Young Investigators, 2008

19. Prognostic / Predictive Markers • Prognostic markers are markers that associate with the disease outcome regardless of the treatment • For example, stage, performance status • Different outcomes in different marker groups (e.g., Stage I, II, or III) using std tx or BSC. • Same difference between marker groups holds across all treatments. (assumption too strong) • Predictive markers are markers which predict differential treatment efficacy in different marker groups • e.g., In Marker (-), tx does not work but in Marker (+), tx works

20. Biomarkers for Personalized Medicine (Cancer)

21. Biomarkers for Personalized Medicine

22. How to summarize the predictive effect of markers in multiple studies? Forest Plot and Meta-Analysis

23. INTACT Trial IDEAL Trial

25. Where do we go next?

26. Don’t know what to do? Be Adaptive!

27. How to design a trial withtwo treatments andone biomarker?

28. 1. Simple Randomization Design A: Standard Therapy Registration Randm. B: Targeted Therapy • Can test whether new treatment works in the whole group. • Can apply the conditional post-hoc analysis to test whether • Does targeted therapy work in Marker ()? • Does targeted therapy work in Marker (+)? • Is marker predictive (Marker x Treatment Interaction)? • Marker distribution may be unbalanced in the two treatment groups

29. 2. Marker x Treatment Interaction Design A: Standard Therapy Randm. Marker− B: Targeted Therapy Registration C: Standard Therapy Testing Markers Marker + Randm. D: Targeted Therapy Can Answer 4 Questions: 1. Does targeted therapy work in Marker ()? (A vs. B) 2. Does targeted therapy work in Marker (+)? (C vs. D) 3. Is marker prognostic? (A vs. C) 4. Is marker predictive (MK x TX Interaction)? (A/B vs. C/D)

30. 3. Bayesian Adaptive Randomization (AR) Design • Design Structure is similar to Marker x Treatment Interaction Design but, • Instead of using equal randomization, apply adaptive randomization with the randomization rate proportional to the treatment effectiveness. • Bayesian AR Designs (a) Subgroup analysis under the hierarchical Bayes model (b) Bayesian logistic regression analysis (c) Bayesian Cox regression analysis • Model based

31. 2. Marker x Treatment Interaction Design 1:1 1:1 A: Standard Therapy Randm. Marker− B: Targeted Therapy Registration C: Standard Therapy Testing Markers Marker + Randm. D: Targeted Therapy

32. 3. Bayesian Adaptive Randomization Design AR 2:1 AR 1:1 AR 1:1 AR 1:4 AR 1:3 AR 1:1 A: Standard Therapy Randm. Marker− B: Targeted Therapy Registration C: Standard Therapy Testing Markers Marker + Randm. D: Targeted Therapy

33. Simulation Settings • N=150 with 1,000 simulation runs • Prob(MK+) = 0.3 and 0.5 • Two analysis methods were compared for Designs 1, 2, and 3 • Subgroup Comparison – pairwise comparisons between different subgroups • Logistic Regression – logistic regression model was fit with marker effect, treatment effect, and their interaction • Two Bayesian Adaptive Randomization Designs were evaluated • Hierarchical Bayes Model for subgroup comparison • Declare TX difference if Prob(q0 > q1 ) > 0.965 or Prob(q1 > q0 ) > 0.965 where q is the posterior response rate • AR rate for TX 1: q1 / (q0 + q1) • Bayesian Logistic Regression • Declare TX difference if Prob(bi > 0) > 0.975 or Prob(bi < 0) > 0.975 where bi is the posterior regression coefficient for i = marker, treatment, or interaction • AR rate for TX 1: Prob(q1 > q0) • The first 50 patients were equally randomized followed by adaptive randomization

34. Two treatments, One marker, Binary endpoint Scenario 1: Marker Prognostic TX Marker (-) Marker (+) 0 0.2 0.4 1 0.2 0.4 Scenario 0: Null Case TX Marker (-) Marker (+) 0 0.2 0.2 1 0.2 0.2 Scenario 3: Marker Prog/Pred Scenario 2: Marker Predictive

35. Table 1. Statistical Power for Designs 1, 2, and 3 Prob(MK+)=0.5

36. Table 2. Patient Allocation

37. What have we learned? • The parameters in Bayesian designs can be calibrated to control the Type I error. • Bayesian AR design allocates more patients in more effective treatments. It gains efficiency through modeling but AR could result in mild loss in statistical power. There is a tradeoff between individual ethics versus group ethics. • Bayesian AR design continues to learn about the effects of markers, treatments, and their interactions along the trial and adjust the randomization proportion accordingly. The efficiency can be further improved (smaller sample size) by adding early stopping rules due to futility or efficacy

38. How to design a trial withmultiple treatments andmultiple biomarkers?

39. BATTLE (Biomarker-based Approaches of Targeted Therapy for Lung Cancer Elimination) • Patient Population: Stage IV recurrent non-small cell lung cancer (NSCLC) • Primary Endpoint: 8-week disease control rate [DCR] • 4 Targeted treatments • 11 Biomarkers • 200 patients • 20% type I error rate and 80% power Zhou X, Liu S, Kim ES, Lee JJ. Bayesian adaptive design for targeted therapy development in lung cancer - A step toward personalized medicine (Clin Trials, 2008).

40. Biomarker Profile and Adaptive Randomization Sorafenib Vandetanib Erlotinib + Bexarotene Erlotinib Four Molecular Pathways Targeted in NSCLC: BATTLE Program Enrollment into BATTLE Umbrella Protocol Endpoint: Progression-free survival at 8 weeks – Disease Control Rate (DCR)

41. Bayesian Hierarchical Probit Model • Probit model with hyper prior (Albert et al, 1993) • Notation • -- ith : subject, i=1 , ..., njk • -- jth : treatment arm, j=1 , …, 4 • -- kth : marker group, k=1 , …, 5 • -- yijk: 8-week progression-free survival status: 0(no) vs 1(yes) • -- zijk : latent variable • -- jk: location parameter • -- j: hyper-prior on jk • -- gjk: disease control rate (DCR) • -- 2,2: hyper-parameters control borrowing across MGs • within and between treatments

42. Computation of the Posterior Probability via Full Conditional Distribution –Gibbs Sampling • The random variables are generated from their complete posterior conditional distributions as follows. • The latent variable zijk is sampled from a truncated normal distribution centering at μjk. • The full conditional distribution of μjk and Φj are the linear combination of the prior distribution and the sampling distribution.

43. Equal Randomization (ER) Followed By Adaptive Randomization (AR) • ER is applied in the first stage for model development • AR will be applied after enrolling at least one patient in each (Treatment x MG) subgroup. • Adaptively assign the next patient into the treatment arms proportional to the marginal posterior disease control rates. • Randomization Rate (RR): proportional to the marginal posterior DCR. • set a minimum RR to 10% to ensuring a reasonable probability of randomizing pts in each arm • Suspend randomization of a treatment in a biomarker group if • Probability(DCR > 0.5 | Data) < 10% • Declare a treatment is effective in a biomarker group if • Probability(DCR > 0.3 | Data) > 80%

44. Response Adaptive Randomization e.g., a pt w/ EGFR mutation (+), K-ras (-), VEGF (+), RXR (-) & Cyclin D1 (-) TX P(DCR) P(Rand) After Tx P(Rand) P(DCR) .50 .75 1 .60 .56 .10 .08 2 .10 .07 .20 .17 3 .20 .15 .25 .30 .22 4 .30 Next pt received TX=1 and had a Disease Control 1.20 1.35

45. Simulation – Scenario 1 • One effective treatment for MG 1-4, no effective treatment for MG 5, adaptive randomization (AR),with vague prior

46. Simulation Results, Scenario 1(without early stopping)

47. Simulation Results, Scenario 1(with early stopping)

48. Conventional Design • Simon’s optimal two-stage design in each of the 4 x 5 = 20 trt x MG combinations • H0: p  p0 vs. H1: p  p1 p0 = 0.3, p1 = 0.5,  = 0.20, 1-  = 0.80 n1 = 6, r1 = 1, n= 20, r= 7, • Total N up to 20 x 20 = 400

49. Potential Benefits • Smaller trials • More accurate conclusions • More questions can be considered in a single trial • An umbrella trials for uniform tissue collection and biomarker analysis • Modular approach with each treatment trial consists of one treatment modality which can be plug in and out from the umbrella trial • Treat patients better in trials • Faster, more efficient drug development through rational learning using the interim data • Lower costs of medical care

50. Cumulative Accrual for BATTLE Accrual Rate: 235/26 = 9 pts / month (original estimate 7-8 pts/mon) Randomization Rate: 177/26 = 6.8 pts / month