1. 1 Designs for Oncology MTD Finding Yevgen Tymofyeyev MERCK & Co., Inc September 12, 2008

2. 2 Acknowledgement Linda Sun Keaven Anderson Jason Clark Chen Cong Lisa Lupinacci Yang Song

3. 3 Outline Objectives of Phase I Oncology Trials Considered designs:  3+3 Design, Group Designs, Cumulative Cohort Design  Modified Ji Bayesian Design  Continual Reassessment Method (CRM)  Misc. techniques Isotonic regression Simon’s acceleration Some design comparison and recommendations

4. 4 Phase I Oncology Trials Cancer cells are cells with uncontrolled growth. Most oncology drugs are somewhat toxic to kill tumor cells or to control the growth. Therefore, Phase I oncology trials start with cancer patients directly, instead of healthy subjects like in other therapeutic areas.

5. 5 Objectives of Phase I Oncology Trials The general belief of oncologists is that the more toxic a regiment is, the more efficacious.  For all designs we assume monotonic dose-toxicity relation The primary objective of Phase I oncology studies is to find the maximum tolerated dose (MTD). MTD – highest dose where Dose Limiting Toxicity (DLT) rate is acceptable. MTD will be carried to Phase II trials for proof of concept evaluation in terms of efficacy.

6. 6 Traditional 3+3 Design This is an adaptive design, since we allocate patients according to what we have learned during the study.  Start from the lowest dose level  Adapt every cohort of 3 patients  Dose escalate until unacceptable toxicity rate Variants of design include “A+B”, accelerated titration design, etc.

7. 7 Dose 3 patients DLTs? Dose is Not Safe (de-escal- ate) Dose Is Safe (escalate) Dose 3 more patients Total DLTs? >2/3 1/3 0/3 >2/6 =1/6 Traditional 3+3 Design

8. 8 Comments on Traditional 3+3 Design Pros:  Simple and intuitive algorithm  Easy to implement and monitor  Model free: don’t have to assume dose response curve Cons:  Target DLT rate for MTD is about 20% (unclear)  The safety and tolerability of the final dose is only tested with a maximum of 6 patients  Require to observe toxicity outcome in the current cohort

9. 9 A+B designs Lin and Shin (2001) 3+3 is a special case, when A=B=3 Applicable for targeting wide range DLT Require to observe toxicity outcome in the current cohort (longer study duration and problem with lost to follow-up) Ivanova (2006) provides rules on how to construct A+B designs and group up-and- down designs

10. 10 Group Up-and-Down Designs Wetherill (1963); Gezmu and Flournoy (2006) Subjects are treated in cohorts of size s X(dj) – number of toxicities observed in the last cohort at dose j, j=1,…,K Design denoted by UD(s,c L,c U ), c L and c U are set in a way to “target” given Γ, i.e MTD  0 ≤ c L ≤ c U ≤ s The next cohort is assigned to  (i) dose d j+1 if X(dj) ≤ c L  (ii) dose d j-1 if X(dj) ≥ c U  (iii) dose d j if c L <X(dj)< c U

11. 11 Cumulative Cohorts Design (CCD) for Dose Finding Ivanova, Flournoy, Chung (2005) Treatment allocation rule is similar to the group up- and-down designs Let q = X(dj)/ N(dj), where N(dj) –sample size on dose dj  If q ≤ Γ- Δ, increase dose  If q ≥ Γ+Δ, decrease dose  If Γ- Δ ≤ q ≤ Γ+Δ, repeat dose Note: For a given Γ,the same Δ is recommended for all N(dj).

12. 12 CCD (cont.) Treatment allocation rule based on not only the most resent cohort of subjects (as for A+B and group-up-down designs) but rather on all cumulative information at the current dose Simple and have good operating characteristics; “Time to event” (TITE) modification of CCD is available to use in studies where the follow-up response time is long (similar to TITE CRM) Performance results form the literature  CCD ~ CRM  CCD is often more preferable than group designs

13. 13 Modified Ji Bayesian Design To address the issues with traditional 3+3 design, Merck oncology group started to use a two-stage Bayesian adaptive design which modifies Ji’s (2007) design. Stage 1: Dose Escalation  Mimic 3+3 design Stage 2: Dose Confirmation  Adaptively allocating patients around the potential MTD dose to confirm the safety and tolerability of the final selected dose

14. 14 An Example of Modified Ji Design MTD: the target DLT rate is 20% The maximum sample size is 50  This number is largely determined by budget/resource Stage 1: Dose Escalation  Follow the scheme of 3+3 design  Until 2 out of 3 patients or 2 out of 6 patients experience DLTs at a given dose

15. 15 An Example of Modified Ji Design (Cont’) Stage 2: Dose Confirmation  Start to allocate patients continuously (or in cohorts) at the dose right below the highest tested dose.  Once each enrolled patient DLT information is available, use the monitoring table provided to determine whether to put the next patient to the next higher dose, or the next lower dose, or the same dose. The monitoring table is determined by Bayesian statistics  This Stage ends when Either there is a dose with 3 or fewer patients out of 14 having DLT Or all 50 patients have been enrolled Final analysis:  Pooled Adjacent Violator Algorithm (PAVA), ref. Robertson at. al. (1988), to select the dose which has DLT rate most close to the target rate.

16. 16 An Example of Modified Ji Design (Cont’)

17. 17 Bayesian Statistics Used in modified Ji Design Put non-informative prior to DLT rate of each dose  Beta (1, 1) for all doses  That is, this design is also model free and doesn’t have to assume dose response curve Once patient toxicity information becomes available, update the posterior distribution of DLT rate of the testing dose  Allocate the next patient according to how the posterior distribution relates to the target DLT rate.

18. 18 Illustration of Ji’s Algorithm

19. 19 Ji Design Decision Rules Current tried dose is i; p T - target toxicity prob. of MTD Posterior probability of the intervals at dose i  q D = P (p i -p T > K 1 σ i | data)  q S = P (-K 2 σ i ≤ p i -p T ≤ K 1 σ i | data)  q E = P (p i -p T < - K 2 σ i | data)  σ i is the posterior std. dev. of p i Compute J=I( P (p i+1 >p T | data ) > ξ) Choose max { q D, q S, q E (1-J) } which results in  D – “De-escalate”  S – “Stay”  E – “Escalate” Parameters K 1, K 2, ξ, are prior parameters can be adjusted according to study specifics

20. 20 Comments on the modified Ji Bayesian Design Pros:  Keep all the pros of 3+3 design: model free, easy to implement and monitor, dose-escalation is transparent to physicians  Address issues of 3+3 design: the final dose can be selected with greater confidence/assurance. Cons:  Can’t handle partial information. Time-to-event CRM, TITE-CCD may be applicable

21. 21 Continual Reassessment Method (CRM), simple version Bayesian parametric model  E.g., Probability of toxicity at dose k, ψ k = (a k ) θ θ – parameter with non - informative prior (a 1, …, a m ) – fixed pre-specified values  Typical example: (.05,.1,.2,.3,.5,.7 ) Rules applied after each new response(s) :  Update posterior for θ, hence update ψ k for all dose levels k=1,…,m  Allocate next patient (s) to the dose suggested to be the closes to MTD reconciling constrains  Check for early stopping criteria

22. 22 Example of CRM run

23. 23 Example of potential CRM problems, DLT target = 0.30 Dose123456789 N3454——2—— # DLT0000——2—— (A) Posterior summaries ak0.010.0150.020.0250.030.040.050.10.17 ψkψk 0.0690.0850.010.110.120.1440.1630.2420.33 (B) Posterior summaries (equidistant ak) ak0.0630.1250.1880.250.3130.3750.4380.50.563 ψkψk 0.0240.0540.090.130.1760.2260.2810.3410.405

24. 24 Early Stopping for CRM Zohar and Chevret (2001) Stopping criteria  All doses are unacceptable toxic  All doses are of unacceptably low toxicity  The current dose is expected to be the best estimate of the MTD Suitability on the dose scale Suitability on the response probability scale  Based on point estimated  Based on precision in estimates

25. 25 Evaluation of modified Ji design and competing designs What are the operating characteristics of the modified Ji design?  accuracy  speed  safety Do we need the first, “3+3”, design stage? How does the design compare to other competing designs?

26. 26 Versions of the Modified Ji Design The following rules are very similar:  Two stage design  Skipping the 3+3 stage and working with the table when response from subjects is analyzed in cohorts of size 3 Number of patients at current dose Number of toxicities 123456 0SEEEEE 1DUDSSSE 2 DDD 3 4 Table for MTD= 20%

27. 27 Versions of the Modified Ji Design (Cont.) Put “S” in the grey entries of the table. Number of patients at current dose Number of toxicities 123456 0SEEEEE 1DUDSSSE 2 DDD 3 4 Table for MTD= 20% Equivalently, each newly tested dose starts with 3 patients, and then cohort size of 1

28. 28 Simon’s Acceleration Purpose: design a trial so that fewer patients are treated at sub-therapeutic dose levels Method: only one patient per cohort until one patient experienced dose-limiting toxic effects after that switch to 3+3 approach for further escalation Extension: (3 stage design) accelerated escalation → (3+3) → confirmation Performance from simulations: As expected,  good when target dose is in the high dose range (good dose finding and short study duration)  Poor when target dose is in the low dose range (poor dose finding, larger number of DLTs)

29. 29 Isotonic Regression Robertson at. el (1988) Nonparametric (robust) shape constrained fit (least square error fit subject to order restriction) “Borrow” strength cross doses Typically isotonic regression improve probability of right selection of the target dose Better describe dose-toxicity relation Performed when trial is finished Example

30. 30 Isotonic regression

31. 31 Estimation Bias of Isotonic Regression

32. 32 Criteria for Design Evaluation Total number of observed DLTs Probability of the correct selection of the target dose (accuracy) Expected total sample size Distribution of subjects to dose levels Other things to look at  Design flexibility Tuning parameters Cohort size Stopping rules  Simplicity (implementation and study conduct)

33. 33 Design NameDesign Description n at MTD Max N 1Traditional 3+3 Once we see 2/6, the next lower dose is claimed to be the target dose 6N/A 2 Original Ji design with cohort size 1 Dose adaptation according to the monitoring table from the beginning of the study 14 50 3Two-stage modified Ji Stage 1: dose escalation, 3+3 Stage 2: dose confirmation, cohort sz 1 1450 4 Modified Ji's design (cohort size 1 after the first 3 pts) or modified table entries for n=1,2 No stages, each newly tested dose starts with 3 patients, and then cohort size of 11450 5 Three-stage modified Ji (Objective: allocate fewer pts in lower doses) Stage 1: dose escalation, cohort sz 1 (Simon's accelerated titration) Stage 2: dose escalation, (3+3) Stage 3: dose confirmation, cohort sz 1 1450 6CRM One param. Bayesian model, with early stopping for dose misspec. 1440

34. 34

35. 35 Simulation results (,, ): Accuracy, Speed, Safety Target dose (scenario #) Performance of Design 3+3 Original Ji w/ chrt sz=1 Modif. Ji 2 stage Ji w/ 3 sub. at new dose Simon’s + 2 stage CRM middle dose(s) w/ moderate spacing (1-4) LHHLHH LAALAA ALAALA ALAALA AHLAHL HHLHHL middle dose(s) – closer spacing (11) L H (18) H (.13) L A (25) A (.16) H L (31) A (.16) H L (32) A (.16) A A (26) L (.19) H H (23) L (.20) The highest dose or higher than all (5,6) H H (20) N / A L A (24) N / A A - H L (30) N / A H L (31) N / A H H (21) N / A H H(20) N / A Lower than all doses (7) L (.70) H (5.7) H (0.44) H (.93) H (5.4) H(0.43) A (.90) L (8.3) H (0.42) A (.91) L (7.7) H (0.43) A (.92) L (10) A (0.48) H (.95) H (6.0) L (0.78) Multiple doses with toxicity = 0.2, (9,10) N / A H (14,13) H (0.18) N / A A (24,15) A (0.17) N / A L (27,20) A (0.19) N / A L (28,22) A (0.19) N / A L (26,20) L (0.23) N / A A(24,21) L (0.24) “H” = High, “A”= Average, “L”= Low

36. 36 Conclusions CCD and Ji design have similar methodology but were not compared directly here The modified Ji design and its versions improve the 3+3 design (confirm the MTD is tolerable by using moderate number of patients) The modified Ji design in general performed well in our simulation studies in terms of finding MTD and safety One parameter CRM tends to provide better (but comparable to Ji design) estimation of MTD BUT is criticized for exposing subjects to highly toxic doses and dependency on parameter tuning. CRM remains a sound alternative design and two parameter version will be investigated in the future. Modified Ji design is easy to implement as dose assignments for new patients are readily determined in the monitoring table which is created and validated before study beginning.

37. 37 References Durham, S.D., Flournoy, N. Random walks for quantile estimation. Statistical Decision Theory and Related Topics V, Berger, J. and Gupta, S., eds. Springer-Verlag, New York 1994 467-476. Gezmu, M., Flournoy, N. Group up-and-down designs for dose fundings. J. Statist. Plann. Inference 2006 136:1749-1764 Ivanova, A., Flournoy, N., Chung, Y. Cumulative cohort design for dose finding. Journal of Statistical Planning and Inference (2007) Ivanova, A. Escalation, up-and-down and A+B designs for dose-finding trials. Statistics in Medicine 2006 25:3668-3678 Ji, Y., Li, Y., Bekele, N. Dose-finding in phase I clinical trials based on toxicity probability intervals. Clinical Trials 2007 4:235-244 Lin, Y., Shih, W.J. Statistical properties of the traditional algorithm-based designs for phase I cancer clinical trials. Biostatistics 2001 2:203-215. O'Quigley, J., Pepe, M., Fisher L. Continual reassessment method: A practical design for phase I clinical trials in cancer. Biometrics 1990 46:33 - 48. Wetherill, G.B. Sequential estimation of quantal respose curves. J. Roy. Statist. Soc. 1963 B 25: 1-48 Zohar, S., Chevret, S. The continual reassessment method: comparison of Bayesian stopping rules for dose-ranging studies. Statistics in Medicine 2001 20 2827-2843

38. 38 Recommended Literature Chevret, S. ed. Statistical Methods for Dose Finding. 2006. John Wiley. Ting, N. ed. Dose Finding in Drug Development. Springer-Verlag. 2006 New- York.