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Designs for Oncology MTD Finding . Yevgen Tymofyeyev MERCK & Co., Inc September 12, 2008. Acknowledgement. Linda Sun Keaven Anderson Jason Clark Chen Cong Lisa Lupinacci Yang Song. Outline. Objectives of Phase I Oncology Trials Considered designs:

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designs for oncology mtd finding

Designs for Oncology MTD Finding

Yevgen Tymofyeyev

MERCK & Co., Inc

September 12, 2008

  • Linda Sun
  • Keaven Anderson
  • Jason Clark
  • Chen Cong
  • Lisa Lupinacci
  • Yang Song
  • 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
phase i oncology trials
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.
objectives of phase i oncology trials
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.
traditional 3 3 design
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.

Traditional 3+3 Design

Dose is

Not Safe








Dose 3 more


Dose 3





Dose Is Safe


comments on traditional 3 3 design
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
a b designs
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
group up and down designs
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,cL,cU), cL and cU are set in a way to “target” given Γ, i.e MTD
    • 0 ≤ cL ≤ cU ≤ s
  • The next cohort is assigned to
    • (i) dose dj+1 if X(dj) ≤ cL
    • (ii) dose dj-1 if X(dj) ≥ cU
    • (iii) dose dj if cL <X(dj)< cU
cumulative cohorts design ccd for dose finding
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
    • IfΓ- Δ≤ q ≤ Γ+Δ, repeat dose
  • Note: For a given Γ,the same Δ is recommended for all N(dj).
ccd cont
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
modified ji bayesian design
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
an example of modified ji design
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
an example of modified ji design cont
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.
bayesian statistics used in modified ji design
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.
ji design decision rules
Ji Design Decision Rules
  • Current tried dose is i; pT- target toxicity prob. of MTD
  • Posterior probability of the intervals at dose i
    • qD = P (pi-pT > K1σi | data)
    • qS = P (-K2σi ≤ pi-pT ≤ K1σi | data)
    • qE= P (pi-pT < - K2σi | data)
    • σiis the posterior std. dev. of pi
  • Compute J=I( P (pi+1>pT | data ) > ξ)
  • Choose max { qD, qS, qE(1-J) } which results in
    • D – “De-escalate”
    • S – “Stay”
    • E – “Escalate”
  • Parameters K1, K2, ξ, are prior parameters can be adjusted according to study specifics
comments on the modified ji bayesian design
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
continual reassessment method crm simple version
Continual Reassessment Method (CRM), simple version
  • Bayesian parametric model
    • E.g., Probability of toxicity at dose k, ψk = (ak )θ
      • θ – parameter with non - informative prior
      • (a1, …, am ) – 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 ψk 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
early stopping for crm
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
evaluation of modified ji design and competing designs
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?
versions of the modified ji design
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

Table for MTD= 20%

versions of the modified ji design cont
Versions of the Modified Ji Design (Cont.)

Table for MTD= 20%

Put “S” in the grey entries of the table.


each newly tested dose starts with 3 patients, and then cohort size of 1

simon s acceleration
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)
isotonic regression
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


criteria for design evaluation
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)
simulation results accuracy speed safety
Simulation results ( , , ): Accuracy, Speed, Safety

“H”=High, “A”=Average, “L”= Low

  • 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.
  • 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
recommended literature
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.