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Bayesian Adaptive Designs for Dose Escalation Studies Midwest Biopharmaceutical Statistics Workshop

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Title: Bayesian Adaptive Designs for Dose Escalation Studies Midwest Biopharmaceutical Statistics Workshop


1
Bayesian Adaptive Designs for Dose Escalation
StudiesMidwest Biopharmaceutical Statistics
Workshop
Anna McGlothlin 20 May 2009
2
Contents
  • Traditional Dose Escalation Design
  • (and its shortcomings)
  • The Continual Reassessment Method
  • An example trial using CRM
  • Simulation and Operating Characteristics
  • Overview of other novel designs
  • Summary

3
Motivation
Why should you care about novel designs for dose
escalation studies?
Traditional designs are not reliable for
selecting the correct maximum tolerated dose
Wrong dose carried forward to future trials.
Standard design tends to treat a high percentage
of patients at doses outside of the therapeutic
range.
Novel designs are better for patients!
4
Dose Escalation Studies
  • Typically small, uncontrolled studies.
  • GOAL Determine the maximum tolerated dose (MTD),
    and/or a recommended Phase II dose.
  • Two Approaches
  • Algorithm-based designs
  • 33 (or the more general AB)
  • MTD is identified as the dose with fewer than
    some proportion of dose limiting toxicities (e.g.
    lt1/3).
  • Model-based designs
  • MTD is estimated as a quantile of the
    dose-toxicity curve
  • Design may be modified to allow for a control.
    This will be briefly discussed later.

5
Standard 3 3 Design
Note DLT Dose Limiting Toxicity
Enter 3 patients at dose level i
0/3 DLTs
1/3 DLTs
gt 1/3 DLTs
Add 3 patients to dose level i
1/6 DLTs
gt 1/6 DLTs
Escalate to dose level i 1
Stop and declare dose level i 1 as the MTD
One common variation allows de-escalation, as in
the following example.
6
Example 3 3 Design
At the end of the trial, dose level 3 is declared
the MTD.
7
Problems with Standard 3 3 Design
  • The 3 3 design tends to treat a high proportion
    of patients at low, possibly ineffective dose
    levels.
  • There is no statistical estimation of the MTD.
  • The probability of stopping at an incorrect dose
    level is higher than generally believed (Reiner,
    Paoletti, OQuigley 1999).
  • This design uses data only from the most recent
    cohort, and ignores data from previous cohorts.

If a dose has true DLT rate of 25, there is a
60 chance that the algorithm will escalate to a
higher dose for the next cohort.
8
Model-based Designs
  • Model-based designs use a statistical model to
    describe the relationship between dose and
    outcome
  • Continual Reassessment Method (CRM)
  • OQuigley, Pepe, Fisher (1990)
  • Faries (1994)
  • Goodman, Zahurak, Piantadosi (1995)
  • Escalation with Overdose Control (EWOC)
  • Babb, Rogatko, Zacks (1998)
  • Joint Toxicity/Efficacy
  • Braun (2002)
  • Thall and Cook (2004)

9
Continual Reassessment Method
  • Start with a prior estimate of Pr(DLT) for each
    dose level.
  • Select a mathematical model to describe the
    relationship between dose and Pr(DLT).
  • Describe uncertainty about the model by a prior
    distribution.
  • After each patient, update the model, and
    estimate the probability of toxicity for each
    dose level.
  • Treat the next patient at the dose whose estimate
    is closest to some pre-specified target (say,
    25).
  • Stop when a maximum sample size is reached.

Reference OQuigley, Pepe, and Fisher (1990)
10
Statistical Models for CRM
  • Let the toxicity response be yj Binomial(nj,
    pj) for doses j 1, , J.
  • The following models are commonly used with CRM
  • Hyperbolic Tangent
  • Logistic
  • Power
  • Prior for ß Unit Exponential, Uniform, Gamma,
    etc.

11
Transformation of Dose Levels
  • These single-parameter curves are only defined
    over a restricted set of xs.
  • Therefore, the doses must be transformed to
    ensure that they lie in the appropriate range.
  • The x-hat values are calculated to give the
    defined prior probabilities on the dose-toxicity
    curve, assuming that ß 1 (its prior mean)

12
Modifications to the CRM
  • To address concerns surrounding the original
    implementation of CRM, several modifications have
    been proposed, including
  • Always start at the lowest dose level.
  • Limit the escalation increment.
  • Escalate by cohorts rather than single patients.
  • Definition of MTD
  • Dose whose Pr(DLT) is closest to target, or
  • Highest dose where Pr(DLT) is below target
  • Early stopping rules
  • Stop if CRM recommends a dose level at which XX
    number of cohorts have already been treated.
  • Stop if any dose has probability gt XX of being
    the MTD.
  • Stop if the (1 a)100 credible interval for
    MTD is sufficiently narrow.

Notable references Faries (1994) Goodman,
Zahurak, Piantadosi (1995)
13
A Hypothetical Trial
  • Consider a dose escalation study with the
    following design characteristics
  • Cohort Size 3 subjects
  • Maximum Sample Size 10 cohorts (30 subjects)
  • 6 Dose Levels
  • Doses must be explored in sequential order (no
    skipping), starting with the lowest dose.
  • MTD is defined as the dose level at which the
    probability of DLT is nearest to 25.
  • Early Stopping Rule Stop if 3 cohorts have been
    treated at a dose, and CRM predicts the same dose
    for the next cohort
  • Model Hyperbolic tangent Unit exponential prior
    for ß
  • Prior Probability of DLT at each dose

14
Hypothetical Trial
15
Simulation Overview
  • The preceding slide demonstrated the performance
    of CRM for a single hypothetical trial.
  • We now ask the question How does the method
    perform on average? This question is addressed
    by simulation
  • Assume we know the true curve
  • Conduct a hypothetical trial using data generated
    from the true curve
  • Repeat many times
  • Operating Characteristics
  • How often is each dose level chosen as MTD at the
    end of the trial?
  • Average sample size (overall and per dose level)
  • Etc.

16
Simulation Scenarios
  • Three different curves to represent a possible
    dose-toxicity curve
  • MTD1 Dose Level 2
  • MTD2 Dose Level 4
  • MTD3 Dose Level 5
  • For each scenario, simulate 1000 trials.
  • Summarize each scenario and compare to standard
    design.
  • Prior probabilities

17
Simulation Results
3 3 chooses lowest dose in over 50 of
simulated trials!
18
Simulation Results
Again, 3 3 often chooses a dose that is below
the true MTD. CRM chooses the correct dose 53
of the time.
19
Simulation Results
20
Simulation Results
CRM treats higher proportion of patients at doses
close to the MTD.
21
CRM with No Early Stopping
The probability of selecting the correct dose
improves when the CRM continues to the maximum
trial size with no early stopping.
22
CRM vs. 33
  • The standard design is easy to understand and
    implement.
  • The 33 design tends to choose a dose below the
    true MTD.
  • The CRM tends to treat patients at doses close to
    the MTD, whereas 33 treats a higher proportion
    of patients at low, possibly ineffective, doses.
  • The CRM provides a statistical estimate of the
    MTD, and allows for uncertainty around this
    estimate.
  • CRM can target any relevant DLT rate.
  • CRM incorporates available data from all cohorts,
    while the 3 3 design uses information from only
    the most recent cohort.

23
Operational considerations
  • Allow sufficient time prior to protocol approval
    to conduct simulations and assess operating
    characteristics.
  • Statistician will need timely access to data
    during the trial in order to update the model.
  • Model updates can be performed prospectively
    Given the current data, what will the
    model-predicted dose be if
  • The next patient has a DLT?
  • The next patient has no DLT?

24
Other Dose Escalation Designs
  • 1. Two-sample CRM
  • Suppose there are two distinct, but related,
    populations.
  • Examples
  • TRTSOC and TRT alone
  • Different dosing schedules
  • It may be reasonable to assume that there is some
    information common to both populations.
  • The dose-toxicity curves may be modeled to
    account for this shared information.
  • Logistic
  • Hyperbolic Tangent

Reference OQuigley, Shen, Gamst (1999).
25
Other DE Designs (continued)
  • 2. Escalation with Overdose Control (EWOC)
  • Model
  • Reparameterization
  • Marginal posterior cdf of the MTD ?k(x)
  • Escalation Scheme The kth patient is allocated
    to dose so that the posterior
    probability of exceeding MTD is equal to the
    feasibility bound, a.

where ? MTD ?0 Pr(DLT) at xmin
References Babb J, Rogatko A, Zacks S (1998)
Chu et al. (2009)
26
Other DE Designs (continued)
  • 3. Bivariate CRM
  • Suppose that interest lies in two outcomes
    toxicity and efficacy.
  • Joint model
  • Where
  • p1 and p2 are the probabilities of toxicity and
    efficacy respectively
  • y and z binary indicators of toxicity and
    efficacy
  • k(p1,p2,?) is a normalizing constant
  • ? is the probability of combined toxicity and
    efficacy.
  • Two-stage design
  • Estimate MTD using the previously described CRM.
  • Then subjects are allocated to the dose whose
    probability of efficacy is closest to some
    pre-defined target.

Reference Braun (2002) Alternative design for
toxicity and efficacy outcomes Thall and Cook
(2004).
27
Other DE Designs (continued)
  • 4. CRM for Ordered Outcomes
  • Suppose that toxicity is measured on an ordinal
    scale

Define MTD as the dose for which Pr(grade 3 or
above) is closest to some pre-specified target
(say, 25). Use information from lower grade
toxicities to improve estimation of
MTD. Alternatively, Bekele and Thall (2004)
propose a design to incorporate information from
multiple ordinal toxicities, weighted according
to importance.
28
Summary
  • Traditional designs for dose escalation are not
    optimal for selection of MTD, and may expose a
    high proportion of patients to low doses.
  • Novel designs such as CRM are under-utilized, and
    should be considered for dose escalation studies.
  • Novel designs have been proposed to address
    different trial objectives (efficacy/toxicity,
    two-samples, etc.)
  • Simulations are vital to understanding the
    operating characteristics of the trial design.
  • The most common implementation of CRM is for
    phase 1 oncology trials. But its use should not
    be confined to just one therapeutic area.
  • Trial design may be modified to allow a control
    arm
  • Within each cohort, randomized subjects to TRT
    dose or placebo.
  • The placebo information may be incorporated into
    the dose-toxicity model.

29
Key References
  • Bekele BN, Thall PF (2004). Dose-finding based on
    multiple toxicities in a soft tissue sarcoma
    trial. Journal of the American Statistical
    Association, 99 26-35.
  • Babb J, Rogatko A, Zacks S (1998). Cancer phase I
    clinical trials Efficient dose escalation with
    overdose control. Statistics in Medicine, 17
    1103-1120.
  • Braun TM (2002). The bivariate continual
    reassessment method extending the CRM to phase I
    trials of two competing outcomes. Controlled
    Clinical Trials, 23 240-256.
  • Chu P-L, Yong L, Shih WJ (2009). Unifying CRM and
    EWPC designs for phase I cancer clinical trials.
    Journal of statistical planning and inference,
    139 1146-1163.
  • Faries D (1994). Practical modifications of the
    continual reassessment method for phase I cancer
    clinical trials. Journal of Biopharmaceutical
    Statistics, 4147-164.
  • Goodman SN, Zahurak ML, Piantadosi S (1995). Some
    practical improvements in the continual
    reassessment method for phase I studies.
    Statistics in Medicine, 141149-1161.
  • Heyd JM, Carlin BP (1999). Adaptive design
    improvements in the continual reassessment method
    for phase I studies. Statistics in Medicine,
    181307-1321.
  • Ishizuka N, Ohashi Y (2001). The continual
    reassessment method and its applications a
    Bayesian methodology for phase I cancer clinical
    trials. Statistics in Medicine, 202661-2681.
  • Lasonos A (2008). A comprehensive comparison of
    the CRM to the standard 33 dose escalation
    scheme in Phase I dose finding studies. Clinical
    Trials, 5 465-477.
  • OQuigley J, Pepe M, Fisher L (1990). Continual
    reassessment method A practical design for phase
    I clinical trials in cancer. Biometrics,
    4633-48.
  • OQuigley J, Shen Z, and Gamst A (1999).
    Two-Sample Continual Reassessment Method. Journal
    of Biopharmaceutical Statistics, 9 17-44.
  • Rogatko, et al. (2007). Translation of Innovative
    Designs Into Phase I Trials. Journal of Clinical
    Oncology, 25 4982-4986.
  • Thall PF, Cook JD (2004). Dose-Finding Based on
    Efficacy-Toxicity Trade-Offs. Biometrics, 60
    684-693.
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