Adaptive Designs for Clinical Trials Frank Bretz Novartis 24 April 2013, Tel Aviv.
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Transcript of Adaptive Designs for Clinical Trials Frank Bretz Novartis 24 April 2013, Tel Aviv.
Three definitions of adaptive designs
By adaptive design we refer to a clinical study design that uses accumulating data to decide how to modify aspects of the study as it continues, without undermining the validity and integrity of the trial.
PhRMA White Paper (2006)
A study design is called “adaptive” if statistical methodology allows the modification of a design element (e.g. sample-size, randomisation ratio, number of treatment arms) at an interim analysis with full control of the type I error.
EMEA Reflection Paper (2007)
An adaptive design clinical study is defined as a study that includes a prospectively planned opportunity for modification of one or more specified aspects of the study design and hypotheses based on analysis of data (usually interim data) from subjects in the study.
FDA Draft Guidance for Industry (2010)
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Major types of adaptive designs
Adaptive randomization• Adaptive modifications of treatment randomization probabilities
Adaptive dose finding• Adaptive dose escalation in, for example, Oncology Phase I trials
• Adaptive dose finding in Phase II studies
Group sequential designs• Early stopping either for futility or success (frequentist or Bayesian
rules)
Adaptive sample size re-estimation• Blinded or unblinded sample size re-estimation based on interim data
Adaptive designs for confirmatory trials• Adaptive designs in the sense of the EMEA Reflection Paper (2007)4
Prior to study the true position of dose response curve is unknown
Res
pons
e
Dose
Initial doses
In the adaptive dose finding approach, a small number of patients on many initial doses are used to outline the unknown dose-response.
As the dose response emerges more patients are allocated to doses (including new doses) within the dose- range of interest. In addition the number of patients allocated to ‘non-informative’ doses (‘wasted doses’) is decreased.
Adaptive dose finding – The idea
X = Mean dose response after a pre-defined number of patients
X X X
XX X
Region of interest
X
X
X
X
X
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Benefit of adaptive dose finding designs
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When evaluating adaptive designs from a purely inferential perspective (precision in estimating target dose or dose response) via simulations:• moderate gains in most scenarios
• substantial gains in some scenarios
− e.g. extreme mis-specification of initial design
• but sometimes adaptive designs perform similar or even worse than fixed designs
Can mathematical/analytical considerations confirm these findings and provide more insight• When does an adaptive design pay off?
• Consider a simplified setup, to remove interfering factors
Results from Dette, Bornkamp and Bretz (2013)
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• Goal: Estimate the parameters θ in a non-linear model
• Compare two designs (in terms of mean squared error)
1. Fixed design: N observations according to optimal design based on initial parameter guess θ0
2. Two-stage adaptive design: • Stage 1: N0 = p0N observations according to design based on θ0
• Interim: Estimate θ with maximum likelihood
• Stage 2: Remaining N – N0 observations according to the optimal design based on the interim estimate
At trial end calculate the maximum likelihood estimate based on complete set of N observations
Which design is more efficient and estimates θ more precisely?
Exponential Regression Model
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• Assume the model
with unknown parameterguess θ and initial guess guess θ0
• Exponential model with unknown parameter θ = 1 and initial guesses θ0 = 1.2, 2, 3
• Which design estimates θ more precisely: the fixed design or the two-stage adaptive design?
Exponential Regression Model – Results
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Relative efficiency of adaptive versus non-adaptive design for N = 100, θ = 1. Efficiency > 1 indicates that the adaptive design is better.
Main factors: variability / sample size at interim, timing of interim, suitability of start design
Treatment selectionOverview
Dose A
Dose B
Dose C
Placebo
Dose A
Dose B
Dose C
Placebo
Interim Analysis
Phase II
Phase III
Stage 1
Stage 2
Time
Test Dose B against Placebo using data from both stages
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Type I error rate controlSources and related approaches
Sources of potential
Type I error rate inflation
Approaches for error rate control
Early rejection of null hypotheses at
interim analysis
Classical group sequential plans (e.g. α- spending approach)
Adaptation of design features and combination of information across trial stages
Combination of p-values
(e.g. inverse normal method, Fisher’s combination test)
Multiple hypothesis testing (e.g. with adaptive selection of hypotheses at interim analysis)
Multiple testing methodology
(e.g. closed test procedures)
All three approaches can be combined
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Continue to second stage futility stop; retain H
reject H retain H
reject H
p
0 1 0 1
Stage 1
0 1
Stage 2
Principles of adaptive designs
q
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• Single null hypothesis H (no treatment difference)• Two stages, i.e., one interim analysis
Principles of adaptive designs
2exp, 2,4 cpqqpC
Fisher‘s product combination test (Bauer and Köhne, 1994) At interim, stop if p ≤ α1 (reject H) or p ≥ α0 (retain H)
Else, α1 < p < α0, continue the study, resulting in q
Final decision:
Reject H, if and only if Alternatively, define the conditional error function
and reject H, if and only if q ≤ A(p)
Weighted inverse normal method (Lehmacher and Wassmer,
1999; Cui, Hung, and Wang, 1999)
01
0
1
,
,0
,1
reject )(
ppc
p
p
pHPpA H
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General principle to construct powerful multiple test procedures Schematic diagram for 2 hypotheses H1 and H2:
Rejection rule: Reject H1 (say) at overall α, if H1 and H12 are rejected, each at local level α.
Operationally:
• Test H12 at local level α; if rejected, proceed; otherwise stop
• Test H1 and H2 each at local level α. Reject H1 (H2) overall if H12 and H1 (H2) are rejected locally
Type I error rate control in the strong sense
Closed test procedure
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Multiple testing in adaptive designs
Test all (intersection) hypotheses with combination tests
p12
p1 p2
q12
q1 q2
C(pI, qI)
..
.
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Generic example
Treatment selection: assume that at interim it is decided to continue with the first treatment
H1 is rejected if q1 < min{A(p12), A(p1)}
Similar: subgroup selection, endpoint selection
p12
p1 p2
q12 = q1
q1
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Summary
Variety of different adaptive designs available for clinical trials
Potential advantages offered by adaptive designs need to be balanced against any perceived risks or complexities
Some types of adaptations convey limited information for which it seems difficult to envision how the trial might be compromised.
Others convey more information, but extra steps might be implemented to mitigate the risk
Extensive regulatory guidance is available, mostly applicable in the context of confirmatory drug development.
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