Adaptive Designs
for Clinical Trials
Frank Bretz
Novartis
24 April 2013, Tel Aviv
What are
Adaptive Designs?
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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FDA Draft Guidance for Industry (2010)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
•4 Adaptive designs in the sense of the EMEA Reflection Paper (2007)
Adaptive
Dose Finding
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Adaptive dose finding – The idea
Prior to study the true position of
dose response curve is unknown
Region of interest
Response
X
X
X
X
X
X
X
X
X
X X
Initial
doses
Dose
X = Mean dose response after a pre-defined number of patients
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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 ‘noninformative’ doses
(‘wasted doses’) is
decreased.
Benefit of adaptive dose finding designs
 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
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Results from Dette, Bornkamp and Bretz (2013)
• 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?
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Analytical approximation
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Analysis
•
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One obtains for the approximate (inverse) covarinace
matrices
Exponential Regression Model
•
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?
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Exponential Regression Model – Results
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
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Adaptive Designs for
Confirmatory Trials
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Treatment selection
Overview
Phase II
Phase III
Dose A
Dose B
Dose C
Placebo
Time
Stage 2
Stage 1
Dose A
Dose B
Test Dose B against Placebo
using data from both stages
Dose C
Placebo
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Interim Analysis
Type I error rate control
Sources 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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Principles of adaptive designs
• Single null hypothesis H (no treatment difference)
• Two stages, i.e., one interim analysis
p
Stage 1
1
0
reject H
0
Continue to second stage
1
futility stop; retain H
q
Stage 2
0
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1
reject H
retain H
Principles of adaptive designs
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:
2


C
p
,
q

pq

c

exp


4, 2
Reject H, if and only if
 Alternatively, define the conditional error function
p  1
1,

A( p )  PH reject H p   0,
p  0
c p ,   p  
1
0



and reject H, if and only if q ≤ A(p)
Weighted inverse normal method (Lehmacher and Wassmer,
1999; Cui, Hung, and Wang, 1999)
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Closed test procedure
 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
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Multiple testing in adaptive designs
Test all (intersection) hypotheses with combination tests
p12
p1
q12
p2
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
p12
p1
q12 = q1
p2
q1
 H1 is rejected if q1 < min{A(p12), A(p1)}
 Similar: subgroup selection, endpoint selection
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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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