1. Adaptive Designs for Clinical Trials
Frank Bretz
Novartis
24 April 2013, Tel Aviv

2. What are
Adaptive Designs?

3. 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FDA Draft Guidance for Industry (2010) 3

4. 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)
| Introduction to Drug Development and Pharmaceutical Statistics |Adaptive Design | 2012

5. Adaptive
Dose Finding

6. Adaptive dose finding – The idea
Prior to study the true position of dose response curve is unknown
In the adaptive dose finding approach, a small number of patients on many initial doses are used to outline the unknown dose-response.
Region of interest X X X X X
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.
Response X X X X X X
Initial doses
Dose
X = Mean dose response after a pre-defined number of patients

7. 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 7 7 7

8. 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)
Fixed design: N observations according to optimal design based on initial parameter guess θ0
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? 8 8 8

9. Analytical approximation9 9 9

10. Analysis One obtains for the approximate (inverse) covarinace matrices10 10 10

11. 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? 11 11 11

12. 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 12 12 12

13. Adaptive Designs for Confirmatory Trials

14. Treatment selection Overview
Phase II
Phase III
Dose A
Dose B
Dose C
Placebo
Time
Stage 1
Stage 2
Dose A
Dose B
Dose C
Test Dose B against Placebo using data from both stages
Placebo
Interim Analysis

15. 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

16. Principles of adaptive designs
Single null hypothesis H (no treatment difference)
Two stages, i.e., one interim analysis p
0  
Stage 1
reject H
Continue to second stage
futility stop; retain H
Stage 2 q
reject H
retain H

17. 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:
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)
1) A(p1) is based on the assumption of p1, p2 being independently U[0, 1] distributed (but recall the p-clud condition)
2) A(p1) is the maximum value p2 can achieve, s.t. we reject H at the final stage

18. 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

19. Multiple testing in adaptive designs
Test all (intersection) hypotheses with combination tests
1) So far, we have no adaptive choice of hypotheses at interim. In what follows I will show some examples, on how to adapt the results on this slide to some standard problems (both generic and more specific problems). But before I come to the examples, here is a flow chart ...

20. 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

21. 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.