Estimating the interesting part of a
dose-effect curve: When is a
Bayesian adaptive design useful?
Frank Miller
AstraZeneca, Södertälje, Sweden
Multiple Comparison Procedures 2007, Vienna
July 11
Frank Miller, AstraZeneca, Södertälje
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Thanks to
Wolfgang Bischoff (Univ. of Eichstätt-Ingolstadt),
Holger Dette (University of Bochum),
Olivier Guilbaud (AstraZeneca, Södertälje),
Ulrika Wählby Hamrén (AstraZeneca, Mölndal),
Matts Kågedal (AstraZeneca, Södertälje)
Frank Miller, AstraZeneca, Södertälje
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Content
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•
•
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“Interesting part” of the dose-effect curve
Bayesian optimal design (non-adaptive)
Bayesian adaptive design
When is a Bayesian adaptive design useful?
(compared to the non-adaptive)
Frank Miller, AstraZeneca, Södertälje
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Background and Design
• Dose finding study, 300 patients
• Continuous primary variable
• Possible treatment arms:
•
•
•
placebo, 20mg, 40mg, 60mg,
80mg, 100mg/day
Proportions of patients per dose?
Traditional: Balanced design with
equal allocation (16.7% each) to
all groups
Unbalanced design can allocate
different proportions of patients
to doses
Frank Miller, AstraZeneca, Södertälje
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Objective: The “interesting part” of
the dose-effect curve
• Effects of <5 (compared to
•
•
•
placebo-effect) are of no
medical interest
 estimate effect between
smallest relevant and highest
dose (100mg)
This is the “interesting part”
If no “interesting part” exists
 estimate effect at highest
dose
Frank Miller, AstraZeneca, Södertälje
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Objective: The “interesting part” of
the dose-effect curve
• We consider the asymptotic
•
•
variance of the LS-estimate
of Effect(dose) - Effect(0)
Minimise average variance of
all LS-estimates of
Effect(dose) - Effect(0) with
dδ<dose<100
(IL-optimality; Dette&O’Brien,
Biometrika, 1999)
If no “interesting part” exists,
minimise variance of LSestimate of
Effect(100) - Effect(0)
Frank Miller, AstraZeneca, Södertälje
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dδ
Anticipations (scenarios)
Emax-sigmoid model
seems to be good and
sufficient flexible:
Emax  dose
Effect(dose)  E0 

ED50
 dose
Frank Miller, AstraZeneca, Södertälje
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Bayesian optimal design
• Optimal design
•
calculated for each
scenario
Based on a priori
probabilities, the overall
optimal design
allocates
• 38% to placebo
• 4% to 20mg
• 6% to 40mg
• 10% to 60mg
• 12% to 80mg
• 30% to 100mg
“Bayesian optimal
design”
Frank Miller, AstraZeneca, Södertälje
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Efficiency of designs
Gain in efficiency when changing the balanced design
to the Bayesian optimal design
Bayes
39%
Optimistic
21%
Pessimistic
96%
Good-high-doses
- 5%
This means:
balanced design
needs 39% more
patients than this
Bayesian optimal
design to get
estimates with
same precision.
Frank Miller, AstraZeneca, Södertälje
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Adaptive design
(Bayesian adaptive design)
•
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Stage 1: Observe 100 patients according to Bayesian
optimal design
Interim analysis
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Recalculate probabilities for scenarios based on
observed data (using Bayes formula)
Calculate ”new” Bayesian optimal design for Stage 2
• Stage-1-overrun: When interim analysis ready, 40
•
patients more randomised according Stage-1-design
Stage 2: Randomize according to calculated design
Frank Miller, AstraZeneca, Södertälje
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Adaptive design (Example)
n=100
OverSt 1 run
n=40
n=160
Stage 2
Plac
20 mg
40 mg
60 mg
80 mg
100 mg
Study time
Interim Design
change
OPT 35%
PES 35%
GHD 30%
OPT 64%
PES 24%
GHD 12%
Frank Miller, AstraZeneca, Södertälje
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Efficiency of designs
Gain in efficiency when changing the balanced design
to the Bayesian optimal design and further to the
Bayesian adaptive design
Bayes
39%a
4%b
Optimistic
21%
10%
Pessimistic
96%
+- 0%
Good-high-doses
- 5%
2%
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aAsymptotic
relative efficiency
bbased on 4000 simulations
Why is there no bigger gain from
adaptation?
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Distribution functions of
mean square error
(MSE) of simulations for
non-adaptive and
adaptive design
(optimistic scenario)
For 96% of simulations
(MSE<750), adaptive
design is better
For high MSE, adaptive
design even worse
(misleading interim
results!)
Frank Miller, AstraZeneca, Södertälje
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When is a Bayesian adaptive
design useful?
•
b
Efficiency + 4%
+ 12%
Useful
Frank Miller, AstraZeneca, Södertälje
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When is a Bayesian adaptive
design useful?
- 1%
Not useful
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+- 0%
When is a Bayesian adaptive
design useful?
•
If differences between possible scenarios
large (in relation to variability of data in interim
analysis), there is gain from adaptive dosing
•
If scenarios similar or variance large,
decisions based on interim data could lead
into wrong direction
Frank Miller, AstraZeneca, Södertälje
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References
Dette, H, O'Brien, TE (1999). Optimality criteria for
regression models based on predicted variance.
Biometrika 86:93-106.
Miller, F, Dette, H, Guilbaud, O (2007). Optimal designs
for estimating the interesting part of a dose-effect curve.
Journal of Biopharmaceutical Statistics to appear.
Frank Miller, AstraZeneca, Södertälje
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