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Frank Miller, AstraZeneca, Södertälje
Estimating the interesting part of a dose-effect curve: When is a Bayesian adaptive design useful?Frank MillerAstraZeneca, Södertälje, Sweden
Multiple Comparison Procedures 2007, ViennaJuly 11
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Frank Miller, AstraZeneca, Södertälje
Thanks toWolfgang 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, Södertälje3
Content
• “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, Södertälje4
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, Södertälje5
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, Södertälje6
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 LS-estimate of Effect(100) - Effect(0) dδ
Frank Miller, AstraZeneca, Södertälje7
Anticipations (scenarios)
doseED
doseEEdoseEffect
50
max0)(
Emax-sigmoid modelseems to be good andsufficient flexible:
Frank Miller, AstraZeneca, Södertälje8
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, Södertälje9
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, Södertälje10
Adaptive design (Bayesian adaptive design)
• Stage 1: Observe 100 patients according to Bayesian optimal design
• Interim analysis• 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, Södertälje11
Adaptive design (Example)
Plac
20 mg
Over-run
40 mg60 mg80 mg100 mg
Study timeDesignchange
St 1
Interim
n=100 n=40
Stage 2
n=160
OPT 35%PES 35%GHD 30%
OPT 64%PES 24%GHD 12%
Frank Miller, AstraZeneca, Södertälje12
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%aAsymptotic relative efficiencybbased on 4000 simulations
Frank Miller, AstraZeneca, Södertälje13
Why is there no bigger gain from adaptation?
• 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, Södertälje14
When is a Bayesian adaptive design useful?
• b
Efficiency + 4% + 12%Useful
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When is a Bayesian adaptive design useful?
- 1% +- 0%Not useful
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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
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Frank Miller, AstraZeneca, Södertälje
ReferencesDette, 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.