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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.