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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. Thanks to Wolfgang Bischoff (Univ. of Eichstätt-Ingolstadt),

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estimating the interesting part of a dose effect curve when is a bayesian adaptive design useful

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

slide2

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

content
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, Södertälje

background and design
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

objective the interesting part of the dose effect curve
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

objective the interesting part of the dose effect curve1
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)

Frank Miller, AstraZeneca, Södertälje

anticipations scenarios
Anticipations (scenarios)

Emax-sigmoid modelseems to be good andsufficient flexible:

Frank Miller, AstraZeneca, Södertälje

bayesian optimal design
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

efficiency of designs
Efficiency of designs

Gain in efficiency when changing the balanced design to the Bayesian optimal design

This means:balanced design needs 39% more patients than this Bayesian optimal design to get estimates with same precision.

Frank Miller, AstraZeneca, Södertälje

adaptive design bayesian adaptive design
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, Södertälje

adaptive design example

n=160

Stage 2

Adaptive design (Example)

n=40

n=100

Over-run

St 1

Plac

20 mg

40 mg

60 mg

80 mg

100 mg

Study time

Interim

Designchange

OPT 35%

PES 35%

GHD 30%

OPT 64%

PES 24%

GHD 12%

Frank Miller, AstraZeneca, Södertälje

efficiency of designs1
Efficiency of designs

Gain in efficiency when changing the balanced design to the Bayesian optimal design and further to the Bayesian adaptive design

aAsymptotic relative efficiencybbased on 4000 simulations

Frank Miller, AstraZeneca, Södertälje

why is there no bigger gain from adaptation
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, Södertälje

when is a bayesian adaptive design useful
When is a Bayesian adaptive design useful?
  • b

Efficiency + 4%

+ 12%

Useful

Frank Miller, AstraZeneca, Södertälje

when is a bayesian adaptive design useful1
When is a Bayesian adaptive design useful?

- 1%

+- 0%

Not useful

Frank Miller, AstraZeneca, Södertälje

when is a bayesian adaptive design useful2
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

slide17

References

Dette, H, O'Brien, TE (1999). Optimality criteria for regression models based on predicted variance. Biometrika86:93-106.

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