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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. 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?

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  1. 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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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, Södertälje

  7. Anticipations (scenarios) Emax-sigmoid modelseems to be good andsufficient flexible: Frank Miller, AstraZeneca, Södertälje

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. When is a Bayesian adaptive design useful? • b Efficiency + 4% + 12% Useful Frank Miller, AstraZeneca, Södertälje

  15. When is a Bayesian adaptive design useful? - 1% +- 0% Not useful Frank Miller, AstraZeneca, Södertälje

  16. 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

  17. 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

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