1 Frank Miller, AstraZeneca, Södertälje 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

2 Frank Miller, AstraZeneca, Södertälje 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 d δ <dose<100 (I L -optimality; Dette&O’Brien, Biometrika, 1999) If no “interesting part” exists, minimise variance of LS- estimate of Effect(100) - Effect(0) dδdδ

Frank Miller, AstraZeneca, Södertälje 7 Anticipations (scenarios) E max -sigmoid model seems to be good and sufficient 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 Bayes39% Optimistic21% Pessimistic96% 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 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 Adaptive design (Example) Plac 20 mg Over- run 40 mg 60 mg 80 mg 100 mg Study time Design change 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, 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 Bayes39% a 4% b Optimistic21%10% Pessimistic96%+- 0% Good-high-doses- 5%2% a Asymptotic relative efficiency b based 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

17 Frank Miller, AstraZeneca, Södertälje References Dette, H, O'Brien, TE (1999). Optimality criteria for regression models based on predicted variance. Biometrika 86: 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.