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 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
This means: balanced design needs 39% more patients than this Bayesian optimal design to get estimates with same precision.
Bayes
39%
Optimistic
21%
Pessimistic
96%
Good-high-doses
- 5%
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)
Stage 2
n=160
n=40
n=100
Over- run
St 1
Plac
20 mg
40 mg
60 mg
80 mg
100 mg
Study time
Interim
Design change
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
Bayes
39%a
4%b
Optimistic
21%
10%
Pessimistic
96%
+- 0%
Good-high-doses
- 5% 2%
aAsymptotic relative efficiency bbased 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?
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. 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.
Frank Miller, AstraZeneca, Södertälje