Bayesian Dose Response Analysis for Concave, Linear, and Convex - PowerPoint PPT Presentation

Bayesian Dose Response Analysis for Concave, Linear, and Convex Monotone DR Curves Michel Friesenhahn and Paul Manser May 12, 2017 Confidential — do not copy, distribute or use without prior written consent.

Introduction 2  Who are we? – Work at Genentech/Roche supporting early development non oncology – CNS (e.g. Alzheimer’s Disease, ALS, Pain) – Ophthalmology  Why do we worry about dose-response characterization? – Safety and tolerability – Manufacturing (particularly for certain large molecules) – Minimize patient burden (e.g. frequency of dosing in ophthalmology)  We believe there are advantages to expressing uncertainty with Bayesian methods. This can aid informed dose selection, but … – How to select good priors, particularly when there is no prior information on shape? – Model selection? Model averaging?  Propose fitting a novel single family of concave, linear, and convex DR curves – Has very geometrically interpretable parameters to aid in setting of priors – Reduces or eliminates need for model selection/averaging Confidential — do not copy, distribute or use without prior written consent.

Emax Model for Concave and Monotone DR 3 Confidential — do not copy, distribute or use without prior written consent.

Re-parameterize 4 Tested Dose Range Maximum treatment effect over tested dose range is: Confidential — do not copy, distribute or use without prior written consent.

Re-parameterize 5 Diagonal 1 Diagonal 2  Maximal distance from Diagonal 1 is on Diagonal 2 (Point B)  Tangent at point B is parallel to Diagonal 1 Confidential — do not copy, distribute or use without prior written consent.

Lambda is Geometrically Interpretable 6  Re-parameterized Emax has directly interpretable parameters: Confidential — do not copy, distribute or use without prior written consent.

Also Spans Linear and Convex DR Curves 7  Natural mapping from to Concave , Linear and Convex DR curves  We call this a Concavex DR family  Could use MLE, perhaps with one further re-paramterization: Confidential — do not copy, distribute or use without prior written consent.

Setting Prior for λ 8  Theoretically-Motivated Non-informative – Jeffrey’s Prior – Bornkamp’s Prior Parameters considered as points in a metric space • Put uniform prior in the metric space to “spread out” the curves • Induces a prior on the parameters • – Approximations to Jeffrey’s and Bornkamp’s priors? Work in progress  Pragmatically-Motivated Non-informative – Uniform – Beta(1/3,1/3)  Interpretability of λ should aid in setting prior when some information is available Confidential — do not copy, distribute or use without prior written consent.

Example for Trial in Knee Pain 9 Concavex Priors Confidential — do not copy, distribute or use without prior written consent.

Posterior Parameter Distributions 10 θ 1 = 1.092 (0.570, 1.589) P(θ 1 > Efficacy Threshold C Some text here C) 0 points 0.999 0.5 points 0.968 0.75 points 0.864 1 point 0.617 Confidential — do not copy, distribute or use without prior written consent.

Basic Dose-Response Characterization 11 Confidential — do not copy, distribute or use without prior written consent.

Characterizing Efficacy Risks vs Dose 12 Target Efficacy Risks Suboptimal Efficacy Risks Ph 3 Efficacy Risks Confidential — do not copy, distribute or use without prior written consent.

Standard Emax with Uniform Prior on ED 50 13 Emax Priors Concavex Priors Confidential — do not copy, distribute or use without prior written consent.

Summary for Concavex Model 14  Single model family for concave, linear and convex dose response curves  Eliminates (or reduces) need for model selection or model averaging  Could be fit using maximum likelihood, but would suggest one further re- parameterization of λ  We focus on efficacy risk profiles as a meaningful input to dose selection – Most naturally obtained via Bayesian framework – Interpretability of Concave model aids in setting transparent priors  Development version of concavex R package currently available on GitHub – github.com/paulmanser/concavex Confidential — do not copy, distribute or use without prior written consent.