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

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Introduction

• 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

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Emax Model for Concave and Monotone DR

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Re-parameterize

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Tested Dose Range Maximum treatment effect over tested dose range is:

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Re-parameterize

• Maximal distance from Diagonal 1 is on

Diagonal 2 (Point B)

• Tangent at point B is parallel to Diagonal 1

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Diagonal 1 Diagonal 2

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Lambda is Geometrically Interpretable

• Re-parameterized Emax has directly interpretable parameters:

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Also Spans Linear and Convex DR Curves

• 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:

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Setting Prior for λ

• 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

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Example for Trial in Knee Pain

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Concavex Priors

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Posterior Parameter Distributions

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Some text here

Efficacy Threshold C P(θ1 > C)

0 points 0.999 0.5 points 0.968 0.75 points 0.864 1 point 0.617

θ1 = 1.092 (0.570, 1.589)

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Basic Dose-Response Characterization

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Characterizing Efficacy Risks vs Dose

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Target Efficacy Risks Suboptimal Efficacy Risks Ph 3 Efficacy Risks

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Standard Emax with Uniform Prior on ED50

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Concavex Priors Emax Priors

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Summary for Concavex Model

• 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

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