Design Space A Risk Based Approach

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Design Space A Risk Based Approach
Paul McAllister,Statistical Sciences
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Outline

• Pharmaceutical industry context
• Definition
• Example tablet granulation and compression
• Reporting design space
• Example extended release compression
• Making the process rugged

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Pharmaceutical Products

• Require licensure from regulatory bodies around
  the world
• Company must demonstrate efficacy and safety
  through clinical trials
• New Drug Application (NDA) includes extensive
  sections on Chemistry Manufacturing Controls
  (CMC) how will the product be manufactured ?

(Drug substance active ingredient Drug
product form given to patient)
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The Regulatory Landscape..
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Regulatory Landscape ....
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Regulatory Landscape ....
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Regulatory Landscape ....
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Regulatory Landscape ....
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Conceptual framework for product manufacture
Regulatory Agreement Specifications for quality
attributes (QAs) Process description including
process parameters with proven acceptable ranges
(PARs)
Target or Normal operating ranges (NORs)
CQA critical quality attribute PP process
parameter
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The New guidance for the Quality Overall Summary
(QOS) of the NDA..
Regulatory Landscape ....

• Convey the design intent for the Drug Product wrt
  patient safety, requirements and efficacy
• Provide a summary of information on both Drug
  Substance and Drug Product
• Product knowledge process understanding
  identification and justification of Critical
  Quality Attributes (CQAs) and Critical Process
  Parameters (CPPs) and in-process controls.
• Convey the relationship between CQAs and QPPs for
  Drug Substance and Drug Product
• Convey the Design Space for Drug Substance and
  Drug Product
• Where relevant incorporate unbiased, scientific
  and risk-based assessments/analysis and
  conclusions of each critical and overall product
  quality aspect
• Emphasise the process understanding from pilot
  scale to manufacturing scale
• Clearly identify regulatory commitments for
  carrying forward into the Regulatory Agreement

(Drug substance active ingredient Drug
product form given to patient)
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Definition of Design Space

• Design Space is
• the multidimensional combination and interaction
  of input variables (e.g. material attributes) and
  process parameters that have been demonstrated to
  provide assurance of quality. ICH Q8 (2006),
  Guidance for Industry Q8 Pharmaceutical
  Development, page 11.

• We interpret Quality to mean patient safety and
  efficacy.
• We do not interpret assurance to mean 100
  certainty.

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Design Space A Risk Based Approach

• Risk based approach to assurance of quality.
• Accounts for the multivariate nature of the
  critical quality attributes.
• Uses a quantitative model linking critical
  quality attributes to input attributes and
  process parameters.

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Design Space A Risk Based Approach
Risk Assessment Process
Design of Experiments (DoE)
Perform the Experiments
?
Knowledge (from DoE) And Design Space
Control Strategy Derived from Design Space
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Example 1 Granulation and Compression
Compression
Granulation
CQAs

• Three CQAs (Ys)
• Disintegration time lt 15 minutes (As)
• Friability lt 0.8 loss after 12 min at 25 rpm
• Hardness 8-14kp

• Three Compression parameters (Xs)
• Main compression force
• Main compression/pre-compression ratio
• Speed
• 8 combinations plus three centre points on
  compression

• Three granulation parameters (Xs)
• Quantity of water added
• Rate of water addition
• Wet massing time
• 7 combinations plus two centre points on
  granulation

All granulation combinations combined with all
compression combinations to give a total of 99
runs
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With the data fit models to each response, plot
Overlapping Contours
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Based on Point Prediction

• Provides confidence intervals and prediction
  intervals for each response at various factor
  settings.
• Useful way to see which responses have large
  intervals.
• The probability of being in spec can be
  calculated for each response individually.
• Does not account for uncertainty in model
  parameters or correlation among responses.

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Describing Design Space
Design space consists of the set of all values
and combinations of the controllable parameters
(Xs) that are predicted to yield all of the
critical quality attributes (Ys) within their
specifications (As) with a probability of at
least 1-a.
(A Bayesian posterior predictive distribution is
used to calculate probabilities)
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Key Elements

• The definition of Design Space requires
  calculation of the multivariate probability that
  all of the CQAs simultaneously meet their
  required specifications.
• We write explicit equations that predict this
  multivariate probability from the target values
  assigned to all of the controlled parameters
  the Xs. These equations can be derived from a
  combination of prior scientific knowledge and
  empirical model building from observed data using
  experimental design principles.

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Example 1 Granulation and Compression
Compression
Granulation
CQAs

• Three CQAs (Ys)
• Disintegration time lt 15 minutes (As)
• Friability lt 0.8 loss after 12 min at 25 rpm
• Hardness 8-14kp

• Three Compression parameters (Xs)
• Main compression force
• Main compression/pre-compression ratio
• Speed
• 8 combinations plus three centre points on
  compression

• Three granulation parameters (Xs)
• Quantity of water added
• Rate of water addition
• Wet massing time
• 7 combinations plus two centre points on
  granulation

All granulation combinations combined with all
compression combinations to give a total of 99
runs
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Example 1 Granulation and Compression

• We use our 99 runs to build an empirical model
  relating the process parameters to the CQAs.

HSWG high shear wet granulation
1 This is only part of a much bigger table of
data.
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Example 1 Granulation and Compression
Multivariate Analysis Linear Models

• Friability
• Water Addition Quantity
• Wet Massing Time
• Main Compression Force
• Ratio Main to Pre Force
• Interactions 1 by 5 3 by 4 3 by 5 1 by 3 by 4

• Disintegration Time
• Water Addition Quantity
• Water Addition Rate
• Wet Massing Time
• Main Compression Force
• Interactions 2 by 4 3 by 4

• Hardness
• Water Addition Quantity
• Water Addition Rate
• Wet Massing Time
• Interactions 1 by 2 2 by 3 1 by 3

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Table of Probabilities of Passing Specs for given
x
Control Parameter Combinations
Marginal Probabilities
1 This is only a small portion of a much bigger
table.
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Reporting Design Space

• Mathematical definition of design space is
  precise, but may not be easy to represent on a
  flat piece of paper.
• May not be easy to specify the bounds of any
  particular controllable parameter, Xj since the
  multivariate nature of the Xs may mean that the
  bounds for Xj depend on the values of the other
  Xs.
• May choose a regularly spaced region with fixed
  limits specified for each controllable parameter,
  Xj, but true shape of the actual design space may
  mean that such an inscribed rectangular region
  is limiting especially as the number of Xs
  increase

Dark green represents the calculated design
space. Light green is the rectangular space.
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Example 1 Displaying the Knowledge Space
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Design Space A Risk Based Approach
?
?
?
Risk Assessment Process
Design of Experiments (DoE)
Perform the Experiments
?
Statistical Analysis of DoE (Build a
quantitative model)
Apply a 50 level of quality assurance. (to
quantitative model)
Knowledge Space from DoE
Design Space
?
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Example 1 Granulation and Compression Design
Space, with 1-a 50
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Example 1 Granulation and Compression Design
Space, with 1-a 70
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Example 2 Extended Release Compression Study
Compression
Quality Attributes

• Four CQAs (Ys)
• Dissolution T20 gt 4 mins
• Dissolution T75 gt13 mins
• Tablet thickness 7.35 to 7.85mm
• Tablet hardness 18-29kN

• Five Compression parameters (Xs)
• Pre-compression force
• Main compression force
• Turret speed
• Die-depth
• Feed rate
• Physical Property (Input)
• API particle size, lt 50um

API active pharmaceutical ingredient
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Example 2 Displaying the Knowledge Space from DoE
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Example 2 Extended Release Compression Design
Space, with 1-a 90
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Rugged to API particle size

• Having zoomed into the DoE

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Knowledge Space Rugged to API particle size
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Example 2 Extended Release Compression Design
Space, Rugged to API particle size, with 1-a
80
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Summary
Design space provides a risk-based approach
for regulatory approval and potential
flexibility. The level of assurance is
characterized as the simultaneous probability
of meeting all quality requirements. The
multidimensional description of design space
is a challenging problem.
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Acknowledgements

• John Peterson Research Statistics Unit
• Michael Denham Statistical Sciences
• Kevin Lief Statistical Sciences

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References and Advocacy
ICH Q8 (2006), Guidance for Industry Q8
Pharmaceutical Development. ICH Q8 (2007),
Pharmaceutical Development Annex to
Q8 Miró-Quesada, G., del Castillo, E., and
Peterson, J. J. (2004), A Bayesian Approach to
for Multiple Response Surface Optimization with
Noise Variables, Journal of Applied Statistics,
31, 251-270. Peterson, J. J. (2004), A
Posterior Approach to Multiple Response Surface
Optimization, Journal of Quality Technology,
Peterson, J. J. (2007) A Bayesian Approach to
the ICH Q8 Definition of Design Space.
Proceedings of The American Statistical
Association, Biopharmaceutical Section. (Also to
appear in the Journal of Biopharmaceutical
Statistics in fall 2008.) Peterson, J. J.
(2008). A Bayesian Reliability Approach to
Multiple Response Surface Optimization with
Seemingly Unrelated Regressions Models, Quality
Technology and Quantitative Management, (to
appear). Stockdale, G. and Chen, A. (2008),
Finding Design Space and Reliable Operating
Region using a Multivariate Bayesian Approach
with Experimental Design, Quality Technology and
Quantitative Management, (to appear). 2007
Gregory Stockdale presented Bayesian Design Space
concepts to the PhRMA CMC Statistical Expert
Team. 2007 John Peterson presented Bayesian
Design Space concepts at the 2007 FDA/Industry
Statistics Workshop. 2008 John Peterson
invited to present at the 2008 International
Biopharmaceutical Symposium at Shanghai (by Tim
Schofield (Merck) and Yi Tsong (Deputy Director,
Division of Biometrics VI), the head CMC
statistician at FDA).
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Appendix
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Prediction Models
The Standard Multivariate Regression Model
The Seemingly Unrelated Regressions model
Other models? e.g. Nonlinear, PLS,Wavelets, etc.
x (x1,xk) vector of predictive variables r
no. of response types.
Fitted models give us predicted responses, i.e.
but we need toknow the variances
of the also to assess risk.
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Reliability Model
How much assurance do we have of meeting
specifications?
Consider If we knew we could
define a Design Space as for some reliability
level R. From a Bayesian perspective one
could consider the posteriorexpectation
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Aside.what is a posterior predictive
distribution?

• A posterior predictive distribution is used to
  compute
• If is the pdf for Y , then
  g(y x, data) is the posterior predictivepdf
  with
• where is the posterior
  distribution of b and S.
• So

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• In most situations, Markov Chain Monte Carlo
  techniques will be used to compute

MCMC
,....,
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Design Space
From a Bayesian perspective one could consider
the posteriorexpectation

• Computationally,
  is straightforward to compute using MCMC.
• Experiments with multiple batches, split plots,
  missing data, noise variablesand even
  heavy-tailed residual distributions can be
  handled with MCMC.
• In theory it is also possible to handle latent
  variable models that may be needed for
  functional data from in-process measurements
  (e.g. BayesianPLS, Wavelets, etc.)
• The classical multiple response surface
  approaches found in Design Expert, JMP,
  Statistica, etc. fall short of providing a good
  reliability models!