1. Using PK/PD Modeling to Simulate Impact of Manufacturing Process Variability
Alan Hartford
Agensys
Tim Schofield
Biologics Consulting Group, Inc.
The 32nd Annual Midwest Biopharmaceutical Statistics Workshop
May 18 – 20, 2009, Muncie, Indiana

2. Introduction
The manufacturer has the responsibility of keeping manufacturing process variability of the dose in control.
One method for assuring that a product, after a re-formulation, is viable is to perform a clinical trial showing bioequivalence (BE) of exposure endpoints.

3. Investigate with Modeling
PK/PD models can be used to simulate the impact of variations of dose on the response cascade of
dose → exposure → pharmacodynamics → clinical outcome
These models can address the appropriateness of
the BE study
choice of bounds
Specific information from clinical development is needed as input for this PK/PD modeling.
Important information from nonclinical development can also be incorporated to save clinical resources.

4. Outline Introduction Bioequivalence (BE) bounds PK/PD Models
Predict effect of process variation on clinical outcome
Required clinical information
Collaborative modeling nonclinical/clinical
Summary

5. Current Practice
When a new formulation is developed, the current practice is to perform a clinical study to show the new formulation is “bioequivalent” to a previously studied formulation.
This allows for inference of conclusions from earlier studies for the new formulation.
i.e., efficacy results from a Ph III study can be inferred to a new formulation

6. BE Requirements
Strict bioequivalence (BE) bounds are used for exposure endpoints (AUC and Cmax)
The geometric mean for AUC and Cmax is calculated for both formulations.
If the formulations are similar, the ratio of exposure for new formulation / old formulation ≈ 1.
For BE, AUC and Cmax of new formulation compared to approved formulation must have 90% CI of GMRs to be within (0.80, 1.25)

7. BE Requirements (cont.)
This strict BE requirement is standard for many clinical comparisons (e.g., interaction studies, elderly/young studies, insufficiency studies)
But (0.80, 1.25) may not be appropriate for clinical reasons
(0.80, 1.25) is standard for when no clinical justification can be given for other bounds
If victim drug has wide therapeutic window, then wider bounds are appropriate

8. BE Requirements (cont.)
For drug interaction studies, FDA suggests that boundaries can be justified by a sponsor based on population average dose, concentration-response relationships, PK/PD models, or other
So the onus is on the sponsor to justify other comparability bounds
FDA Guidance: Drug Interaction Studies--Study Design, Data Analysis, and
Implications for Dosing and Labeling (draft 2006)

9. Example of Using Alternate Comparability Bounds
In the case of testing if a new antibody has an effect on the exposure of a standard of care chemotherapy
Not ethical to sample many patients with cancer for this interaction trial
Variability of the chemo (AUC, Cmax) was high
FDA accepted plan with small N which required GMR to be within (0.80, 1.25) but that the 90% CI to be within (0.70, 1.43)

10. FDA Guidance to Clinical
FDA Guidance for some studies (e.g., interaction studies) allows for some leeway for sponsor to clinically justify alternative bounds
PK/PD modeling can be used to justify different bounds for comparing formulations

11. Modeling & Simulation
PK/PD M&S and Clinical Trial Simulation can provide insight to
Effect of variation in dose on exposure
Effect of variation in exposure on PD
Effect of PD on clinical endpoint

12. Example: Selection of Dose to Achieve 40% Effect
Example: Assume Emax model is appropriate for a drug
Target of 40% Response
This target of exposure not appropriate.
Does not allow for variability in exposure or effect.

13. Suppose Clinical Selection of Dose was to Achieve 40%†
†For this example, 40% was chosen completely arbitrarily and not generally a target
chosen for most drugs.
Range of exposure for patient population
due to variability in PK parameters {
Increase dose to ensure mean exposure high enough (~38) to conclude statistical significantly  40% effect

14. Assume the following dose-linear relationship is observed/verified
Need exposure of ~38 for desired clinical effect
Needed dose is then ~15 mg
And should have been confirmed
in clinical development

15. Manufacturing Variability
Every manufacturing process has specification limits
Product from this process is allowed to vary within these limits
In this manner, the dosage of drug is not constant across a batch
The effect of the manufacturing variability is what we need to understand

16. Incorporating Manufacturing Variability
To determine effect of manufacturing variability on the sequence of
Dose:Exposure:Response
Perform simulations
Assume manufacturing variability limits
Using dose linear relationship and incorporating PK model with inter-subject variability, determine effect of additional variability due to manufacturing process on exposure
Using PK/PD model (e.g., Emax), determine effect of compounded variability in exposure in step 2 on clinical or PD effect

17. Effect on Exposure due to Manufacturing Variability and Subject-to-Subject Variability in PK
May need to increase dose beyond 15 mg to ensure exposure for all above 38, but only if safe

18. Increase Effect Target to Account for Variability in Exposure
Mean target for response is now >40% to account for variability in exposure

19. Limits for Effect
Note that the 40% effect size was determined from Ph III development and not an effect size targeted in earlier studies
Likewise, an upper limit for effect to be determined by the safety profile observed throughout clinical development
Simulations using PK/PD models will help to determine acceptable limits of manufacturing variability

20. Including Safety Information from Clinical Development
In clinical development, there is a maximum dose studied or maximum dose found to be safe
This clinical information provides an upper limit for manufacturing variability on dose.

21. Required Clinical Information
The information needed from clinical development includes
Upper limit on exposure due to safety
Target response for efficacy

22. Required Clinical Information (cont.)
Additionally, clinical information is needed to build the PK/PD model
Need to sample responses across wide range of exposure values to understand what model is appropriate
Note that this can be at odds with goals of adaptive designs

23. Dose-Exposure Relationship
Earlier, we assumed a linear dose-exposure relationship
However, this relationship might not be known for patients for a new formulation
Nonclinical and preclinical modeling could be used to provide this information

24. Additional Modeling Opportunities
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Modeling approaches are used widely across drug development
These different modeling efforts can be linked across nonclinical and clinical

25. Expanded Problem statement
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How can nonclinical development collaborate with clinical development to demonstrate that a manufacturing process is delivering product to the patient that is safe and effective?

26. Potential paths Process Parameters (x’s) Patient Outcomes (z’s)
Pro: Can directly study impact of process parameters on patient outcome
Con: Too many combinations to study
Patient Outcomes (z’s)

27. Potential paths (cont.)
Process Parameters (x’s)
Pro: Can study many combinations of process parameters in a homogeneous population
Con: Uncertain relationship of response in animals to response in humans
Preclinical
Models (ẑ’s)
Patient Outcomes (z’s)

28. Potential paths – nonclinical and preclinical
Allometric
Scaling
Process Parameters (x’s)
Pro: Can study many combinations of process parameters in a homogeneous population
Con: Uncertain relationship of response in animals to response in humans
Preclinical
Models (ẑ’s)
Patient Outcomes (z’s)
Exposure (ž)

29. Potential paths – nonclinical
Process Parameters (x’s)
Pro: Can study many combinations of process parameters in vitro
Con: Less certain relationship of response in vitro to response in humans
Quality
Attributes (y’s)
Patient Outcome (z’s)

30. The pieces Specifications-6 6 12 18 24 30 36
Specifications
Shelf-Life
Release
Limits
Capability
Minimum Specification
Maximum Specification
Starts with clinically supportable maximum and minimum limits (specifications)
Maximum release calculated from release assay variability
Minimum release calculated from shelf life, stability, and release assay variability's
A key to the linkage between manufacturing and the clinic is development of specifications, and a release strategy which helps assure quality throughout product shelf life. Clinically supportable maximum and minimum limits (specifications) are determined from the relationship between critical quality attributes (y, measurements of product quality) and patient outcome (z), sometimes through a surrogate such as PK. Once limits are established which forecast satisfactory clinical response, chemistry, manufacturing and control (CMC) attributes such as release assay variability and stability loss and uncertainty can be used to determine release specifications which help assure patient benefit.

31. The pieces Design Spacey
UCL
USL
LCL
LSL
Upstream of specifications are limits on processing parameters (x) which help assure that quality attribute measurements (y) will fall within specifications. This is accomplished through multifactor experimental design, where process factors such as X1 and X2 are varied and the mathematical relationship between (X1,X2) and a quality attribute (y) is determined, then the region in (X1,X2) is determined where y falls between the lower specification limit (LSL) and the upper specification limit (USL). This region in (X1,X2) is the “design space” for the process. The manufacturer then operates within the normal operating ranges (NOR) for these process factors.
Design
Space
NOR X1
Knowledge
Space X2
Dave Christopher
PhRMA CMC SET

32. The pieces Design Space (cont.)
Posterior Predicted Reliability with
Temp=20 to 70, Catalyst=2 to 12, Pressure=60, Rxntime=3.0
Rxntime
Pressure 70
0.7
0.6 60
= Design Space
0.5
Contour plot
of p(x) equal to
Prob (y is in A
given x & data).
The region inside the
red ellipse is the
design space. 50
0.4
x2=
Temp
Enhancements in the definition of “design space” have been proposed, including the variability in the mathematical modeling and the data. One solution is to use results from the multifactor DOE to calculate the posterior probability of a measurement falling within specifications – Prob(y is in A given x & data). The design space can be defined as the region where this probability is of acceptable magnitude, i.e., > 1 – alpha.
0.3 40
0.2 30
0.1
0.0 20 2 4 6 8 10 12
x1=
Catalyst
John Peterson, GSK
June 11, 2008, Graybill Conference, Ft. Collins, CO

33. The pieces IVIVC
An in-vitro in-vivo correlation (IVIVC) has been defined by the FDA as “a predictive mathematical model describing the relationship between an in-vitro property of dosage form and an in-vivo response”
Main objective is to serve as a surrogate for in vivo bioavailability and to support biowaivers
Might also be used to bridge in vitro and in vivo activity along the pathway from manufacturing process to patient outcome
IVIV relationship (IVIVR) more appropriate to the goal – g(y)=ž
IVIVC has been a longstanding initiative in the industry. The main objective is to bridge in vitro response such as dissolution with in vivo response such as PK. The primary use historically has been to support biowaivers, waiving of in vivo studies bioequivalence based on predictability of PK response from in vitro testing. It has been commonly acknowledged that the true intent is to establish the in vitro in vivo relationship (IVIVR) rather than in vitro in vivo correlation IVIVC).

34. Potential paths – IVIVC
Design
Space
IVIVC
PK/PD
Modeling
Process Parameters (x’s)
Quality
Attributes (y’s)
PK Profile (ž’s)
Patient Outcome (z’s)

35. IVIVC FDA guidance offers 5-levels of correlation
Level A correlation comes closest to defining IVIVR – the purpose of level A correlation is to define a direct relationship between in vivo data such that measurement of in vitro dissolution rate alone is sufficient to determine the biopharmaceutical rate of the dosage form
The ideal is to determine the relationship (with uncertainty) such that measurement of in vitro activity alone (e.g., dissolution rate) is sufficient to determine the biopharmaceutical rate (PK) of the dosage form.
Fdiss=fraction dissolved
Fabs=fraction absorbed

36. The pieces IVIVC (cont.)
IVIVR established from “link model” among in vitro dissolution, in vivo plasma levels, and in vivo absorption
Fraction absorbed is obtained in one of 3-ways:
Wagner-Nelson method
CT = plasma [C] at time T
KE = elimination rate constant
Loo-Riegelman method
(XP)T = [C] in peripheral comp. after oral
VC = volume in central compartment
K10 = elimination rate constant after IV
Numerical deconvolution
Linkage functions are used to relate in vitro dissolution with in vivo plasma levels with in vivo absorption. Some of those methods are commonly utilized throughout the pharmaceutical industry.

37. The Full Cascade of Information
Processing Parameters (x’s)
Quality Attributes (y’s)
PK (exposure) Parameters (ž’s)
PD or Clinical Outcome (z’s)

38. Potential paths (cont.)

39. Summary
A process has been outlined for using information from different stages of drug development to determine process limits
Process will inform decision about needing additional clinical trials for new formulations

40. Summary (cont.) Clinical information is needed for successful modeling
Target for efficacy
Safety
In total, the therapeutic window
IVIVC or IVIVR models needed to inform about exposure

41. Summary (cont.)
Both PK/PD Modeling and IVIVC modeling are time-consuming and tedious and must be integrated early into development
Designs of clinical trials must be designed so that information needed for building models is available