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Determining Replicates and Number of Dosage Units for Composite Sample Preparation in Drug Product Assay
Nonclinical Biostatistics Conference
14 October 2015
Objective• Develop strategy for determining number of dosage
form units and replicates to use in preparing a sample for potency analysis
• Able to implement early in method development when data is scarce
• Based on current, defined compendia criteria• Includes all solid oral dosage forms• Recommendations appropriate per stage of
development
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DP Assay – Sample Composite Strategy
Outline• Define a Drug Product Composite Sample
Replicate Strategy for Potency Assays– What data is available?– What estimates required?– How deal with confounding?
• How Criterion Defined to Measure Adequacy
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Example: Experimental Model – Drug Product Potency Assay
• A potency assay consist of a number of dosage units prepared into a sample of which there may be a number of replicate (r) sample preparations composited to form the reportable assay value. The below schematic illustrates such an experimental run.
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Approach
Where, S = sample preparation du = dosage unit
Drug Product Assay Variability
The Criterion we hold ourselves to for SE potency may be more restrictive if other components are significant contributors.
du1...dun
S1 S2 Sr
...du1...dun du1...dun
method/sample preparation variability
dosage unit variability
𝑌𝑖𝑗 = 𝜇+ 𝜀𝑖 + 𝜂𝑖𝑗 𝑖 = 1 𝑡𝑜 𝑟; 𝑗= 1 𝑡𝑜 𝑛
Approach used to Develop the Drug Product Sample Composite Strategy
How?
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Experimental Model 1 – Uniformity of Dosage Units
• To compute the uniformity of dosage (UDU), individual dosage units are prepared each into an individual sample preparation . The below schematic illustrates such an experimental run.
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Approach – Total Variability Ests from UDU
Where, S = sample preparation du = dosage unit
Variance attributed to method/sample preparation
Variance attributed to dosage unit
𝑌𝑖 = 𝜇+ 𝜀𝑖 + 𝜂𝑖 𝑖 = 1 𝑡𝑜 𝑟 du1
S1
du2
S2
...Sr
dur
𝑽𝒂𝒓(𝒚) = ൣ�൫𝝈𝜺𝟐 + 𝝈𝜼𝟐൯൧
Approach – UDU and Assay Same Method
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Content Uniformity: CU
2 = ε2 + η
2
(1) Potency Assay Repeatability:POTENCY
2 = ( ε 2 + η
2/k)/r (with k dosage units per r sample composites)(2)
Same Analytical Method used for UDU and Potency (and data for both): Taking (1) – r×(2) gives:(CU
2 - rPOTENCY2 ) = ( ε
2 + η 2) – ( ε
2 + η 2/k)
k(CU2 - rPOTENCY
2 ) = kp2 - η
2
k(CU2 - rPOTENCY
2 ) = (k-1) η 2
k(CU2 - rPOTENCY
2 )/(k-1) = η 2
(3) Taking r×k×(2) – (1) gives:(krPOTENCY
2 - CU2 ) = (k ε
2 + η 2) – ( ε
2 + η 2)
(krPOTENCY2 - CU
2 ) = (k-1) ε 2
(krPOTENCY2 - CU
2 )/(k-1) = ε 2
(4)
Approach – UDU and Assay Same Method
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Content Uniformity: CU
2 = ε2 + η
2
(1) Potency Assay Repeatability:POTENCY
2 = ( ε 2 + η
2/k)/r (with k dosage units per r sample composites)(2)
Required Data:
Content Uniformity per Lot
Replicate Potency per Lot
Approach – UDU and Assay Different Method
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Content Uniformity: CU
2 = μ2 + η
2
(1) Potency Assay Repeatability:POTENCY
2 = ( ε 2 + η
2/k)/r (with k dosage units per r sample composites)(2)
Different Analytical Method used for UDU and Potency:
Requires an independent measure of each method variability
Content Uniformity Data Potency Data
Experimental Model – Using Accuracy Experiment to Estimate Method/Sample preparation variability• To Evaluate the Accuracy of an analytical potency method, spikes of
known analyte amount are prepared each into an individual preparation . The below schematic illustrates such an experimental run. Preparation may be a pure placebo or a mix of product excipients to more closely mimic a typical product sample preparation.
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Approach – UDU and Assay Different Method
Where, C = Concentration
preparationSp = spiked amount
Variance attributed to concentration preparation
Variance attributed to spiked amount
Sp1
C1
Sp2
C2
... Spr
Cr
𝑌𝑖 = 𝜇+ 𝜀𝑖∗+ 𝜂𝑖∗ 𝑖 = 1 𝑡𝑜 𝑟 𝑽𝒂𝒓(𝒀) = ൣ�൫𝝈𝝐∗𝟐 + 𝝈𝜼∗𝟐 ൯൧
Experimental Model – Using Accuracy Experiment to Estimate Method/Sample preparation variability• Because () represents the variability about measured concentrations
that are exceedingly precise, it is logical to assume () is approximately zero. Then, () is thought to be a good approximation to () as long as there exists no unrealized effect of dosage unit manufacture that is not captured in this spiking experiment, i.e., () is not an exaggerated underestimate of ().
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Approach – UDU and Assay Different
Approximately equivalent to ?
~0
𝑽𝒂𝒓(𝒀) = ൣ�൫𝝈𝝐∗𝟐 + 𝝈𝜼∗𝟐 ൯൧ 𝝈𝜺𝟐
Approach – SOP Flow Chart• Content Uniformity:
(1)
• Potency Assay:(2)
(with k dosage units per r sample composites)
• Accuracy Experiments– Obtain (method variability from Accuracy
experiment) for BOTH the UDU and Potency methods
Subtract method variance of UDU from Eqn. 1 to get dosage unit Variance.
Use method variance of Potency from Accuracy experiment in calculation.
Subtract Eqn. 2 from Eqn 1. Get variances of method & dosage unit. Use these estimates in
calculation.
Obtain Method Variance estimates
from UDU and Potency Accuracy
Experiments
UDU and Potency the Same Method?
Composite Strategy Complete
Yes
No
Calculate Standard Error of
Potency for k and r
Meet SE Criterion of ≤ 1.3?
Increase k and/or r
Yes
No
Prototype Tool
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Approach used to Develop the Workflow
How define the Maximum Criterion?
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Approach used to Develop the Standard Error (SE) Criteria
• Proposition – Determining a conservative SE criteria requires minimizing the SE(potency) equation– Smallest numerator – – Largest denominator – k
• Using current compendia …– Maximum k: TGO<78> – k=20– Minimum : = 0 not practical …
• Uniformity of Dosage Units (UDU) - Ph. Eur. 2.9.40/USP 905 • , and must be less than 15
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Determine SE criterion
• TGO-78 criteria for n=20– Most conservative regulatory recommendation: n=20 dosage units for
potency assay
5.75Maximum SE potency using n=20
• This strategy provides guidance on number of units for assay composite and replicates
• Provides early stage of development assessment
• Requires limited data – Unit Dosage Uniformity and Assay Accuracy Estimate
• General Solution allows for different UDU and Potency Assay Methods
• Using surrogate method variability to estimate components of variance
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Summary
DP Sample Composite LDT Members
• Marc Barber • David Giamalva • Michele Guo • Carlos Lee • Beverly Nickerson • Garry Scrivens • Loren Wrisley
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Acknowledgements
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& Questions