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.

66

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.

1010

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 ().

1111

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