Scale Down Model (SDM) for Bioprocess: Equivalence Acceptable Criteria (EAC)
/ Practical Significant Difference (PSD) & Sample Size Calculation
Determining the right equivalence acceptance criteria and statistically valid sample size is one of the most critical — and often underestimated — challenges in scale-down model qualification.
Determining the right equivalence acceptance criteria and statistically valid sample size is one of the most critical — and often underestimated — challenges in scale-down model qualification. This article explains how to calculate EAC/PSD from reference manufacturing data, how to interpret the sample size formula, and how Graphtal supports your biopharma team through this process.
Understanding EAC, PSD and Equivalence Margin
Before calculating, it's important to understand what each term means and how they relate to SDM qualification decisions.
The statistically derived boundary within which the 90% confidence interval for the difference in means must fall for the SDM to be declared equivalent. EAC is derived from manufacturing batch data.
The minimum difference between scale-down and commercial scale that is considered practically meaningful. PSD defines the equivalence margin in terms of real-world process impact.
Derived from reference (manufacturing scale) data. A wider margin means more tolerance for difference; a narrower margin demands closer alignment between SDM and commercial scale performance.
Manufacturing scale batch data forms the reference set. The number of available batches directly determines how many standard deviations (k) should be used — a critical input for sample size.
Calculating EAC / PSD from Manufacturing Scale Data
The sample size formula provides the mathematical foundation for determining how many reference batches are required to achieve a given statistical power at a specified confidence interval.
How to use this formula: Given your available manufacturing batches (N), solve for k to determine how many standard deviations you can use as equivalence margin. A larger k (wider margin) requires fewer batches; a smaller k (tighter margin) requires more batches.
Sample Size Calculator — Example Table
The table below illustrates calculated sample sizes across different combinations of confidence interval, power, and standard deviation factor (k).
| CI | α | Power | 1−(α/2) | Z at 1−(α/2) | Z at (1−β) | Z Sum | Z Sum² | SD (k) | Sample Size (N) |
|---|---|---|---|---|---|---|---|---|---|
| 95% CI | 0.05 | 0.95 | 0.975 | 1.96 | 1.64 | 3.6 | 12.96 | 1 | 25.92 |
| 0.05 | 0.95 | 0.975 | 1.96 | 1.64 | 3.6 | 12.96 | 2 | 6.48 | |
| 0.05 | 0.95 | 0.975 | 1.96 | 1.64 | 3.6 | 12.96 | 3 | 2.88 | |
| 90% CI | 0.05 | 0.9 | 0.975 | 1.96 | 1.28 | 3.24 | 10.49 | 1 | 20.99 |
| 0.05 | 0.9 | 0.975 | 1.96 | 1.28 | 3.24 | 10.49 | 2 | 5.25 | |
| 0.05 | 0.9 | 0.975 | 1.96 | 1.28 | 3.24 | 10.49 | 3 | 2.33 |
How to Interpret the Calculator Results
The number of available manufacturing batches determines the appropriate standard deviation factor (k):
If you have 26+ batches of data, use k = 1 (1 Standard Deviation) — the tightest and most rigorous criterion.
If you have 6+ batches of data, use k = 2 (2 Standard Deviations) — a moderate criterion for mid-phase.
If you have 3+ batches of data, use k = 3 (3 Standard Deviations) — for early-stage or limited data scenarios.
Key insight: As k increases (wider margin), fewer reference batches are needed. This trade-off must be scientifically justified for regulatory submission.
Step-by-Step EAC Calculation Process
Compile manufacturing batch data
Gather all available at-scale manufacturing data. The quantity of batches determines your k factor selection.
Select confidence interval and power
Define α and 1−β. For SDM qualification, 90% CI (α = 0.05, power = 0.90) is standard TOST guidance.
Determine appropriate k
Match your batch count to k = 1 (≥26), k = 2 (≥6), or k = 3 (≥3).
Calculate EAC
Apply the formula to derive the sample size and define the EAC boundary based on manufacturing standard deviation × k.
Document Justification
Use derived EAC in TOST and provide clear scientific rationale for the choice of k and batch count.
Graphtal's Offering for Bioprocess SDM Qualification
Graphtal offers advanced analytics solutions specifically for mAb development and scale-down model qualification.
TOST & Equivalence Margin Setting
Expert support in deriving statistically robust EAC boundaries from manufacturing datasets for TOST validation.
MVDA Integration
Using MVDA to identify patterns and qualify models across multiple attributes simultaneously for improved accuracy.
Customised Calculations
Tailored sample size and EAC calculations adapted to your specific data constraints and regulatory context.
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