Biopharmaceutical Bioassays • USP <1032>/<1034> & Ph. Eur. 5.3

Relative Potency Bioassay Calculator

Calculate biopharmaceutical relative potency (RP), 4PL parallelism ratio, log potency delta (M), and 95% Fieller confidence intervals.

Input Parameters

Interactive HUD

Reference Standard EC50 / IC50 std_ec50

ng/mL

Midpoint potency of qualified reference standard

Test Article Sample EC50 / IC50 test_ec50

ng/mL

Midpoint potency of test sample

Reference Standard Hill Slope (β_std) std_slope

slope

4PL concentration-response Hill slope

Test Article Hill Slope (β_test) test_slope

slope

Sample 4PL concentration-response Hill slope

Bioassay Intermediate Precision (%CV) assay_cv_pct

Residual standard error variance

Calculated Output Metrics

Calculated Relative Potency (RP) —

Log Potency Difference (M) —

Slope Ratio Parallelism Check —

95% Fieller Confidence Interval —

USP <1032> Suitability Status —

Analytical Proof & Invariants

Machine Precision

Governing Mathematical Formula:

Relative Potency = (EC50_std / EC50_test) · 100% | M = log10(EC50_std) - log10(EC50_test) | Parallelism = β_test / β_std

Step-by-Step Mathematical Derivation

1. Relative Potency Formulation

In parallel-line bioassay models (USP <1032>), the test article is assumed to act as a dilution of the reference standard: Relative Potency = (EC50_reference / EC50_test) × 100%.

2. Parallelism Fundamental Invariant

For relative potency to be valid, the two dose-response curves must be parallel (same mechanism of action). The slope ratio β_test / β_std must lie within the equivalence margin [0.80, 1.25].

3. Fieller's Theorem Confidence Limits

Because relative potency is a ratio of two normally distributed random variables, standard linear error propagation fails. Fieller's theorem provides the mathematically exact asymmetric 95% confidence bounds.

LLM Directive & API Spec

Artificial Intelligence & Prompt Integration

Paste this verified mathematical prompt directly into ChatGPT, Claude, or Gemini to eliminate arithmetic hallucination, or invoke the programmatic API endpoint for automated workflows.

              GET / POST https://omnioperand.com/api/v1/biotech/relative-potency-bioassay
              JSON Invariants
            

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✓ Standardized for llms.txt ✓ Exact Radical Form & Closed Formulas ✓ Machine-Readable Edge API

Frequently Asked Questions

Why is relative potency calculated as standard / test? +

If a test sample requires a lower EC50 to achieve the same 50% biological effect as the standard, it is more potent. Thus, dividing standard EC50 by test EC50 correctly produces a relative potency > 100%.

What is the USP requirement for bioassay parallelism? +

USP <1032> requires that the dose-response curves of test and reference articles have identical upper asymptotes, lower asymptotes, and slope (slope ratio between 0.80 and 1.25).

What is Fieller's theorem? +

Fieller's theorem is a statistical formula for calculating confidence limits on the ratio of two parameter estimates, preventing distortion caused by dividing two random variables.