PharmaCalc

This guide explains shelf-life estimation from long-term stability data using linear regression, following ICH Q1E, Evaluation for Stability Data. The method fits assay (% label claim) against time, computes the one-sided lower 95% confidence limit on the regression line, finds where that limit crosses the acceptance criterion, and then applies the Q1E limit on extrapolation beyond the observed data.

Two guidelines govern this work. ICH Q1A(R2) defines the study design — batches, storage conditions, time points, and the data package required at submission. ICH Q1E defines how to evaluate the data and how far a shelf life may extend beyond it.

Where this is used:

• Establishing the shelf life proposed in a new drug application or marketing authorisation.
• Ongoing/annual stability review of commercial product.
• Evaluating whether long-term data support an extension of an approved shelf life.
• Trending assay or degradation-product data against specification over time.

Storage conditions (drug product, general case, ICH Q1A(R2) §2.2.7.1):

If 30°C/65% RH is chosen as the long-term condition, there is no intermediate condition. Q1A(R2) requires a minimum of 12 months of long-term data on at least three primary batches at submission — long-term data through the full proposed shelf life are not required; Q1E exists precisely because extrapolation beyond the observed data is permitted within defined limits.

Multiple batches: shelf life is established on a minimum of three batches. Before pooling into one regression, test poolability (equality of slopes and intercepts, e.g. ANCOVA); Q1E directs a significance level of 0.25 to compensate for the low power of the design. If batches cannot be pooled, the shelf life is based on the worst-performing batch. In the calculator the poolability analysis is opt-in: enable it to run the α = 0.25 tests; left off, multiple batches are evaluated individually and the worst-performing batch governs — conservative and Q1E-acceptable, but no poolability test is performed.

Scenario: long-term data at 25°C/60% RH, acceptance criterion ≥ 90.0% LC. A real submission requires at least three batches and a poolability assessment; a single batch is shown here to illustrate the arithmetic only.

1. Assemble the long-term data.
   Example Data

   t (months): 0, 3, 6, 9, 12, 18, 24
   y (% LC): 100.2, 99.8, 99.1, 98.6, 98.0, 97.1, 96.3
2. Fit the regression.
   Calculation

   n = 7; t̄ = 10.2857; ȳ = 98.4429; Sₓₓ = 429.4286; Sₓᵧ = −71.4857
   Slope b = −71.4857 / 429.4286 = −0.16647 %/month
   Intercept a = 98.4429 + 0.16647 × 10.2857 = 100.155 % LC
   RSS = 0.0771 → s = √(0.0771/5) = 0.1242 · R² = 0.9936
3. Take the one-sided t value: t(0.95, 5) = 2.015 — one-sided, per Q1E §2.6.
4. Find where the lower bound crosses 90.0% LC.
   Calculation

   Solving Lower bound(t) = 90.0 numerically gives t ≈ 57.5 months.
   (The point estimate alone crosses at 61.0 months — the confidence bound must cross earlier.)
5. Apply the extrapolation cap — do not skip this step.
   Calculation

   Data cover 24 months → ceiling = min(2 × 24, 24 + 12) = 36 months
   The statistical crossing point is not the shelf life. Q1E §2.4.1.1: the proposed shelf life “can be up to twice, but should not be more than 12 months beyond, the period covered by long-term data.” Q1E §2.3 adds that extrapolation assumes the same change pattern continues, and that an extrapolated shelf life must be verified by additional long-term data as it becomes available.
6. Conclude.
   Interpretation

   Supportable shelf life: 36 months — not the 57.5-month statistical crossing.

• What passes: the one-sided lower 95% confidence limit must remain at or above the criterion through the proposed shelf life, and the shelf life must respect the Q1E cap — no more than twice, and no more than 12 months beyond, the long-term coverage.
• Direction of the bound: for an increasing attribute (e.g. a degradation product), use the upper one-sided 95% limit; for attributes that can move either way, use both (two-sided at 95%).
• R² measures linearity of fit, not compliance. The confidence-bound crossing and the cap decide.
• Linearity: zero-order change assumed over the observed range; check residuals, consider transformation per Q1E if not linear.
• Batches: single batch shown, three required, with poolability tested at significance 0.25 (opt-in in the calculator; otherwise the worst-performing batch governs).
• Extrapolation risk: commitment-batch and ongoing data must confirm the assumed pattern.
• One attribute: shelf life is set by the worst-case attribute across all specification parameters that change on storage.

• ICH Q1A(R2), Stability Testing of New Drug Substances and Products. database.ich.org
• ICH Q1E, Evaluation for Stability Data. database.ich.org