Analytical Method Validation Calculator (ICH Q2(R2))
Linearity, recovery, precision and range from your data, against your protocol’s criteria.
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About the Analytical Method Validation Calculator (ICH Q2(R2))
Turns the data of an analytical method validation into the statistics and tables of its report, as ICH Q2(R2) Validation of Analytical Procedures asks for them: linearity (slope, y-intercept and their confidence intervals, r and r², the residual standard deviation, every residual and the y-intercept as a percentage of the response at 100%, with a residual plot), accuracy (the recovery of every determination, the mean and its confidence interval at each level), repeatability (SD, RSD and their intervals), intermediate precision (a one-way analysis of variance over days, analysts or instruments), the reportable range that Table 2 of the guideline gives for the use of the procedure, and the quantitation and detection limits.
Each result is compared with the acceptance criterion you enter from your protocol and gets a verdict. Without a pass it shows a free preview: Q2(R2)’s requirements, your criteria and every verdict, with the computed statistics hidden; the statistics, the residual plot, the PDF, the XLSX file, the printed copy and the copied text unlock with a Premium pass.
How to use it
- Choose the use of the procedure — an assay, content uniformity, dissolution, an impurity test, purity or potency — and fill in what its reportable range depends on (the specification limits, the reporting threshold, or the range from your protocol).
- Enter or paste the linearity points: the level (as % of declared content, or of the specification limit for an impurity), the concentration and the response.
- Enter or paste the accuracy determinations (level, amount added, amount found), the repeatability results and the intermediate precision results with the condition of each.
- Enter your protocol’s acceptance criteria: the smallest r, the largest y-intercept and residuals, the recovery limits and the largest RSDs. A criterion left empty is reported but not judged.
- Add the signal-to-noise at the QL and DL if you used that approach, and pick the confidence level for the intervals.
- Read the summary, the checks and each table. Without a pass the report stays a free preview with its statistics hidden; the PDF, XLSX, print and copy unlock with a Premium pass.
Examples
20, 30, 40, 50 and 60 µg/mL · responses 401.2, 600.8, 803.5, 1001.9, 1199.6 · 40 µg/mL at 100%
Slope 19.979 · y-intercept 2.24 (0.28% of the response at 100%) · r = 0.99999 · s(y/x) = 1.619
The y-intercept as a percentage is 2.24 ÷ (2.24 + 19.979 × 40) × 100 = 0.28%.
8.0, 10.0 and 12.0 mg added · found 7.96, 8.03, 7.98 / 9.94, 10.05, 10.01 / 11.92, 12.05, 11.98
Mean recoveries 99.88%, 100.00% and 99.86% · overall 99.91%, 95% interval 99.56–100.26%
Day 1: 99.5, 100.1, 99.8 · Day 2: 100.6, 100.9, 100.3
Repeatability RSD 0.30% · intermediate precision RSD 0.62% · F = 10.67, p = 0.031
s(IP) = √(MS within + (MS between − MS within) ÷ n0) = √(0.09 + 0.29) = 0.616.
Common uses
- A QC or analytical development scientist evaluating validation data and drafting the report tables.
- A reviewer re-checking the statistics of a validation report.
- Method transfer and partial revalidation after a change, with the same statistics on the new data.
- Training in the statistics behind analytical method validation.
What ICH Q2(R2) asks for
- Linearity (section 3.2.2.1): a plot of the data, the correlation coefficient or coefficient of determination, the y-intercept and the slope; an analysis of the residuals for any non-random pattern; a minimum of five concentrations across the range.
- Accuracy (3.3.1.4): an appropriate number of determinations over the reportable range (for example 3 concentrations with 3 replicates each), reported as the mean percent recovery with a 100(1 − α)% confidence interval that is compatible with the acceptance criteria.
- Repeatability (3.3.2.1): a minimum of 9 determinations covering the range (for example 3 concentrations with 3 replicates each), or a minimum of 6 at 100% of the test concentration.
- Intermediate precision (3.3.2.2): the effects of random events such as different days, environmental conditions, analysts and equipment; the SD, RSD and an interval are reported (3.3.2.4).
- Quantitation and detection limits (3.2.3): a signal-to-noise ratio of at least 10:1 for the QL and of 3:1 for the DL, or QL = 10σ ÷ S and DL = 3.3σ ÷ S from the standard deviation of the response and the slope; for impurity tests the QL at or below the reporting threshold (3.2.3.5).
The reportable ranges of Table 2
- Assay of a product: 80% to 120% of the declared content, or 80% of the lower to 120% of the upper specification acceptance criterion.
- Potency: the lowest specification acceptance criterion −20% to the highest +20%.
- Content uniformity: 70% to 130% of the declared content.
- Dissolution, immediate release: for a one-point specification from Q − 45% of the lowest strength, for a multiple-point specification from the lower limit of the reportable range (as justified by the specification) or the QL, up to 130% of the declared content of the highest strength; modified release from the lower limit of the reportable range or the QL, to the same high end.
- Impurity: the reporting threshold to 120% of the specification acceptance criterion.
- Purity (as area %): 80% of the lower specification acceptance criterion to the upper criterion or 100%.
- Assay and impurities in one test with a single standard: linearity from the reporting level of the impurities up to 120% of the assay’s specification acceptance criterion (the note to Table 2).
The calculator works the range out for an assay, content uniformity, an impurity and purity; for potency and dissolution enter the two ends your protocol derives from the wording above. The range the data cover is the span of levels studied for both linearity and accuracy.
How the statistics are worked out
- Least squares: slope b = Sxy ÷ Sxx, intercept a = ȳ − b·x̄, r = Sxy ÷ √(Sxx·Syy), residual standard deviation s(y/x) = √(Σ(y − ŷ)² ÷ (n − 2)); intervals b ± t·s(y/x) ÷ √Sxx and a ± t·s(y/x)·√(1/n + x̄² ÷ Sxx).
- y-intercept as % of the response at 100%: a ÷ (a + b·x100) × 100, using the fitted response at the 100% concentration.
- Mean and interval: mean ± t·s ÷ √n with n − 1 degrees of freedom; the SD interval from the chi-square distribution.
- Intermediate precision: a one-way ANOVA over the conditions gives the repeatability variance (MS within) and the between-condition variance (MS between − MS within) ÷ n0, zero when negative; their sum is the intermediate precision variance. n0 is the effective number of results per condition when the numbers differ.
Acceptance criteria are yours
ICH Q2(R2) sets out what to study and report, not the numbers to meet: the criteria come from your validation protocol, justified for the product and the purpose of the procedure. The calculator compares each result with the criterion you enter and reports, without judging, any result whose criterion you leave empty.
Limitations
- It covers procedures with a linear response; non-linear calibration models (four- or five-parameter logistic curves) and multivariate models are not fitted.
- Specificity, robustness and system suitability are judged from chromatograms and experiments, not from numbers entered here; record them in your report.
- DL and QL from the whole linearity line are estimates; Q2(R2) bases them on a calibration curve near the limits and asks for an estimated QL to be confirmed with samples at or near it.
- A calculation aid, not a validated computerised system: the signed validation report remains the record.
- The requirements and the reportable ranges of Table 2 are summarised, with changes in wording, from ICH Q2(R2) (© ICH); read the guideline itself for its full text. MySmartCoPilot is not affiliated with or endorsed by ICH.
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Frequently asked questions
What do I get without a pass?
Without a pass, Analytical Method Validation Calculator (ICH Q2(R2)) shows the method, the limits that apply and the verdict for your input; computed figures stay hidden until the pass. Until you unlock it, the result can’t be downloaded, copied or printed. A Premium or Ultimate pass, a one-time payment that never renews, unlocks the full result. The pricing page lists the passes and their prices.
What does the free preview show?
Your data, what Q2(R2) asks for, your acceptance criteria and every verdict — meets, review or does not meet — with the checks in words. The computed statistics (slope, intercept, r, residuals, recoveries, RSDs, the ANOVA and the limits) show as “•••” and the residual plot is left out; they, the PDF, the XLSX file, the printed copy and the copied text unlock with a Premium pass.
How many concentrations does linearity need?
ICH Q2(R2) recommends a minimum of five concentrations, appropriately distributed across the range. The calculator counts the distinct concentrations and flags fewer than five.
How is the y-intercept expressed as a percentage?
As the intercept divided by the fitted response at the 100% concentration, × 100. With a = 2.24, b = 19.979 and 40 µg/mL at 100%: 2.24 ÷ (2.24 + 19.979 × 40) × 100 = 0.28%.
What is the difference between repeatability and intermediate precision?
Repeatability is the precision under the same conditions over a short time (one analyst, one instrument, one day). Intermediate precision adds the variation between days, analysts or equipment in the same laboratory; the analysis of variance separates the two.
How are the DL and QL worked out from the calibration line?
DL = 3.3σ ÷ S and QL = 10σ ÷ S, with S the slope and σ the standard deviation of the response — here the residual standard deviation of the regression line (ICH Q2(R2) section 3.2.3.3).