Linearity Verification Interpreter
Linearity Verification Interpreter
You ran a dilution series and one level sits off the straight line. CLSI EP06-Ed2 does not ask whether that deviation is statistically significant — it asks whether it is bigger than the deviation you decided in advance you could tolerate. This page applies that comparison, and then answers the question that actually follows: can the measuring interval be truncated, or is the method nonlinear inside it? For the fit itself, see the Deming regression calculator.
Is the method linear across its claimed interval?
Dilution series → linear or notA dilution series with five levels and four replicates each. The worst deviation is 16 units at the level whose expected concentration is 120 units, and it is at the top of the interval. The laboratory declared an allowable deviation from linearity of 5 units absolute or 10% relative, whichever is greater.
The allowable deviation from linearity, and what changed in 2020
Deviation at a level = mean of the replicates at that level − value predicted by the straight-line fit
EP06-Ed2 (2020, current): linear if the deviation at every level is within that level’s ADL
EP06-A (2003, superseded): fit 1st-, 2nd- and 3rd-order polynomials; if a higher-order coefficient is statistically significant, quantify nonlinearity as the difference between the linear fit and the best-fitting nonlinear model
- why the change
- the polynomial test asks whether a bend exists, and with enough replicates the answer is always yes. EP06-Ed2 asks instead whether the bend is large enough to matter, level by level. The CLSI preview of the second edition describes the shift as being to "clinical acceptability of deviations … as opposed to a global pass-or-fail assessment based solely on internal statistical criteria"
- which is current
- EP06-Ed2, published 2020, with a CLSI correction notice dated 9 September 2021 amending equations 28 and 29 so that the quantile is Z(1 − alpha/2) rather than Z(alpha). EP06-A is superseded but is still in wide circulation in validation templates and in older analyser documentation, which is why both are printed here
- absolute and relative together
- a purely relative allowance goes to zero at zero concentration and a purely absolute one is absurdly generous at the top of the interval. Taking the greater of the two at each level is the same hybrid form the CLIA proficiency limits use — potassium at a flat 0.3 mmol/L, creatinine at 0.2 mg/dL OR 10%, whichever is larger
- what an ADL is NOT
- it is not the method’s imprecision, and it is not derived from the data. It is a statement about clinical consequence made before the study, from biological variation, from the scheme or regulatory limit you are held to, or from the width of a decision zone. Setting it after seeing the deviations turns the whole procedure into a formality
Worked example
A dilution series with five levels and four replicates each. The worst deviation is 16 units at the level whose expected concentration is 120 units, and it is at the top of the interval. The laboratory declared an allowable deviation from linearity of 5 units absolute or 10% relative, whichever is greater.
The relative allowance at 120 units is 10% of 120 = 12 units
The absolute allowance is 5 units. The greater of the two is 12, so the ADL at this level is 12 units
The observed deviation is 16 units, which is larger than 12 → the level fails
16 is not more than three times 12 (= 36), so this is an ordinary end-of-range deviation rather than a gross one
The deviation is at the top of the interval, so it can be removed by truncation: set the upper reportable limit at the highest level that passed, and dilute above it
Change one number and the verdict changes with it. Had the worst deviation been at the level whose concentration is 40 units, the ADL there would be the greater of 5 and 4, so 5 units — and the same 16-unit deviation would be more than three times the allowance rather than a third over it
EP06-A against EP06-Ed2
| EP06-A (2003, superseded) | EP06-Ed2 (2020, current) | |
|---|---|---|
| The question asked | Is a higher-order polynomial term statistically significant? | Is the deviation at each level clinically acceptable? |
| Design | Five equally spaced levels, four replicates each | Sized from the allowable deviation, the acceptable risk and the method SD; at least two replicates per level |
| Statistic | Nonlinearity = linear fit minus best-fitting nonlinear model | Deviation = level mean minus straight-line fit, at each level |
| Verdict | Global pass or fail for the series | Level by level, against that level’s allowable deviation |
| Failure mode | Large replicate counts make trivial bends significant | A generous or after-the-fact allowable deviation makes everything pass |
What each position in the interval means you can do
| Worst deviation is | Can truncation fix it? | First thing to check |
|---|---|---|
| At the top | Yes — lower the upper reportable limit | Whether the deviation is downwards, which in immunoassay means hook effect |
| At the bottom | Yes — raise the lower reportable limit | Whether it agrees with an independently determined limit of quantitation |
| In the middle | No | The calibration curve fit, and whether one intermediate dilution was mis-made |
Why EP06 stopped asking whether a bend is significant
The 2003 edition of EP06 approached linearity as a hypothesis test. You fitted a straight line, a parabola and a cubic to the dilution series, asked whether the higher-order coefficients were statistically significant, and if one was, the method was declared nonlinear. It is a clean procedure and it has a fatal property: the answer depends on how many replicates you ran. With two replicates per level a real and clinically important bend can fail to reach significance; with ten, a bend of no consequence whatever will reach it comfortably. Two laboratories with identical instruments and different workloads could reach opposite conclusions about the same method, and both would be correct on their own terms.
The second edition, published in 2020, replaced the question. It asks, at each level of the series, how far the mean of the replicates sits from the straight-line fit, and compares that distance with an allowable deviation from linearity that the laboratory declares in advance. If every level is inside its allowance, the method is linear over the interval tested. The statistical machinery has not disappeared — it moved to the design stage, where the number of replicates is now chosen so that the study has adequate power to detect a deviation of the size that matters — but the verdict itself is a clinical comparison, not a p value.
That shifts the burden onto the allowable deviation, and this is where linearity studies go wrong in practice. The allowance has to be set before the data are seen, from something external: within-subject biological variation, the limit the proficiency scheme holds you to, the width of a clinical decision zone, or the manufacturer’s own claim. Set afterwards, from the deviations observed, it guarantees a pass and documents nothing. Set from what the instrument can do rather than from what the patient needs, it is a description of the method rather than a specification for it.
The other thing EP06 does not do is establish accuracy. A method can be perfectly linear and uniformly wrong, because a straight line with the wrong slope is still a straight line. Linearity says the relationship between what is there and what is reported has no bend in it; it says nothing about where that line sits. Trueness is a separate study against a comparative method or a reference material, and the deviation of that line from identity at each medical decision point is what decides whether the method is fit to use.
Frequently asked questions
Which edition of CLSI EP06 should I be working to?
EP06-Ed2, published in 2020, which is the current edition and which replaced the polynomial-order approach of EP06-A (2003) with a per-level comparison of deviation against an allowable deviation from linearity. Check also for the CLSI correction notice dated 9 September 2021, which amends equations 28 and 29 so that the quantile used is Z(1 − alpha/2) rather than Z(alpha). Both editions are still in circulation in validation templates, so record the per-level deviations even if your local template asks for a polynomial test.
Where should the allowable deviation from linearity come from?
From outside the study, and from the clinical consequence of being wrong at that concentration — within-subject biological variation, the acceptance limit of the proficiency scheme you are enrolled in, the width of a decision zone, or a documented manufacturer claim. It has to be fixed before the data are seen. An allowance chosen after the deviations are known is not a specification, and it turns the verification into a formality.
Why does the allowance combine an absolute and a percentage figure?
Because a percentage allowance shrinks to nothing at the bottom of the measuring interval and becomes very generous at the top. Taking whichever of the two is larger at each level gives a sensible floor at low concentrations and sensible proportionality at high ones. It is the same hybrid form the CLIA proficiency limits use — potassium at a flat 0.3 mmol/L, creatinine at 0.2 mg/dL or 10%, whichever is greater.
The deviation is at the top of my interval. Can I just dilute those samples?
Only if the diluted result has itself been shown to be accurate, because dilution linearity is a separate claim and often a matrix-dependent one. Lower the upper reportable limit to the highest level that passed, verify the dilution protocol independently, and make sure the new limit reaches the laboratory information system and the report comments. One warning: if the deviation at the top runs downwards in an immunoassay, that is a hook effect, and a hook produces a plausible-looking low result from a grossly raised sample rather than an obvious flag.
Does passing a linearity study mean my results are accurate?
No. Linearity says the relationship between the true concentration and the reported one has no bend in it. A method that reads 15% high at every concentration is perfectly linear. Accuracy is a separate question, answered by comparing against a reference or comparative method and looking at the predicted bias at each medical decision point.
Related calculators
References
- CLSI EP06-Ed2. Evaluation of the Linearity of Quantitative Measurement Procedures. 2nd ed. Clinical and Laboratory Standards Institute; 2020.
- CLSI. Correction notice to EP06, 2nd edition, 9 September 2021 (equations 28 and 29; Z(1 − alpha/2)).
- CLSI EP06-A. Evaluation of the Linearity of Quantitative Measurement Procedures: A Statistical Approach. Clinical and Laboratory Standards Institute; 2003. [Superseded]
- Centers for Medicare & Medicaid Services. Clinical Laboratory Improvement Amendments of 1988 (CLIA) Proficiency Testing Regulations Related to Analytes and Acceptable Performance. Final rule. Fed Regist. 2022;87(131):40946-41014.
Medical Disclaimer: The tools and content provided here are for educational and reference purposes only. They are not intended to substitute for professional medical advice, diagnosis, or treatment. Clinical decisions should always be based on the comprehensive assessment of a qualified healthcare professional.