STATISTICS
be 15% biased). Precision is a different question again. Replicate agreement tells you about repeatability, not whether a level was prepared correctly or whether the material is representative of patient specimens. Most laboratories aren’t establishing a new claim from scratch. They’re verifying that a manufacturer’s stated interval holds up locally, which is a smaller undertaking than the manufacturer’s original validation. Either way, ‘linearity passed’ isn’t a usable conclusion on its own. A defensible statement needs to say what interval was tested, in what specimen type, against what acceptance limit, and whether it was validation or verification. Table 1 shows the terminology used here. It’s worth being clear about what
linearity does not tell you. It says nothing about the lowest concentration you can reliably report. That depends on detection capability and imprecision near zero, which is a separate evaluation (covered in the next article in this series). And a mixing-based linearity study, using expected values calculated from high/ low pool proportions rather than an independent reference method, is not a trueness or method comparison study. If the endpoint values themselves are biased, that bias simply carries through into every calculated expectation in the series.
Designing a study that actually challenges the claim As mentioned in previous articles, a study is only as good as its design. Define the interval, specimen type and acceptance limit before you look at any data, otherwise there’s a real risk of quietly adjusting the target to match what came out of the analyser. The acceptance limit itself should reflect the clinical and analytical stakes of the measurand, not just whatever number to which the software defaults. A percentage limit alone tends to be unreasonably strict
Expected (units) 10 30 50 70 90
110 130 150
Mean measured 10.1 30.0 49.8 70.2 89.9
107.0 121.0 132.0
Design element Materials
Levels Replicates Practical guidance
Patient pools preferred over commercial panels/calibrators where feasible; record source, matrix and preparation
≥6–8 across the interval; extra points near both boundaries and any decision concentration
Typically 2–4 per level, to separate imprecision from real trend
Acceptance limit Set in advance; absolute, relative, or combined. Never R² alone Run order
Table 2. Study design checklist.
near zero, while a fixed absolute limit can become too generous at the top end, so many laboratories use a combination of the two. Use patient-like material wherever
you can. Mixing a high- and low- concentration patient pool in known proportions is usually better than serially diluting one high sample with water or saline, because plain dilution progressively changes the specimen matrix as well as the concentration. Whichever approach you use, test enough intermediate levels. Two endpoints only prove you can draw a line between them, that will always be straight. Include extra points near the proposed boundaries and any clinically important decision concentration. Replicate each level (commonly in triplicate) so random noise can be told apart from a genuine trend, and randomise or balance the run order so drift or carryover doesn’t masquerade as a concentration effect. Elements of study design are shown in
Table 2. Materials and matrix effects
The material you choose is not a side issue. It can determine whether your result is even relevant to patients. Commercial linearity panels and calibrators are convenient and stable, but they may be stabilised, lyophilised or formulated in a matrix that behaves
Fited response 13.8 31.6 49.5 67.3 85.2
103.0 120.9 138.7
Table 3. Worked example data (fited line: ลท = 4.84 + 0.893x; R² = 0.992). 18
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Deviation −3.7 −1.6 +0.3 +2.9 +4.7 +4.0 +0.1 −6.7
differently from fresh plasma or serum during measurement or dilution. A panel can fail in a way that’s purely material specific, or equally, pass while masking a problem that would show up in real patient specimens. Where the assay is known to be matrix sensitive, or the clinical stakes are high, confirm any unexpected finding using independently prepared patient material before drawing conclusions about the assay itself. Mixing to create intermediate levels can behave non-additively because of interactions between proteins and inhibitors. A calculated mixing proportion is not a guarantee of a proportional result.
Analysing the data: R2
isn’t enough Plot the individual replicates before you fit anything. This is where you catch transcription errors, an unusually scattered replicate, or an obvious upper end plateau. Then fit a regression of measured against expected concentration and look at the deviation from that fitted line at each level, not just the overall slope, intercept or R². In a study spanning a wide interval, most of the variation in the data comes from the concentration range itself, not from any local departure. A dataset with real curvature at one end can still return an R² above 0.99. A statistically significant curvature test isn›t decisive either.
Linearity describes whether measured results stay
proportional to the measurand’s true
concentration across a stated interval
Randomised or balanced to avoid confounding concentration with drift/carryover
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