STATISTICS
With very precise data, even a trivial and clinically unimportant wobble can reach significance, while a genuinely important departure can go undetected if replication is thin. The question that actually matters is simple. Is the deviation at each concentration inside the predefined allowable limit? One further point. Ordinary regression
assumes the scater around the line is roughly constant across the interval, but analytical imprecision often increases with concentration. Where that’s a real effect, an unweighted fit lets the high end drag the line around, which is part of why the worked example below behaves the way it does. This is a detail rather than something to memorise, but it’s a reasonable question to ask when a fited line looks odd against the raw points. A deviation plot (expected
concentration on the x-axis, deviation from the fited line on the y-axis, allowable limits marked) makes this easy to see at a glance, and is usually far more informative than the raw measured versus expected scater. Figure 1, from the worked example below, shows why.
Worked example A laboratory verifies a manufacturer’s claimed interval of 10–150 units, using eight mixed patient pool levels in triplicate, with a (deliberately illustrative) allowable deviation of ±5 units (Table 3). R² is 0.992! Reassuring on its own – but the deviation at 150 units breaches the ±5 unit limit, and the pattern of differences (negative, then positive, then sharply negative again) is a classic signature of curvature, not random scatter. Note too that 130 units shows only +0.1 deviation, yet it would be wrong to call that acceptable. The fitted line has been dragged down by the failing upper points, and both 130 and 150 units show clear negative recovery against their nominal concentrations. The defensible conclusion is that the full 10–150 claim is not verified. A provisional upper
8 6 4 2 0
-2 -4 -6
Allowable deviation (±5 units) -8 0 20 40 Fig 1. Deviation plot for the worked example.
boundary nearer 100 units needs focused, independently prepared confirmation before adoption. Not simply deleting the top two levels and refitting.
When a study fails – and extending the interval with dilution A failed study doesn’t automatically mean the assay is non-linear. Work through preparation records, calibration and QC status, run order, and replicate behaviour before blaming the test. A systematic dilution error, an unstable endpoint pool, or simple drift across the run can all produce a curvature-shaped result.
Repeat testing is only useful if it’s targeted at a specific suspected cause. Repeating blind until you get a pass is a well- recognised way to manufacture a false reassurance – don’t do it! Never simply delete the concentrations that failed and refit. That can hide genuine saturation or a local discontinuity. Never set a revised boundary at ‘the highest level that happened to pass’ without additional data confirming the transition. It’s also worth distinguishing where
the failure sits. A problem confined to one boundary usually just means adopting a narrower, still continuous interval
60 80 100 Expected concentration (units) 120 140 160
Ordinary regression assumes the scatter around the line is roughly constant across
the interval, but analytical imprecision often increases with concentration
September 2026
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Deviation from fited linear response (units)
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