Bias at clinical decision limits: what a method comparison misses

Two questions, not one

A method comparison answers a numerical question: how far apart are results from the old and the new measurement procedure, and is that within what the laboratory will accept [CLSI EP09]. Near a decision limit there is a second, interpretive question: does the same patient land in the same category on both? The two can disagree. Numerically similar results can fall on opposite sides of a limit, and a difference outside the allowable error can leave a patient’s category unchanged [Cai et al., 2026].

The second question matters because clinical decisions are made at limits, not at averages. A laboratory that reports a difference in percent has answered the first question. Clinicians and quality managers usually need the second.

The comparison line: Passing-Bablok and Bland-Altman in brief

Passing-Bablok regression fits a straight line of new results on old without assuming either method is free of error, and is robust to outliers [Passing and Bablok, 1983]. Its slope says whether the difference grows with concentration (proportional) and its intercept whether there is a fixed offset (constant). Both come with intervals, usually from the method’s own procedure or from bootstrap resampling.

Bland-Altman analysis plots each pair’s difference against its mean and reports the average difference with limits of agreement, the range in which most differences fall [Bland and Altman, 1986]. It is the familiar summary of agreement across the whole range.

Both are standard tools for verifying comparability in a medical laboratory, alongside Deming regression and paired difference tests [Abdel Ghafar and El-Masry, 2021]. Neither, on its own, says what happens at a particular limit.

Bias at the limit, with an interval

With a comparison line in hand, the systematic error at any concentration can be read off it: that is how method-validation practice estimates error at medical decision concentrations rather than as one average [Westgard]. At a decision limit L, with slope b and intercept a:

bias at L = (b × L + a) − L

Expressed as a percentage of L, this is the figure to set against the laboratory’s acceptance limit at that concentration. Repeating the fit on bootstrap resamples of the pairs gives an interval for it. The point is not the formula, which is simple, but the habit: report bias at each limit the laboratory publishes, not once for the whole range. A proportional difference that looks small on average can be large at a high limit, and a constant offset matters most at a low one.

Counting patients across a line

Bias at a limit is still a property of the method. The number the clinician asks for is a count: how many patients were in one category on the old analyser and in another on the new. From the paired results this is direct. Place each pair’s old result and new result into the categories the limits define, and count the pairs whose category differs, separately for each limit and each direction.

Direction matters. A new analyser that reads lower moves patients down across a limit; one that reads higher moves them up; a change in slope can do both at different limits. A table of old category by new category shows all of it at once.

Why repeat testing sets the baseline

Some of those crossings would have happened with no change at all. Measure a sample twice on one analyser and a result close to a limit can land on either side of it, purely from imprecision. So a raw count of crossings overstates what the change did.

The baseline comes from the analyser’s repeat-test imprecision (its coefficient of variation). For each result, take the probability that a repeat measurement on the same analyser would put it in a different category; summed over all results, that is the number of crossings to expect from repeat testing alone. The change’s own effect is the excess of observed crossings over that expectation. If the laboratory has QC or duplicate data, the imprecision should be measured; if a default is used, the report should say so.

A re-test band follows naturally. Results that land within a narrow range of a limit on the new analyser are the ones most likely to have crossed because of the change or by chance. Re-testing them during the transition catches much of the excess for a known share of extra tests, and the share can be fixed in advance as a budget.

A worked example

Sample

The example uses a public CD4 method comparison: 1,885 paired counts from an open-access deposit in which one flow-cytometry platform replaced another [Coetzee and Glencross, 2017]. We ran it through our program as if a laboratory had exported it, with decision limits at 100, 200, 350, 500 cells/µL. It is a sample built from public data: no laboratory commissioned or reviewed it, and repeat-test imprecision is assumed.