Estimating bias at a medical decision point A method comparison’s real output is not the regression line — it is the bias at the concentrations where clinical decisions turn. How to estimate it, bound it, and judge whether it matters.

A method comparison produces a slope and an intercept, and it is tempting to treat those as the answer. Slope and intercept describe the relationship across the whole range. What a clinician, a reviewer or an auditor actually needs to know is narrower.

At the concentration where a decision gets made, how far apart are the two methods? Is that gap small enough not to change the decision? The answer is the bias at the medical decision point, and it is the number a method comparison exists to deliver.

Why the decision point, not the average

Average agreement can hide trouble exactly where it matters. A method can sit almost on top of its comparator across most of the range and still diverge at one particular concentration. If a clinical threshold happens to fall there, that local bias is what reclassifies patients from treat to do not-treat.

A medical decision point is a concentration where clinical action changes: a diagnostic cut-off, a treatment threshold, an alert level. The bias that matters is the bias at those points, not the bias averaged over a range that mostly lies where no decision is made.

Estimating the bias from the regression

Fit an appropriate regression to the comparison data: Deming or Passing–Bablok rather than ordinary least squares, for the reasons that guide covers. Then use it to predict, at each decision point, what the new method reads when the comparative method reads the decision value. The difference between the two is the estimated bias at that point.

Both a constant offset and a proportional slope feed into the bias, so the bias at a low decision point can differ entirely from the bias at a high one. Estimate it point by point rather than reading a single average. That is what makes the answer trustworthy.

A method-comparison scatter with a fitted regression line and a dashed line of identity; at a marked decision value, the vertical gap between the two lines is bracketed as the bias.
Bias at a decision point is the vertical gap between the fitted regression and the line of identity at that value. Because slope and intercept both feed into it, the bias at a low decision level can differ from the bias at a high one.

Put a confidence interval on it

The estimated bias is a prediction from a fitted line, so it carries the line’s uncertainty. That uncertainty varies along the range, typically tightest near the centre of the data and wider towards the extremes.

Report the bias at each decision point with its confidence interval. A bias of 4% with an interval of 2–6% supports a firm conclusion. The same 4% with an interval of −3% to 11% does not. Quoting the point estimate alone would hide how little the data actually pin it down.

Judge it against an allowable bias

An estimated bias means nothing until it is compared against how much bias is tolerable at that decision point. That allowable bias comes from outside the comparison: from biological variation, from regulatory limits, or from clinical judgement about how much change would alter management. With a limit in hand, the question becomes a proper test. Is the bias, and its confidence interval, comfortably inside the allowable limit?

An equivalence framing is appropriate here. You are trying to show the methods are close enough to be interchangeable, not just failing to prove they differ. A wide confidence interval that happens to straddle zero is not evidence of equivalence. It is evidence of an underpowered study, which is a different finding entirely.

A worked example

The workbook below fits all five method-comparison regressions to the same data and reports the bias at a medical decision point of 5 µg/L, each with a confidence interval and a hypothesis test. Comparing the decision-point bias across the fits is instructive in itself. Where the five fits agree, the bias estimate is robust. Where they diverge, the choice of regression affects the result and deserves scrutiny.

A forest plot of the bias at a 5 microgram-per-litre decision point for five regression fits, each with its 95% confidence interval, against a shaded allowable band of plus or minus 6 percent: ordinary least squares minus 0.6%, weighted least squares minus 7.5% (outside the band), Deming minus 1.0%, weighted Deming plus 3.7%, Passing-Bablok plus 0.4%.
The bias at the 5 µg/L decision point for all five fits (CLSI EP09-A3, Example 2), each with its 95% confidence interval, against the allowable ±6% band. Ordinary least squares, Deming and Passing–Bablok agree near zero; weighted least squares lands at −7.5%, outside the band — here the choice of regression changes whether the bias meets the limit.

Downloads

Download the CLSI EP09-A3 method comparison example workbook (.xlsx) — five regression fits with the bias at a 5 µg/L decision point, each with a confidence interval and hypothesis test, ready to open in the Analyse-it trial.

Common mistakes

Reporting the slope and intercept and stopping there. They are the means, not the end. Translate them into the bias at the decision points that drive clinical action.

Quoting one average bias for the whole range. Bias can differ at low and high decision points. Estimate it at each one.

Dropping the confidence interval. The decision-point bias is a prediction with uncertainty that widens towards the extremes. Report the interval, not just the estimate.

Reading “not significantly different” as equivalent. A wide interval that includes zero means underpowered, not interchangeable. Test against an allowable bias, not against zero.

Estimate bias at a decision point with Analyse-it

Analyse-it estimates the bias where it matters clinically, from your own comparison data, inside Excel:

  • Bias at any medical decision point, predicted from the fitted method-comparison regression
  • A confidence interval on each estimate, and a test against an allowable bias
  • The decision points you name, rather than a single figure for the whole range

Every feature from all five editions for 15 days. The regression fits are in the Method Validation and Ultimate editions, from US$ 475 a year; the Medical edition estimates bias at decision points from Bland–Altman agreement, from US$ 340 a year. Validated against NIST and CLSI reference datasets. See also choosing a regression.