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Excel’s LINEST function and chart trendline fit an ordinary least-squares line and stop. All the measurement error is assumed to be in Y; the reference method is treated as error-free. In a method comparison both methods have error, and ignoring the error in X biases the slope towards zero. Deming regression corrects for that, but the correction depends on whether precision is constant or varies with concentration. Use the wrong model and the bias estimate is wrong.
Is precision constant across the measuring range, or proportional to concentration? Is the bias a fixed offset, a proportional one or both? Is the scatter about the line what the within-run precision predicts, or is something in the matrix inflating it? And at the concentrations where clinical decisions are made, does the bias matter?
Both models are in the same analysis, so you can fit both and choose with evidence. Deming when precision is constant across the range (constant SD), Weighted Deming when it varies with concentration (constant CV). Fit both, compare the residual patterns and keep the one that matches the data. Slope and intercept come with jackknife confidence intervals, and the scatter plot shows the fit with its confidence band, the identity line and the allowable error bands.
Deming regression needs the imprecision of both methods, and there are two ways to supply it. For singlicate measurements, specify it as an SD, a %CV or the ratio of the two — from an EP05-A3 precision study or the manufacturer’s claim. For duplicates or replicates, imprecision and the within-subject variance are estimated directly from the data, and the precision of each method is reported. Compare using the mean of the replicates, the first replicate only or the first replicate of the test method against the mean of the reference.
A single bias figure hides whether the offset is fixed across the range or scales with concentration. Constant bias (the intercept) and proportional bias (the slope) are reported separately, each with a confidence interval, so you can see which component drives the difference. Syx is an independent estimate of the scatter about the line, to compare with the expected within-run precision. A larger Syx points to matrix-related effects inflating the differences, which warrant investigation before the bias conclusion is final. Pearson r summarises the correlation.
The slope gives the average bias; clinical decisions are made at specific concentrations. Predict the mean bias, with a confidence interval, at any decision threshold. Test equality (is the difference zero?) and equivalence (is it inside the allowable difference?) at each point per EP09-A3. Specify the allowable difference as an absolute concentration, a percentage or a combination — such as “10%, with a minimum of 5 mg/dL”.
Precision that changes across the measuring range is not served by one regression. Partition the data into separate measuring intervals, each with its own regression, bias estimates and comparability assessment, or reduce the interval to the range the comparison supports. Use any fit within each interval, and give each its own allowable difference, as EP09-A3 specifies. A method can pass on bias and still fail in use. EP21-A combines the bias estimate with the imprecision of the test method and compares the total against the allowable error at each decision point. The result is one pass/fail assessment for both. The difference plot and the mountain plot show the differences against the same allowable band.
See Deming and Weighted Deming results in detail — systematic error decomposition, Syx, bias at decision points and total analytical error. Each analysis uses a CLSI example dataset you can download and follow along with.
10 pages
EP09-A3 — Appendix IDeming and Weighted Deming are two of five regression methods in the method comparison analysis. For a non-parametric approach, see Passing-Bablok regression. To see the distribution of differences and limits of agreement, see Bland-Altman.
Related guides in the Learn section: choosing a regression for method comparison and bias at a medical decision point.
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