Deming and Weighted Deming regression for method comparison Deming and Weighted Deming per EP09-A3 — constant and non-constant precision, jackknife CIs, systematic error decomposition, and Syx for independent precision estimation.

The parametric regression for when precision is characterised

Ordinary linear regression assumes all the measurement error is in the Y variable. In a method comparison, both methods have error — and ignoring the X error biases the slope toward zero. Deming regression corrects for this by accounting for imprecision in both methods, but that correction depends on whether precision is constant or varies with concentration. Use the wrong model and the bias estimate is wrong. Use an ordinary regression and it’s definitely wrong.

Analyse-it provides both Deming and Weighted Deming in the same analysis, so you can compare directly and choose with evidence. Systematic error is decomposed into constant and proportional components, and Syx gives an independent check on precision that can flag matrix effects before they contaminate the bias estimate.

Analyse-it has a tremendous advantage in its ease of use. With other programs, you really have to study how to use them, but Analyse-it makes it so easy, and at the same time offers the advanced procedures we need like Weighted Deming regression.

Marco Balerna, Ph.D.
Clinical Chemist
Ente Ospedaliero Cantonale, Switzerland
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What's included

Deming for constant precision, Weighted Deming for non-constant

Both available in the same analysis. Deming when precision is constant (constant SD), Weighted Deming when it varies with concentration (constant CV). Fit both, compare the residual patterns, and choose the one that matches your data. Jackknife confidence intervals on slope and intercept.

Specify imprecision or estimate it from replicates

For singlicate measurements, specify imprecision as SD, %CV, or relative ratio — from an EP05-A3 precision study or the manufacturer’s claimed imprecision. For replicates, imprecision is estimated directly from the data. Compare using mean of replicates, first replicate only, or first replicate of test against mean of reference.

Systematic error decomposed into constant and proportional bias

Constant bias (intercept) and proportional bias (slope) reported separately, each with confidence intervals. Identify whether the offset is fixed across the range or scales with concentration, and which component is driving the difference.

Syx for independent precision and matrix effect detection

Syx provides an independent estimate of scatter around the regression line. Compare it against expected within-run precision — if Syx is larger, matrix-related effects may be inflating the differences and warrant investigation before finalising the bias conclusion.

Bias at clinical decision points with equality and equivalence tests

Predict mean bias with confidence intervals at any decision threshold. Test equality and equivalence at each point per EP09-A3. Allowable difference as absolute concentration, percentage, or a combination — such as “10%, with a minimum of 5 mg/dL.”

Partition the measuring range

Partition the data into separate measuring intervals, each with its own regression, bias estimates, and comparability assessment. Use any fit within each interval. Each interval gets its own allowable difference specification per EP09-A3.

Total analytical error per EP21-A

Combine the bias estimate with the imprecision of the test method and compare the total against allowable error at each decision point. One pass/fail assessment that accounts for both bias and imprecision.

Example analyses

See Deming and Weighted Deming results in detail — systematic error decomposition, Syx, bias at decision points, and total analytical error — using CLSI example datasets you can download and follow along with.

EP09-A3 — Appendix I
All five fits with decision point testing. 79 observations. Deming and Weighted Deming alongside OLS, Weighted OLS, and Passing-Bablok. Bias at decision point 5 μg/L with CI and equality test.

EP21-A — Table 2
LDL Cholesterol total analytical error. 100 observations. Mountain plot, limits of agreement, and allowable difference ±10 mg/dL.

Part of the method comparison workflow

Deming and Weighted Deming are two of six 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.

Software you can trust

Validated calculations you can defend at inspection Every calculation is performed by Analyse-it — no Excel formulas, no third-party functions. Results are validated against CLSI reference datasets, published datasets, and thousands of internal test cases before every release. See how we develop and validate Analyse-it →

Data stays in your facility Analyse-it runs entirely within Microsoft Excel on your PC. No cloud processing, no data transmission. Pre-submission data, patient-adjacent data, and in-process results stay within your facility under your own data governance controls.

Standard Excel workbooks anyone can open Every analysis is an ordinary .xlsx workbook. Share with colleagues, submit to regulatory affairs, archive for audit, open on any PC with Excel. No proprietary format, no licence required to view results. Colleagues and auditors see exactly what you see.

Results that can’t be accidentally broken Analysis output contains computed values, not formulas. Nothing to accidentally overwrite, no cell references to break, no formula errors to introduce. The results you reported are exactly what you’ll find when you reopen the workbook months or years later for an audit.

Technical details

CLSI protocols

EP09-A3: Measurement Procedure Comparison and Bias Estimation Using Patient Samples
EP21-A: Estimation of Total Analytical Error for Clinical Laboratory Methods

Deming regression

Deming regression (constant precision)
Weighted Deming regression (non-constant precision)
Slope and intercept with jackknife confidence intervals
Systematic error: constant and proportional bias with CIs
Syx independent precision estimate
Imprecision: SD, %CV, or relative ratio (singlicate)
Automatic imprecision estimation from replicates

Bias estimation

Predict bias with confidence intervals at clinical decision points
Equality and equivalence (within allowable difference) tests
Allowable error: absolute, percentage, or combination

Study design

Singlicate, duplicate, and replicate measurements
Compare using mean, 1st replicate, or 1st vs mean of reference
Within-subject variance estimation
Reduce or partition measuring interval new in v4.00
Total analytical error per EP21-A

Diagnostics

Pearson r correlation coefficient
Precision (SD or CV) for each method

Plots

Scatter plot with fit line, confidence bands, identity line, and allowable error bands
Difference / relative difference / ratio plot with allowable difference band
Mountain plot with allowable difference band new in v3.71
Residual plot (raw and standardised) with histogram
Vary colour of points by a factor