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Passing-Bablok Regression Calculator
Compare two measurement methods with a robust, non-parametric regression — Passing-Bablok slope and intercept with confidence intervals — and copy the exact R command behind the result. A full guide follows below. Validated against R 4.3.3.
In Simple Words
Passing-Bablok regression fits a line between two measurement methods without assuming which one is error-free and without assuming a particular error distribution. The slope is the median of all pairwise slopes between data points, which makes it robust to outliers and to measurement error in both methods.
The result is read through its confidence intervals: if the slope’s interval includes 1 and the intercept’s includes 0, the two methods agree without proportional or constant bias. A slope away from 1 indicates proportional bias; an intercept away from 0 indicates constant bias.
When to Use Passing-Bablok
Use Passing-Bablok for method-comparison studies in clinical chemistry and laboratory medicine, especially when both methods carry measurement error and the data may contain outliers. It is recommended by method-comparison guidelines precisely because it makes no distributional assumptions.
It complements, rather than replaces, a Bland-Altman plot: the regression characterises systematic bias across the range, while the plot shows the spread of differences. When the error ratio between methods is known, Deming regression is an alternative. Ordinary least squares is not appropriate when both methods have error. Unsure which to use? Our Test Selector can help.
Expected: 2 columns: Method 1 values | Method 2 values
Drop a CSV here or click to choose. Parsed in your browser: nothing is uploaded.
Expected: 2 columns: Method 1 values | Method 2 values
library(mcr)
m1 <- c({m1})
m2 <- c({m2})
mcreg(m1, m2, method.reg = "PaBa")User guide
When to use. Non-parametric method comparison robust to outliers and measurement error in both methods.
Assumptions. Continuous paired measurements; no assumption on error distribution.
Common mistakes. Needs a reasonable measurement range to estimate the slope reliably.
Worked example
Click Load example data above, then Run Analysis to see a fully worked result with figure, formula and interpretation for this test.
References
- Passing H, Bablok W. A new biometrical procedure for testing the equality of measurements. J Clin Chem Clin Biochem. 1983;21:709-720.
Worked Examples
Example 1 — Methods agree
Passing-Bablok gives a slope of 1.02 (95% CI 0.95 to 1.09) and an intercept of 0.1 (95% CI −0.5 to 0.7). Because the slope interval contains 1 and the intercept interval contains 0, there is no evidence of proportional or constant bias — the methods agree.
Example 2 — Proportional bias
If the slope is 1.15 with a 95% interval of 1.08 to 1.22, the interval excludes 1. One method reads progressively higher than the other as values rise — proportional bias — which a single bias figure would miss but the regression captures.
Assumptions to Check
Paired continuous measurements. Each sample is measured by both methods on the same continuous scale.
A reasonable measurement range. The slope is estimated from pairwise slopes, so a spread of values across the analytical range is needed for a reliable estimate.
A roughly linear relationship. Passing-Bablok assumes the relationship between the two methods is linear; strong curvature requires a different approach.
Common Mistakes
Using ordinary least squares instead
OLS assumes the x-method is error-free, which is false in method comparison. Passing-Bablok (or Deming) accounts for error in both methods.
Judging bias from the point estimates alone
A slope of 1.05 may or may not indicate bias; the confidence interval decides. Always interpret slope and intercept through their intervals.
Too narrow a measurement range
If all samples cluster in a small range, the slope is poorly determined. Span the analytical interval where possible.
Applying it to clearly non-linear data
Passing-Bablok estimates a single straight line; if the methods relate non-linearly, the fit is misleading and a different model is needed.
Frequently Asked Questions
Why is Passing-Bablok preferred for method comparison?
It makes no assumption about which method is the reference or about the error distribution, and it is robust to outliers, which suits real laboratory data.
How do I read the slope and intercept?
If the slope’s confidence interval includes 1 and the intercept’s includes 0, the methods agree; values outside indicate proportional or constant bias.
When should I use Deming instead?
Deming regression is appropriate when the ratio of the methods’ analytical errors is known; Passing-Bablok needs no such assumption.
Does the result match R?
Yes. The calculator uses the standard Passing-Bablok estimator and shows the R command (mcr package) so you can reproduce slope, intercept, and intervals.
Related Calculators
References
- Passing H, Bablok W. A new biometrical procedure for testing the equality of measurements from two different analytical methods. Part I. J Clin Chem Clin Biochem. 1983;21(11):709–720. PMID 6655447.
- Passing H, Bablok W. Comparison of several regression procedures for method comparison studies and determination of sample sizes. Part II. J Clin Chem Clin Biochem. 1984;22(6):431–445. PMID 6481307.
- CLSI. Measurement Procedure Comparison and Bias Estimation Using Patient Samples. EP09c. 3rd ed. Wayne, PA: Clinical and Laboratory Standards Institute; 2018.
Need This Analysis Done for Your Manuscript?
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