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Passing-Bablok regression

Command:Statistics
Next selectMethod comparison & evaluation
Next selectPassing-Bablok regression

Description

Passing & Bablok (1983) have described a linear regression procedure with no special assumptions regarding the distribution of the samples and the measurement errors. The result does not depend on the assignment of the methods (or instruments) to X and Y. The slope B and intercept A are calculated with their 95% confidence interval. These confidence intervals are used to determine whether there is only a chance difference between B and 1 and between A and 0.

Required input

Dialog box for Passing-Bablok regression - method comparison

Results

When you have completed the dialog box, click OK to proceed. The following results will be displayed in a text window.

Passing-Bablok regression - method comparison - results

Optionally, the program reports Spearman's rank correlation coefficient (rho) with P-value and 95% Confidence Interval. Note that Passing & Bablok (1983) discourage reporting the correlation coefficient in method comparison studies. We have found that Passing & Bablok regression does not work when correlation is low; we report it not as a method-comparison statistic, but as a factor in the evaluation of the validity of the Passing-Bablok regression procedure itself.

Scatter diagram and regression line

This graph shows the observations with the regression line (solid line), the confidence interval for the regression line (dashed lines) and identity line (x=y, dotted line):

Passing-Bablok regression - method comparison - scatter diagram

Extrapolation

MedCalc only shows the regression line in the range of observed values. As a rule, it is not recommended to extrapolate the regression line beyond the observed range. To allow extrapolation anyway, right-click in the graph and select Allow extrapolation in the pop-up menu.

Allow extrapolation

Residuals plot

Passing-Bablok regression - method comparison - residuals

The residual plot allows for the visual evaluation of the goodness of fit of the linear model. If the residuals display a certain pattern, you can expect the two variables not to have a linear relationship.

Outliers

Since it is in essence a non-parametric procedure, Passing-Bablok regression is not influenced by the presence of one or relative few outliers. Nevertheless, outliers - defined here as residuals outside the 4 SD limit - are plotted in a different color in the residuals plot. Linnet & Boyd (2012) recommend that these measurements should not just be rejected automatically, but the reason for their presence should be scrutinized.

Bablok & Passing (1985) recommend that "Samples which produced deviant values should be analysed again by both methods. Any measurement value should only be termed as an outlier and be excluded from the data, if an analytical error was identified or the analyser declared the result as questionable. If the distribution of the data is known, a statistical test for detecting outliers can be used."

Importance of sample size

When sample size is small, the width of the 95% Confidence Intervals for intercept and slope will be large, and will more likely contain the values 0, resp. 1 (see also Mayer et al, 2016). The result is that method comparison studies based on small sample sizes are biased to the conclusion that the laboratory methods are in agreement.

Therefore a correct and large enough sample size needs to be used.

Passing & Bablok W (1984) and Bablok & Passing (1985) give tables with suggested adequate sample sizes (ranging from 30 to 90). Bablok & Passing (1985) advise to have at least 30 samples. Ludbrook (2010) cites a sample size of at least 50.

Notes

Literature

See also