Passing-Bablok regression (Passing & Bablok, 1983) finds the line of best fit using a shifted median of all possible pairwise slopes between points. It does not make assumptions of the distribution of the measurement errors, and the variance of the measurement errors need not remain constant over the measuring interval though their ratio should remain proportional to β² (the slope squared, in many cases β ≈ 1).
There is a modification to the procedure for use when the methods measure on different scales, or where the purpose is to transform results from one method to another rather than to compare two methods for equality (Passing & Bablok, 1988).
Confidence intervals for parameter estimates are based on a normal approximation or bootstrap. Confidence curves around the regression line and at specific points on the line are obtained by bootstrap.
From the Statistical Reference Guide for Analyse-it 6.24.0: https://analyse-it.com/docs/user-guide/method-comparison/passing-bablok-regression
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