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Passing–Bablok regression is a method from robust statistics for nonparametric regression analysis suitable for method comparison studies introduced by Wolfgang Bablok and Heinrich Passing in 1983.^[1]^[2]^[3]^[4]^[5] The procedure is adapted to fit linear errors-in-variables models. It is symmetrical and is robust in the presence of one or few outliers.

The Passing-Bablok procedure fits the parameters $a$ and $b$ of the linear equation $y=a+b*x$ using non-parametric methods. The coefficient $b$ is calculated by taking the shifted median of all slopes of the straight lines between any two points, disregarding lines for which the points are identical or $b=-1$ . The median is shifted based on the number of slopes where $b<-1$ to create an approximately consistent estimator. The estimator is therefore close in spirit to the Theil-Sen estimator. The parameter $a$ is calculated by $a=\operatorname {median} ({y_{i}-bx_{i})}$ .

In 1986, Passing and Bablok extended their method introducing an equivariant extension for method transformation which also works when the slope $b$ is far from 1.^[6] It may be considered a robust version of reduced major axis regression. The slope estimator $b$ is the median of the absolute values of all pairwise slopes.

The original algorithm is rather slow for larger data sets as its computational complexity is $O(n^{2})$ . However, fast quasilinear algorithms of complexity $O(n$ ln $n)$ have been devised.^[4]^[5]

Passing and Bablok define a method for calculating a 95% confidence interval (CI) for both $a$ and $b$ in their original paper,^[1] which was later refined,^[4] though bootstrapping the parameters is the preferred method for in vitro diagnostics (IVD) when using patient samples.^[7] The Passing-Bablok procedure is valid only when a linear relationship exists between $x$ and $y$ , which can be assessed by a CUSUM test. Further assumptions include the error ratio to be proportional to the slope $b$ and the similarity of the error distributions of the $x$ and $y$ distributions.^[1] The results are interpreted as follows. If 0 is in the CI of $a$ , and 1 is in the CI of $b$ , the two methods are comparable within the investigated concentration range. If 0 is not in the CI of $a$ there is a systematic difference and if 1 is not in the CI of $b$ then there is a proportional difference between the two methods.

However, the use of Passing–Bablok regression in method comparison studies has been criticized because it ignores random differences between methods.^[8]

References

^ ^a ^b ^c Passing H, Bablok W (1983). "A new biometrical procedure for testing the equality of measurements from two different analytical methods. Application of linear regression procedures for method comparison studies in Clinical Chemistry, Part I". Journal of Clinical Chemistry and Clinical Biochemistry. 21 (11): 709–20. doi:10.1515/cclm.1983.21.11.709. PMID 6655447. S2CID 45557122.
^ Passing H, Bablok W (1984). "Comparison of several regression procedures for method comparison studies and determination of sample sizes. Application of linear regression procedures for method comparison studies in Clinical Chemistry, Part II" (PDF). Journal of Clinical Chemistry and Clinical Biochemistry. 22 (6): 431–45. doi:10.1515/cclm.1984.22.6.431. PMID 6481307. S2CID 26235878.
^ Bilić-Zulle L (2011). "Comparison of methods: Passing and Bablok regression". Biochem Med. 21 (1): 49–52. doi:10.11613/BM.2011.010. PMID 22141206.
^ ^a ^b ^c Dufey, F (2020). "Derivation of Passing–Bablok regression from Kendall's tau". The International Journal of Biostatistics. 16 (2). doi:10.1515/ijb-2019-0157. PMID 32780716.
^ ^a ^b Raymaekers, Jakob; Dufey, Florian (2022). "Equivariant Passing-Bablok regression in quasilinear time". arXiv:2202.08060 [stat.ME].
^ Bablok W, Passing H, Bender R, Schneider B (1988). "A general regression procedure for method transformation. Application of linear regression procedures for method comparison studies in clinical chemistry, Part III" (PDF). Journal of Clinical Chemistry and Clinical Biochemistry. 26 (11): 783–90. doi:10.1515/cclm.1988.26.11.783. PMID 3235954. S2CID 4686716.{{cite journal}}: CS1 maint: multiple names: authors list (link)
^ EP09-A3: Measurement Procedure Comparison and Bias Estimation Using Patient Samples; Approved Guideline (Third ed.). CLSI. August 30, 2013. ISBN 978-1-56238-888-1.
^ "A note on Passing-Bablok regression". MedCalc Software bvba. Retrieved 19 October 2016.

[PB1983-1] Passing H, Bablok W (1983). "A new biometrical procedure for testing the equality of measurements from two different analytical methods. Application of linear regression procedures for method comparison studies in Clinical Chemistry, Part I". Journal of Clinical Chemistry and Clinical Biochemistry. 21 (11): 709–20. doi:10.1515/cclm.1983.21.11.709. PMID 6655447. S2CID 45557122.

[PB1984-2] Passing H, Bablok W (1984). "Comparison of several regression procedures for method comparison studies and determination of sample sizes. Application of linear regression procedures for method comparison studies in Clinical Chemistry, Part II" (PDF). Journal of Clinical Chemistry and Clinical Biochemistry. 22 (6): 431–45. doi:10.1515/cclm.1984.22.6.431. PMID 6481307. S2CID 26235878.

[biliczulle2011-3] Bilić-Zulle L (2011). "Comparison of methods: Passing and Bablok regression". Biochem Med. 21 (1): 49–52. doi:10.11613/BM.2011.010. PMID 22141206.

[dufey2020-4] Dufey, F (2020). "Derivation of Passing–Bablok regression from Kendall's tau". The International Journal of Biostatistics. 16 (2). doi:10.1515/ijb-2019-0157. PMID 32780716.

[raymaekers2022-5] Raymaekers, Jakob; Dufey, Florian (2022). "Equivariant Passing-Bablok regression in quasilinear time". arXiv:2202.08060 [stat.ME].

[PB1986-6] Bablok W, Passing H, Bender R, Schneider B (1988). "A general regression procedure for method transformation. Application of linear regression procedures for method comparison studies in clinical chemistry, Part III" (PDF). Journal of Clinical Chemistry and Clinical Biochemistry. 26 (11): 783–90. doi:10.1515/cclm.1988.26.11.783. PMID 3235954. S2CID 4686716.{{cite journal}}: CS1 maint: multiple names: authors list (link)

[EP09A3-7] EP09-A3: Measurement Procedure Comparison and Bias Estimation Using Patient Samples; Approved Guideline (Third ed.). CLSI. August 30, 2013. ISBN 978-1-56238-888-1.

[8] "A note on Passing-Bablok regression". MedCalc Software bvba. Retrieved 19 October 2016.

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