Passing–Bablok regression is a method from

robust statistics Robust statistics are statistics that maintain their properties even if the underlying distributional assumptions are incorrect. Robust Statistics, statistical methods have been developed for many common problems, such as estimating location parame ...

for

nonparametric regression Nonparametric regression is a form of regression analysis where the predictor does not take a predetermined form but is completely constructed using information derived from the data. That is, no parametric equation is assumed for the relationshi ...

analysis suitable for method comparison studies introduced by Wolfgang Bablok and Heinrich Passing in 1983. The procedure is adapted to fit linear

errors-in-variables models In statistics, an errors-in-variables model or a measurement error model is a regression model that accounts for measurement errors in the independent variables. In contrast, standard regression models assume that those regressors have been me ...

. 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(

. 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. It may be considered a robust version of

reduced major axis regression In applied statistics, total least squares is a type of errors-in-variables regression, a least squares data modeling technique in which observational errors on both dependent and independent variables are taken into account. It is a generaliza ...

. 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 In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations ...

O(n^2)

. However, fast quasilinear algorithms of complexity

O(n

n)

have been devised. Passing and Bablok define a method for calculating a 95% confidence interval (CI) for both

a

and

b

in their original paper, which was later refined, though bootstrapping the parameters is the preferred method for in vitro diagnostics (IVD) when using patient samples. The Passing-Bablok procedure is valid only when a linear relationship exists between

x

and

y

, which can be assessed by a

CUSUM In statistical process control, statistical quality control, the CUSUM (or cumulative sum control chart) is a sequential analysis technique developed by E. S. Page of the University of Cambridge. It is typically used for monitoring change detecti ...

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. 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.

References

{{DEFAULTSORT:Passing-Bablok regression Analytical chemistry Medical statistics