This tutorial will show you how to set up and interpret a Passing & Bablok regression to compare methods in Excel using the XLSTAT statistical software.
Method comparison with the Passing and Bablok regression
When developing a new method to measure the concentration or the quantity of an element (molecule, micro organism, …) you might want to check whether it gives results that are similar to a reference or comparative method or not.
Passing and Bablok (1983) developed a regression method that allows comparing two measurement methods, which overcomes the assumptions of the classical linear regression that are inappropriate for this application. XLSTAT-Life provides the Passing and Bablok regression to evaluate the performance of a method compared to another.
Dataset for method comparison with the Passing and Bablok regression
An Excel sheet with both the data and the results can be downloaded by clicking on the button below:
Download the data
The data correspond to a medical experiment during which the concentration of an antibody is measured for 8 mice submitted to 8 different doses of a new molecule being tested. For each mouse, a blood sample has been taken and divided into four homogeneous sub-samples. Two methods are being tested each on 2 of the 4 sub-samples. The first method is currently considered as the reference, but it is much more expensive than the second and new method.
Our goal is to check if it is possible to use the new method instead of the reference one.
Setting up a Passing and Bablok regression
Once XLSTAT has been started, select the Method validation / Passing and Bablok regression feature.
The Passing and Bablok regression dialog box appears.
In the General tab, select the data that correspond to the first method, then to the second method.
In the Options tab, two methods of estimation are proposed:
Part I - same scale: This is the first method developed by Passing and Bablok (1983). It should be used when both methods are on the same scale and move in the same direction (positive correlation between X and Y).
Part III - different scale: This method of estimation developed by Bablok et al. in 1988 is an improvement of the method known as Part I. It is more robust and can be used to compare two methods on different scales with possibly a negative correlation between X and Y.
Choose the first method and click OK to start the computations.
Interpreting the results of a Passing and Bablok regression
The first table displays the descriptive statistics for the two methods. The new method has a larger mean but a larger variance as well.
Then, the model coefficients are displayed.
The intercept value is -1.970 with a confidence interval including 0. This value measures that the systematic difference between the two methods is not significantly different from 0.
The slope coefficient is equal to 1.214 with confidence interval including 1. That means that the proportional difference between the two methods is equal to 1. If 1 is included in the confidence interval then the hypothesis that the slope is equal to 1 is not rejected.
We can say that there no systematic and no proportional differences between the two methods.
The regression plot confirms these remarks:
Before drawing any conclusion, we should test that our model fits a linear model. For that purpose a test of linearity is applied.
Since the test is not rejected, we can say that both methods have no significant difference and that the new less expensive method could be used to replace the former one.