Bland-Altman analysis is a statistical method for evaluating the consistency of two measurement methods, and is widely used mainly in the fields of medicine and manufacturing. Below is a graph called a " Bland-Altman plot" that is used when performing Bland-Altman analysis. In this plot, the difference between two measurements is plotted on the vertical axis, and the average of the two measurements is plotted on the horizontal axis, allowing the bias and consistency between measurements to be evaluated.
Figure: Bland-Altman plot
JMP introduced Bland-Altman analysis as an option for "matched pairs" in version 17, and the latest version 18 adds even more functionality.
In this blog, we will explain the overview of Bland-Altman analysis, the steps for performing the analysis using JMP, and points to note.
Data used
We will use the JMP sample data "Method Comparison.jmp", which contains the measurement results for 20 objects using the "Standard Method" and "Measurement Method 1". We will use this data to evaluate the agreement between the measurement methods.
In this data set, the measurement results for each object using the standard method and measurement method 1 correspond, so the data is paired . Using Graph Builder, a scatter plot was drawn with the standard method on the horizontal axis and measurement method 1 on the vertical axis, and a straight line (blue) where the values on the horizontal and vertical axes match.
If the plotted points are on a straight line, it means that the two measurements are consistent. In this example, most of the data points are close to the straight line., but you can see that there are some plots where some points deviate from a straight line.
Bland-Altman analysis assumes that the difference between the two measurements follows a normal distribution.
Bland-Altman analysis
When you have data like the ones above, where the measurements you want to compare are entered across two columns, JMP performs a Bland-Altman analysis in the following steps:
- In Analyze > Advanced Modeling > Matched Pairs , specify the two columns you want to compare as Y, Paired Response .
- Select Bland Altman Analysis from the red triangle button to the left of the report "Y, Matched Pairs."
The "Bland-Altman analysis" report will be displayed at the bottom of the report.
In Bland-Altman analysis, the values shown in the red box in the figure above are important.
Bias : The average of the difference between measurement method 1 and the standard method. For each data point, calculate "measurement method 1 value - standard method value" and take the average of these values. In this example, the bias is 0.113.
Lower and upper tolerance limits : These are the widths of the intervals that are acceptable for the measurements to match. If we can assume that the mean difference follows a normal distribution, we would expect approximately 95% of the data to fall within these ranges. In JMP, this is calculated using the 97.5% point (Z(0.975)) of the standard normal distribution as follows:
Bias ± Z(0.975) * (standard deviation of bias)
(Note: The value of Z(0.975) is 1.95996, but in Bland-Altman analysis, the value of 1.96 is often used for convenience.)
The tolerance limits in this example are (-3.229, 3.455).
Bland-Altman plot
The Bland-Altman plot is a graph that plots the bias and tolerance limits calculated in the Bland-Altman analysis described above, allowing you to visually check the agreement between measurements.
Note that the graph shown in the JMP Matched Pairs report is not the exact Bland-Altman plot. The dotted red lines in this graph are often mistaken for tolerance limits, but they are 95% confidence limits for the mean difference, calculated based on the standard errors.
On the other hand, since the tolerance limits for the Bland-Altman plot are calculated based on the standard deviation , to draw this plot, you need to edit the report graph by following steps (1) and (2).
(1) Hide the dotted confidence interval lines
Right-click on any graph in the Matched Pairs report and select Customize from the menu.
In the Customize Graph window, set the following:
- Click the up arrow icon (↑) several times on the left items "Upper Line" and "Lower Line" to move them up.
- Click on the line color and change the color from red to white.
(2) Setting tolerance limits
Double-click the vertical axis of the graph and set the lower and upper tolerance limits as reference lines in the Y-axis settings.The figure below is an example of setting a reference line.
Using these steps, we can produce the following Bland-Altman plot, where the solid red line shows the bias values.
As mentioned above, the plot points are calculated using the following formula:
Vertical axis : Difference between two measurements
Horizontal axis : average of two measurements
The vertical axis is the difference in the measurements, so if there is almost no difference, it will be plotted near Y=0. If the difference in the measurements falls within the lower and upper limits of the tolerance range (blue dotted lines), the agreement is considered good. In this example, all points except for one fall within the tolerance range, so the agreement is generally good. However, for any points that are outside the range, you should go back to the data and consider the cause.
It is also important to consider how the difference on the vertical axis changes with respect to the average value of the measurement method on the horizontal axis. If the difference increases as the measurement value increases, as in the figure below, then proportional error exists. In such cases, it becomes difficult to evaluate agreement using a simple average difference.
Assess Concordance by Percentage Change (New in JMP 18)
The Bland-Altman analysis shown so far has evaluated agreement using the difference between two measurements, but the percentage change (the percentage change of one measurement method compared to another measurement method) can also be used. For example, when measuring with two types of scales (A and 
, the increase in scale B compared to scale A may be 0.1%.
Thinking in terms of rate of change is also one way of dealing with the proportional error shown above when it exists.
The latest version of "JMP 18" adds a function that allows you to examine the consistency between measurements by the rate of change . You can select the option to analyze the rate of change from the red triangle button of the report "Matched Pairs" (red frame in the image below).
The rate of change in this example is calculated as follows and plotted as the value on the vertical axis:
by Naohiro Masukawa (JMP Japan)
Naohiro Masukawa - JMP User Community
