Bland-Altman Plot Dialog

Design 1: One data-pair per subject

A Bland-Altman plot is used to compare two measurements of the same variable. That is, it is a method comparison technique. In the initial design of this analysis, that has been used for many years, each of the two measurement methods is used once on each subject. You need to provide two input data columns, one for each measurement method, via the Method 1 and Method 2 list boxes. The Subject box should be set to None in this design. A big drawback of this simple design is that no repeatability parameter can be computed.

Considering n paired observations for method 1 (M_1k) and method 2 (M_2k), with k = 1, 2,...,n, the simplest form of a Bland-Altman plot is obtained by plotting the differences d_k = M_1k - M_2k on the Y axis versus the pair means (M_1k + M_2k)/2 on the X axis.

A horizontal line representing the bias is drawn at the mean difference: d_mean = ∑d_k/n.

Two other horizontal lines, known as the limits of agreement (LoA ) are added to the plot at:

LoA_up,low = d_mean ± 1.96 S_d

where S_d is the standard deviation:

S_d = [1/(n-1)∑(d_k - d_mean )²]^1/2

Sometimes the 1.96 multiplier for the standard deviation is replaced with 2 or with another value. The default value in the Multiplier (SD) box is therefore set to 1.96 and can be freely modified.

There are four display modes available for the X axis of a Bland-Altman plot:

There are three display modes available for the Y axis of a Bland-Altman plot:

Design 2: Repeated measurements for each method

Multiple observations by each method on each subject are needed in order to compare the repeatability of the two methods. For this more complex design of the Bland-Altman analysis three columns of input data are required: one with the measurements of the first method, one with the measurements of the second method and one with the subject values.

In this design only one display mode is available for the Y axis of a Bland-Altman plot: the default Difference mode. Also, the result curve displays the data points corresponding to each subject with a different color.

Two methods are available for calculating the Confidence interval for the limits of agreement (LoA) in the case of replicated measurements: Delta method and MOVER (Method of Variance Estimates Recovery). The calculation steps for each of these two methods are explained in detail by GY Zou in his paper Confidence interval estimation for the Bland-Altman limits of agreement with multiple observations per individual, Statistical Methods in Medical Research, 2013 Dec;22(6):630-42.

The use of the option True Value is Constant is very clearly explained by Bland and Altman in their paper from 2007 Agreement between methods of measurement with multiple observations per individual, Journal of Biopharmaceutical Statistics, 17: 571-582: "There are two different situations to consider for replicated data. We can think of the observations for the same subject as a series of measurements of a quantity that does not vary over the period of observation... Or we can think of them as pairs of measurements by two methods of a changing quantity, where it is the instantaneous measurement for the subject which we want to capture....The distinction is important, as it determines whether we need to consider pairing of observations by the two methods. Indeed, for the first (constant) case we do not require equal replication of each method for each individual, whereas this is a requirement for the second (non-constant) case."

If the option True Value is Constant is checked, the data columns for Method 1 and Method 2 may have a different number of input cells, since pairing is not required. The calculations for the limits of agreement and the corresponding confidence intervals will take into account the different number of observations for each method, nevertheless, only paired observations will be displayed by the output result curve.

By checking the option Plot Subjects as Bubbles, it is possible to group the measurements for each subject and represent them as one bubble with the center located at the following coordinates: mean of group (X) and mean difference (Y). The sizes of the bubbles are proportional to the number of replicates. This option does not affect in any way the calculations of the various reported values, only the drawing of the result data curve.