Method comparison & evaluation
The Bland-Altman plot (Bland & Altman, 1986 and 1999), or difference plot, is a graphical method to compare two measurements techniques. In this graphical method the differences (or alternatively the ratios) between the two techniques are plotted against the averages of the two techniques. Alternatively (Krouwer, 2008) the differences can be plotted against one of the two methods, if this method is a reference or "gold standard" method.
Horizontal lines are drawn at the mean difference, and at the limits of agreement, which are defined as the mean difference plus and minus 1.96 times the standard deviation of the differences.
If you have duplicate or multiple measurements per subject for each method, see Bland-Altman plot with multiple measurements per subject.
After you have selected Bland-Altman plot in the menu, enter the variables for the two different techniques in the following dialog box:
You can select the following variations of the Bland-Altman plot (see Bland & Altman, 1999; Krouwer, 2008):
- Plot against (X-axis)
In the original Bland-Altman plot (Bland & Altman, 1986) the differences* between the two methods are plotted against the averages of the two methods (recommended, Bland & Altman, 1995).
Alternatively, you can choose to plot the differences* against one of the two methods, if this is a reference or "gold standard" method (Krouwer, 2008). Finally, you can also plot the differences* against the geometric mean of both methods.
*or ratios when this option is selected (see below).
- Plot differences
This is the default option corresponding to the methodology of Bland & Altman, 1986.
- Plot differences as %
When selecting this option the differences will be expressed as percentages of the values on the axis (i.e. proportionally to the magnitude of measurements). This option is useful when there is an increase in variability of the differences as the magnitude of the measurement increases.
- Plot ratios
When this option is selected then the ratios of the measurements will be plotted instead of the differences (avoiding the need for logarithmic transformation). This option as well is useful when there is an increase in variability of the differences as the magnitude of the measurement increases. However, the program will give a warning when either one of the two techniques includes zero values.
- Click the Subgroups button if you want to identify subgroups in the Bland-Altman plot. A new dialog box is displayed in which you can select a categorical variable. The graph will use different markers for the different categories in this variable.
- Draw line of equality: useful for detecting a systematic difference.
- Draw lines for 95% CI of mean of differences*: the 95% Confidence Interval of the mean difference illustrates the magnitude of the systematic difference. If the line of equality is not in the interval, there is a significant systematic difference.
- Draw lines for 95% CI of limits of agreement: shows lines for the 95% confidence interval for both the upper and lower limits of agreement.
- Draw regression line of differences*: this regression line may help to detect a proportional difference. The regression parameters are shown in the graph's info panel. Optionally, you can select to show the 95% confidence interval of this regression line.
*or ratios when this option is selected.
After you click OK you obtain the following graph:
The graph displays a scatter diagram of the differences plotted against the averages of the two measurements. Horizontal lines are drawn at the mean difference, and at the limits of agreement, which are defined as the mean difference plus and minus 1.96 times the standard deviation of the differences.
To get more statistical information, right-click in the graph window and select the Info option in the popup menu:
The Bland-Altman plot is useful to reveal a relationship between the differences and the magnitude of measurements (examples 1 & 2), to look for any systematic bias (example 3) and to identify possible outliers. If there is a consistent bias, it can be adjusted for by subtracting the mean difference from the new method.
If the differences within mean ± 1.96 SD are not clinically important, the two methods may be used interchangeably.
Some typical situations are shown in the following examples.
Example 1: Case of a proportional error.
Example 2: Case where the variation of at least one method depends strongly on the magnitude of measurements.
Example 3: Case of an absolute systematic error.
The Bland-Altman plot may also be used to assess the repeatability of a method by comparing repeated measurements using one single method on a series of subjects. The graph can then also be used to check whether the variability or precision of a method is related to the size of the characteristic being measured.
Since for the repeated measurements the same method is used, the mean difference should be zero. Therefore the Coefficient of Repeatability (CR) can be calculated as 1.96 (or 2) times the standard deviation of the differences between the two measurements (d2 and d1):
This coefficient can be read from the Bland-Altman plot by subtracting the mean difference from the upper 95% limit of agreement, but can also be calculated using Summary statistics. E.g. if the names of the variables for 2 repeated measurements for FSH concentration are FSH1 and FSH2, then you define a new variable as FSH2-FSH1 and calculate the summary statistics for it. By multiplying the calculated standard deviation by 2 you obtain the coefficient of repeatability.
- Bland JM, Altman DG (1986) Statistical method for assessing agreement between two methods of clinical measurement. The Lancet i:307-310. [Abstract]
- Bland JM, Altman DG (1995) Comparing methods of measurement: why plotting difference against standard method is misleading. The Lancet 346:1085-1087. [Abstract]
- Bland JM, Altman DG (1999) Measuring agreement in method comparison studies. Statistical Methods in Medical Research 8:135-160. [Abstract]
- Dewitte K, Fierens C, Stöckl D, LM Thienpont (2002) Application of the Bland-Altman plot for interpretation of method-comparison studies: a critical investigation of its practice. Clinical Chemistry 48:799-801. [Abstract]
- Hanneman SK (2008) Design, analysis, and interpretation of method-comparison studies. AACN Advanced Critical Care 19:223-234. [Abstract]
- Krouwer JS (2008) Why Bland-Altman plots should use X, not (Y+X)/2 when X is a reference method. Statistics in Medicine 27:778-780. [Abstract]