Bland & Altman plot

Command:

Statistics Method comparison Bland & Altman plot

Description

The Bland & Altman plot (Bland & Altman, 1986 and 1999) is a statistical 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. 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.

Required input

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 one of the following three variations of the Bland & Altman plot (see Bland & Altman, 1999):

• Plot differences

  This is the default option corresponding to the methodology of Bland & Altman, 1986.

• Plot differences as % of averages

  When selecting this option the differences will be expressed as percentage of the averages. 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 log 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.

Options

• Click the Subgroups button if you want to identify subgroups in the scatter diagram. 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* versus averages: 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 was selected.

After clicking the OK button, or pressing the Enter key, 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 averages (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.

Repeatability

The Bland and 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 deviations of the differences between the two measurements (d₂ and d₁):

This coefficient can be read from the Bland & Altman plot, 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.

Literature

• 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 (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]

See also

• Mountain plot
• Deming regression
• Passing & Bablok regression
• Format graph
• Graph legend
• Add graphical objects
• Reference lines