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Bland-Altman plot

Command:Statistics
Next selectMethod comparison & evaluation
Next selectBland-Altman plot

Description

The Bland-Altman plot, or difference plot, is a graphical method to compare two measurements techniques (Bland & Altman, 1986 and 1999). 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.

Required input

Dialog box for Bland-Altman plot

You can select the following variations of the Bland-Altman plot (see Bland & Altman, 1995; Bland & Altman, 1999; Krouwer, 2008):

Options

(*) or ratios when this option is selected.

It is recommended (Stöckl et al., 2004; Abu-Arafeh et al., 2016) to enter a value for the "Maximum allowed difference between methods", and select the option "95% CI of limits of agreement".

How to define the Maximum allowed difference

Jensen & Kjelgaard-Hansen (2010) give two approaches to define acceptable differences between two methods.

  • In the first approach the combined inherent imprecision of both methods is calculated (CV2method1 + CV2method2)1/2, or in case of duplicate measurements [(CV2method1 /2)+ (CV2method2)/2)]1/2.
  • In the second approach acceptance limits are based on analytical quality specifications such as for example reported by the Clinical Laboratory Improvement Amendments (CLIA).

A third approach might be to base acceptance limits on clinical requirements. If the observed random differences are too small to influence diagnosis and treatment, these differences may be acceptable and the two laboratory methods can be considered to be in agreement.

Results

MedCalc creates a graph and a report.

Graph

Bland-Altman plot

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.

The limits of agreement (LoA) are defined as the mean difference ± 1.96 SD of differences. If these limits do not exceed the maximum allowed difference between methods Δ (the differences within mean ± 1.96 SD are not clinically important), the two methods are considered to be in agreement and may be used interchangeably.

Proper interpretation (Stöckl et al., 2004) takes into account the 95% confidence interval of the LoA, and to be 95% certain that the methods do not disagree, Δ must be higher than the upper 95 CI limit of the higher LoA and −Δ must be less than the lower %95 CI limit of the lower LoA:

Schematic presentation of Bland-Altman plot.

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.

Confidence intervals

Optionally, confidence intervals may be displayed for the average difference and for the limits of agreement. These confidence intervals can be represented as error bars or horizontal lines. Right-click on the error bar to set formatting options.

See Video: How to format confidence intervals in Bland-Altman plots.

Report

The report contains the exact values and confidence intervals for average difference and the limits of agreement.

Bland-Altman plot - report
Bland-Altman plot

Method A

TEST1

Method B

TEST2

Sample size

67

Option

Plot differences

Arithmetic mean

-6.4514

95% Confidence interval

-10.7484 to -2.1545

P (H0: Mean=0)

0.0038

Lower limit

-40.9793

95% Confidence interval

-48.3594 to -33.5992

Upper limit

28.0764

95% Confidence interval

20.6963 to 35.4565

Examples

Some typical situations are shown in the following examples.

Bland-Altman plot example showing proportional error
Example 1: Case of a proportional error.

Bland-Altman plot example where at least one method depends strongly on the magnitude of measurements
Example 2: Case where the variation of at least one method depends strongly on the magnitude of measurements.

Bland-Altman plot example showing an absolute systematic error
Example 3: Case of an absolute systematic error.

Repeatability

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) (Bland & Altman, 1986):

Coefficient of Repeatability $$CR = 1.96 \times \sqrt{\frac{\sum_{}^{}{(d_2-d_1)^2}}{n}} $$

The 95% confidence interval for the Coefficient of Repeatability is calculated according to Barnhart & Barborial, 2009.

To obtain this coefficient in MedCalc you

The coefficient of repeatability is not reported when you have selected the "Plot ratios" method.

Literature

See also

External links