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 (LoA), which are defined as the mean difference plus and minus 1.96 times the standard deviation of the differences. If the differences within mean ± 1.96 SD are not clinically important, the two methods may be used interchangeably.
The plot is useful to reveal a relationship between the differences and the averages, to look for any systematic biases and to identify possible outliers.
The Bland and Altman plot may also be used to assess the repeatability of a technique by comparing repeated measurements using one single method on a series of subjects. In this case, the graph can also be used to check whether the variability or precision of a method is related to the size of the characteristic being measured.
- Select the variables for the two methods to compare.
- Optionally select a filter to include a subset of cases.
- Plot against: 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 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.
- Maximum allowed difference between methods: (optionally) the pre-defined clinical agreement limit. Differences below this limit are clinically irrelevant or neglectable. Depending on the option (Plot differences or ratios) selected above, a difference, a difference expressed as a percentage, or a ratio must be entered.
- Draw line of equality: useful for detecting a systematic difference.
- Show 95% CI of mean: shows an error bar representing for the 95% confidence interval (CI) for the mean difference. The 95% CI 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.
- Show 95% CI of limits of agreement: shows an error bar representing for the 95% confidence interval for both the upper and lower limits of agreement.
- Draw regression line: this regression line may help to detect a proportional difference.
- Draw 95% CI of regression line: Optionally, you can select to show the 95% confidence interval of this regression line.
The Bland-Altman plot 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:
- Bland JM, Altman DG (1986) Statistical method for assessing agreement between two methods of clinical measurement. The Lancet i:307-310.
- Bland JM, Altman DG (1995) Comparing methods of measurement: why plotting difference against standard method is misleading. The Lancet 346:1085-1087.
- Bland JM, Altman DG (1999) Measuring agreement in method comparison studies. Statistical Methods in Medical Research 8:135-160.
- Hanneman SK (2008) Design, analysis, and interpretation of method-comparison studies. AACN Advanced Critical Care 19:223-234.
- 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.
- Stöckl D, Rodríguez Cabaleiro D, Van Uytfanghe K, Thienpont LM (2004) Interpreting method comparison studies by use of the Bland-Altman plot: reflecting the importance of sample size by incorporating confidence limits and predefined error limits in the graphic. Clinical Chemistry 50:2216-2218.
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