

BIOSTATISTICS 

Year : 2017  Volume
: 3
 Issue : 1  Page : 110111 

Bland–Altman plot: A brief overview
Parampreet Kaur, Jill C Stoltzfus
Department of Research and Innovation, The Reseach Institute, St. Luke's University Health Network, Bethlehem, PA 18015, USA
Date of Web Publication  7Jul2017 
Correspondence Address: Parampreet Kaur 801 Ostrum Street, Bethlehem, PA 18015 USA
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/IJAM.IJAM_54_17
In healthcare research, it is common to compare two methods of measurement to determine the overall degree of agreement. The Bland–Altman (BA) plot is an alternative to traditional correlational analyses. The BA plot portrays the agreement graphically by creating statistical limits of agreement using the mean and standard deviation of the differences between two measurements. The difference (Test #1 − Test #2) is constructed on the vertical axis while the mean ([Test #1 + Test #2]/2) is depicted on the horizontal axis. Within this plot, one can detect bias between the mean differences, as well as estimate an agreement interval. If the data points are normally distributed, 95% of differences will lie between the limits, but smaller sample sizes may be unreliable for estimating larger population parameters. Although nonparametric methods can estimate limits of agreement with nonnormally distributed data, they may be less reliable than logarithmically transforming the data before creating the plot. The following core competencies are addressed in this article: Practicebased learning and improvement, Medical knowledge.
Keywords: Agreement, bias plot, Bland–Altman plot, measurement methods
How to cite this article: Kaur P, Stoltzfus JC. Bland–Altman plot: A brief overview. Int J Acad Med 2017;3:1101 
In healthcare research, it is common practice to compare two methods of measurement to determine how well they agree with each other. Although correlational analyses are used to assess the strength of association – with higher correlations indicating stronger relationships – they do not show the degree to which two measures are comparable.^{[1]}
Given this reality, Altman and Bland devised an alternative approach in 1983, which involves plotting graphically the agreement between two quantitative measurements by creating statistical limits of agreement using the mean and standard deviation of the differences between these measurements.^{[2]}
The Bland–Altman (BA) graph consists of a scatter plot in which the difference between two measures (Test #1 − Test #2) is constructed on the vertical axis, while the mean of the two measures ([Test #1 + Test #2]/2) is depicted on the horizontal axis. While this is the standard way of presenting the BA plot, one may also represent the differences between two measures as percentages or ratios.^{[1]}
The traditional Bland–Altman plot appears as follows:^{[3]}
Within this plot, one is able to detect bias between the mean differences of two measures, as well as estimate an agreement interval. Within this interval, 95% of the data points should fall within ± 2 standard deviations of the mean difference. Therefore, the agreement interval allows one to assess the range of variability between the two methods, and this interval must be decided upon before constructing the plot based on clinical objectives. However, the BA plot only defines the intervals of agreement – it does not indicate whether these limits are reasonable or justifiable for a particular clinical purpose.^{[1]}
Some important considerations should be noted when interpreting a Bland–Altman plot. First, one must assess where the mean difference falls, since this gives a general sense of whether one method of measurement tends to overestimate (i.e., the mean difference is above zero) or underestimate (i.e., the mean difference is below zero). The closer the mean difference is to zero, the better the agreement between the measures. It is then prudent to calculate the 95% confidence interval (CI) of the mean difference to determine the precision of this outcome. If the line representing zero falls outside the 95% CI, there is a significant difference between measures, meaning one method either overestimates or underestimates the other.^{[1]} Second, one must determine the spread of the limits of agreement, since the standard deviation of the differences between measures reveals random variation around the mean. Wider limits of agreement indicate less precision while narrower limits suggest that the two methods are reasonably comparable.
Finally, if the data points are normally distributed, 95% of differences will lie between the limits, but with smaller sample sizes, the 95% limits of agreement may be unreliable for estimating larger population parameters. Therefore, one should have a sufficient sample size to ensure greater precision. Furthermore, one should always verify, both graphically and statistically, whether the data are normally or nonnormally distributed, similar to what is done before using inferential statistical methods to ensure that the correct measure of central tendency is captured (in this case, means versus medians). If data are not normally distributed, one should try transforming the data logarithmically, then creating a new Bland–Altman plot.^{[1]} Alternatively, one could use a nonparametric approach to estimate limits of agreement, although this method may be less reliable, especially with small samples.^{[4]}
It should also be noted that the standard Bland–Altman plot cannot be used to estimate agreement when there are repeated measures for each subject. In this case, a random effect model may be used to estimate the withinsubject variation, with the appropriate Bland–Altman plot created based on these results.^{[5]} In addition, it is important to use appropriate statistical agreement methods according to the type of data. For categorical and ordinal variables, agreement is generally assessed using Cohen's kappa and weighted kappa methods.^{[6]}
In conclusion, Bland–Altman plots are a simple way to visually assess the agreement between two methods of measurement, provided one keeps in mind the scope of usage and basic limitations.
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Conflicts of interest
There are no conflicts of interest.
References   
1.  Giavarina D. Understanding Bland Altman analysis. Biochem Med (Zagreb) 2015;25:14151. [ PUBMED] 
2.  Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 1986;1:30710. [ PUBMED] 
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4.  Bland JM, Altman DG. Measuring agreement in method comparison studies. Stat Methods Med Res 1999;8:13560. [ PUBMED] 
5.  Myles PS, Cui J. Using the BlandAltman method to measure agreement with repeated measures. Br J Anaesth 2007;99:30911. [ PUBMED] 
6.  Watson PF, Petrie A. Method agreement analysis: A review of correct methodology. Theriogenology 2010;73:116779. [ PUBMED] 
