Bland-Altman-Analysis

A MATLAB function for Bland-Altman Analysis of agreement between measurement methods.

Bland-Altman Analysis is a statistical method published by J. Martin Bland and Douglas G. Altman in the 1980s and further developed later on. It is used to determine the agreement between two measurement methods that measure the same quantity. It is a popular method in biostatistics and chemistry.

Syntax

s = ba(x,y) performs Bland-Altman Analysis on x and y, which are data from two measurement methods for the same quantity respectively. x and y must be numeric vectors of the same length. The calculations are done at a significance level of alpha = 0.05. Output s is a structure containing multiple fields with descriptive statistics about the agreement of x and y. For more details on s see section Output below.

s = ba(x,y,alpha) specifies the significance level to calculate the limits of agreement and confidence intervals with. alpha must be a scalar in the interval [0,1]. If alpha is not specified a value of 0.05 is used by default to calculate 95% limits of agreement and confidence intervals.

s = ba(__,Name,Value) specifies additional options using one or more name-value pair arguments, in addition to any of the input arguments in the previous syntaxes. For example, you can specify to create the mean-difference plot using the'PlotMeanDifference'` name-value pair argument.

ba(__) can be used to plot the data without returning an output argument.

__ = ba(f,__) specifies the figure(s) f in which to create the plots specified with the corresponding name-value pairs. The number of figures in f must equal one or the number of specified plots.

__ = ba(ax,__) specifies the (array of) axes in which to create the plots specified with the corresponding name-value pairs. The number of axes in ax must equal the number of specified plots.

Examples

See and run the ba1999demo.m script for examples of the syntax of ba used with data from the 1999 article by Bland and Altman. Calling ba without input arguments also runs the demonstration script.

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments to access various options. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: 'XName','X','YName','Y'

'XName': Name of x variable

inputname of input argument x (default) | string

Name of x variable, specified as a string. 'XName' is used in the plot titles.

Example: 'XName','X' sets the first measurement's name to 'X'.

'YName': Name of y variable

inputname of input argument y (default) | string

Name of y variable, specified as a string. 'YName' is used in the plot titles.

Example: 'YName','Y' sets the second measurement's name to 'Y'.

'Exclude': Observation pairs to exclude

[] (default) | logical indices | numeric indices

Observation pairs to exclude, specified as logical or numeric indices to index into x and y. The specified elements are removed from x and y before any calculations or plots.

Example: 'Exclude',[1, 3, 4] excludes elements 1, 3 and 4 from x and y.

Example: 'Exclude',[0 0 1 0 1 1 0 0 1] excludes the true elements from x and y.

'PlotMeanDifference': Create mean-difference plot

false (default) | true

Create the mean-difference plot if the specified value is true. The mean-difference plot is a scatter plot of the difference between observations versus their mean. Specifying the 'PlotAll' Name-Value pair argument as true creates the mean-difference plot, regardless of the 'PlotMeanDifference' value.

'PlotCorrelation': Create correlation plot

false (default) | true

Create the correlation plot if the specified value is true. The correlation plot is a scatter plot of x and y. Specifying the 'PlotAll' Name-Value pair argument as true creates the correlation plot, regardless of the 'PlotCorrelation' value.

'PlotAll': Create all plots

false (default) | true

Create mean-difference and correlation plots if the specified value is true. Setting 'PlotAll' to true overrides any value given to the 'PlotMeanDifference' and 'PlotCorrelation' Name-Value pair arguments. However, setting it to false does not override the individual plot Name-Value pair arguments.

'PlotStatistics': Add statistics to the created plots

'none' (default) | 'basic' | 'extended'

Add statistics to the created plots, specified as 'basic' or 'extended'. 'basic' specifies a basic set of statistics to add. 'extended' adds a more extended set of statistics to the plots. The following statistics are added to the plots.

• The basic set adds labelled lines for the limits of agreement to the mean-difference plot. It also adds the Spearman rank correlation coefficient to the legend of the mean difference plot. Furthermore, the Pearson correlation coefficient is added to the legend of the correlation plot.
• The extended set adds the statistics of the basic set. Additionally, the confidence intervals of the mean difference and limits of agreement are plotted as error bars in the mean-difference plot. The extended set does not add statistics other than the basic set to the correlation plot.

If no plots are created, the 'PlotStatistics' value is ignored.

'PlotLeastSquares': Add a least-squares line to the created plots

false (default) | true

Add a least-squares line to the created plots if the specified value is true. The least-sqares line describes the simple linear relationship between x and y in the correlation plot and the mean and difference in the mean-difference plot.

Output

The only output argument s is optional. It is a scalar structure containing multiple fields with descriptive statistics about the agreement of x and y. s contains the following fields:

• muD: the mean difference between x and y, also called the bias.
• muDCI: the 95% (default, depending on alpha) confidence interval of the mean difference.
• loa: the 95% (default, depending on alpha) limits of agreement, a 2 element vector. The first element is the lower limit of agreement, the second is the upper.
• loaCI: the 95% (default, depending on alpha) confidence interval of the limits of agreement, a 2x2 matrix. The first column corresponds to lower limit of agreement, the second to the upper limit. The first and second row correspond to the lower and upper confidence interval bound respectively.
• sD: the standard deviation of the differences.
• rSMuD: the Spearman rank correlation between mean and difference.
• pRSMuD: the p-value of the Spearman rank correlation for testing the hypothesis of no correlation against the alternative that there is a nonzero correlation.

About

This MATLAB function is an implementation of the methods in the 1999 article by Bland and Altman: Measuring agreement methods in comparison studies. You might not have access to this article. Access it through your institution's library or buy it.

The article comprises of 5 methodological sections (sections 2-6). The current version of this MATLAB file (8 september 2016) implements the first methodological section. More sections will be added in the future.

The demonstration script ba1999demo.m is an implementation of the calculations done by Bland and Altman in the article. Their article contains a number of example data sets, which they use in their methods. The demonstration script illustrates the same results and the syntax used to obtain them.