## Wednesday, June 15, 2011

### Bland-Altman Plot for Assessing Agreement

Bland-Altman plot is a scatter plot of variable means plotted on the horizontal axis and the differences plotted on the vertical axis which shows the amount of disagreement between the two measures (via the differences) and lets you see how this disagreement relates to the magnitude of the measurements.

When I was in graduate school, the statistical analysis of microarray data just started to be a hot topic. In collaboration with Dr Rick Song, we looked at the microarray data and wrote a manuscript titled “On Graphical Presentation and Quantitative Analysis of cDNA Microarray Data” and we presented in JSM. In this manuscript, we proposed to use Bland-Altman plot. In clinical trials, I have not got a chance to apply this approach, but I do often see articles using the Bland-Altman plot. For example, an article titled “Using the Bland–Altman method to measure agreement with repeated measures” from British Journal of Anaesthesia.

When data is appropriate, Bland-Altman plot can be a handy tool to use. It is worth relaying the paragraphs from our original paper on graphical presentation of micro-array data using Bland-Altman plot.

“Graphical presentation is usually the first step for data analysis of microarray data. In the case without duplication (this is typical in microarray experiment), scatter plots will be drawn and then a regression line drawn through the data. This helps the eye in gauging the degree of agreement between two measurements and also may help us to identify the "outliers" that represent the differentially expressed genes in microarray experiment.

In clinical medicine, to assess agreement between two methods of clinical measurement, Bland and Altman proposed to plot the difference between the methods (A-B) against the mean (A+B)/2[12,13,14,15]. This approach has been extensively used in medical research for assessing measurement error and comparing different measurements for the same quantity. Bland and Altman’s method can be also applied to the microarray data. We can plot (Rm-Gm) against (Rm+Gm)/2 (figure2 above).

Calculating or plotting a regression line is not our focus as we are not concerned with the estimated prediction of one color intensity by another but with the theoretical relationship of equality and deviations from it.

There are several advantages for presenting the microarray data using Brand and Altman’s approach:

The plot of difference against mean allows us to investigate any possible relationship between the discrepancies and the true value. The plot will also show clearly any extreme or outlying observations. If two different samples are used in the experiment, these extreme or outlying observations could indicate the differentially expressed genes. It is often helpful to use the same scale for both axes when plotting differences against mean values. This feature helps to show the discrepancies in relation to the size of the measurement.

Brand and Altman's method makes it easier for us to estimate the precision of the estimated limits of agreement between two color intensities. We want a measure of the agreement that is easy to estimate and to interpret for a measurement on the color intensity of an individual gene. An obvious starting point is the difference between measurements by the two channels on the same gene. There may be a consistent tendency for one channel to exceed the other. This is called calibration factor and can be estimated by the mean difference. There will also be variation about this mean, which we can estimate by the standard deviation of the differences. These estimates are meaningful only if we can assume that calibration factor and variability are uniform throughout all genes.”

More references on Bland-Altman Plot: