Bland Altman Plot - Do the variables have to be normally distributed ?
jaf...@pobox.com
While plotting a Bland Altman plot to measure agreement between two
measurements, do the measurements (or differences between measurements)
have to be normally distributed ? Can someone please also shed light
what assumptions (if any) does one have to meet before doing a BA plot
?
Much appreciated
Fahim H. Jafary, MD
Aga Khan University Hospital
Karachi, Pakistan
mb...@york.ac.uk
This all started with a paper Doug Altman and I wrote on measuring
agreement between two methods of measurement. We were criticising
applications of correlation and regression in this context and we thought
we should say what we thought was a correct method of analysis. We
suggested calculating the differences between the two methods and finding a
95% range for differences by mean difference plus or minus 1.96 standard
deviations of the differences. We thought that this was simple and obvious
from first principles of statistics. We later called this range the the 95%
limits of agreement.
To do this we must assume that the mean and SD of the differences are
uniform, i.e. they must not be related to the magnitude of the quantity
being measured. To check this assumption, we suggested plotting difference
against mean of the pair of measurements, as the best estimate of the
magnitude.
So the plot is a check on the assumptions of the 95% limits of agreement.
The differences should be Normal for the 1.96 to work, but this should be
fairly robust. It is the uniformity which is more important.
If there is a relationship between mean and/or standard deviation and
magnitude, we proposed two methods to deal with this: a log transformation
and a more general regression method.
You can find the original papers on my website.
Martin
--
J. Martin Bland
Prof. of Health Statistics, Dept. of Health Sciences,
University of York, Heslington, York YO10 5DD
Email: mb...@york.ac.uk
Phone: 01904 321334
Web site: http://www-users.york.ac.uk/~mb55/
jaf...@pobox.com
Fahim Jafary