Meaning of positive vs. negative slope in a Bland-Altman plot

[John Sorkin]

Colleagues,
I know that if there is perfect agreement a Bland-Altman plot (difference plotted against the mean) will show a line with a slope of zero. It is also clear that a slope of zero with an intercept that is non-zero indicates a systematic bias. It is also clear that in the face of random error (i.e. noise) the plot with show a non-zero slope. I am trying to understand if there is any inference to be drawn when the slope is positive vs. negative, for example a slope of 0.5 vs. -0.5. I don't think the sign of the slope is important, but I would like to hear what other list members have to say.
John

John David Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
University of Maryland School of Medicine Division of Gerontology
Baltimore VA Medical Center
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[Bland, M.]

The sign of the slope, if any, depends on which measurement you choose
to subtract from which. If your measurements are labelled X and Y, if
you plot X - Y against (X+Y)/2 then a negative slope means that for
subjects with large values of the quantity being measured will have
relatively large Y compared to X, a positive slope will mean that large
X compared to Y.

The famous plot was intended to as a visiual check on the assumption
that bias and variability are constants, i.e. unrelated to magnitude,
that's all. This was so that we could estimate these as single numbers.

Martin

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[Doug Altman]

You refer to numerical values for the slope which implies regressing the difference on the mean, which is not part of the basic method that we proposed. Regression of difference on mean can be done of course, and this may be  useful when the differences vary with the size of measurement; we discussed this with an example in our 1999 paper in SMMR.

However, the sign of the slope surely depends on which method you all A and which you call B (or X and Y). It cannot have any meaning.

~Doug

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[John Sorkin]

Thank you.
Could you send me a copy of the SMMR paper?
Thanks,
John

John David Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
University of Maryland School of Medicine Division of Gerontology
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
(Phone) 410-605-7119

(Fax) 410-605-7913 (Please call phone number above prior to faxing)>>> Doug Altman <doug....@csm.ox.ac.uk> 1/14/2010 12:58 PM >>>

~Doug

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[John Sorkin]

Prof. Altman,
I am not sure I sent a copy of my reply to you.
First, thank you for responding. Could you send me a copy of your SMMR paper?
Thanks,
John

John David Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
University of Maryland School of Medicine Division of Gerontology
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
(Phone) 410-605-7119

(Fax) 410-605-7913 (Please call phone number above prior to faxing)>>> Doug Altman <doug....@csm.ox.ac.uk> 1/14/2010 12:58 PM >>>

You refer to numerical values for the slope which implies regressing

~Doug

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[BXC (Bendix Carstensen)]

I the curent issue of Statistics in Medicine (Volume 29 Issue 3, 10 February 2010)
you will find:

Comparing methods of measurement: Extending the LoA by regression (p 401-410)
Bendix Carstensen
Published Online: Dec 8 2009 11:00AM
DOI: 10.1002/sim.3769

where this issue is discussed in some more detail.

Best regards,
Bendix