[R] Regression versus functional/structural relationship?

Ravi Varadhan
Wed, 29 Oct 2008 23:00:39 -0000

Hi,

I am dealing with the following problem.  There are two biochemical assays,
say A and B, available for analyzing blood samples.  Half the samples have
been analyzed with A.  Now, for some insurmountable logistic reasons, we
have to use B to analyze the remaining samples.  However, we can do a
comparative study on a small number of samples where we can obtain
concentrations using both A and B.  This gives us the data of the form (x,
y), where x are values from A and y from B.  Now, my question:  Can we
simply use the regression equation from regressing y on x, to convert all
the x values for which only method A was used?  Or do we need to obtain the
functional (or structural) relationship between X and Y (the true values
without measurement error) and use that to do this conversion.  It seems to
me that since we can only observe error-prone x, and we should be predicting
the expected value of error-prone y (i.e E[y | x]).  Therefore, we can
simply use the ordinary regression equation.  However, I have seen papers
using the Deming's orthogonal regression or something equivalent in the
clinical chemistry literature to address this problem.  Deming's method
would make sense if I am interested in obtaining the functional relationship
between X and Y (the true values of two assays), but I don't see why I
should care about that. Am I right?

I would appreciate any clarifying thoughts on this.  I apologize for posting
this methodological, non-R question.

Thank you,
Ravi.
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Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan@jhmi.edu

Webpage:  http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html



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