Hi Leif,

Thank you for your response. I went back and carefully read a classic paper

by Dennis Lindley (JRSSB 1947). He makes clear the distinction between

regression and functional relationship. Here I quote his summary from his

paper:

"(A) The functional relationship is required for the statement of laws in th

eempirical sciences which would hold if no errors existed.

(B) The regression line is required for prediction of either true or

observed values of one variate from observation of of the other whether or

not the latter is in error; it being understood that the x from which y is

to be predicted comes from the same population as those x's used in the

estimation of the regression line."

Thus, according to Lindley, for my purposes, which is the prediction of most

likely (or expected) values of one assay given the observed values (with or

without error) of the another assay, a simple linear regression of y on x is

what is needed. Note that more advance methods such as orthogonal

regression (and your suggestions) would be required, if we are interested in

the functional relationships between true values, X and Y.

Best,

Ravi.

----------------------------------------------------------------------------

-------

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 at jhmi.edu

Webpage:

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

--------

-----Original Message-----

From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On

Behalf Of Leif Peterson

Sent: Wednesday, October 29, 2008 9:19 PM

To: r-help at r-project.org

Subject: Re: [R] Regression versus functional/structural relationship?

The two test outcomes will have correlated results, so you will need to look

at either bivariate probit regression or seemingly unrelated regression.

For either of these two methods, you will need to constrain all independent

variable coefficients to be equal, or you will have difficulty making sense

of the results. Stata has biprobit and sureg, and also a constraint

command. (Also bivariate probit requires binary dependents, so you will

need to apply a "clinically interesting" cutpoint of (+)/(-) test results.

If you can't find anything like these in R you will likely need to perform

quantile normalization of both dependents (x,y) before regression. Look at

the qnorm package in bioconductor, by Bolstad. LP

-----Original Message-----

From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On

Behalf Of Ravi Varadhan

Sent: Wednesday, October 29, 2008 6:01 PM

To: r-help at stat.math.ethz.ch

Subject: [R] Regression versus functional/structural relationship?

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.

----------------------------------------------------------------------------

-------

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 at jhmi.edu

Webpage:

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

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______________________________________________

R-help at r-project.org mailing list

https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide

http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.