Grokbase Groups R r-help October 2008
FAQ
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@jhmi.edu

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



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

Search Discussions

  • Leif Peterson at Oct 30, 2008 at 1:18 am
    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



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



    [[alternative HTML version deleted]]

    ______________________________________________
    R-help at r-project.org mailing list
    https://stat.ethz.ch/mailman/listinfo/r-help
    PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
    and provide commented, minimal, self-contained, reproducible code.
  • Ravi Varadhan at Oct 30, 2008 at 4:14 pm
    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



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



    [[alternative HTML version deleted]]

    ______________________________________________
    R-help at r-project.org mailing list
    https://stat.ethz.ch/mailman/listinfo/r-help
    PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
    and provide commented, minimal, self-contained, reproducible code.

    ______________________________________________
    R-help at r-project.org mailing list
    https://stat.ethz.ch/mailman/listinfo/r-help
    PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
    and provide commented, minimal, self-contained, reproducible code.

Related Discussions

Discussion Navigation
viewthread | post
Discussion Overview
groupr-help @
categoriesr
postedOct 29, '08 at 11:00p
activeOct 30, '08 at 4:14p
posts3
users2
websiter-project.org
irc#r

2 users in discussion

Ravi Varadhan: 2 posts Leif Peterson: 1 post

People

Translate

site design / logo © 2017 Grokbase