Ravi Varadhan
2008-Oct-29 23:00 UTC
[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@jhmi.edu Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html ---------------------------------------------------------------------------- -------- [[alternative HTML version deleted]]
Leif Peterson
2008-Oct-30 01:18 UTC
[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.