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From |
David Hoaglin <dchoaglin@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Is it valid to use the individual ratios (i.e. Xi/Yi) in the dependent or independent part of a regression model? |

Date |
Sun, 27 May 2012 07:35:51 -0400 |

Dear Jinn-Yuh, My answer is, "It depends." In an earlier message, you explained that ACR is used to standardize urinary concentration (of urinary albumin, I think) to ensure comparability of albuminuria among individual patients. "Standardize" may be a bit too strong; it may be that dividing by urinary creatinine merely adjusts for variation among patients. If ACR is the variable that clinicians work with, you can definitely use ACR as either the dependent variable or an explanatory variable. Sometimes it is preferable to work with concentration data in a log scale (either explicitly or by leaning on the -poisson- command to use quasi-likelihood to fit a linear predictor in the log scale without transforming the data --- the latter approach is a separate discussion, and I won't pursue it here). One can use regression for a variety of purposes. You may be interested mainly in prediction, or in the values of one of the coefficients in the regression (for example, how ACR varies with cholesterol when you adjust for the contributions of age and gender). (These two do not exhaust the list of purposes.) A regression model for either of these purposes could have ACR as the dependent variable. Depending on the research that led to the use (adoption?) of ACR, it might also be instructive to use urinary albumin as the dependent variable and urinary creatinine as one of the explanatory variables. I could also see working with log(ACR) and with log(urinary albumin) and log(urinary creatinine) in parallel analyses. I'm not familiar with the physiology, so I don't know whether it is meaningful to have ACR as the dependent variable and cholesterol as an explanatory variable and also to have cholesterol as the dependent variable and ACR (or urinary albumin and urinary creatinine) as an explanatory variable. As an explanatory variable, ACR is one function of urinary albumin and urinary creatinine; but you could reasonably consider other functions, such as the linear combination of urinary albumin and urinary creatinine that arises from using those two as explanatory variables or the nonlinear function in which the explanatory variables in that part of the model are urinary albumin, urinary creatinine, and their product (for this version, it would be a good idea to center the two variables by subtracting suitable values before taking their product). I have focused mainly on model building. That is probably the main issue. Fortunately, you have enough data (about 500 patients) to develop a reasonable model. You may have been looking for a straightforward answer, and I have given you a rather complicated one. In practice, careful analyses of data are seldom simple. In this instance, if you are not already familiar with regression diagnostics, it would be worthwhile to learn about them. They should be helpful as you proceed with the analysis of your data. David Hoaglin On Sun, May 27, 2012 at 5:07 AM, <guhjy@kmu.edu.tw> wrote: > Dear David: > In a sample (not a survey sample) of about 500 hospital chronic kidney > disease patients, I am using ACR as the: > 1. Dependent variable: regress ACR age gender cholesterol (Is it > better to regress urinary albumin on urinary creatinine, age, gender > and cholesterol?) > 2. Independent variable: regress cholesterol age gender ACR (Is it > better to regress cholesterol on age, gender, urinary albumin and > urinary creatinine?) > "Patients with chronic kidney disease" is the population in the > inferential statistics. The population ACR (but not the population > totals of urinary albumin or urinary creatinine) are my concerns. > > Thank you. > Jinn-Yuh > > > 2012/5/27 David Hoaglin <dchoaglin@gmail.com>: >> Dear Jinn-Yuh, >> >> In a notation that is customary in survey sampling, X/Y (perhaps more >> commonly Y/X) is the ratio of two population totals. Please tell us >> more about the population for which you would like to estimate the >> ratio of the population total of urinary albumin to the population >> total of urinary creatinine. >> >> If you are calculating ACR for individual patients, and that is the >> variable that you are using in your regressions, how are the >> population totals related to those regressions? The relevance of the >> biases that you have mentioned to your analysis is not yet clear. It >> would help if you described one of the multiple regression models that >> you are using. >> >> David Hoaglin >> >> On Sat, May 26, 2012 at 9:02 PM, <guhjy@kmu.edu.tw> wrote: >>> ACR (urinary albumin creatinine ratio, i.e. urinary albumin [Xi] >>> divided by urinary creatinine [Yi]) is used to standardize for urinary >>> concentration to ensure comparability of albuminuria among individual >>> patients (http://en.wikipedia.org/wiki/Microalbuminuria). I am using >>> ACR as the dependent or independent variable in multiple linear >>> regressions. However, "ratio of means" and "mean of ratios (ACR >>> [Xi/Yi] in this case)" are both biased estimates for the population >>> ratio [X/Y] (Mean of ratios or ratio of means or both?: >>> http://www.sciencedirect.com/science/article/pii/S0378375801001811). >>> In view of these problems and the many pitfalls of ratios mentioned in >>> many references, is it better to use X (or Y) to adjust for Y (or X) >>> in regressions (despite its clinical usefulness in individual >>> decisions)? >>> >>> Thank you. >>> Jinn-Yuh >> * >> * For searches and help try: >> * http://www.stata.com/help.cgi?search >> * http://www.stata.com/support/statalist/faq >> * http://www.ats.ucla.edu/stat/stata/ > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Is it valid to use the individual ratios (i.e. Xi/Yi) in the dependent or independent part of a regression model?***From:*Phil Clayton <philclayton@internode.on.net>

**Re: st: Is it valid to use the individual ratios (i.e. Xi/Yi) in the dependent or independent part of a regression model?***From:*guhjy@kmu.edu.tw

**References**:**st: Is it valid to use the individual ratios (i.e. Xi/Yi) in the dependent or independent part of a regression model?***From:*guhjy@kmu.edu.tw

*From:*Nick Cox <njcoxstata@gmail.com>

*From:*Steve Samuels <sjsamuels@gmail.com>

*From:*guhjy@kmu.edu.tw

*From:*Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com>

*From:*guhjy@kmu.edu.tw

*From:*Nick Cox <njcoxstata@gmail.com>

*From:*guhjy@kmu.edu.tw

*From:*David Hoaglin <dchoaglin@gmail.com>

*From:*guhjy@kmu.edu.tw

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