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

[guhjy@kmu.edu.tw]

Dear David:
Thank you for your detailed explanations.
It helps me a lot.
P.S.: The motivation for my question was the fact that the ratio
distribution is very complicated
(http://en.wikipedia.org/wiki/Ratio_distribution) with no means and
variances (http://www.mathpages.com/home/kmath042/kmath042.htm).

Jinn-Yuh


2012/5/27 David Hoaglin <dchoaglin@gmail.com>:
> 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
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