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

[Cameron McIntosh <cnm100@hotmail.com>]

Jinn-Yuh, 

I would suggest you have a look at the following as well:

Bradshaw, Y., & Radbill, L. (1987). Method and Substance in the Use of Ratio Variables. American Sociological Review,52(1), 132-135.

Firebaugh, G. (1988). The Ratio Variables Hoax in Political Science. American Journal of Political Science, 32(2), 523-535.

Liu, Y., & Schutz, R.W. (2003). Statistical validity of using ratio variables in human kinetics research. Research Quarterly in Exercise and Sport, 74(3), 226-235.

Liermann, M., Steel, A., Rosing, M., & Guttorp, P. (2004). Random denominators and the analysis of ratio data. Environmental and Ecological Statistics, 11(1), 55-71.

Cam

> From: guhjy@kmu.edu.tw
> Date: Mon, 28 May 2012 22:47:24 +0800
> 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?
> To: statalist@hsphsun2.harvard.edu
> 
> 1. Why is the ACR of a group of patients not a ratio distribution?
> 2. The coefficient of variation is always higher for the ratio (X/Y)
> than for either X or Y (http://www.ncbi.nlm.nih.gov/pubmed/17434158).
> 3. In the PREVEND (Prevention of Renal and Vascular End-stage Disease)
> study (http://www.ncbi.nlm.nih.gov/pubmed/22383750):
> 1) The hazard ratio (95% CI) for predicting CV events were 1.41 (1.25,
> 1.58) for spot urine ACR, 1.26 (1.1, 1.43) for spot urine urinary
> albumin concentration, and 1.16 (1.01, 1.32) for the reciprocal of
> spot urine creatinine, respectively. The 95% CI of the three HR
> overlapped (i.e. the three HR were similar) although the author
> claimed that ACR predicts better than either urinary albumin or
> urinary creatinine.
> 2) Body weight, 24 hour-urinary creatinine excretion, age and gender
> predict ACR independent of 24 hour-urinary albumin excretion. In other
> words, 24 hour-urinary albumin excretion is not the only determinant
> of ACR.
> 4. In "Ratio index variables or ANCOVA? Fisher's cats revisited
> (http://www.ncbi.nlm.nih.gov/pubmed/19337988), Tu YK cautioned about
> the use of ratios wherever the underlying biological relationships
> among epidemiological variables are unclear (urinary concentration is
> not the only determinant of urinary creatinine in this case), and
> hence the choice of statistical model is also unclear.
> 
> Jinn-Yuh
> 
> 
> 2012/5/28 David Hoaglin <dchoaglin@gmail.com>:
> > Dear Jinn-Yuh,
> >
> > Your analysis is not actually concerned with the ratio distribution as such.
> >
> > Your first message, at the start of this thread, assumed that X and Y
> > were normally distributed.  Real data, however, are never normal, so
> > results for a ratio of normal variables are mainly of theoretical
> > interest.
> >
> > In particular, from Phil Clayton's comments, it seems that urinary
> > albumin and urinary creatinine are not close to having normal
> > distributions.  You could investigate the distribution shape of
> > urinary albumin, urinary creatinine, and ACR empirically in your
> > patients, though they are probably not a random sample from any
> > well-defined population.
> >
> > In your analyses, if ACR is the dependent variable, a more important
> > consideration is the distribution of the variation of the part of ACR
> > that remains after the contributions of the predictor variables have
> > been removed.  In other words, the residual variation (or the
> > so-called "error term").  You can investigate that also, by using the
> > residuals from the fitted regression model.
> >
> > If ACR is an explanatory variable (I avoid the term "independent
> > variable" because "independent variables" are seldom "independent" in
> > any reasonable sense), the underlying theoretical distribution is much
> > less important than the way ACR is distributed in your patients.
> >
> > David Hoaglin
> >
> > On Sun, May 27, 2012 at 9:23 AM,  <guhjy@kmu.edu.tw> wrote:
> >> 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).
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