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]

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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