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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   David Hoaglin <>
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   Mon, 28 May 2012 14:04:04 -0400

Dear Jinn-Yuh,

1.  ACR is clearly a ratio variable.  If you are using ACR as the
dependent variable in a regression, however, you are not dealing with
its distribution as a free-standing variable (see my earlier comment).

2.  The article on propagation of error and CV assumes a ratio of
independent random variables, each of which has a normal distribution.
 (For each of the links that you sent, I looked only at the abstract.)
 It is not clear how, if at all, to apply its results to ACR, which is
the ratio of quantities that are (as I understand it) not independent
and not normally distributed.

3. 1) The abstract of the article from the PREVEND study says that the
association is stronger for spot urine ACR than for spot urinary
albumin concentration or the reciprocal of spot urine creatinine.  I
read that statement as interpreting the three values of the hazard
ratio (1.41 vs. 1.26 and 1.16).  It would be stronger if the
difference were significant.  Each of those hazard ratios is per SD in
the log scale, which is a reasonable unit, but perhaps not the only

3. 2) As a statistician, I claim no expertise on the choice of
predictor variables for inclusion in your models.  Though widespread,
language such as "independent of" is not helpful in reporting results.
 Without reading the article, I suspect that the statement means that,
after adjusting for the contribution of 24-hour urinary albumin
excretion to ACR, body weight, 24-hour urinary creatinine excretion,
age, and gender made significant contributions.  If all of those
variables were predictors in a single multiple-regression model, the
results give the contribution of each after adjusting for the
contributions of all of the others.  If each was used in a separate
regression, with 24-hour urinary albumin excretion as the only other
predictor, then the adjustment is only for 24-hour urinary albumin
excretion.  Determining which variables should be included in a
regression on the data of your patients is part of your analysis.

4.  The abstract for "Ratio index variables or ANCOVA" contains too
little information for me to understand what the authors did.  As I
discussed in an earlier message, in advance of the model-building
phase of an analysis, the choice of statistical model is usually
unclear.  Clarifying the choice for a particular set of data requires
both statistical judgment and substantive (clinical) judgment.  Even
if a model were well established in the literature, some skeptical
model-building would often be appropriate.  Models sometimes become
established without adequate analysis.

David Hoaglin

On Mon, May 28, 2012 at 10:47 AM,  <> wrote:
> 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 (
> 3. In the PREVEND (Prevention of Renal and Vascular End-stage Disease)
> study (
> 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
> (, 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
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