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

[Phil Clayton <philclayton@internode.on.net>]

On 27/05/2012, at 9:35 PM, David Hoaglin wrote:

>  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

What we're interested in, biologically, is the 24-h urinary albumin excretion.

The reason the albumin is divided by creatinine is that the ACR is used to estimate the 24-h urinary albumin excretion from a single urine specimen rather than asking someone to collect their urine for a day. The urinary concentration can vary several fold (eg if you're dehydrated it goes up) which changes the albumin concentration in that specimen - but it changes the creatinine concentration by a similar amount, and we know the normal 24-h excretion of creatinine, so we divide the albumin by the creatinine to estimate the 24-h albumin excretion.

So biologically ACR should be a ratio and must be nonnegative. You could include it in a regression model as a surrogate for the 24-h urine albumin excretion, but would need to careful how to model it as it generally has a nonlinear effect. For example it is commonly modelled as a categorical variable - normal, microalbuminuria, macroalbuminuria.

Phil
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