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st: ratios


From   David Airey <david.airey@vanderbilt.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: ratios
Date   Mon, 24 Nov 2003 13:45:24 -0600

This is a somewhat independent follow-up to my recent post on ratio calculation.

In the biological sciences, ratios are often used, but some deprecate their use. I have been told the ratio sometimes remains correlated with the denominator, and so the use of ratios to control for or normalize to the denominator may not do the trick. The distribution of the ratio or percent is also sometimes difficult to deal with, and may benefit transformation. Finally, since there are two hidden components to a ratio, one doesn't always know whether an increase in a ratio is due to an increase in the numerator or a decrease in the denominator. This would seem particularly vexing in more complex experimental settings with interactions.

I recently read a note from Cornell on spurious results from using ratios, especially when more than one ratio is used:

<http://www.human.cornell.edu/admin/statcons/statnews/stnews03.htm>

Now, care of Alex Tsai, I have read:

Goldman DP, Smith JP. Methodological biases in estimating the burden of
out-of-pocket expenses. Health Serv Res. 2001 Feb;35(6):1357-64;
discussion 1365-70. Comment on: Health Serv Res. 1999 Apr;34(1 Pt
2):241-54.

which is a surprisingly recent dispute on the merits and pitfalls of ratios in statistics between experts, with quite serious implications for policy change.

So, the question I have, is it not possible to ask all the same questions using the numerator and denominator separately in a model that are asked by using the ratio? If all questions cannot be answered via analysis of the components of the ratio, in case where they can, is this not preferred?

-Dave

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