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:
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?
