When you take the log of the ratio, keep in mind what what that is: $log({a \over b}) = log(a) - log(b)$
Does using this value as a dependent variable make sense in your problem?
Now, as to using the raw ratio - this can be problematic. Kronmal 1993 makes the argument that a regression with a ratio as the dependent variable:
$ {Y \over Z} = \alpha_0 + \alpha_XX + \epsilon$
which can be described as
$ Y = Z1_n\alpha_0 + ZX\alpha_X + Z^{-1}\epsilon $
is a submodel of
$ Y = \beta_0 + \beta_XX + Z1_n\alpha_0 + ZX\alpha_X + Z^{-1}\epsilon $
aka...
- Regress numerator by original independent variables, denominator, and denominator times the original variables
- Weight regression by (inverse) denominator
Only in the case where $\beta_0$ and $\beta_X$ were zero would the original regression model be valid.
Caveat - I'm not convinced I have a complete understanding of ratios eithereither.
