What about taking the log of the response variable? The difference between the treatment means is the log of the ratio, and confidence bounds around the ratio can be calculated from the confidence interval on the difference by exponentiating the results.
OK. Percent change from baseline is the same as an analysis of covariance, with the regression coefficient for the pretreatment value fixed at negative one (that's pretty loose, but it's a fair analogy). How about a log transform of all values before calculating the change from baseline? Then you are looking at the ratio change from baseline. Or, you could use the log of the pretreatment value as a covariate, and look at the difference in group least squares means, giving the ratio after adjusting all subjects to an equivalent pretreatment value.
Now what to do when the response is equal to 0? I considered adding a constant to the response variable, but then the results are dependent on the constant I choose. The baseline response is always > 0, but the post-baseline response can be equal to 0.
Zeros. My first reaction is to start swearing, but since that doesn't solve the problem, I went googling for nonparametric methods. The EU recommends a nonparametric approach in many cases. There were also some bootstrapping methods returned in the search. I have to admit that I am out of my comfort realm with these; I just know that they have been used.
I just looked up the EMEA guidance, and it now specifies that non-parametric analyses should NOT be used, so my previous posting should be crumpled and tossed in the nearest waste receptacle. It seems I was ten years out of date, and I apologize.
That leaves bootstrapping and Bayesian methods, so far as I can determine.