## Confidence interval for ratio of means, parallel design

Occasional Contributor
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# Confidence interval for ratio of means, parallel design

I am looking for a way to use Proc GLM to calculate the confidence interval for the ratio of means with treatment and center as factors for testing bioequivalence. I found the following reference:

http://www.lexjansen.com/pharmasug/2008/sp/sp04.pdf

but this calls for a crossover design. For the type of products we test here, we run a parallel design with clinical endpoints.

Any suggestions?
Posts: 2,655

## Re: Confidence interval for ratio of means, parallel design

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.

Steve Denham
Occasional Contributor
Posts: 8

## Re: Confidence interval for ratio of means, parallel design

The response variable is % change from baseline and can be negative and positive. Of course we can't take the log of a negative number.
Posts: 2,655

## Re: Confidence interval for ratio of means, parallel design

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.

Would that approach be workable?

Steve Denham
Occasional Contributor
Posts: 8

## Re: Confidence interval for ratio of means, parallel design

Good suggestions, thanks!
Occasional Contributor
Posts: 8

## Re: Confidence interval for ratio of means, parallel design

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.
Posts: 2,655

## Re: Confidence interval for ratio of means, parallel design

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.

Good luck,

Steve Denham
Posts: 2,655