Confidence Interval for the ratio of means

[CraigWW]

I often need to get the CI for the ratio of means for bioequivalence testing. I know using a log transformation on the data and then converting back the associated CIs accomplishes this. The problem I have is the data contains negative values (% change in lesion counts). I have tried adding a constant, but the resulting CIs change depending on the constant I use. I am using the following code to convert the CI of the difference of the treatment means into a CI for the ratio of means:

*getconfidence interval for difference of treatment means;

odslisting close;

odsoutput lsmeandiffcl=cla(rename=(dependent=_name_));

procglm data=pp(where=(extrt ne 'Vehicle'));

      class extrt siteid;

      model pchinf=extrt siteid;

      lsmeans extrt/out=lsm alpha=0.10stderr pdiff cl; *get lsmeans for treatment;

run;

quit;

odslisting;

dataequci&outvar;

merge cla lsm(where=(extrt='Reference'));*usereference lsmean for denominator;

      by _name_;

      length ciles $30;

      *reverse sign because above CI calculatedon reference-test difference instead of test-reference difference;

      ciles='('||cats(put((-uppercl/lsmean)+1,5.3))||','||cats(put((-lowercl/lsmean)+1,5.3))||')^{super1}';

run;

I believe the method is sound, but I am unable to find any kind of documentation to back it up.

Any comments?

Craig

[SteveDenham]

Does your SAP restrict your response to % change in counts?  If not, I would strongly consider looking at counts as the dependent variable, and modeling an appropriate distribution (poisson, negative binomial, and possibly zero inflated versions of these).

At the FDA/Industry Statistics Workshop held recently in Washington, DC, Dr. Stephen Senn led a short course on statistical issues in drug development.  One slide really struck home (and is applicable here):

Seven Deadly Sins in Measuring Clinical Trial Outcomes

• Using baslines to construct change-scores
• Percentage change from baseline
• Crude corrections in general
• Correcting for post-randomsation covariates
• Ignoring titration
• Treating ordinal data as categorical
• Creating dichotomis from continuous data

It seems to me that this hits the first two. Ratios generally do not have good distributional properties. He suggested analysis of covariance with log(y) as the dependent variable and log(x), i.e., the log of the baseline value as a covariate.

This should get around the negative percentages, but you may be locked in by your SAP.

Good luck,

Steve Denham