Bioequivalence and Bioavailability Forum

Dear Yung-jin, dear ElMaestro,

sorry but I was a little short in time last week to share the discussion, which I have kicked off naively.

Without delving into the details of your arguments/discussion contributions:
The key is that we are fitting a linear model to our data, because we are interested in estimating the difference between our treatments/formulations in respect to some target parameters (AUC, Cmax or whatever, log-transformed or not).

And this from our fitted model, with all the eventually existing cofactors included to account for their influence.

As ElMaestro has pointed out, this can be done via the coefficients of the model (including a 90% confidence interval for the equivalence test) associated to the treatment.

But this is only true if your have only two treatments/formulations of interest, because lm() or lme() estimate the first of the coefficients to zero.
If your order of treatments is so that reference comes first, then T-R is the value of the coefficient associated with test.

If you consider a broader class of cross-over designs with more treatments/formulations, f.i. 3x3 (three treatment, 3 period) or 4x4 cross-over, you have to deal with the estimation of more then one contrast, which you cannot obtain from the confidence intervals of the coefficients itself.
You have to estimate the difference between the coefficients of interest, with their variation and associated 90% confidence intervals.

If you deal with that via LSMeans or not, is a matter of taste I think.
If I understand the SAS ESTIMATE statement and the R counterpart described on the WEB site I pointed to above .
All stuff in respect of LSMeans (coefficients to average over all other effects present in the model) vanishes, if you go to the LSMeans differences. The only task left is to estimate differences in the treatment associated model coefficients.

Then the only task is to identify which piece of R will do the task for you. Or you must/can do it by yourself using the coefficients and the residual variance and associated df of the fitted model.

BTW: @ElMaestro:
Seems part of the R community is seeing SAS as "The dark side of the power (to know)".
Seems every one needs some M$ (in german "Klein weich") to claim one self can do better.
(this is not meant in respect to you personally, but a BTW to your answer to me above concerning Rusers and Rdevelopers)