Bioequivalence and Bioavailability Forum

Dear Yjlee,

❝ Because each subject just has one and the only one seq in a crossover study, so subj:seq is just the same as subj.

Ah good. That means you are using uniquely coded subjects. Full point from Belgium!

❝ However, it is interesting to find out that R treats the model of (lnAUC ~ seq + prd + trt + subj) and the other model of (lnAUC ~ seq + prd + trt + subj:seq) sightly differently through drop1() function to calculate type III SS that we've already had many discussion when we announce bear at this Forum.

Well, since you prefer uniquely encoded subject there is no reason to use the ":", so we need not to worry about this (but the secret lies in the model matrix, I think!)

❝ As far as I know, for a balanced 2x2x2 crossover study, the SAS-calculated type III SS should be the same as the type I SS. Both should be the same as those calculated by R's drop1(). You said they're different. Could you explain more? Thanks.

Actually this was exactly what I tried to explain in the previous post. You are in principle right when you say they should be. However, you can also argue that the output R provides is the correct one. Or that the SAS ouput is correct. Confused? Many of us are. Type III SS can be generally calculated by dropping the terms one by one. But dropping Seq makes no difference - there is no "added value" of Seq when Subject is already in the model. Therefore a round 0.0 (sort of) for the Seq SS from R's perspective, and you can say this is correct.
However, we must confess that Seq itself actually does add variation to our data. And therefore the Seq SS is not zero, and therefore SAS does more than just dropping terms one by one. It figures out that in order to make meaningful SS for Seq in this case it needs to play a little trick with the factor inclusions. And so it does (I can later come back to how this can be done in R, but trust me, my proposed solution will be syntactically ugly!), and therefore we have this odd situation where the SAS typeIII output can differ from R's drop1 output.

Finally as for type I SS vs type III SS: yes, they will be identical when the dataset is balanced for sequences.

EM.