We conducted a bioequivalence study with 2 different formulations in 4-period design as follows:
First two periods (1 and 2) tested test (A) against reference ( B formulation in fasting state, last two periods (3 and 4) tested the same test (labelled as C) against the same reference (labelled as D) in fed state.
I wanted to check the food effect on the test formualtion and to perform ANOVA on A vs. C. I excluded Treatment B and Treatment D so in the analysis there were two treatments (A and C), 4 periods (in pairs foe each subjects 1 and 3 or 2 and 4 as in accordance with the respective sequence) and 2 sequences (ABCD and BADC).
ANOVA model used: Sequence+Treatment+Period+Subject(Sequence)
I didnt get any results in Average Bioequivalence (no LSMs, no anything …). Why is this so?
On the other hand, if I exclude “Period” from the model, I get all results but is this model and results even correct? Or what would be the correct model in this case?
Edit: Additionally, if I put “Treatment+Sequence+Period(Treatment)+Subject(Sequence)” in the model, I also get some results (PEs are the same as in the model above without “Period”, but CI are different). This is probably not a correct model but I was just trying to test different models in order to understand everything
the set of factors presented should be able to distinguish each row of your dataset in only one way.
You removed B and D, so in fact you have only one sequence of formulations - AC
So the factors Period and Formulation become collinear, i.e. from known period (say 1) you can foresee what formulation is (for period 1 it is always A). That’s why H matrix is invertible and you cannot get any results.
Now you removed period factor, so there’s no collinearity anymore. But in fact sequence is an intersubject factor and could be thrown away, the results do not depend on that.
so your model represents the difference between the formulations without any intrasubject variability factors (i.e. period) - this is equivalent of
t.test(x = log(), y = log(), paired = TRUE, var.equal = TRUE, conf.level = 0.9)
which I’d suggest to use
when you have added an interaction between treatment and period, the model matrix is invertible, but with deep analysis you can see that it is not fully identifiable (for further analysis you may want to run some collinearity analysis tools in R)
