Bioequivalence and Bioavailability Forum

Hi John,

❝ In a nutshell here is what I am trying to do. I have a set of data from a parital 3-way replicate study (1 Test, reference given twice). I want to find out what happens if I simulate this to a full replicate study. Therefore I need to

❝ 1) Generating a 2nd set of data for the test product

❝ 2) I also want to introduce some intrasubject CVs on the test data

❝

❝ Question 1 can be done with bootstrap on the existing data(Correct?). But how should I approach question 2 so that I can see BE/SABE scenarios with different intrasubject CV on the test?

I assume at this point you have estimates of intrasubj. sigma for Ref and you have an estimated T/R ratio and a between-subject variance estimate.
Usually, when we talk replicated studies it implies a mixed model with compound-symmetric covariance matrix (FDA) or something similarly evaluated through a linear model (EMA).

The model is Y = Treatment + Sequence + Period + (fixed interactions, who cares?) + Subj + error. It is the model that determines how you simulate.

The error is the intra-subject term with mean zero and some variance. The variance is depending on whether the observation comes from Test or Reference.
The Subj term is fixed as preferred by EMA or you can use random (mean zero and some variance) for FDA.
Thus when you simulate the i'th subject who is given the j'th treatment (pardon me if I use i and j in other meanings than Chow and Liu, I don't remember what their i and j and k's were but that's not essential here), then you add the fixed effects and a sampling intra-subject error for the i'th subject being given the j'th treatment and a between-subject sampling error for that subject (FDA). In the dataset you will have several observations for one subject (e.g. subj. X receving two times test and two times ref = 4 observations for subject X). The 'added value' for the Subj term must be the same (constant) across all these four or whatever observations sinced this is a between-variability, but the error term is...well... randomly sampled in all cases for that subject.

All in all, in addition to the fixed effects you may need two-three normal distributions for the sims:
One for the intra-subject error associated with Test.
One for the intra-subject error associated with Ref.
One for the between-subject error (FDA). Note: In many cases you can forget about this one as well as the fixed effects for Sequence and Period.

1)
A starting point is to use the same error for Test as you have ID'ed for Ref. Or you can add a bit or subtract a bit of variance for either depending on your level of optimism, how you have slept, position of Saturn's moons etc.
This isn't a bootstrap since you have no replication for Test which you can resample.

2)
Answered in the previous line I believe.