Bioequivalence and Bioavailability Forum

Hi Ben,

❝ 2. I'm trying to get the degrees of freedom for the following design: one single group, fixed sequence, uncontrolled with respect to time effects (intra-subject design), say n subjects receive k days treatment A, then another k days they receive treatment A and B. More mathematically

❝ log(response) = overall mean + subject + trt effect + error.

❝

❝ Now, consider the following approach. We have 2n values, we lose n-1 df because of the subjects, 2-1 df because of treatment effects and the "usual" -1 because of the overall mean, hence the degrees of freedom is n-1.

❝ I'm wondering whether this is correct or not. Let's say we use the same approach for a 2x2 cross-over design, that is,

❝ log(response) = overall mean + sequence + subject + period + trt effect + error,

❝

❝ then we end up with (assume n₁ = n₂ = n/2) 2n - (n-1) - (2-1) - (2-1) - (2-1) - 1 = n-3.

❝ But we should have n-2 (don't we?) and hence the approach may not be correct at all...?

I think....
In the 2,2,2-BE example you know the sequence if you know the subject's period and treatment coding of the model matrix (or vice versa). Thus you need to add one df in the equation above to get n-2.
For your model, assuming you code A and A+B as two individual factor levels, you might say if there's a tick for A then there's no tick for A+B and vice versa, so loss of 2-1 df here. Then df=n-1 looks right to me.