## Logistic nigthmare [Design Issues]

Hi arl_stat,

I hope you don’t regularly start with the title of a study and then think about the design. I suggest to do it the other way ’round.

There are tons of posts in the forum discussing why the partial replicate (TRR|RTR|RRT) is a lousy design. One may fail to get a result if reference-scaling is not applicable (swR <0.294) with the FDA’s SAS-code for ABE (no convergence of the – over-specified – mixed-effects model). Please forget this design! Use one of the fully replicated designs instead (four periods: TRTR|RTRT, TRRT|RTTR, or TTRR|RRTT; three periods: TRT|RTR or TRR|RTT).

Combining replicates with multiple doses is very, very tricky. In a naïve way one can think about adding n saturation / switch-over administrations and get for the TRT|RTR this:

[n×T] TRT [n×R] RTR [n×R] RTR [n×T] TRT

But wait a minute! The comparisons require that we are in (pseudo) steady state. That would be valid only if the true T/R-ratio is exactly one. Otherwise only the estimates in the first period are correct (since we have n administrations of the respective treatment before) but estimates in the other periods will be biased. You have to guarantee that you are in steady state for each administration. Then you end up with this:

[n×T] T [n×R] R [n×T] T [n×R] R [n×T] T [n×R] R [n×R] R [n×T] T [n×R] R [n×T] T [n×R] R [n×T] T

Good luck with the duration of the study and dropouts…

In general the intra-subject variability in steady state is substantially lower than after a single dose. If your drug is not nasty (extremely high CV) it might well be that you don’t need reference-scaling at all. I suggest to perform a pilot study to get an idea how the CV behaves.

Dif-tor heh smusma 🖖
Helmut Schütz

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