## Will take much more hours still… [R for BE/BA]

Hi ElMaestro,

» I think expressing the G matrix after this fit is a little backward;…

OK, true.

» That SAS and WinNonlin and more do not have a way to make provisions for a solution outside those involving this decomposition, it merely a testament to their development capabilities than to the design itself. If you start defining the the stats model on basis of G and R rather than V then obviously you must create two variance components which are not uniquely estimable, but whose sum is. Therefore, just screw R and G, go directly for V, and present the components without in any way calling them members of G or R - they really aren't when the model is constructed my way.

Yep.

» The 2-trt, 3-seq, 3-per design is good, healthy and appropriate, until now it was just the statistical work on it that has been lagging. The post is an attempt at providing a solution.

I still see no reason to perform a study in one of the partial replicates. Sorry.
What is given as ‘justifications’:
• “We want to limit the blood volume and decrease the chance of dropouts. Hence, we prefer 3 over 4 periods.”
Understandable. However, 3-period full replicates (TRT|RTR or TRR|RTT) require similar sample sizes than the partial replicates (TRR|RTR|RRT or TRR|RTR) but provide additional information about CVwT. If this is a pilot study one gets an incentive for the sample size of the pivotal if CVwT < CVwR (which is often the case). In a partial replicates one has to assume CVwT = CVwR.
Furthermore, one may consider ABEL for AUC (WHO’s rules) where the vari­ability associated with each product has to be compared.
• “This design is recommended by the FDA and the EMA.”
False. The fact that the FDA gives only SAS-code for the partial replicate does not imply that it is the only acceptable one. There are a lot of different designs in the public domain which were accepted by the FDA. The FDA stated already in 2001: “… the two-sequence, three-period design TRR|RTT is thought to be optimal among three-period replicated crossover designs.”
In the EMA’s Q&A the partial replicate is given only as an example. Rev.12 (June 2015) made clear that TRT|RTR is acceptable as well. The only condition is that at least 12 eligible subjects are in sequence RTR. That’s not relevant in practice unless one faced dropout rates of >40% (see there).
• If one has problems with the evaluation and/or want to perform simulations, heterogenicity is a pain in the back. Much easier in full replicates. That’s the reason why the two Lászlós in their early papers simulated TRT|RTR.
Nobody published reference datasets for the mixed-model so far.
Hence, everybody has to believe in the software. As a starter I would expect the same level of error handling, documentation,  like the package replicateBE. Otherwise, assessors would be skeptical.

» The PE will be accessible via the est.b vector. You shuld be able to extract it (difference between first two effects, one good reason to do X without intercept) after the model has converged.

In Section 2:
  Final <- function(Pars) {     CovM <- Create.CovM(Pars)     tmp  <- solve(t(X) %*% solve(CovM) %*% X) %*% t(X) %*% solve(CovM) %*% y     PE   <- exp(as.numeric(tmp["TrtT", ] - tmp["TrtR", ]))     return(PE)   }
At the end:
  PE <- Final(res\$Estimate)   cat("PE:", PE, "\n")
Gives:
  PE: 1.372138
In PHX 1.372138 (Patterson/Jones got in SAS 1.37). Great!
TODO: Get the Satterthwaite’s DFs for the CI.

» If you have a dataset that does not readily converge with SAS then I'd be eager to learn if it does in some flavour of my code.

See this post with links to John’s datasets. Maybe there are others.

Dif-tor heh smusma 🖖
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes