## Some answers [Regulatives / Guidelines]

Hi ElMaestro,

❝ M: "Is it possible to prove that with sims?" - what is it you want to prove? Can you formulate it plain and simple? Sims are totally possible, I just need to figure out the equations, as well as have a purpose.

The idea behind the Group-by-Treatment interaction is that the T/R in one group is different from the other (i.e., we have collinearity with a “hidden” variable). Therefore, simulate a group of subjects with T/R 0.95 and another one with T/R 0.95–1 (CV ad libitum). Merge them to get a “study”. Run model 1 and check the p-value of the Group-by-Treatment interaction. With the simple model you should expect T/R 1.

❝ H: "It should be noted that in rare cases (e.g., extremely unbalanced sequences) the fixed effects model gives no solution and the mixed effects model has to be used." - a realistic linear model will have a single analytical solution unless you make a specification error. Imbalance would not affect that, please describe where/how you came a cross a fit which failed with the lm.

I had one data set where the fixed effects model in Phoenix/WinNonlin showed me the finger. Same in JMP (“poor man’s SAS”). Have to check again.

❝ M+H: FDA are also fitting subject as fixed even when using the random statement in PROC GLM. Some of them just have not realised it

True.

❝ H: "(...) seemingly ~10% of studies show a significant group-by-treatment interaction. " - this is expected by chance. You apply a 10% significance level. By chance 10% will then be significant.

Exactly. That’s the idea of assessing real studies. If there would be a true Group-by-Treatment interaction (i.e., not random alone) we could expect significant results in >10% of studies. This is what I have so far (I hope that the Canadians will come up with another ~100).

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  0.0012  0.2693  0.5573  0.5206  0.7725  0.9925

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 0.00376 0.28731 0.47584 0.49187 0.71717 0.98837

86 studies (60 analytes), 85 data sets for AUC and 86 for Cmax, sample sizes 15 to 74, two to four groups, median interval between groups three days. Significant Group-by-Treatment interaction in 8.24% (AUC) and 12.79% (Cmax) of data sets. Hence, I guess it is a bloody myth.

❝ (and by the way: Which denominator in F did you apply; within or between?)

Numerator DF = Groups – 1
Denominator DF = Subjects – 2 × Groups

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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