Plzeň, Czech Republic,
Posting: # 19642
Dear Helmut and others,
I have several theoretical thoughts about TIE inflation in BE studies under some circumstances.
First of all, I can't see the reason of TIE inflation for FDA 2x2 model with groups (as mentioned at the end of this presentation). In many of cases discussed here on BEBAC forum where TIE inflation presents, it is clear to me why. So it led me to various topics where the TIE inflation is more obvious (as two-stage design because of data evaluation twice or even TIE inflation for replicate designs with widening the acceptance limits - because of floating acceptance limits) - as described in different topics many times.
And this way of thinking bring me to the qustion "Can a pilot study be used as pivotal if 90% CI is in 80-125% (i.e. BE is concluded)?". The answer is regulatory dependend as I read here in several topics with many of reasons (ethical or maybe also obtained intra-subject CV can lead to the same number of subjects in pivotal study as was used in the pilot study, etc.). Though I thought that repetition of the study is not ethical or just increasing the sponsor's risk. I tend to the fact that a pilot study is a pilot study is a pilot study.
For simplicity consider following example: The plan would be to make a pilot study with 24 subjects.
If 90% CI will be in 80-125% - stop - BE concluded.
Else pivotal study will be performed to evaluate BE.
This scenario as the whole plan has an adventage of the increasing the power - as in pilot study we have chance to conclude BE (even for underpowered cases by chance). If BE will not be concluded in pilot study it is planned to have at least 80% or 90% power in the pivotal study.
I.e. in the whole plan we have more power than only in a pivotal study (some not known power for pilot study and desired power for pivotal study).
But TIE is a probability of BE conclusion in case of true GMR=0.8 (or 1.25) so we have 5% TIE for pilot (or maybe less as illustrated here but surely nonzero TIE) and 5% TIE for pivotal.
If the treatments are not bioequivalent (borderline case) and the pilot study is not underpowered (which can happen, nevertheless even for underpowered study the TIE would be still > 0%), we have 5% probability of demonstrating BE in pilot study. Then according to the whole plan stop - BE concluded.
Else pivotal study (e.g. with some more subjects added) will be performed with again 5% TIE. When we look at the plan as whole:
If I imagine simulations:
The pilot study is performed everytime (5% of all cases conclude BE after pilot study - STOP)
95% of cases continue to pivotal (5% from these 95% of cases conclude BE, i.e. 4.75% of all cases conclude BE after pivotal study, as 0.05*0.95=0.0475)
The aggregate TIE is 5+4.75 = 9.75%.
Note this is the maximum TIE, as it was shown in the mentioned topic, the real TIE can be between 5-9.75% (wenn ich mich nicht irre).
I don't know about any problems with regulatory acceptance of that and I found quite similar example with study repetition in this interesting PAR - 90% CIs from study 1 and study 2 do not even overlap but the second larger study concluded BE.
But I see nothing of that in the FDA model with groups which could result in TIE inflation. Maybe I simplified it in my imagination too much...
What I imagine is simulations of studies (similar as above, i.e. borderline case when the treatments are not bioequivalent) where for each simulated study we calculate ANOVA to know the significance of Group*Treatment interaction which splits the cases to 2 ways:
These my expectations are far away from the Helmut's simulations presented in the (mentioned presentation), only maybe the 4.5% for Model II when the groups can be pooled seems to be quite close to my thoughts.
Posting: # 19647
» Dear Helmut and others,
AFAIK: Helmut is downunder and will be back next year in February.
Thus be patient.
For me your estimation of the TIE seems reasonable, but Helmut's results are there and we (I) can't know if something goes wrong in his simulations. Thus we have to wait until Helmut comes by ...