Datacollector ☆ United Kingdom, 20190727 10:09 Posting: # 20448 Views: 1,141 

I was involved with a regular 2 way crossover with a non endogenous compound which is not very exotic. The good news was that the study comfortably met the usual bioequivalence criteria. The less good news was that there were significant period and sequence effects for both AUC and Cmax. We are assured we can ignore the sequence effect as the usual conditions for so doing apply. Looking at the period data (treating as two parallel studies) we find the T/R point estimator lies considerably below the acceptance range, while for period 2, it is rather higher than the BE acceptance range. This has given rise to some concern. Does the observation of the difference between periods negate the finding of equivalence? I should be grateful for any advice or suggestions. I don't have any obvious reason to suspect the design or conduct of the study. Edit: Please follow the Forum’s Policy. [Helmut] 
Helmut ★★★ Vienna, Austria, 20190727 11:15 @ Datacollector Posting: # 20449 Views: 1,077 

Hi Datacollector, » […] a regular 2 way crossover […] comfortably met the usual bioequivalence criteria. Congratulations. » The less good news was that there were significant period and sequence effects for both AUC and Cmax. AUC and C_{max} are highly correlated. If you see significant effects for one likely you see them for the other as well. » We are assured we can ignore the sequence effect as the usual conditions for so doing apply. Correct. A statistically significant sequence effect (better unequal carryover because equal carryover doesn’t matter) can be caused by
A test for carryover is not considered relevant and no decisions regarding the analysis (e.g. analysis of the first period only) should be made on the basis of such a test. The potential for carryover can be directly addressed by examination of the pretreatment plasma concentrations in period 2 (and beyond if applicable). » Looking at the period data (treating as two parallel studies) … Given the above, why did you do that at all? The sequence effect is not relevant. Even more, the period effect is adjusted for in the crossover model anyway (it means out). » … we find the T/R point estimator lies considerably below the acceptance range, while for period 2, it is rather higher than the BE acceptance range. Are you looking for an explanation? Since the two periods are now evaluated as parallel designs there are tons of reasons. If a study would have been planned (!) as a parallel design, the usual conditions should have been observed: It is of utmost importance to keep groups as similar as possible (sex, body weight, agedependent clearance, …). If the drug is subjected to polymorphic metabolism, pheno (or even better geno) typing should be done. This was not the case – and with good reasons. Since in a crossover subjects act as their own reference, we don’t have to care about all that. It is quite possible that – by pure chance – groups were not similar: You think that your are comparing treatments but actually you are comparing treatments + unknown (!) group differences. Confounded effects again. Meaningless. » … This has given rise to some concern. By whom and why? » Does the observation of the difference between periods negate the finding of equivalence? Nope.
— Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
Datacollector ☆ United Kingdom, 20190727 11:34 @ Helmut Posting: # 20450 Views: 1,043 

Hi Helmut, Thanks for your kind and considered response. To answer your question on the origin of the concerns I was not at first unduly concerned the study was submitted. However, a well regarded EU regulatory agency has raised objections on public health grounds. Treatment by period interaction has been mentioned. I can't see how that could arise given that the design of the study is fine and assuming there was no major issue in the conduct of the study. I can only infer that the agency suspects that the study has not been executed correctly but is not prepared to say so in black and white. Have you encountered this kind of response? Thanks & Regards 
Helmut ★★★ Vienna, Austria, 20190727 11:48 @ Datacollector Posting: # 20451 Views: 1,045 

Hi Datacollector, » […] a well regarded EU regulatory agency has raised objections on public health grounds. Treatment by period interaction has been mentioned. I can't see how that could arise given that the design of the study is fine and assuming there was no major issue in the conduct of the study. I can only infer that the agency suspects that the study has not been executed correctly … OK, then the agency should trigger an inspection^{1} rather than just ‘suspect’ sumfink. Again: Statistics^{2} cannot help. BTW, it is yet another – all too common – misconception that the pvalue gives the probability that the Nullhypothesis is true. » … but is not prepared to say so in black and white. Well, they are happy to speculate in black and white. As I wrote before, only a failure in randomization can be assessed in an inspection. Everything else: No way. » Have you encountered this kind of response? Yes. By the German BfArM three days (‼) ago. Potential serious risk to public health not already raised by the RMS as major objection.
— Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
ElMaestro ★★★ Belgium?, 20190727 11:50 @ Datacollector Posting: # 20452 Views: 1,050 

Hi DC, can you show me a plot or table of: ln(T) in period 1 ln(T) in period 2 ln(R) in period 1 ln(R) in period 2 you can use LSMeans. Many thanks. — I could be wrong, but... Best regards, ElMaestro 
Helmut ★★★ Vienna, Austria, 20190727 14:55 @ ElMaestro Posting: # 20453 Views: 1,007 

Hi Elmaestro, like DC’s the study I have on my desk passed with flying colors. Balanced sequences, equal number of subjects in both periods. pvalues for AUC: 0.576 (treatment), 7.17·10^{–8} (subjects), 2.42·10^{–8} (sequence), 0.0321 (period). Geometric means ±SD. R in blue and T in red:
— Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
ElMaestro ★★★ Belgium?, 20190727 15:38 @ Helmut Posting: # 20454 Views: 991 

Hi Hötzi, this is either an element of chance or something else. Clearly. — I could be wrong, but... Best regards, ElMaestro 
Datacollector ☆ United Kingdom, 20190727 17:13 @ ElMaestro Posting: # 20455 Views: 981 

Hello Helmut & Elmaestro, Mine is Bfarm also Not sure if this is still wanted, but just in case (AUC data only)...
Period 1 lnauc Thanks & Regards 
Helmut ★★★ Vienna, Austria, 20190727 21:53 @ Datacollector Posting: # 20456 Views: 971 

Hi Datacollector, looks familiar. Since we are in the same boat and out of curiosity: pvalues of the sequence effect were given by the CRO and also by the BfArM with 0.0077 (AUC) and 0.0252 (C_{max}). Recalculated in Phoenix WinNonlin 8.1 and R 3.6.1 (function lm() of stats ):
Extending what I wrote at the end of this post (not for you – as an obvious initiate – but the archive). Let’s assume that the two groups randomized to sequences TR and RT differ (by chance) in their body weights. Might happen cause we don’t stratify in a crossover for anything. Both T and R have a relative BA of 1. Hence, T/R should be 100%. I assumed that the response with a body weight of 70 would be exactly 1. Due to different volumes of distribution the response will be higher in the group with low BW and vice versa. Two cases (the responses are the means of groups):
One might be tempted to be prepared for the worst (i.e., bizarre deficiency letters) and aim at a stratified randomization keeping body weights as close as possible. But where will it end? Having a single slow metabolizer in one group and none in the other could already be the killer. Doesn’t make any sense. — Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
mittyri ★★ Russia, 20190728 13:19 @ Helmut Posting: # 20457 Views: 895 

Hi Helmut, » Since we are in the same boat and out of curiosity: pvalues of the sequence effect were given by the CRO and also by the BfArM with 0.0077 (AUC) and 0.0252 (C_{max}). » Recalculated in Phoenix WinNonlin 8.1 and R 3.6.1 (function lm() of stats ):»
which one sequence effect are you referring to? — Kind regards, Mittyri 
Helmut ★★★ Vienna, Austria, 20190728 13:59 @ mittyri Posting: # 20458 Views: 885 

Hi Mittyri, » which one sequence effect are you referring to? Are you trying to confuse me? The crappy nested model (sorry, my Capt’n), all effects fixed. AUC only. PHX/WNL Hypothesis Numer_DF Denom_DF SS MS F_stat P_value R Df Sum Sq Mean Sq F value Pr(>F) — Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
mittyri ★★ Russia, 20190728 14:20 @ Helmut Posting: # 20459 Views: 888 

Hi Helmut, Sorry for confusion I meant to divide the MS of the sequence effect by the MS of subject(sequence), not by the MS of the residual error (same manner you did in famous Rscript published). F is about 7.9, sorry R is not available at the moment to check p value — Kind regards, Mittyri 
Helmut ★★★ Vienna, Austria, 20190728 14:36 @ mittyri Posting: # 20460 Views: 878 

Hi Mittyri, » I meant to divide the MS of the sequence effect by the MS of subject(sequence), not by the MS of the residual error Oops, how stupid! Analysis of Variance Table ✖period 1 0.296 0.2959 4.953 0.0321 * ✔Residuals 38 14.0770 0.37045 ✖period 1 0.372 0.3718 4.737 0.0358 * ✔Residuals 38 12.7310 0.33501 THX! I stand corrected. — Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 