martin ★★ Austria, 20121105 17:31 Posting: # 9504 Views: 4,111 

Dear all! I have a question regarding a special case of a replicated cross over trials where the number of periods is fixed in advance. Three products (one test and 2 reference products) will be investigated in n “subjects” where each “subject” will be treated 6 times (=fixed number of periods). Using a kind of block randomization with block size = 3 will lead to the following sequences: Sequence 1: A, B, C ; A, B, C Sequence 2: A, C, B ; A, C, B Sequence 3: B, A, C ; B, A, C Sequence 4: B, C, A ; B, C, A Sequence 5: C, A, B ; C, A, B Sequence 6: C, B, A ; C, B, A Can the study design be improved when using different sequences than the six mentioned above when the number of periods is fixed in advance? Any ideas and suggestions are highly appreciated!! best regards martin 
martin ★★ Austria, 20121106 11:50 @ martin Posting: # 9508 Views: 3,722 

Dear all! Some more information: Using 3 treatements, a Williams design can be used leading to 6 sequences with 3 periods Sequence 1: A, B, C Sequence 2: A, C, B Sequence 3: B, A, C Sequence 4: B, C, A Sequence 5: C, A, B Sequence 6: C, B, A we are also planning to perform replicates and the question is: how should the order of replicates be specified? 1) Replicated Williams design: the order of treatments are identical for first and second part: Sequence 1: A, B, C ; A, B, C Sequence 2: A, C, B ; A, C, B Sequence 3: B, A, C ; B, A, C Sequence 4: B, C, A ; B, C, A Sequence 5: C, A, B ; C, A, B Sequence 6: C, B, A ; C, B, A 2) Replicated Williams design where the order of treatments in the second part is determined randomly, for example: Sequence 1: A, B, C ; B, C, A Sequence 2: A, C, B ; C, A, B Sequence 3: B, A, C ; A, B, C Sequence 4: B, C, A ; A, C, B Sequence 5: C, A, B ; B, A, C Sequence 6: C, B, A ; C, B, A I would be happy to receive some comments regarding the pros and cons for these two designs best regards Martin 
ElMaestro ★★★ Denmark, 20121106 12:09 @ martin Posting: # 9509 Views: 3,614 

Hi Martin, why would it be an aim to replicate administration of the test product? Save a period? I ask because I think most sponsors only wish to replicate due to scaling options, and then only replication of the ref. comes into play. Is your situation somehow demanding knowledge of intrasubject variability for all formulations? Anyways, from a theoretical standpoint I guess the higher order of carryover is interesting but in my experience agencies aren't too concerned. After all, there are many more obvious assumptions and shortcuts in play when we do BE; mandatory parametric statistics as one example, neglection of nuisance effects as a prominent other example. So in practice carryover is just something that is of practical concern to you when the girlfriend has spent 9 hours shopping and needs assistance to get 17 bags of clothes transferred to your car in the parking lot. If your test subjects have long tails and eat cheese then I wouldn't know how it would be assessed, though. — I could be wrong, but... Best regards, ElMaestro 
martin ★★ Austria, 20121106 12:29 @ ElMaestro Posting: # 9510 Views: 3,573 

Hi ElMaestro! Thank you for your quick reply with my attempt to answer the questions: I was told that this design is standard for this kind of studies (one test and 2 references) and I think that straightforward doubling the sequence was intuitive with the aim to decrease the number of subjects (no power calculations available) No idea regarding the intrasubject variability but this information may be important for planning upcoming studies Scaling would be definitely an option if it turns out that the CV>30% (it's a NONGXP study) hope this helps Martin 
ElMaestro ★★★ Denmark, 20121106 12:43 @ martin Posting: # 9511 Views: 3,576 

Hi Martin, ok, I'd then just aim for 5 periods. 1xTest, 2xRefA and 2xRefB, and not too advanced regarding the nature/number of sequences. — I could be wrong, but... Best regards, ElMaestro 
Helmut ★★★ Vienna, Austria, 20121106 14:07 @ martin Posting: # 9513 Views: 3,693 

Hi Martin! » I was told that this design is standard for this kind of studies (one test and 2 references) […] There’s a hint in EMA’s BE GL p.22 (“3 treatment, 3 period, 6 sequence design”). Williams’ designs are variancebalanced for (firstorder) carryover, which should be avoided by a suitable washout anyway. I have learned from Detlew that Latin Squares should do as well. — Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
Ben ★ 20121107 21:10 @ Helmut Posting: # 9521 Views: 3,733 

» I have learned from Detlew that Latin Squares should do as well. That sounds interesting to me Would fit to this post... Detlew mentioned that the advantage of first order carry over can only be an advantage if effect of carry over is part of the model. But due to the design isn't it the case that a Williams design will give more reliable results in any case  even without adjusting for carry over in the model? Ben 
d_labes ★★★ Berlin, Germany, 20121108 08:29 @ Ben Posting: # 9524 Views: 3,669 

Dear Ben! » ... But due to the design isn't it the case that a Williams design will give more reliable results in any case  even without adjusting for carry over in the model? Why should it? Same number of subjects, same number of degrees of freedom, same design constant. At least if we talk about the usual evaluation. So what mysterious feature should let to more reliable results? In case we talk about the 'robust' evaluation (aka Senn's basic estimator) we have to analyse the TR contrasts (in the log domain) via an ANOVA with sequence as effect in the model. The degrees of freedom to use are then Nnseq, where N=number of subjects, nseq=number of sequences. That gives us: Latin square Williams A slight advantage of the Latin square in case of a 3treatment3period study. Else also identical design features. — Regards, Detlew 
Ben ★ 20121109 18:20 @ d_labes Posting: # 9530 Views: 3,547 

Dear Detlew, » So what mysterious feature should let to more reliable results? The idea was because of the fact that the number of subjects who receive formulation i in some period followed by formulation j in the next period is the same for all i # j. You don't have this in a Latin square. Note that I was not talking about 'more precise' results. Otherwise I fully agree with what you have stated! Thanks, Ben 
d_labes ★★★ Berlin, Germany, 20121111 14:14 @ Ben Posting: # 9531 Views: 3,511 

Dear Ben, » Note that I was not talking about 'more precise' results. I did! Originally you talked about " ... more reliable results ... ". So give me an impression what this could be and how to quantify this? — Regards, Detlew 
Ben ★ 20121118 13:20 @ d_labes Posting: # 9544 Views: 3,398 

Dear Detlew, » So give me an impression what this could be and how to quantify this? Good question, next queston! Intuitively, since each treatment precedes each other treatment the same number of times as it follows each other treatment any carryover from say, for example treatment A should be averaged over all other treatments. Even though we are not able to estimate the carryover effects (since not included in the model), we should have balanced out potential carryover effects. That was my initial thoughts, unfortunately I am struggling to quantify that. [Moreover, maybe one can add an additional argument, namely the fact that all pairwise treatment comparisons have the same variance: In a Latin square one treatment comparison can be much worse (by chance due to higher variability) than the other one, you simply don't know. This cannot happen in a Williams design, results are more reliable in the sense that you know a priori all comparisons will behave equally.] Best, Ben 
Helmut ★★★ Vienna, Austria, 20121118 14:48 @ Ben Posting: # 9545 Views: 3,330 

Dear Ben! » […] results are more reliable in the sense that you know a priori all comparisons will behave equally. — Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
Ben ★ 20121118 15:28 @ Helmut Posting: # 9547 Views: 3,281 

Well, cough The only thing I wanted to refer to is the same variance... 