martin
★★

Austria,
2012-11-05 18:31
(3863 d 06:43 ago)

Posting: # 9504
Views: 5,001

## Replicated cross over with fixed number of periods [Design Issues]

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,
2012-11-06 12:50
(3862 d 12:24 ago)

@ martin
Posting: # 9508
Views: 4,513

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,
2012-11-06 13:09
(3862 d 12:05 ago)

@ martin
Posting: # 9509
Views: 4,358

## Quick Q for my clarification

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 intra-subject variability for all formulations?

Anyways, from a theoretical standpoint I guess the higher order of carry-over 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 carry-over 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.

Pass or fail!
ElMaestro
martin
★★

Austria,
2012-11-06 13:29
(3862 d 11:45 ago)

@ ElMaestro
Posting: # 9510
Views: 4,325

## Quick Q for my clarification

Hi ElMaestro!

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 intra-subject 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 NON-GXP study)

hope this helps

Martin
ElMaestro
★★★

Denmark,
2012-11-06 13:43
(3862 d 11:31 ago)

@ martin
Posting: # 9511
Views: 4,322

## 5 periods

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.

Pass or fail!
ElMaestro
Helmut
★★★

Vienna, Austria,
2012-11-06 15:07
(3862 d 10:06 ago)

@ martin
Posting: # 9513
Views: 4,450

## Latin Squares ↔ Williams’ designs

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 variance-balanced for (first-order) carry-over, which should be avoided by a suitable washout anyway. I have learned from Detlew that Latin Squares should do as well.

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

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

2012-11-07 22:10
(3861 d 03:04 ago)

@ Helmut
Posting: # 9521
Views: 4,536

## Latin Squares ↔ Williams’ designs

❝ 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,
2012-11-08 09:29
(3860 d 15:45 ago)

@ Ben
Posting: # 9524
Views: 4,424

## Williams’ designs more reliable?

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 T-R contrasts (in the log domain) via an ANOVA with sequence as effect in the model. The degrees of freedom to use are then N-nseq, where N=number of subjects, nseq=number of sequences.
That gives us:
          Latin square  Williams 3-period    N-3           N-6 4-period    N-4           N-4
A slight advantage of the Latin square in case of a 3-treatment-3-period study. Else also identical design features.

Regards,

Detlew
Ben
★

2012-11-09 19:20
(3859 d 05:54 ago)

@ d_labes
Posting: # 9530
Views: 4,307

## Williams’ designs more reliable?

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,
2012-11-11 15:14
(3857 d 10:00 ago)

@ Ben
Posting: # 9531
Views: 4,271

## Williams’ designs more reliable?

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
★

2012-11-18 14:20
(3850 d 10:53 ago)

@ d_labes
Posting: # 9544
Views: 4,259

## Williams’ designs more reliable?

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 carry-over from say, for example treatment A should be averaged over all other treatments. Even though we are not able to estimate the carry-over effects (since not included in the model), we should have balanced out potential carry-over 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,
2012-11-18 15:48
(3850 d 09:26 ago)

@ Ben
Posting: # 9545
Views: 4,113

## Frequentists vs. Bayesians

Dear Ben!

❝ […] results are more reliable in the sense that you know a priori all comparisons will behave equally.

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

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

2012-11-18 16:28
(3850 d 08:46 ago)

@ Helmut
Posting: # 9547
Views: 4,024

## Frequentists vs. Bayesians

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