The power of a loop design is always better than the power of a 
reference design with the same number of arrays.  The minimum power 
will always decrease as the loop expands, and there are probably 
better designs with 10 or more treatments.

"Interwoven" loop designs are always better than duplicating a loop 
design if you can double the sample size.

I have a paper under revision for Genetical Research that discusses 
these issues.  A preprint can be found at:
<http://www.stat.psu.edu/%7Ewzhao/bcc/respapers/AltmanInterface04.doc>Extending 
the Loop Design for Microarray Experiments. Naomi Altman (Paper)

Another paper on the subject is:

Wit, E, Agostino, N. and Khanin, R. 2005,  Near-optimal designs for 
dual-channel microarray studies Applied Statistics, 54, 817 - 830.

Neither paper gives the power computations, however.

I have a student working on an R routine for power for loop 
designs.  However, he has only done completely balanced incomplete 
block designs, which are designs in which every pair of treatments 
are together on an array, so it applies only to loops of size 3 and 
(double) interwoven loops of size 5.  We will make this available as 
soon as his thesis is approved (by Dec.)  Hopefully, the next 
interested student can take this work and extend it to loop designs. 
THere are no technical difficulties, just time ...

--Naomi

At 09:39 AM 10/21/2006, Nadia Messerschmidt wrote:
>Hi,
>
>I'm am currently a postgraduate bioinformatics student at the University
>of Pretoria, South Africa.
>
>My background is from computer science, and I'm trying to create
>software that would enable biologists to get a better feel for what the
>statistics behind the experiments are. And how different experimental
>designs (loop or reference) would influence the statistics.
>
>I thought I would start with time course experiments since they are used
>quite a lot at our lab. I will need a generic approach that enables all
>time point comparisons and the profiles of genes across all time points.
>
>If you for instance do a small pilot study (would the design matter
>here?) and find that the population coefficient of variability is 30 %
>for argument's sake, you can enter that value into the power.t.test and
>get a feel for the different possibilities (changing sig level, power ect).
>
>But now, for the large-scale study, the question is, would a loop or a
>reference design be better? Would it be possible to adapt the
>power.t.test parameters somehow so that is would reflect the different
>designs, or would you have to do two pilots studies, one loop and one
>reference, get the var of each and put those into the power.t.test? Or
>is there some way that you can take the variance from the pilot study,
>say using a loop design, and adjust that to reflect a ref design?
>
>Is what I'm trying to achieve feasible at all? Because I read another
>paper saying that the effectiveness of the loop design becomes less if
>you have more than 10 time points - something that surely can't be
>accounted for in the power.t.test params?
>
>Any help would be greatly appreciated.
>
>Regards,
>Nadia Messerschmidt
>
>ACGT Bioinformatics and Computational Biology Unit
>University of Pretoria
>South Africa
>
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Naomi S. Altman                                814-865-3791 (voice)
Associate Professor
Dept. of Statistics                              814-863-7114 (fax)
Penn State University                         814-865-1348 (Statistics)
University Park, PA 16802-2111

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