[BioC] Q1, efficiency of experimental designs

[magates at u.washington.edu]

Dear all, 
 
I have a series of transcription factor overexpression studies in fruitflies 
that use what is known as the UAS/Gal4 system . Essentially,I can consider 
this as a ?two factor? (called L and B below) experiment, each of which is 
either present or absent. 
 
I have 6 sets of biological replicates (includes equal numbers with dye 
reversals) of 5 of the 6 possible direct comparisons: 
1)LB -> WB 
2)WB -> WW 
3)WW -> LW 
4)LW -> LB	 
5)WW -> LB 
 
(30 arrays total) 
 
What I am most interested in those genes that are differentially regulated due 
to the ?interaction effect? - when both L and B are present, as well as 
estimates of  the ?main effects?. 
 
For future similar experiments, I would like to know the following: 
Given what I want to estimate (interaction effect), did I gain anything over a 
?loop? design by running the one ?diagonal? (LB vs WW) set of arrays? 
 
More generally, if  I had 60 arrays, which of the following experimental 
designs would be ?best?  in terms of most precision for estimating interaction 
effect? Or am I asking a wrong headed question? 
 
a) 10 repeats of  the ?saturated? design (all 6 possible direct comparisons) 
b) 15 repeats of the 4 array ?loop? design. (no diagonals directly compared) 
c) (12 repeats of my 5 direct comparisons.) 
 
In my naive understanding, it would seem that a) gives more ways of estimating 
the interaction effect per ?set of experiments", but has less (10 instead of 
15) sets of experiments. B) gives more replicate sets (15 vs 10), but within a 
"set", less ways to estimate the interaction.  Or quite possibly, my thinking 
is completely wrong. Any enlightening comments would be greatly appreciated. 
 
Thanks very much, 
Michael Gates