[BioC] 2x2 factorial loop without common reference (pool)

[Naomi Altman]

I would use single channel analysis for 
this.  The only problem is that Limma allows only 
1 level of random effects.  Hence, you will need to average the dye-swaps.

Anyways with single channel analysis, you have a 
balanced incomplete block design with factorial 
treatments, and the analysis is much simplified.

--Naomi

At 01:41 PM 4/23/2006, francois fauteux wrote:
>Hi;
>
>We are doing an experiment with agilent 44K (3 biological reps,
>complete dye-swap):
>
>a - control
>b - treatment 1
>c - treatment 2
>d - treatment 1 + treatment 2
>
>and I would like to output evidence of the interaction between two
>treatments and effect on gene expression.
>
>24 chips:
>
>SlideNumber     Cy3     Cy5
>1       a1      b1
>2       a2      b2
>3       a3      b3
>4       b1      a1
>5       b2      a2
>6       b3      a3
>7       a1      c1
>8       a2      c2
>9       a3      c3
>10      c1      a1
>11      c2      a2
>12      c3      a3
>13      b1      d1
>14      b2      d2
>15      b3      d3
>16      d1      b1
>17      d2      b2
>18      d3      b3
>19      c1      d1
>20      c2      d2
>21      c3      d3
>22      d1      c1
>23      d2      c2
>24      d3      c3
>
>I've done several tests with limma to isolate significant results in
>the following:
>1- a vs b;
>2- a vs c;
>3- b bs d;
>4- c vs d;
>
>with this "targets.txt":
>
>SlideNumber     Cy3     Cy5
>1       a       b
>2       a       b
>3       a       b
>4       b       a
>5       b       a
>6       b       a
>7       a       c
>8       a       c
>9       a       c
>10      c       a
>11      c       a
>12      c       a
>13      b       d
>14      b       d
>15      b       d
>16      d       b
>17      d       b
>18      d       b
>19      c       d
>20      c       d
>21      c       d
>22      d       c
>23      d       c
>24      d       c
>
>First option:
>
> > f <- paste(targets$Cy3, targets$Cy5, sep = ".")
> > f <- factor(f, levels = c("a.b", "b.a", 
> "a.c", "c.a", "b.d", "d.a", "c.d", "d.a"))
> > design1 <- model.matrix(~0 + f)
>
> > design
>    a.b b.a a.c c.a b.d d.b c.d d.c
>1    1   0   0   0    0    0    0    0
>2    1   0   0   0    0    0    0    0
>3    1   0   0   0    0    0    0    0
>4    0   1   0   0    0    0    0    0
>5    0   1   0   0    0    0    0    0
>6    0   1   0   0    0    0    0    0
>7    0   0   1   0    0    0    0    0
>8    0   0   1   0    0    0    0    0
>9    0   0   1   0    0    0    0    0
>10   0   0   0   1    0    0    0    0
>11   0   0   0   1    0    0    0    0
>12   0   0   0   1    0    0    0    0
>13   0   0   0   0    1    0    0    0
>14   0   0   0   0    1    0    0    0
>15   0   0   0   0    1    0    0    0
>16   0   0   0   0    0    1    0    0
>17   0   0   0   0    0    1    0    0
>18   0   0   0   0    0    1    0    0
>19   0   0   0   0    0    0    1    0
>20   0   0   0   0    0    0    1    0
>21   0   0   0   0    0    0    1    0
>22   0   0   0   0    0    0    0    1
>23   0   0   0   0    0    0    0    1
>24   0   0   0   0    0    0    0    1
>
>This gives significant results for each one of the "levels" but does
>not take into account the dye-swap (i.e "a.b" and "b.a" are considered
>independent).
>
>Other tested option is:
> > design2 <- modelMatrix(targets,ref="a")
>
> > design
>       p  s sp
>ab1   0  1  0
>ab2   0  1  0
>ab3   0  1  0
>ba1   0 -1  0
>ba2   0 -1  0
>ba3   0 -1  0
>ac1   1  0  0
>ac2   1  0  0
>ac3   1  0  0
>ca1  -1  0  0
>ca2  -1  0  0
>ca3  -1  0  0
>bd1  0 -1  1
>bd2  0 -1  1
>bd3  0 -1  1
>db1  0  1 -1
>db2  0  1 -1
>db3  0  1 -1
>cd1 -1  0  1
>cd2 -1  0  1
>cd3 -1  0  1
>dc1  1  0 -1
>dc2  1  0 -1
>dc3  1  0 -1
>
>This gives results for "b" effect, "c" effect, and "d" effect.
>However, I could'nt get results for the 4 comparisons of interest
>(even though the matrix is coherent).
>
>Questions:
>
>1 - What would be the best option (design and operations) to get to
>contrasts of interest considering that the experiment has a 4
>treatments in a factorial design without common reference  (a vs b, a
>vs c, b vs d, c vs d) and taking into account the dye-effect;
>
>2- Is this method (4 contrasts) the best one considering that
>treatment "d" is a combination of treatments "b" and "c" (factorial
>type design). How could one directly get to identify genes
>differentially expressed due to the interaction between treatment "b"
>and treatment "c" (i.e effect of "d" over "b" and "c").
>
>In Limma Users Guide and elsewhere on this forum, I could not find a
>clear description of how this type of analysis should be performed,
>even though it is a simple design (i.e 2X2 factorial without a common
>reference - two color arrays - complete dye swap).
>
>Thanks for your time, best regards.
>
>François Fauteux
>Étudiant à la maîtrise en biologie végétale
>Centre de recherche en horticulture
>Université Laval
>francois.fauteux at gmail.com
>
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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